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Diss. ETH No. 18139
Thermodynamic Database of the La-Sr-Mn-Cr-O Oxide
System and Applications to Solid Oxide Fuel Cells
DISSERTATION
for the degree of
DOCTOR OF SCIENCES
of the
SWISS FEDERAL INSTITUTE OF TECHNOLOGY ZURICH
presented by
ERWIN POVODEN-KARADENIZ
Mag. rer. nat.
born on March 18, 1973
Citizen of Austria
accepted on the recommendation of
Prof. Dr. Ludwig J. Gauckler, examiner
Prof. John T.S. Irvine, co-examiner
Dr. Ming Chen, co-examiner
Zurich, 2008
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Dedicated to my parents
Whatever creates or increases happiness
or some part of happiness,
we ought to do;
whatever destroys or hampers happiness,
or gives rise to its opposite,
we ought not to do.
Aristoteles
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Acknowledgements
I am deeply grateful to my supervisor Professor Gauckler. He gave me a great chance by
taking me into the boat: a boat that is not only sailed to scientific success. It took me away
from an insecure float wobbling in the surf and approaches a promising future.
Endless gratitude belongs to my wife who stays by my side throughout highs, downs, and
distances, preventing me from losing the way; she is my firm anchor.
I am greatly indebted to Nicholas Grundy for open doors, his patience of a saint, great
teaching, and picky reviewing. He catalyzed my way into the field of thermodynamic
modeling, airing the “modeling is fun” approach at any time.
I would further like to thank Ming Chen for continuing scientific support and advising; he
was often motivating me to spin the wheel of accurate and fast modeling and publishing.
I owe thanks to Franc and Flavia Dugal-Borsari who saved me from an unintentional outdoor
adventure in Zurich during a time when it was extremely difficult to find a new
accommodation. It was a very pleasant time in Zollikon.
I thank Brandon Bürgler and Jennifer Rupp for their pleasing office companionship at the
beginning of my work: they facilitated my jump into the ETH waters.
I would also like to thank Toni Ivas for abiding collegiality, cooperation, and friendship.
I thank the rest of the office crew, Thomas Ryll and Rene Tölke, for always enjoyable
working hours.
Zurich, December 2008
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Table of Contents
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Table of Contents
Summary 7
Zusammenfassung 9
1 Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-
alloy interconnects 11
1.1 Introduction 11
1.1.1 Principles of SOFC 11
1.1.2 The problem of chromium “poisoning” 13
1.2 Volatilization of Cr2O3 14
1.3 Literature survey 17
1.3.1 Degradation of SOFC caused by chromium from the interconnect 17
1.3.2 The role of current load on electrical losses of degraded SOFC 22
1.3.3 Impedance spectroscopy measurements and implications on the
degradation process 24
1.3.4 Microstructures in degraded SOFC 24
1.3.5 Amounts of chromium in SOFC tested with and without current
load 27
1.3.6 Critical assessment of proposed mechanisms of chromium
“poisoning” 28
1.4 Proposed strategies against chromium “poisoning” and their effectiveness 36
1.4.1 Increasing the Cr-tolerance of conventional SOFC with
Cr-interconnects and LSM cathodes 36
1.4.2 New ways – alternative materials 37
2 Aim of study 45
3 Method 46
3.1 Benefits of the thermodynamic La-Sr-Mn-Cr-O oxide database for the
understanding of Cr-poisoning of SOFC 46
3.2 Thermodynamic modeling 47
3.2.1 Stoichiometric solid oxides 47
3.2.2 Solid solution phases – the Compound Energy Formalism (CEF) 48
3.2.3 Vacancies and the concept of reciprocal reactions 49
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3.2.4 Calculation of defect chemistry using the Calphad approach 51
3.3 Optimization of model parameters 52
4 Thermodynamic assessments 53
4.1 Thermodynamic reassessment of the Cr-O system in the framework of
SOFC research 53
4.1.1 Technology 53
4.1.2 Experimental data 54
4.1.3 Previous assessments of the Cr-O System 58
4.1.4 Thermodynamic modeling 59
4.1.5 Optimization of parameters 66
4.1.6 Results and discussion 67
4.1.7 Conclusions 73
4.2 Thermodynamic assessment of the Mn-Cr-O system for SOFC materials 77
4.2.1 Introduction 77
4.2.2 Experimental 78
4.2.3 Thermodynamic modeling 86
4.2.4 Optimization of parameters 89
4.2.5 Results 93
4.2.6 Discussion 96
4.2.7 Applications on SOFC 97
4.3 Thermodynamic assessment of the La-Cr-O system 101
4.3.1 Introduction 102
4.3.2 Literature review of the La-Cr system 103
4.3.3 Literature review of the La-Cr-O system 103
4.3.4 Thermodynamic modeling and optimization 109
4.3.5 Results and discussion 117
4.3.6 Conclusions 128
4.4 Thermodynamic La-Sr-Mn-Cr-O oxide database for SOFC applications 134
4.4.1 Introduction 134
4.4.2 Assessment of data from the literature 135
4.4.3 Modeling and optimization 137
4.4.4 Results and discussion 140
4.4.5 Conclusions 143
5 Thermodynamic calculations of impacts of chromium on Sr-doped
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manganite (LSM) cathodes for SOFC 148
5.1 Introduction 149
5.2 Method 150
5.3 Results 152
5.3.1 Thermodynamic calculations of La0.9Sr0.1MnO3-δ contaminated
by chromium 152
5.3.2 Thermodynamic calculations of (La0.8Sr0.2)0.9MnO3-δ contaminated
by chromium 157
5.3.3 Thermodynamic testing of LSM with Mn-deficiency 160
5.3.4 Formation of Cr2O3 162
5.4 Discussion 163
5.5 Conclusions 165
Appendix 170
Thermodynamic La-Cr database 169
Thermodynamic La-Sr-Mn-Cr-O-(H) oxide database 172
Curriculum Vitae 190
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Summary
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Summary
The thermodynamic La-Sr-Mn-Cr-O oxide database is established by assessing oxide
subsystems using the CALPHAD (Calculation of phase diagrams) approach. The new
database is applied to the problem of chromium “poisoning” of Sr-doped lanthanum
manganite cathodes ((La1−xSrx)1-yMnO3-δ or LSM) for Solid Oxide Fuel Cells (SOFC)
stemming from gaseous Cr species from the high-Cr containing alloy of the interconnect. The
chromium is known to deteriorate the electrical performance of the cathodes.
In chapter 1 the basics of planar SOFC are briefly explained, and previous findings of
chromium “poisoning” of SOFC are critically reviewed. Based on the findings from the
literature it gets clear that several questions about the key mechanisms of the chromium
“poisoning” have not been answered yet, and the aim of this study (chapter 2) is to gather a
deeper understanding of these unsolved problems by using thermodynamics. In the third
chapter the reader learns, how thermodynamic calculations can lead to a better understanding
of a system, even if the system is in a thermodynamic non-equilibrium state, and the modeling
approach used in this study is presented. Chapter 4 deals with the construction of the La-Sr-
Mn-Cr-O oxide database based on the assessments of subsystems. The new database is
applied to the problem of chromium “poisoning” of SOFC with Cr-interconnects and LSM
cathodes in chapter 5: a consistent phenomenological description of the process of chromium
“poisoning” of SOFC cathodes is established that is in line with both experimental findings
reported in the literature and thermodynamic calculations using the presented database. It is
shown that chromium “poisoning” of SOFC cathodes is a rather complex process consisting
of several steps, some of them probably occurring simultaneously. Some of these processes
are governed by thermodynamics, and some are kinetically controlled.
A key role is played by the adsorption of gaseous CrO3(g) (g = gaseous) and chromium-
oxyhydroxides stemming from the interconnect on LSM and reaction of chromium with LSM.
The associated chemical changes of the LSM phase, as well as the formation of a new spinel
phase occur under thermodynamic control: decreasing concentrations of vacancies in LSM
that contains chromium are calculated at decreased oxygen partial pressure reflecting SOFC
operation at high current load. This has calamitous consequences for the electrochemical
properties of the cathode. Furthermore spinel blocks pores and thus impedes the oxygen
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Summary
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reduction required for the function of the cell. Cr2O3(s) (s = solid) that hampers the diffusion of
oxygen into the electrolyte is a metastable phase in LSM contaminated by chromium.
With this contribution the prevailing question is resolved, which of the phenomena in a
chromium-“poisoned” LSM cathode are governed by thermodynamics. Appropriate measures
can be foreseen preventing the long-term degradation of SOFC cathodes in combination with
high-chromium containing interconnects.
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Zusammenfassung
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Zusammenfassung
Die thermodynamische La-Sr-Mn-Cr-O Oxid-datenbank wird basierend auf dem Assessment
oxidischer Subsysteme mit dem CALPHAD-ansatz (Berechnung von Phasendiagrammen)
aufgebaut. Die neue Datenbank wird auf das Problem der „Chromvergiftung“ von Sr-
dotierten Lanthan-Manganit-kathoden ((La1−xSrx)1−yMnO3-δ oder LSM) für Festoxid-
Brennstoffzellen (SOFC) angewandt, welches von gasförmigen Cr spezies der hochgradig Cr-
führenden Interkonnektor-Legierung herrührt. Es ist bekannt, dass das Crom die elektrische
Leistung der Kathoden verschlechtert.
In Kapitel 1 werden die Grundlagen von planaren SOFC kurz erklärt, und es wird ein
kritischer Überblick über bisherige Erkenntnisse der „Chromvergiftung“ von SOFC gegeben.
Basierend auf den Erkenntnissen aus der Literatur wird klar, dass einige Fragen, welche die
Schlüsselmechanismen der „Chromvergiftung“ betreffen, noch nicht beantwortet wurden. Das
Ziel dieser Studie (Kapitel 2) ist es, unter Verwendung der Thermodynamik ein tieferes
Verständnis dieser ungelösten Probleme zu erlangen. Im dritten Kapitel lernt der Leser, wie
thermodynamische Berechnungen zu einem besseren Verständnis eines Systems führen
können, selbst wenn dieses System sich in einem thermodynamischen
Ungleichgewichtszustand befindet, und der in dieser Studie verwendete Modellansatz wird
vorgestellt. Kapitel 4 beschäftigt sich mit der Konstruktion der La-Sr-Mn-Cr-O Oxid-
Datenbank, basierend auf den Assessments der Subsysteme. In Kapitel 5 wird die neue
Datenbank auf das Problem der „Chromvergiftung“ von SOFC mit Cr-interkonnektoren und
LSM-kathoden angewandt: Eine konsistente phenomenologische Beschreibung des Prozesses
der „Chromvergiftung“ von SOFC-kathoden wird gegeben, welche sowohl im Einklang mit
experimentellen Erkenntnissen in der Literatur als auch mit thermodynamischen
Berechnungen unter Verwendung der präsentierten Datenbank steht. Es wird gezeigt, dass
„Chromvergiftung“ von SOFC-kathoden ein ziemlich komplexer Vorgang mit mehreren,
teilweise gleichzeitig in der Zelle ablaufenden Schritten ist. Manche dieser Prozesse sind
thermodynamisch kontrolliert, und manche laufen unter kinetischer Kontrolle ab.
Eine Schlüsselrolle spielt die Adsorbtion von gasförmigem CrO3(g) (g = gasförmig) und
Chromium-oxyhydroxiden, welche vom Interkonnektor stammen, an LSM und die Reaktion
von Chrom mit LSM. Die damit verbundenen chemischen Änderungen der LSM-phase und
die Bildung einer neuen Spinellphase finden unter thermodynamischer Kontrolle statt. Die
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Zusammenfassung
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Berechnungen ergeben abnehmende Konzentrationen der Leerstellen in Cr-hältigem LSM
unter erniedrigtem Sauerstoffpartialdruck, und somit bei Betrieb von SOFC unter hohem
Laststrom . Das hat katastrophale Konsequenzen für die elektrochemischen Eigenschaften der
Kathode. Weiters blockiert Spinell Poren und behindert so die für die Funktion der Zelle
notwendige Sauerstoffreduktion. Cr2O3(s) (s = fest), welches die Diffusion von Sauerstoff in
den Elektrolyt erschwert, ist eine metastabile Phase in Cr-kontaminiertem LSM.
Mit diesem Beitrag werden einige der vorherrschenden Fragen über „Chromvergiftung“ von
SOFC geklärt, und geeignete Maßnahmen zur Verhinderung der Langzeitdegradation von
SOFC-kathoden in Kombination mit hochgradig Chrom-führenden Interkonnektoren können
vorhergesagt werden.
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1 Degradation of planar solid oxide fuel cells (SOFC) with
LSM cathodes and Cr-alloy interconnects
E. Povoden and L.J. Gauckler, to be submitted to Int. J. Mater. Rev.
For the use of LSM cathodes in planar SOFC a comprehensive understanding of the
mechanisms of the cell degradation caused by chromium diffusing from the interconnects into
the cell is needed. This “poisoning” has been intensively investigated over the last decade. In
this paper the affects of Cr on the degradation of SOFC with LSM cathodes and Cr-alloy
interconnects are reviewed: the suggested models of chromium “poisoning” of planar SOFC
with chromium-alloy interconnects and (La1-xSrx)1-yMnO3-δ (LSM) cathodes from the
literature are critically assessed. Taking into account all available experimental findings on
the affects of chromium on Sr-doped lanthanum manganite cathodes in planar solid oxide fuel
cells, it can be concluded that several “poisoning” processes contribute to the deterioration of
the cell performance. The review of all available experimental findings on the degradation of
SOFC caused by chromium allows predictions, as to how the extent of degradation caused by
chromium depends on the current load, operation temperature, operation time, as well as the
amount of chromium diffusing from the interconnect.
1.1 Introduction
1.1.1 Principles of SOFC
A fuel cell directly converts chemical energy into electrical energy. A solid oxide fuel cell
consists of two porous electrodes that are separated by a dense, oxygen ion-conducting
electrolyte. A simple schematic of the electrochemical process is shown in Fig. 1.1.1 (next
page).
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Fig. 1.1.1 Scheme of the electrochemical processes in a fuel cell with O2 oxidant and H2 fuel.
White circles symbolize pores. a = anode, c = cathode, e = electrolyte.
The oxygen, supplied at the cathode reacts with electrons from the external electric circuit to
form oxygen ions. These ions migrate through the electrolyte to the anode. At the anode the
oxygen ions react with hydrogen of the fuel to form water and release electrons. The electrons
flow from the anode through the external electric circuit to the cathode. The direct-current
electricity is produced by the electron flow through the external electric circuit.
In an SOFC, cathode and electrolyte consist of refractory solid oxide ceramics, and ceramic-
metal composites are used for the anode. The materials for the cell components need to have a
sufficient chemical and structural stability at rather high temperatures up to 1273 K that occur
during cell production as well as during cell operation. The electrodes are required to have
high reactivity and the electrolyte must allow high oxygen ion diffusion. All the components
of the cell need to be matched in their thermal expansion in order to minimize mechanical
stresses.
A single cell produces a voltage of 0.7 to 1 V and power around 0.5 to 1 W cm-2. Normally
many cells are electrically connected in series by an interconnect, as shown in Fig. 1.1.2 (next
page) for the widely used planar-design SOFC, forming a cell stack to obtain higher voltage
and power.
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Fig. 1.1.2 Planar design of SOFC
The interconnect separates the fuels and oxidants in adjacent cells. It is the most demanding
component in a planar SOFC as it should have a high electronic conductivity, a low ionic
conductivity; stability in both oxidizing and reducing atmospheres at the high cell operating
temperature (from about T = 973 K to 1273 K); low permeability for oxygen and hydrogen to
minimize direct combination of oxidant and fuel during cell operation; a thermal expansion
coefficient close to that of the cathode and the anode; and chemical compatibility (no
reactions) with other cell materials.
1.1.2 The problem of chromium “poisoning”
In the 1990is LaCrO3-based ceramics were intensively investigated for interconnect
applications in SOFC, as the thermal expansions of LaCrO3-based interconnect and
conventional perovskite cathode materials are similar, the electronic conductivity of several
LaCrO3-based ceramics under SOFC operating conditions is high, and their thermal and
redox-stability is satisfying[1]. However high costs of these materials, difficulties in sintering
and manufacturing and low mechanical strength[2] required the development of alternative
interconnect materials. Nowadays the state-of-the-art interconnect is commonly a chromium-
containing metal plate[3-5], as chromium alloys come close to all desired properties. However
high-valent gaseous Cr-oxide and Cr-oxyhydroxides diffuse from the Cr2O3(s) scale covering
the interconnect into the cathode up to the cathode-electrolyte interface and cause the
degradation that results in the strong deterioration of the electrical performance of SOFC.
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In the last decade a lot of effort was made to elucidate the degradation mechanisms, and it
was suggested that high-valent gaseous Cr-oxide and Cr-oxyhydroxides detrimentally affect
the O2 -adsorbtion, -reduction, and -diffusion processes.
1.2 Volatilization of Cr2O3
Early investigations[6-9] revealed that oxidation of Cr-containing alloys at high temperatures
leads to the redeposition of Cr2O3(s) crystals at cooler parts of the experimental apparatus from
the gas phase. This was a surprising result, as the film of Cr2O3(s) covering the alloy specimen
would have been expected to act as a diffusion barrier preventing the migration of Cr that has
a high vapour pressure from the alloy through the Cr2O3 layer. Furthermore, neither the
vapour pressure of Cr2O3(s) nor its dissociation pressure is high enough to account for the
quantities of deposits observed[10]. Because of the high vapour pressure of Cr it was thus first
considered that the metal itself would diffuse along oxide grain boundaries of the barrier film,
or at discontinuities such as fractures in the film and would then evaporate. But when it was
learned that Cr2O3(s), in the absence of metal, lost weight when heated in oxygen, it became
evident that a volatile Cr-oxide was being formed[10].
Caplan and Cohen[10] investigated the evaporation of Cr2O3(s) by measuring the weight loss
when Cr2O3(s) pellets with 1.2 cm in diameter and height were heated at T = 1273 K in
stagnant air, and at T = 1373 and 1473 K in flowing dry and wet oxygen as well as in dry and
wet argon. Appreciable volatilization occurred in dry oxygen, the weight loss being 0.6 mg at
T = 1373 K and 2.3-2.6 mg at T = 1473 K at a gas flow rate of 200 ml min-1 after 20 h. The
volatilization in wet oxygen was significantly higher after 20 h at the same gas flow rate:
2.1 mg at T = 1373 K and 5.6 mg at T = 1473 K. In stagnant air the volatilization was 0.3 mg
at T = 1273 K after 72 h. Volatilization of Cr2O3(s) was neither observed in dry nor in wet
argon. The observation that no loss of Cr2O3(s) occurs in argon confirms that volatilization
does neither occur by dissociation of the oxide nor as Cr2O3(g) vapor. Since weight loss takes
place under oxidizing conditions, the volatile species must be a higher oxide of chromium. A
known volatile oxide of Cr is CrO3, but its formation by the reaction
2 3(s) 2(g) 3(g)Cr O 3 2O 2CrO+ → (1.2.1)
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
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is thermodynamically unfavourable at high temperatures[10], Δ°G of Eq. 1.1 is calculated to be
+321 kJ at T = 1273 K using assessed thermodynamic data for Cr2O3(s) from Povoden et
al.[11], data for O2(g) from Dinsdale[12], and for CrO3(g) from Ebbinghaus[13]. As gaseous CrO3(g)
was detected experimentally by mass spectrometry when Cr2O3(s) was heated under oxidizing
conditions, the formation of CrO3(g) occurs under kinetic control[10].
The existence of gaseous Cr-oxyhydroxides as oxidation products (Eqs. 1.2.2 and 1.2.3) in
wet atmosphere was experimentally proven in several studies[14-17]. Their formation by
oxidation of Cr2O3 in wet air reads:
2 3(s) 2(g) 2 (g) 2 2(g)Cr O 1 2O 2H O 2CrO (OH)+ + → (1.2.2)
2 3(s) 2(g) 2 (g) 2 (g)Cr O 1 2O H O 2CrO (OH)+ + → (1.2.3)
Δ°G of reaction 1.2 is calculated to be −158 kJ at T = 1273 K using combined data from Opila
et al.[18] and Ebbinghaus[13], and Δ°G of reaction 1.3 is calculated to be +134 kJ at T = 1273 K
using combined data from Kim and Belton[14] and Ebbinghaus[13]. Ebbinghaus[13] estimated a
significantly higher partial pressure of CrO2(OH)2(g) compared to CrO3(g) in wet atmosphere
up to T = 1600 K based on available thermodynamic data of gaseous Cr-species, and this was
affirmed by thermodynamic modeling[19]. However, in a recent combined experimental and
modeling study[18] these earlier findings are rejected for high temperatures: in wet atmosphere
CrO2(OH)2(g) is predominant in the gas from T ≤ 1173 K, whereas at higher temperatures the
gas phase mainly contains CrO3(g) and CrO2OH(g). This tendency is shown in Fig. 1.2.1 (next
page): the calculated amounts of main Cr-species in the gas phase as a function of temperature
in humid air of 2H Op = 2000 Pa at constant chemical potential of oxygen, μ(O) being −300 J
mol-1 referred to pure oxygen gas result from combined thermodynamic data[11-14,18] cited
above. These findings are supported by the higher volatilization of Cr2O3(s) in wet air.
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Fig. 1.2.1 Calculated amounts of gas molecules in Cr-gas as a function of temperature for
constant 2H Op = 2000 Pa at μ(O) = −300 J mol-1 referred to 100000 Pa O2(g)
Transpiration experiments of Cr2O3(s) from T = 673 K to 1223 K resulted in the following
partial pressures of Cr at a flow rate of 150 m min-1: pCr = 2.12x10-5 Pa at T = 673 K and
increases as a function of increasing temperature, reaching pCr = 4.57x10-3 Pa at
T = 1223 K[20]. Mass loss of Cr2O3(s) at T = 973 K and 1073 K was measured in air with
different amounts of water, the mass loss being higher at higher water content and higher
temperature: the constant rate of mass loss was 0.6 μg h-1 for 3 mol% H2O in air at T = 973 K,
3.2 μg h-1 for 3 mol% H2O in air at T = 1073 K, and 18.3 μg h-1 for 25 mol% H2O in air at
T = 1073 K.
Cr-vaporization in SOFC:
Konysheva et al.[21] used a transpiration method proposed by Gindorf et al.[20] to measure the
vaporization rate of Cr from Cr5Fe1Y2O3 (Ducrolloy) and Crofer22APU (high-Cr ferritic
steel), two high-chromium alloy interconnects widely used in SOFC, at T = 1073 K for a time
period of about 500 h. The Cr-vaporization rate of Cr5Fe1Y2O3 exceeds that of Crofer22APU
by about a factor of 3 in the temperature range from T = 1023 K to 1173 K, and the
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
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vaporization rate increases with increasing temperatures for both alloys. With increasing
humidity the difference in the vaporization rates between the two alloys increases. However,
for an SOFC setup with a Cr5Fe1Y2O3 interconnect plate, an LSM cathode, an yttrium-
stabilized zirconia (YSZ) electrolyte and a Ni-zirconia cermet (ceramic-metallic composite)
anode operated at T = 1173 K and 1273 K, Badwal et al.[22] mentioned significant amounts of
deposited Cr2O3(s) in the air exhaust of the cell; thus quantitative chromium “poisoning” rates
affecting the cathode are difficult to determine. This is in line with the experimental
observation[21] that only a fraction of the chromium deposited at the cathode side contributes
to the strong degradation of SOFC with LSM cathodes and Cr-alloy interconnects that were
tested under a current load of 200 mA cm-2 for 393 h. The amount of Cr in these degraded
cells was 140 μg cm-2 with Cr5Fe1Y2O3, this value being by about a factor of 2.5 higher than
with Crofer22APU.
1.3 Literature survey
1.3.1 Degradation of SOFC caused by chromium from the interconnect
Considering the experimental data from Caplan and Cohen[10], the volatilities of gaseous
CrO3(g) and gaseous Cr-oxyhydroxides are negligible under the low oxygen partial pressure at
the fuel side of the cell, and the chromium problem is restricted to the interconnect-cathode-
electrolyte region of SOFC.
Experimental results[21-29,31,32,34,35] of the degradation of SOFC with LSM cathodes caused by
chromium are listed in Table 1.3.1, pp. 18-21.
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
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Table 1.3.1 Results of chromium poisoning of SOFC with and without Cr-containing
interconnects with LSM cathodes collected from the literature
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The degrading effect of gaseous chromium species that form at the Cr2O3 scale under
oxidizing conditions and diffuse into the cathode on the cell performance was first reported in
1995 by Taniguchi et al.[23]. These authors measured an increase of cathode polarization and
decrease of cell voltage in an SOFC consisting of an LSM cathode with the compositions
La0.9Sr0.1MnO3-δ, a YSZ electrolyte and a NiO/YSZ anode with a piece of a Ni-Cr-Fe-alloy
(Inconel 600) attached on top of a Pt mesh used as current collector. The cell was
electrochemically tested at T = 1273 K under a current load of 300 mA cm-2 for 400 h. The
cell voltage decreased over this time from initially about 0.7 V to about 0.1 V, and intensity
measurements using electron probe microanalysis showed that Cr was concentrated at the
cathode-electrolyte interface. In a test of the same setup under open circuit conditions for
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300 h no deterioration of the cell performance was observed, and Cr was randomly distributed
across the cathode. Taniguchi et al.[23] thus linked the cell degradation to the time that the
discharge current was applied, and to chromium deposited at the LSM-YSZ interface filling
pores, hindering the supply of oxygen gas and decreasing the number of reaction sites for the
oxygen reduction. Later these results were confirmed by Badwal et al.[22]: these authors tested
the cell performance of an SOFC with a Cr5Fe1Y2O3 interconnect plate, an LSM cathode, a
YSZ electrolyte and a Ni-zirconia cermet anode at T = 1273 K and a current density of
250 mA cm-2. Experiments without a Cr-based interconnect plate with Pt mesh serving as
current collectors were conducted at T = 1205 K and 188 mA cm-2 current density using the
same electrodes and electrolyte. The cell performance without interconnect plate deteriorated
only little by less than 0.1 V during an operation time of 2500 h. On the other hand the
voltage of the cell with Cr-Fe-alloy interconnect decreased rapidly as a function of operation
time, the voltage drop being 0.4 V after only 16 h. A comparison of measurements of the
overpotentials of SOFC with LSM cathode and high-Cr alloy interconnect with measurements
without interconnect[24-27] or LaCrO3-based interconnect[28] led to the following results: the
overpotentials without interconnects or with LaCrO3-base interconnects consistently became
less negative with time, whereas the opposite was observed for SOFC with Cr-alloy
interconnect. Simner et al.[29] presented cell performance data of an SOFC with LSM cathode,
a Sm2O3-CeO2 interlayer between cathode and electrolyte, a YSZ electrolyte and a Pt counter
electrode (in the following SOFC with Pt counter electrode are denoted as half-cell) with and
without Crofer22APU interconnect at T = 1073 K, holding the cells at 0.7 V: without the
interconnect steel, the cell performance was stable for 110 h, the power density being
0.48 W cm-2. But using a Cr-Fe-alloy interconnect, the cell started to degrade severely after
20 h of testing, its power density decreasing from a maximum of 0.2 W cm-2 to 0.05 W cm-2
after 110 h.
All these experimental studies[22-29] unambiguously proved that chromium stemming from the
alloy interconnect causes the degradation of SOFC.
1.3.2 The role of current load on electrical losses of degraded SOFC
Badwal et al.[22] reported that the degradation rate of SOFC with a Cr5Fe1Y2O3 interconnect
plate, an LSM cathode, a YSZ electrolyte and a Ni-zirconia cermet anode at T = 1173 K and
T = 1273 K was more related to the period of current passage and was less dependent on the
time when no current was flowing through the cell: Badwal et al.[22] ascribed the voltage
decrease to increasing losses of cathodic overpotential, whereas ohmic losses (resistance to
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
23
flow of electrons through the cathode) increased only insignificantly during the cell tests. The
overpotential losses were higher and the cell deterioration was faster at higher current density.
At the beginning of the cell tests, losses increased sharply and reached their maximum values
after only 15 h of cell operation. Konysheva et al.[21], using a half-cell with a Cr5Fe1Y2O3
interconnect, a La0.65Sr0.3MnO3-δ/LSM+YSZ double layer cathode and a YSZ electrolyte
confirmed the strong dependence of the voltage drop on the current density during 450 h cell
tests at T = 1073 K: at 70 mA cm-1 the voltage decrease was 0.07 V, whereas at 280 mA cm-1
the voltage dropped by 0.6 V. A plateau of degradation was reached after about 400 h of
testing. Konysheva et al.[30] tested the reversibility of degradation in a half-cell setup with Cr-
Fe-alloy interconnect, LSM cathode and YSZ at a current density of 100 mA cm-2 at
T = 1073 K and found that the rapid degradation was reversible and disappeared after
switching off the current load, in agreement with earlier findings[22,23,28,31]. However the cell
degraded rapidly again when the current was switched on again.
Matsuzaki and Yasuda[28] measured an overpotential loss from initially −500 mV to
−2000 mV after 14 h in a half-cell setup with an Inconel 600 interconnect, La0.6Sr0.4MnO3-δ
cathode and a YSZ electrolyte at 300 mA cm-2 current density. Zhen et al.[27] measured a
rapid decrease of cell polarization from initially −350 to −750 mV after only 10 minutes in a
half-cell with Cr-Fe-alloy (RA446) interconnect, LSM cathode and a YSZ electrolyte tested at
T = 1173 K and a current density of 200 mA cm-2. In earlier studies using the same setup a
rapid decrease from −360 to −560 mV after 10 minutes[25,26] was observed. In reference tests
without Cr-Fe-alloy interconnect the results were opposite to the tests with Cr-Fe-alloy
interconnects: the polarization increased from −550 to −300 mV[27] or −420 to −170 mV [24,25]
at 1173 K and a current density of 200 mA cm-2. The polarization behavior of SOFC with Cr-
containing interconnect was explained by the strong inhibiting effect of gaseous Cr-species on
the oxygen reduction in LSM[27], in general agreement with Jiang et al.[24,25,32,33].
Paulson and Birss[34] reported rapid deterioration of the performance of a half-cell setup with
a stainless steel disk containing 15.21 % Cr on top of a (La0.8Sr0.2)0.98MnO3-δ cathode and a
YSZ electrolyte over 5 to 10 h at T = 1073 K applying a −0.5 V potential, with a tendency of
stabilization of the cell performance after this testing period at much lower magnitude of
output current.
The total polarization resistance (Rpol) of a half-cell setup using a Cr-Fe-alloy interconnect, an
LSM/LSM-YSZ cathode double layer and a YSZ electrolyte tested for 400 h was markedly
dependent on the thickness of the LSM-YSZ layer, Rpol being 0.5 Ohm cm2 for a thickness of
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
24
50 μm, 0.75 Ohm cm2 for 13 μm, and 2 Ohm cm2 for 7 μm[30]. The total polarization
resistance was also higher at higher current load.
Influence of temperature on the degradation:
SOFC with LSM cathodes and high-chromium 430 stainless steel were tested at T = 973 K
and 1073 K for 300 h[35]. The degradation was higher at higher temperatures at 0.7 V; it
deteriorated from 500 mA to 350 mA at T = 1073 K and from 300 mA to 150 mA at
T = 973 K over the testing time of 200 h and then remained constant.
Jiang et al.[32] observed less overpotential losses at lower temperatures in a half-cell with Cr-
Fe-alloy interconnect, LSM cathode and a YSZ electrolyte: they measured an overpotential
change from initially −300 mV to −650 mV after 10 minutes at T = 1173 K, from −900 to
−1200 mV at T = 1073 K, and from −800 to −1120 mV at T = 973 K after 10 minutes.
1.3.3 Impedance spectroscopy measurements and implications on the degradation
process
Badwal et al.[22] observed an increased size of the high frequency arc during the current
passage in half-cell tests using a Cr5Fe1Y2O3 interconnect plate, an LSM cathode and a YSZ
electrolyte as a function of operation time, reflecting increasing cathode resistance. Mazusaki
and Yasuda[28] concluded from the interpretation of impedance spectra of a half-cell with an
Inconel 600 interconnect, a La0.6Sr0.4MnO3-δ cathode and a YSZ electrolyte operated at
T=1073 K and 300 mA cm-2 current load that the degradation in the electrode caused by
chromium was due to the increase in both charge-transfer resistance and surface diffusion
resistance, but not due to the increase in ohmic resistance. Zhen et al.[27] reported the
existence of a high frequency and a low frequency arc in impedance spectra of a half-cell with
Cr-Fe-alloy interconnect, LSM cathode and YSZ electrolyte tested at T = 1173 K and a
current density of 200 mA cm-2. The increase of both arcs over the testing time was ascribed
to the affect of Cr on the oxygen diffusion processes in the LSM cathode and across the LSM-
electrolyte interface and is in line with the interpretations from Jiang[25,33] and Jiang et
al.[24,26,32].
1.3.4 Microstructures in degraded SOFC
Cathodic polarization:
Taniguchi et al.[23] were the first who reported the occurrence of Cr-Mn-spinel in Cr-
“poisoned” SOFC with an LSM cathode by using XRD analysis. This finding was confirmed
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
25
by Badwal et al.[22] who detected small amounts of Cr-Mn spinel after 100 h of operation of
SOFC with a Cr5Fe1Y2O3 interconnect plate, an LSM cathode, a YSZ electrolyte and a Ni-
zirconia cermet anode at T = 1173 and 1273 K under current load. For the same setup large
quantities of spinel had formed after 2000 to 2500 h of cell operation, in some of the
experiments forming a dense layer of several microns at the cathode-electrolyte interface. In
some cases these authors also observed Cr2O3(s) at the cathode-electrolyte interface;
unfortunately the specific conditions for its formation were not given in more detail. The
amount of spinel at the cathode-electrolyte interface was much larger than within the LSM
cathode particularly after a period of current load. Badwal et al.[22] further observed spinel in
the contact region between interconnect and cathode.
Using a half-cell setup with Inconel 600, LSM cathode and YSZ electrolyte Matsuzaki and
Yasuda[31] reported the formation of a dense layer of Cr-deposit at the LSM-YSZ interface
after a cell test at T = 1073 K and a current density of 300 mA cm-2 over 100 h of polarization.
Zhen et al.[27] observed dense Cr-Mn spinel-deposits exclusively at the LSM-YSZ interface
after a half-cell test of an SOFC with Cr-Fe-alloy interconnect operated for 20 h at
T = 1173 K and a current density of 200 mA cm-2. Using the same setup, Jiang et al.[25,36]
documented spinel formation at the LSM-YSZ interface already after 4 h. The grain size of
spinel was about 0.17 μm after 4 h of cell testing and increased to about 0.7 μm after 50 h.
The zone of these large faceted crystals was followed by a zone of very fine grains (about
0.05 μm) of Cr2O3 towards the cathode-electrolyte interface. The deposition zone broadened
as the polarization time increased from about 60 μm after 50 h to 89 μm after 129 h. Under
the same testing conditions as above, but under anodic polarization very fine grains of Cr2O3
were forming exclusively at the LSM-YSZ interface.
Using the same setup as above, no Cr-deposits formed after 50 h of testing under open circuit
conditions[25,36]. Very small grains of Cr-deposits formed at T = 1373 K under open circuit
conditions, but further details on their spatial distribution and composition were not given.
In a half-cell setup with a Cr-Fe-alloy interconnect, an LSM/LSM-YSZ cathode double layer
and a YSZ electrolyte chromium-deposits were only found in the LSM layer under open
circuit conditions, and the cell-degradation was weak[21]. On the other hand chromium-
deposits were also found in the LSM-YSZ layer and on the surface of the YSZ electrolyte on
increasing the current density up to 280 mA cm-2, and the cell degradation was strong[21]. In
the same setup without LSM-YSZ functional layer no chromium-deposits were detected
without current at T = 1073 K over 393 h. On the other hand Cr-Mn spinel formed already at
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
26
very low current load of 2 mA cm-2 on the surface of the electrolyte and near the LSM-
electrolyte contact. After 160 h of testing at 100 mA cm-2 current load, large gaps between
YSZ grains formed, and spinel crystals were found on the surface of a thin Cr2O3-layer
adjacent to the electrolyte. Cr2O3 was also found inside YSZ, up to 10 μm away from the
LSM-YSZ interface after 160 h of testing, and 30 μm from the LSM-YSZ contact after 940 h.
Cr2O3 completely filled gaps between YSZ grains. Transmission electron microscopy
analyses revealed the layered structure of the composites: a 0.5 μm thick layer directly
adjacent to the YSZ containing mainly Cr2O3 is covered by a spinel layer.
Paulson and Birss[34] investigated the microstructures in a half-cell setup with a stainless steel
disk containing 15,21 % Cr attached on top of a 4 mm2 square (La0.8Sr0.2)0.98MnO3-δ cathode
that rested on a 144 mm2 square YSZ electrolyte, after the half-cell was tested by a sequence
of 8 chronoamperometry experiments at −0.5 V and T = 1073 K. These authors observed the
formation of a 500 μm broad zone of 8 individual, dense Cr2O3-layers at the edge of LSM on
the YSZ surface. Cr-deposits consisting of Cr2O3 and Cr-Mn-spinel were concentrated in an
about 2 μm broad region at the LSM-YSZ interface. A reference test without polarization did
not lead to these features.
Anodic polarization:
After a half-cell test of an SOFC with Cr-Fe-alloy interconnect operated for 6 h at T = 1173 K
and a current density of 200 mA cm-2, Jiang et al.[36] reported the formation of very fine
particles of Cr2O3, exclusively covering the YSZ surface, and the deposition was less
pronounced at T = 1073 K and 973 K. The morphology of the particles was different than the
morphology of the deposits under cathodic polarization.
No spinel formation was observed in these experiments.
Influence of temperature:
Microstructural changes during half-cell tests of a setup consisting of a Cr-Fe-alloy
interconnect, a La0.72Sr0.18MnO3-δ cathode and a YSZ electrolyte were systematically
investigated as a function of time and temperature at a current load of 200 mA cm-2 by Jiang
et al.[32]. After 5 minutes of testing at T = 1173 K very fine Cr-deposits (< 100 nm) already
formed on the YSZ-surface, and the density and size of deposits increased by time. After 20 h
spinel formation was observed forming a 40 to 50 μm wide band at the LSM-YSZ interface.
In direct contact with YSZ about 500 nm large Cr2O3-grains were detected, almost completely
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
27
covering the YSZ surface, associated with large grains (about 1 μm) of spinel. The amount of
Cr-deposits was significantly smaller after 20 h of testing and 200 mA cm-2 current load at
T = 973 K: isolated fine particles (about 100 to 200 nm) were detected on the YSZ surface.
The decreasing degradation at lower temperatures was ascribed to slower diffusion and lower
partial pressure of gaseous Cr-species.
1.3.5 Amounts of chromium in SOFC tested with and without current load
Konysheva et al.[21] compared the total amounts of chromium in half-cells with Cr-Fe-alloy
interconnects, a La0.65Sr0.3MnO3-δ/LSM+YSZ double layer cathode and a YSZ electrolyte
after tests without current showing very small degradation, and under 200 mA cm-2 current
density showing strong degradation as a function of testing time at T = 1073 K. The amounts
of chromium in the half-cell operated under a current was 100 μg cm-2 after 150 h and
150 μg cm-2 after 500 h; this is only 15 to 20 % higher than in the cell operated without
current, although the degradation of the polarized cell was remarkably higher. This was
explained by the following: only under current load chromium deposits are concentrated in
the functional region of LSM close to the contact to YSZ where they inhibit oxygen reduction
and diffusion processes.
In SOFC with LSM cathodes and a Cr-Fe-steel interconnect that were tested at T=1073 K for
300 h at 0.7 V, Krumpelt et al.[35] measured about 2.8 wt.% of Cr at 10 μm distance from the
cathode-electrolyte interface. The Cr-content dropped to about 0.5 wt.% at 14 μm distance
from the contact to the electrolyte. It further decreased slightly towards the interconnect-
cathode interface.
In a half-cell with LSM cathode, a Sm2O3-CeO2 interlayer between cathode and electrolyte
and a YSZ electrolyte with a Crofer22APU interconnect operated at T = 1073 K, holding the
cell at 0.7 V for 120 h, Simner et al.[29] measured 5 at.% Cr in the Sm2O3-CeO2 interlayer, but
no Cr in LSM using energy dispersive scanning electron microscopy.
By using molecular dynamics simulation techniques it was stated recently that only 890 ppm
Cr3+ in LSM significantly increase the formation energy of O2- vacancy within about 10 Å
around Cr3+. This may lead to a dramatic drop of the oxygen diffusion coefficient in LSM by
about 60%[36] and pers. comm.
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
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1.3.6 Critical assessment of proposed mechanisms of chromium “poisoning”
For the mechanisms of chromium “poisoning” two models have been proposed: 1) Reduction
of gaseous Cr-species under polarization[21-23,30-31,33], and 2) Chemical dissociation of Cr-
species on the LSM surface[24-26,32,33,37]. Both reduction and chemical dissociation processes
reflect non-equilibrium conditions.
1) Several authors[21-23,230,31,33] ascribe the mechanism of chromium “poisoning” to the
reduction of gaseous CrO3(g) and Cr-oxyhydroxides at the cathode-electrolyte interface,
described by inverse Eq. 1.2.1. In an LSM cathode the reduction of CrO3(g) is expected to be
localized at the triple phase boundary (TPB) between LSM, YSZ, and gas, where the reaction
partners for the reduction, electron-donating LSM and oxygen-accepting YSZ are
available[38]. This reduction reaction would compete with the oxygen reduction and would
lead to blocking of the active sites at the TPB and subsequent formation of Cr-Mn spinel by
the reaction of Cr2O3(s) with LSM.
Badwal et al.[22] emphasized that chromium “poisoning” would consist of several processes,
including changes of the chemical composition of the LSM surface, reduction of CrO3(g) at the
cathode-electrode interface competing with the normal oxygen reduction reaction, and
blocking of pores by Cr-Mn spinel and Cr2O3(s). In particular they suggest the tight
intercalation between changes of the chemical composition at the surface of LSM particles
and the oxygen adsorption and surface diffusion kinetics in the early stage of chromium
“poisoning”. Badwal et al.[22] ascribe a key role for the late stages of cell degradation to the
formation of Cr-Mn spinel that would block pores and lead to substantial decrease of the TPB
area. Cr-Mn spinel is interpreted by these authors to form in a solid-solid reaction between
Cr2O3(s) and LSM that may have the simplified form of Eq. 1.3.1 when solid solubility of Cr
in LSM[39] is considered and spinel contains the molar fraction of Cr, X(Cr) = 2X(Mn):
1 3 2 3 1 1 3 2 4(s) 2(g)La Sr MnO 3 2 Cr O La Sr Mn Cr O MnCr O 1 4 O− − − − − + ++ →x x yx x yy y yδ δ (1.3.1)
Eq. 1.3.2 is a possible reaction for the formation of spinel with a higher amount of Mn,
X(Mn)= 2X(Cr):
1 3 2 3 1 1 2 3 2 4(s) 2(g)La Sr MnO 1 2 Cr O La Sr Mn Cr O Mn CrO 5 4 O− − − − − + ++ →x x yx x yy y yδ δ (1.3.2)
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
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For equal y in Eqs. 1.3.1 and 1.3.2 less Cr2O3 is needed for the formation of Mn2CrO4, more
oxygen is produced, and LSM gets more deficient in Mn. Oxygen production stems from the
reduction of Mn3+ in perovskite to Mn2+ in spinel. However the formation of spinel can also
be interpreted as a direct solid-gas reaction. Fig. 1.3.1 is a simplified illustration of possible
reaction paths that lead to the end product Cr-Mn spinel.
Fig. 1.3.1 Possible reaction paths for the spinel formation as a function of Gibbs energy.
The true shape of the curves depends on the activation energy Ea and is thus not known.
red = reduction, sp-form = spinel formation.
Which of the possible reaction paths is realized, depends on the activation energy, Ea of the
concerning reaction, and this is not known. The shape of the curves in Fig. 1.3.1 was chosen
based on the consideration that the diffusionless reduction of Cr-gas may have a lower
activation energy than the solid-solid reaction between LSM and Cr2O3(s), and the mobility of
the gas phase is high, thus assuming a lower activation energy for the LSM-Cr-gas reaction.
These assumptions would mean that fast reduction of Cr-gas to Cr2O3(s) occurs as one process,
and the LSM-Cr-gas reaction occurs as a parallel process leading to the formation of spinel.
On the other hand it may last a long time for the Cr2O3(s) that was formed by the reduction
reaction to transform into spinel in the solid-solid reaction with LSM.
As it is not assured if spinel in fact forms in a solid-solid reaction, reactions of direct
formation of spinel by the interaction between Cr-gas and LSM can be formulated (Eqs. 1.3.3
to 1.3.5) considering the main chromium molecules that interact with LSM for spinel with
X(Cr) = 2X(Mn). Such gas-solid reaction can be split into two reaction steps: formation of
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
30
Cr2O3(s) from the gas and subsequent spinel formation from Cr2O3 + LSM. The differences of
oxygen contributions to respective reactions stem from the reaction step of Cr2O3(s) formation:
1 3 1 1 3 2 43(g) 2(g)3La Sr MnO CrO La Sr Mn Cr O MnCr O 5 2 O− − − − − + ++ →x x yx x yy y yδ δ (1.3.3)
1 3 2 2(g)
1 1 3 2 4 2 2(g)H
La Sr MnO CrO (OH)La Sr Mn Cr O MnCr O O(g) +5 2 O
33
xx
x yx y
yy y y
δ
δ
− −
− − − +++ →
(1.3.4)
2(g)
1 3 2 (g)
1 1 3 2 4 2H O
La Sr MnO CrO (OH)La Sr Mn Cr O MnCr O 3 2 O(g) +3 4
3xx
x yx y
yy y y
δ
δ
− −
− − − +++ →
(1.3.5)
2) The chemical dissociation of gaseous Cr-species on the LSM surface for the cell
degradation was proposed as the key process for the degradation of SOFC caused by
chromium by another research group[24-27,32,33,37]: Mn2+ on the surface of LSM at reduced
oxygen partial pressure close to the cathode-electrolyte interface would react with gaseous Cr-
species to Cr-Mn-O nuclei, and consequently to Cr-Mn spinel and Cr2O3(s). As Mn2+ is
associated to vacancy formation in LSM that is necessary for the oxygen diffusion,[24-27,32,33,37]
oxygen diffusion is inhibited by the nuclei-formation. It can be seen from Eqs. 1.3.1 to 1.3.5
that oxygen is produced during the formation of spinel. Thus the 2Op at the locations of the
spinel formation is expected to increase. This in turn will also lead to less Mn2+ in LSM[40]
and consequently lower oxygen diffusion in LSM.
The role of the oxygen vacancy diffusion mechanism in an LSM cathode has been considered
controversially: Mogensen and Skaarup[41] concluded from the low oxygen self-diffusion
coefficients of the order of 4×10-14 cm2 s-1 at T = 1173 K[42] that long range bulk migration of
oxygen ions cannot play a significant role for the cathode performance. However they did not
discuss the dependence of oxygen diffusion upon 2Op . Huang et al.[43] confirmed these early
suggestions by evaluating the ionic conductivity of LSM from pure oxygen to 2Op = 300 Pa at
temperatures from 953 K to 1153 K using YSZ as blocking electrode. The ionic conductivity
was lower at lower oxygen partial pressures, opposite to the trend that would be expected
under the control of the vacancy diffusion mechanism. On the other hand the measured
oxygen tracer diffusion coefficient in LSM strongly increases when the oxygen partial
pressure is decreased from pure oxygen to2Op = 200 Pa[44]. Yasuda et al.[44] concluded that
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
31
oxygen ions in the bulk of LSM diffuse by the vacancy diffusion mechanism. The activation
energy for the diffusion of oxygen for LSM is in the range of 250 to 300 kJ mol-1. This is
close to 270 kJ mol-1 for La0.9Sr0.1CoO3-δ in which oxygen ions are transported by the vacancy
mechanism. This indicates that a vacancy diffusion mechanism also applies to LSM[45]. In an
investigation of active sites for the oxygen reduction at the O2/LSM/YSZ interface[46] for three
different overvoltages of cathode polarization (η = −0.336 V, η = −0.185 V, and
η = −0.090 V) using isotopic oxygen exchange and secondary ion mass spectrometry it was
found that oxygen ions can only diffuse through dense LSM at the high overvoltage of
η= − 0.336 V corresponding to 2Op = 10-4 Pa[46]. The calculated amount of oxygen vacancies
(δ) in La0.8Sr0.2MnO3-δ at 973 K and2Op = 10-4 Pa is δ = 2.4x10-6, compared to δ = 3.94x10-9
in air[23]. This confirms the suggestion that the formation of oxygen vacancies in LSM
contributes to the oxygen diffusion at high current loads[22]. Based on the findings from the
literature it can be summarized that in LSM oxygen diffuses through grain boundaries at high
2Op , as oxygen vacancies are simply not available under these conditions. We believe that the
oxygen vacancy diffusion mechanism contributes to the oxygen diffusion under high current
loads, when the oxygen partial pressure at the cathode-electrolyte interface is decreased
significantly, as it was directly proven by isotopic and tracer diffusion[44] experiments.
Contradictory interpretations[43] from the dependence of the ionic conductivity on2Op need to
be judged with care due to the difficulty of controlling the numerous factors that can influence
the results of the blocking electrode method used.
The electrochemical reduction of CrO3(g) was rejected by the authors favoring the chemical
dissociation approach[24-27,32,33,37]. It is necessary to test the arguments for this claim of
exclusive validity: a strong tendency exists for CrO3(g) to get reduced to Cr2O3(s) at the TPB,
as Δ°G of the reduction being the inversion of reaction Eq. 1.2.1 has a large negative value. It
was also mentioned in the early paper of Caplan and Cohen[10] that substantial precipitation of
Cr2O3(s) from CrO3(g) occurred in the cooler part of the experimental setup. Reduction of
CrO3(g) to Cr2O3(s) was such predominant as to make sampling of gaseous CrO3(g) difficult.
This strong tendency for the precipitation of Cr2O3(s) makes a rejection of the reduction of
CrO3(g) as a possible process contributing to the cell degradation doubtful.
Paulson and Birss[34], as well as Konysheva et al.[21] observed the extension of dense Cr2O3-
layers into YSZ. This phenomenon was well explained by continuous feeding of an initial
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
32
Cr2O3-layer with CrO3(g), the latter becoming reduced at the new TPB consisting of YSZ and
electron-donating Cr2O3(s)[21,34], whereas an explanation by the chemical dissociation approach
is not satisfying. Thus it is obvious that the explanation of the “poisoning” process by the
chemical dissociation approach alone is not without doubt.
Some indications for two independent chromium poisoning mechanisms can be found in the
work from Jiang et al.[24,26,37]: the two phases formed in the scope of a polarized LSM cathode
exhibit distinctive microstructures: spinel forms large grains, whereas the phase that was most
likely identified as Cr2O3 occurs in fine-grained, partly layered structures. The region of
spinel formation extends several microns from the TPB into the cathode, whereas Cr2O3 is
always located directly at the cathode-electrolyte interface. From the occurrence of fine-
grained Cr2O3 the existence of a large number of nuclei for its formation is concluded, which
does not seem to be the case for the spinel phase. Furthermore, from impedance spectra
analyses it was in fact possible to distinguish two distinctive depositions of Cr-species, one
with a lower rate on the LSM surface, and the second with a higher rate on the YSZ
electrolyte surface. Also two different diffusion processes were distinguished, which both
seemed to be inhibited by chromium poisoning.
If CrO3(g) is electrochemically reduced to Cr2O3(s) in a cell, Cr2O3(s) deposition should also
occur under open-circuit conditions, which was definitively not observed. In this case the
contribution of reduction to the Cr-“poisoning” has to be rejected, and the degradation can be
associated to the dissociation process[24-27,32,33,37] and subsequent formation of spinel.
However the situation changes if the reduction of CrO3(g) is under the main control of the
oxygen partial pressure gradient towards the cathode-electrolyte interface, which is increasing
as a function of increasing polarization. In this case no chromium will be deposited at the
cathode-electrolyte interface under open-circuit conditions, whereas in a polarized cathode the
reduction of CrO3(g) takes place and competes with the oxygen reduction leading to Cr2O3(s)
deposition. This explanation is in line with the microstructural features of tested cells both
under open circuit voltage and under current load, and it is also in line with the observed
temporary reversibility of the cell deterioration[22,23,28,30,31]: by switching off the polarization
the competing reduction of CrO3(g) no longer occurs, and the normal charge transfer can take
place by switching it on again.
But how can one explain the strictly localized deposition of Cr2O3 that also occurs under
anodic polarization[37]? Under oxidizing conditions little Mn2+ is expected to be present in
LSM[40], thus the formation of nuclei by the proposed LSM-Cr interaction won’t occur. This
is in contrast with the complicated mechanism for the formation of Cr2O3(s) under anodic
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
33
polarization established by Jiang et al.[37] that includes diffusion of Mn3+/Mn2+ driven by the
oxygen evolution reaction at the cathode/electrolyte interface, again with Mn2+ acting as agent
for the formation of Cr-Mn-O nuclei, the number of the latter being less than under cathodic
polarization, and thus lack of spinel formation. Alternatively, the following simple
explanation for strictly localized Cr2O3(s) formation under anodic polarization can be given: in
an LSM cathode the reduction of gaseous Cr-species is expected to be localized at the triple
phase boundary, where the reaction partners for the reduction, electron-donating LSM and
oxygen-accepting yttrium-stabilized zirconia (YSZ) are available[38]. Oxygen deficiency is
negligible in LSM under high2Op [40], and thus under these conditions LSM has no tendency at
all to accept oxygen, contrary to the situation of a strong 2Op gradient under cathodic
polarization. This is a simple and consistent explanation for a strict localization of Cr2O3(s)
formed by reduction of gaseous Cr-species even under anodic conditions.
In cell tests of a polarized platinum electrode using a Cr-containing interconnect no Cr was
observed, contrary to an LSM electrode. This different behavior of Pt and LSM electrodes
under Cr-poisoning was used as an evidence for the exclusive validity of the dissociation
approach, based on an early finding that LSM behaves like a metallic electrode at low
polarization potentials[47] that was not quantified. However this conclusion was not tested in
the light of the oxygen partial pressure gradient towards the electrode-electrolyte interface:
contrary to platinum, vacancies are expected to form in LSM under increasing polarization,
and in LSM a 2Op gradient is expected under polarization, which is indeed not the case in a
platinum cathode. This once again may favor the reduction of CrO3(g) and gaseous Cr-
oxyhydroxide resulting in Cr2O3(s) deposition at the cathode-electrolyte interface in LSM,
opposite to the situation with a platinum cathode.
It was further mentioned that the existence of Cr-containing products away from the TPB
would be in disagreement with the reduction approach. This is indeed true for the case of
CrO3(g) and Cr-oxyhydroxide reduction being the only Cr-poisoning mechanism. However, if
both the chemical dissociation as well as the reduction of gaseous Cr-species is occurring with
different proportions, this apparent antagonism is abolished. In this context experimental
results of a half-cell test with Cr-Fe-alloy (RA446) interconnect, LSM cathode and a YSZ
electrolyte at T = 1173 K and a current density of 200 mA cm-2 from Zhen et al.[27] are
particularly interesting: the slope of the cathode polarization curve (Fig. 4 b[27]) as a function
of time reveals an inflection point after about 6 1/2 h. This is an indication against one unique
“poisoning” mechanism, but several processes may lead to the deterioration of cell
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
34
performance, and their respective influence on the cell deterioration may vary as a function of
time.
From the considerations in this chapter we conclude that no sustainable arguments exist for
the rejection of the reduction of gaseous Cr-species as one of the controlling mechanisms of
Cr-“poisoning” of SOFC.
The important role of decreased oxygen activity at the LSM-YSZ interface under current load
for the cell degradation was already suggested by Taniguchi et al.[23]. Konysheva et al.[30] give
the following explanation, why the strong oxygen partial pressure gradient in the LSM
cathode under high current densities plays a key role for the degradation: the LSM cathode
has a low electrochemically active area (TPB) near the interface with the electrolyte only.
Under polarization, the oxygen ions formed at this interface are transported from the cathode-
electrolyte interface through the electrolyte. This results in a lower oxygen partial pressure at
the interface as compared to that in air. The higher the current density under SOFC operation,
the lower is the oxygen partial pressure at the contact between LSM and YSZ. The deposition
of chromium followed by its reduction near this interface blocks direct oxygen access to the
electrochemically active sites, thereby still more decreasing the oxygen partial pressure at a
newly formed Cr2O3(s)/electrolyte interface[30]: the TPB between LSM and YSZ diminishes
more and more by the blocking of Cr2O3(s), and oxygen cannot access the TPB. As Cr2O3(s)
has a small electronic conductivity of 0.8 S m-1 at T = 1282 K[48] and 2Op = 1 Pa, the oxygen
ions from this new, weak catalytic reaction diffuse into YSZ, and the chemical activity of the
cell is furthermore deteriorating due to the lack of oxygen supply through the rather dense
Cr2O3 layer to the new TPB. The temporary reversibility of the deterioration by switching the
cell off and on again can also be explained: in contrast to current load operation, under open
circuit the LSM-Cr interactions occur randomly throughout the cathode, thus the remaining
TPB/YSZ active sites are almost unaffected under open current circuit. The small area close
to the new TPB that was strongly depleted of oxygen under current load is filled with air
leaking through remaining pores between LSM and Cr2O3. Applying a current load, the LSM-
Cr interaction is again favored in the region close to YSZ as 2Op decreases at the TPB, even
though the decrease is expected to be less due to less LSM/YSZ active sites caused by the
first degradation. Oxygen is mainly reduced at the new TPB between Cr2O3(s) and YSZ.
Reduction already takes place at higher 2Op at the beginning of the current load operation, as
electronic conductivity of Cr2O3 is significantly higher at higher 2Op (1.8 S m-1 in air[48]).
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
35
Oxygen ions diffuse into YSZ, but new oxygen is not supplied to the new TPB. Active
LSM/YSZ sites further diminish by ongoing formation of spinel and Cr2O3 deposits, and the
degradation increases as a function of time.
Fig. 1.3.2 is a visualisation of the microstructural consequences of chromium in an LSM
cathode. The reported dependence of structural features of the degraded cell on the operation
temperature, current load, and chromium content is schematized in the picture.
Fig. 1.3.2 Model of chromium poisoning of an SOFC with Cr-interconnect and LSM cathode
based on the findings in the literature. Numbers refer to locations of processes that are
decisive for the degradation
Number 1 in Fig. 1.3.2 denotes the interconnect-cathode interface region where oxidation of
Cr2O3(s) to gaseous Cr-oxides and Cr-oxyhydroxides by Eqs. 1.2.1 to 1.2.3 occurs, followed
by diffusion of the gaseous products into the cathode. Number 2 denotes the region of
interactions between LSM and chromium leading to spinel formation by solid-solid reaction,
Eqs. 1.3.1 to 1.3.2, or gas-solid reaction, Eqs. 1.3.3 to 1.3.5, and number 3 denotes the
reduction of gaseous Cr-species by the reverse of Eq. 1.2.1 leading to the redeposition of
Cr2O3(s) at the cathode-electrolyte interface.
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
36
1.4 Proposed strategies against chromium “poisoning” and their
effectiveness
1.4.1 Increasing the Cr-tolerance of conventional SOFC with Cr-interconnects and
LSM cathodes
More than ten years ago Badwal et al.[22] proposed that coating of the Cr-interconnect with a
protective electrically conductive dense layer would be an effective strategy against the
diffusion of Cr-species into the cathode. Several promising materials for coating applications
were developed in the following years that act as chromium diffusion barrier and hinder
growth of chromia scale at the alloy surface, thereby improving the electrical conductivity of
the interconnect-cathode interface[49-69]. However, so far volatilization could not be
suppressed completely.
Application of the following coatings upon the interconnect has been shown to considerably
reduce the diffusion of chromium into the cathode thus decreasing the cell degradation:
Electroplated metallic Co[49,50], Co-Mn, or Cu-Mn[51], sputtered Co, Ni, or Cu[52], Mn, La, or
Mn2CrO4[52], Co3O4
[53], MnCo2O4[54-61], Cu1.4Mn1.6O4
[53,54], Ce0.05Mn1.475Co1.475O4[62],
(La,Sr)CoO3[63], La0.67Sr0.33MnO3
[64], La0.65Sr0.3MnO3[58,65], La0.85Sr0.15MnO3-δ
[50],
La0.6Sr0.4Co0.8Fe0.2O3[58], La0.8Sr0.2Mn0.5Co0.5O3-δ
[66], La0.8Sr0.2Mn0.5Co0.5O3[65],
La0.8Sr0.2FeO3-δ[67], two-segment Cr-Al-Y-O nanocomposite and (Mn,Co)3O4
[68], as well as
(Ti,Al)N[69]. However, as Cr in the ppm range significantly influences the oxygen diffusion in
the LSM cathode[36], coating alone does not solve the problems associated to chromium
poisoning completely, but a combination of the quoted strategies is advisable to further
improve the long-time stability of SOFC performance.
The formation of a dense electrically isolating Cr2O3 layer is probably preventable by using
electrolyte materials or a functional layer between LSM cathode and YSZ electrolyte that can
incorporate Cr in solid solution without affecting the electrical conductivity. Furthermore
such a buffer layer may act as a sink for CrO3(g) thus diminishing nuclei formation on LSM. If
the buffer layer contains an ionic conductor, more active sites for the oxygen reduction will
result in a higher Cr-tolerance. This was recently shown for a cell with a YSZ-LSM functional
layer: a functional LSM-YSZ layer adjacent to the YSZ electrolyte led to a lower cell
degradation[30]: increasing the ionic conductivity of the LSM cathode that is predominantly
electronically conducting down to 2Op = 10-7 Pa[70] by admixture of YSZ results in an
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
37
expanded area of active sites for the oxygen reduction away from the TPB. Thus the number
of active sites is increased, and the cell is more tolerant against chromium[30]. Besides, the
reduction of gaseous chromium will not be restricted to the small area at the TPB due to a
smaller oxygen partial pressure gradient, leading to the formation of more scattered reduction
products instead of a dense layer: thus the block of oxygen diffusion into the electrolyte can
be avoided. The ionic conductivity can be increased by doping the B-site of ABO3 perovskite
with reducible cations. Ideally the selected dopants decrease the mobility of Mn2+ and thus
prevent the formation of nuclei for the adsorption of CrO3(g) without influencing the formation
of vacancies.
1.4.2 New ways – alternative materials
Badwal et al.[22] already considered alternative cathode materials to reduce or stop the
formation of the spinel phase. Matsuzaki and Yasuda[31] concluded from insignificant Cr-
deposits in tested SOFC with Cr-Fe-alloy interconnect, La0.6Sr0.4Co0.2Fe0.8O3-δ (LSCF)
cathode and Ce0.8Sm0.2O1.9 electrolyte that the ratio of the reduction of gaseous CrO2(OH)2(g)
to that of O2(g) at the electrode/electrolyte interface is controlled by the electrochemical
properties of the interface. Based on these findings they predicted that highly Cr-tolerant
cathodes can be developed.
In recent time it was found that new cathode materials such as La1-xSrxCo1-yFeyO3-δ (LSCF),
La(Ni,Fe)O3-δ (LNF), and (La,Ba)(Co,Fe)O3-δ (LBCF) are more tolerant against chromium
“poisoning”. LNF and LBCF revealed extraordinary high tolerance against chromium
poisoning. The highest tolerance against the effects of chromium under SOFC operating
conditions combined with high electrical conductivity has been reported recently for
(La,Ni)FeO3-δ [71,72], which makes this material a promising candidate for a steady long-term
SOFC performance. All these perovskites are mixed electronic-ionic conductors; particularly
LSCF and LNF show rather high ionic contributions to the total electrical conductivity.
Effects of Cr upon the degradation of La1-xSrxCo1-yFeyO3-δ (LSCF)[26,71,73], La(Ni,Fe)O3-δ
(LNF)[71,74], and (La,Ba)(Co,Fe)O3-δ (LBCF)[71,75] cathodes were investigated using
impedance spectroscopy. As for LSM these authors concluded that the mechanism of Cr
poisoning can be explained by chemical dissociation of CrO3(g) to the perovskite-structured
materials and nuclei formation in the cases of LSCF and LNF, whereas no proper nuclei were
reported for LBCF. In all these cathodes Cr-deposition was observed throughout the cathode
both under polarization and without polarization, contrary to LSM. The amount of Cr-
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Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects
38
poisoning of LSCF was considerable. The amount of deposited Cr in LSCF was even larger
without polarization than under polarization, which was explained by a removing effect of
nuclei for the chromium deposition under polarization conditions.
As an alternative to the complicated nuclei mechanism, the following considerations can be
made using the reduction model: For the reduction reaction of CrO3(g) the presence of both an
electron donor and oxygen ion acceptor is necessary, and a typical mixed ionic-electronic
conductor such as LSCF can take over both functions. Thus reduction of CrO3(g) takes place
inside the whole cathode even without being promoted electrochemically by polarization of
the cell. However under strong polarization one can expect that LSCF gets more and more
ionic conducting towards the electrode-electrolyte interface, that is towards lower oxygen
partial pressures, most likely resulting in retarding or inhibiting of the reduction reaction.
Even if the reduction reaction is considered to be the dominant mechanism of chromium
poisoning, nuclei might form in addition, but their influence on the Cr deposition compared to
the reduction of CrO3(g) cannot be decided yet. Opposite to the case of LSM no driving force
for CrO3(g) to migrate to the triple phase boundary exists due to the mixed ionic-electronic
conducting behaviour of the regarding cathodes. The higher the contribution of the ionic
conduction the less complete reduction is expected due to prolonged lack of an electron
donator. Improved inhibition of the reduction of CrO3(g) is predicted for LNF, as this phase
has a particularly high ionic conductivity.
In recent years research activities for LaCrO3-base ceramic interconnector materials were
revitalized by several groups[76-78] to circumvent the problems of chromium “poisoning”.
However, despite rapidly developing processing techniques it is not clear at the moment if the
obstacles of sinterability and low mechanical strength as well as difficult manufacturing
correlated with high costs can be coped.
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70. V.V. Kharton, E.V. Tsipis, I.P. Marozau, A.P. Viskup, J.R. Frade, J.T.S. Irvine, Mixed
conductivity and electrochemical behavior of (La0.75Sr0.25)0.95Cr0.5Mn0.5O3-δ, Solid State
Ionics, 2007, 178, pp. 101-13.
71. Y.D. Zhen, A.I.Y. Tok, F.Y.C. Boey, S.P. Jiang, Development of Cr-tolerant cathodes
for solid oxide fuel cells, Electrochem. Solid St., 2008, 11, pp. B42-6.
72. T. Komatsu, H. Arai, R. Chiba, K. Nozawa, M. Arakawa, K. Sato, Cr Poisoning
suppression in solid oxide fuel cells using LaNi(Fe)O3 electrodes, Electrochem. Solid-
State Lett., 2006, 9, pp. A9-12.
73. S.P. Jiang, S. Zhang, Y.D. Zhen, Deposition of Cr species at (La,Sr)(Co,Fe)O3 cathodes
of solid oxide fuel cells, J. Electrochem. Soc., 2006, 153, pp. A127-A134.
74. Y.D. Zhen, A.I.Y. Tok, S.P. Jiang, F.Y.C. Boey, La(Ni,Fe)O3 as a cathode material with
high tolerance to chromium poisoning for solid oxide fuel cells, J. Power Sources, 2007,
170, pp. 61-6.
75. Y. Zhen, S.P. Jiang, Characterization and performance of (La,Ba)(Co,Fe)O3 cathode for
solid oxide fuel cells with iron-chromium metallic interconnect, J. Power Sources, 2008,
180, pp. 695-703.
76. G.-Y. Lee, R.-H. Song, J.-H. Kim, D.-H. Peck, T.-H. Lim, Y.-G. Shul, and D.-R. Shin,
Properties of Cu, Ni, and V doped-LaCrO3 interconnect materials prepared by Pechini,
ultrasonic spray pyrolysis and glycine nitrate processes for SOFC, J. Electroceram., 2006,
17, pp. 723-27.
77. M. Liu, L. Zhao, D. Dong, S. Wang, J. Diwu, X. Liu, G. Meng, High sintering ability and
electrical conductivity of Zn doped La(Ca)CrO3 based interconnect ceramics for SOFCs,
J. Power Sources, 2008, 177, pp. 451-56.
78. S.P. Jiang, L. Liu, K.P. Ong, P. Wu, J. Li, J. Pu, Electrical conductivity and performance
of doped LaCrO3 perovskite oxides for solid oxide fuel cells, J. Power Sources, 2008,
176, pp. 82-89.
Page 45
Aim of study
45
2 Aim of study
Chromium poisoning of planar SOFC with LSM cathodes and Cr-alloy interconnects is a
complex process consisting of several steps that may occur simultaneously inside the cell.
Mn2+ in LSM plays an important role for the adsorption of gaseous CrO3(g) and Cr-
oxyhydroxide on LSM resulting in blocked oxygen transport from the cathode to the
electrolyte. Reduction of CrO3(g) at the TPB leads to the formation of electrically low
conducting Cr2O3, which further retards the diffusion process of oxygen into the electrolyte.
The causes and consequences of chromium poisoning are clear, and some strategies against
cell degradation caused by chromium have already been successfully applied. However, it
seems that strategies against the cell degradation have been mostly established in a rather
random way so far. For a more systematic and thus more efficient combination of strategies a
strong knowledge about the mechanisms of chromium poisoning of SOFC is required.
Previous experiments have shown that the following factors:
-) High temperature
-) Decrease of oxygen partial pressure at the TPB under current load of SOFC
and processes:
-) Interaction of chromium with LSM leading to Mn-Cr-O nuclei and/or spinel formation
-) Reduction of CrO3(g) to Cr2O3(s) at the TPB
-) Blocking of pores at the TPB by Cr2O3 and/or spinel
govern the degradation of SOFC caused by chromium.
So far it was not possible to define unambiguously, which of these processes play a dominant
role for the degradation and which don’t. In fact it was shown that without sufficient
protection against the diffusion of chromium into the cathode the degradation of SOFC
caused by chromium is not a long-term phenomenon; severe degradation has been observed
after several hours of testing under current load at state-of-the-art SOFC operating
temperatures: from the literature findings it is obvious that the degradation of SOFC caused
by chromium starts immediately after starting SOFC tests under current load. If the process of
chromium “poisoning” were completely governed by thermodynamics, this behaviour would
not be expected, but the effects of chromium would be observed only after thermodynamic
equilibrium is obtained. This means that the kinetic control on the mechanisms of chromium
Page 46
Aim of study
46
is high, and a degrading cell is in a non-equilibrium state particularly at the early stages of the
degradation.
The following questions have remained unsolved so far:
-) Does spinel form by a solid (LSM)-solid (Cr2O3) reaction or directly in a solid (LSM)-gas
(gaseous Cr) reaction?
-) Can the concentration of deposits at the cathode-electrolyte interface under current load be
explained by thermodynamics?
-) How does the LSM phase chemically change due to the interaction with chromium, and can
this change be explained by thermodynamics?
-) Which of the phases observed in LSM contaminated by chromium form under
thermodynamic control, and what are the conditions that favour their formation?
This work aims to answer these questions by the application of thermodynamic calculations.
Therefore the thermodynamic La-Sr-Mn-Cr-O oxide database needs to be established based
on the assessments of low-order subsystems.
In recent times many materials have been tested for SOFC cathodes. In particular LSM
cathodes have been intensively investigated over the last decade, and several studies can be
found regarding the degradation of LSM cathodes caused by chromium. Thus, and as LSM
cathodes are still considered to serve as promising cathodes due to their high electrical
conductivity and stability at SOFC operating conditions, in this study the author focuses on
the effects of Cr on the degradation of SOFC with LSM cathodes.
3 Method
3.1 Benefits of the thermodynamic La-Sr-Mn-Cr-O oxide database for
the understanding of Cr-poisoning of SOFC
A thermodynamic La-Sr-Mn-Cr-O oxide database is highly desirable to enable fundamental
understanding of the mechanisms of chromium “poisoning” of LSM cathodes for SOFC. As a
degrading cell is in a non-equilibrium state, the obvious question why the results of
thermodynamic calculations should be feasible for a deeper understanding of the mechanisms
Page 47
Method
47
of chromium “poisoning” needs some explanation: from the conditions of the non-equilibrium
state at the beginning of the degradation process, including the operating temperature,
composition of LSM, and the rate of chromium diffusion the equilibrium state of chromium
“poisoning”, can be calculated using the thermodynamic La-Sr-Mn-Cr-O oxide database:
Cnon -equilibrium (A) equilibrium (B)⎯⎯→ (3.1.1)
By calculating thermodynamic equilibria for a LSM cathode that is affected by chromium (A)
in the relation above, the theoretical final state of chromium poisoning after a very long time
is found by thermodynamic equilibrium calculations (B). For instance, by choosing the
starting conditions composition of LSM and defined amount of Cr at a specific temperature,
using the thermodynamic database one can calculate the expected thermodynamic
equilibrium, for instance under reducing oxygen partial pressures reflecting the situation at the
TPB under current load. Over time the system LSM + Cr will change from its non-
equilibrium state at the beginning of the Cr-“poisoning” process towards the calculated
equilibrium state. C in Eq. 3.1.1 reflects the path the system takes towards its equilibrium
state. From A and B, C can be predicted for changing cathode compositions, temperatures,
and oxygen partial pressures. Hence, taking into account experimental data on the chromium
“poisoning” of SOFC and using a thermodynamic La-Sr-Mn-Cr-O oxide database, one can
draw conclusions on the evolution of the phase chemistry of degraded LSM cathodes.
The presented thermodynamic database of the La-Sr-Mn-Cr-O oxide system is constructed
using the CALPHAD approach[1]. It contains the optimized Gibbs energy functions of solid
oxide phases: for stoichiometric phases as a function of temperature, and for solid solution
phases as a function of temperature and composition. The optimization of model parameters is
based on the accurate assessment of experimental thermodynamic and phase diagram data of
oxide subsystems.
3.2 Thermodynamic modeling
3.2.1 Stoichiometric solid oxides
The stoichiometric ternary phase α, containing m and n moles of two different sorts of
cations, a with the positive electrical charge r and b with the positive electrical charge q,
Page 48
Method
48
respectively, and p moles of one sort of anions, c with the negative electrical charge s, the
three types of ions sitting in three distinctive crystallographic sublattices, can be described by
the sublattice formula ( ) ( ) ( )qr sm n pa b c . For oxides c = O and charge s = −2. To account for the
charge neutrality criterion, Eq. 3.2.1 is true.
2 0mr nq p+ + = (3.2.1)
The molar Gibbs energy of α, m°Gα at constant pressure is given by
( 1)2 3lnm−° = + + + + +G A BT CT T DT ET FTα (3.2.2)
A, B, C, D, E, and F are model parameters to be optimized by thermodynamic and phase
diagram data. As Cp(α) is defined by
2 22 6 2 −= − − − −pC C DT ET FT (3.2.3)
C, D, E and F are optimized to heat capacity data only. m°Gα can be based on the molar Gibbs
energies of existing binary oxides Ox1: 2-( ) (O )rt ua and Ox2: 2-( ) (O )q
v wb ( , , , N∈t u v w ), if it is
assumed that the heat capacity of the ternary oxide composed by the two binary oxides is
simply the sum of the heat capacities of the composing oxides as shown in Eq. 3.2.4:
22- 2-2-( ) ( ) (O ) ( ) (O )( ) (O ) O (g)
2m m m m m° ° ° ° ° +− −= = + + +
qr qrm n p v wt ua b ba ptv muv nwtm nG G G G G A BTt v tv
α (3.2.4)
m°Gα is the Gibbs energy of formation of the phase α relative to the oxide components. A and B
are optimized by thermodynamic and phase diagram data.
3.2.2 Solid solution phases – the Compound Energy Formalism (CEF)
If in the binary oxide Ox1: 2-( ) (O )rt ua containing cation a with the positive charge r, another
sort of cation with the positive charge q, qb can sit in the same sublattice as a, the sublattice
formula of the resulting solid solution phase β(ss) reads 2-( , ) (O )qrt ua b . Eq. 3.2.5 is the
criterion for charge neutrality:
Page 49
Method
49
( )2
a bt y q y qu
+= (3.2.5)
Using the Compound Energy Formalism (CEF)[2-4], the molar Gibbs energy of the solid
solution phase contains the Gibbs energies of the compounds. For β(ss) the two compounds
read 2-( ) (O )rt ua and 2-( ) (O )q
t ub . The Gibbs energy of β(ss) at constant pressure reads
( )2-2- ( ) (O )( ) (O ) ln lnqr
t ut ur q r r q r
baa a a ab bG y G y G tRT y y y y Gβ β° = + + + +ss ° ° E ss
m m (3.2.6)
where ray is the site fraction of cation a on the cation sublattice, and qby is the site fraction
cation b on the cation sublattice. R=8.31451 J mol-1 K-1. The second-last term accounts for the
configurational entropy of mixing of t moles of a and b. The last term describes the excess
Gibbs energy of mixing due to interactions of ions in the mixture that can be accounted for by
introducing interaction parameters.
3.2.3 Vacancies and the concept of reciprocal reactions
Let us consider the case of a binary oxide phase (A)2(B)3, A standing for the cation sublattice,
and B denoting the anion sublattice, with only one cation a accepting the charge 3+ or 2+ in
the cation sublattice. If the cation is reduced, the charge neutrality criterion is no longer
obeyed by an anionic sublattice that is completely filled with oxygen. Charge neutrality under
such reducing conditions can be remained by the formation of zero-charged vacancies (Va) in
the anionic sublattice resulting in the phase becoming oxygen-nonstoichiometric. In the
sublattice form the phase can be written as 3 2 2-2 3( , ) (O ,Va)+ +a a . The oxygen nonstoichiometry
is denoted “O3-δ”. The molar Gibbs energy of the phase at constant pressure reads
( ) ( )
3 2 2- 3 2- 2 2- 32 3 2 3 2 3 2 3 2 3
3 2- 2 2- 3
2 3 2 2-2 3 2 3
2 3 3 2 2 2- 2-
A O ( , ) (O ,Va) ( ) (O ) ( ) (O ) ( ) (Va)VaO O
( ) (Va) ( , ) (O ,Va)Va Va VaO O
2 ln ln 3 ln ln
a a a a aa a a
a a aa a a a a
G G y y G y y G y y G
y y G RT y y y y RT y y y y G
δ+ + + + +
−+ + +
+ + +
+ + + + +
° °= = + +
+ + + + + +
° ° °m m m m m
° Em m
(3.2.7)
Once again the molar Gibbs energies of all the 4 endmember compounds 3 2-2 3( ) (O )+a ,
2 2-2 3( ) (O )+a , 3
2 3( ) (Va)+a , and 22 3( ) (Va)+a of the phase are required for the molar Gibbs energy
Page 50
Method
50
of the phase. However, the only neutral endmember is 3 2-2 3( ) (O )+a . It thus can exist, and its
molar Gibbs energy can be defined by optimization of model parameters by experiments. The
three other endmembers are charged and cannot exist, but a line of neutral compositions
connects 3 2-2 3( ) (O )+a with the reduced compound 2 2-
2 3( ) (2 3O Va)+a , and its Gibbs energy can
be optimized with experiments that are related to the reduction of the phase, for instance
oxygen nonstoichiometry data.
The composition square of the phase can be seen in Fig. 3.2.1 that is redrawn from Hillert[4],
with the neutral line and the reduced compound, denoted with R, included. The 2+ charged
center composition of the square, 3 2 2-2 3( ) (3 2O 3 2Va)+ +a a , denoted with A in Fig. 3.2.1, is
theoretically obtained by mixing equal amounts of either 3 2-
2 3( ) (O )+a and 22 3( ) (Va)+a or 3
2 3( ) (Va)+a and 2 2-2 3( ) (O )+a .
Fig. 3.2.1 The surface of reference for the Gibbs energy of the reciprocal
phase 3 2 2-2 3( , ) (O ,Va)+ +a a approximating its overall Gibbs energy for Δ°Grec > 0 and Δ°Grec = 0,
plotted above the composition square.
A system that obeys this relation is called a reciprocal system, and 3 2 2-2 3( , ) (O ,Va)+ +a a is a
reciprocal phase[4].
For an unambiguous definition of the molar Gibbs energy of the reciprocal phase it is
necessary to give an arbitrary molar Gibbs energy to a reference. As the chosen molar Gibbs
energy of the reference is unlikely the true value, the reference should favorably be a highly
charged compound, thus far off neutral compositions that can really exist. For the example of
the reciprocal solid solution phase 3 2 2-2 3( , ) (O ,Va)+ +a a the 6+ charged compound 3
2 3( ) (Va)+a is
chosen as reference.
Page 51
Method
51
The surface of reference for the Gibbs energy of the reciprocal phase 3 2 2-2 3( , ) (O ,Va)+ +a a at
very low temperatures (to make the configurational entropic contribution negligible), and
without excess terms for the Gibbs energy is visualized in Fig. 3.2.1 (page 50) and
approximates the whole Gibbs energy of the phase. The morphology of the Gibbs energy
surface depends on Δ°G of the reciprocal reaction 3
2 3( ) (Va)+a + 2 2-2 3( ) (O )+a − 3 2-
2 3( ) (O )+a − 22 3( ) (Va)+a :
3 2 2- 3 2- 2
2 3 2 3 2 3 2 3( ) (Va) ( ) (O ) ( ) (O ) ( ) (Va)rec ° ° °+ + + +° °Δ = + − −a a a aG G G G G (3.2.8)
If Δ°G of the reciprocal reaction, Δ°Grec is positive, the Gibbs energy surface is curved, and
the theoretic compound A will tend to demix to 3 2-2 3( ) (O )+a and 2
2 3( ) (Va)+a by only slightly
oxidizing or reducing it. On the other hand, if Δ°Grec is zero, the Gibbs energy surface is flat
and no tendency of demixing of A exists. In Fig. 3.2.1 (page 50) only the edge of this plane is
seen as bold line. Note that in order to obtain the same Gibbs energy of the reduced
compound R for Δ°Grec > 0 and Δ°Grec = 0, when the Gibbs energies of the endmember 3 2-
2 3( ) (O )+a and the reference 32 3( ) (Va)+a are fixed, the Gibbs energies of the remaining
endmembers are significantly different for Δ°Grec > 0 and Δ°Grec = 0. This is not a problem for
the description of a reciprocal oxide phase, as long as these endmembers are charged and
away from the existing composition range of the phase. Anyway, the true surface shape of a
reciprocal oxide phase with charged endmembers is not known. As no tendency of demixing
was reported for the nonstoichiometric oxide solid solutions that are treated in this study, and
no experiments define a proper value of the reciprocal reaction parameter, it is legitimate to
define Δ°Grec = 0.
3.2.4 Calculation of defect chemistry using the Calphad approach
The Calphad approach is very powerful for the calculation of the defect chemistry of high-
order nonstoichiometric reciprocal solid solution oxide phases[5] such as (A)(B)O3-δ
perovskite with a complex sublattice formula, for instance 3 2 2 3 4 3+ 4+ 2-
3( , ,Va)( , , , , ,Va)(O ,Va)+ + + + +a b c c c d d for a Cr-doped LSM perovskite as a function of
composition, temperature, and oxygen partial pressure. For this purpose model parameters of
the reduced and oxidized compounds are optimized with experimental information on charge
carriers, site fractions and oxygen content.
Page 52
Method
52
3.3 Optimization of model parameters
The optimization of the thermodynamic parameters was performed using the PARROT
module of the Thermo Calc[6] database system. PARROT can take into account all sorts of
thermodynamic and phase diagram data simultaneously. The program minimizes the sum of
squared errors between calculated and experimentally determined phase diagram and
thermodynamic data. As the use of all the experimental data in a simultaneous least square
calculation often leads to divergence, the authors selectively adjusted the relative weight of
each experimental data point and excluded data that were inconsistent with the majority of the
data points during the optimization procedure. This weighting process is based on the accurate
assessment of experimental thermodynamic and phase diagram data.
References
1. N. Saunders, A.P. Miodownik, Calphad Calculation of Phase Diagrams, Pergamon
Materials Series, Vol. 1. Elsevier Science Ltd., 1998, 479 p.
2. J.-O. Andersson, A.F. Guillermet, M. Hillert, B. Jansson, B. Sundman, A Compound-
Energy Model of Ordering in a Phase with Sites of Different Coordination Numbers, Acta
Metall., 1986, 34, pp. 437-445.
3. M. Hillert, B. Jansson, B. Sundman, Application of the Compound-Energy Model to
Oxide Systems, Z. Metallkd., 1988, 79(2), pp. 81-87.
4. M. Hillert, The Compound Energy Formalism, J. Alloy. Cmpd., 2001, 320, pp. 161-76.
5. A.N. Grundy, E. Povoden, T. Ivas, L.J. Gauckler, Calculation of Defect Chemistry Using
the CALPHAD Approach, Calphad, 2006, 30, pp. 33-41.
6. B. Sundman, B. Jansson, J.O. Andersson, The Thermo-Calc databank system, Calphad,
1985, 9(2), pp. 153-90.
Page 53
Thermodynamic assessments
53
4 Thermodynamic assessments
4.1 Thermodynamic reassessment of the Cr-O system in the framework
of solid oxide fuel cell (SOFC) research
E. Povoden, A.N. Grundy, and L.J. Gauckler
J. Phase Equilib. Diff., 2006, 27, pp. 353-62.
A comprehensive compilation and evaluation of experimental and thermodynamic data for the
Cr-O system is presented and, by application of the CALPHAD method, a consistent set of
thermodynamic model parameters is optimized based on new experiments. Nonstoichiometry
of eskolaite (Cr2+xO3) is described using the compound energy model, and the liquid is
described using the two-sublattice model for ionic liquids. Cr3O4 is described as a
stoichiometric compound. Also the magnetic transition in Cr2O3 and the oxygen solubility in
Cr are modeled.
4.1.1 Technology
SOFC offers high fuel conversion efficiencies and, due to the high operating temperature
(>1173 K), combined heat- and power-generation capability. For the planar design SOFC,
which offers low fabrication costs, ceramic and metal interconnect materials have been tested
and evaluated over the years. Meanwhile the use of Cr-based alloy interconnect materials has
gained popularity due to their relative ease of fabrication, low manufacturing costs and high
thermal conductivity[1]. Namely a Cr5Fe1Y2O3 oxide dispersion strengthened alloy with the
composition 94 wt.% Cr, 5 wt.% Fe and 1 wt.% Y2O3 developed jointly by Plansee and
Siemens with satisfying material properties has been promoted as a suitable alternative to the
earth alkaline-doped LaCrO3 ceramics interconnect. However, the use of this alloy as an
interconnect material in SOFC leads to the degradation of the fuel cell performance especially
on the cathode side of the fuel cell. Loss of performance caused by the migration of Cr
originating from the alloy interconnect is well documented by several investigators.
Microstructural analyses of the cathode of SOFC show the formation of Cr2O3 and
(CrMn)3O4, which block active sites as well as pores, thus substantially reducing the triple-
Page 54
Thermodynamic assessments
54
phase boundary area for the normal oxygen reduction reaction at the cathode/electrolyte
interface.
The influence of Cr from the interconnect alloy on the strontium-doped lanthanum manganite
(LSM) cathode can be modelled in terms of an equilibrium thermodynamic view to contribute
to strategies for reducing the SOFC chromium poisoning process by optimizing SOFC
operating conditions and refining SOFC material compositions.
4.1.2 Experimental data
Phase diagram data:
Experimental investigations of phase diagrams in the Cr-O system were made by Ol’shanskii
and Shlepov[2] and Toker[3]. These authors document the existence of a large miscibility gap
between the metallic and the oxide melt. Eskolaite (Cr2O3) is the dominating stable oxide
phase over a wide temperature range. Results of special points in the Cr-O phase diagram
from several studies are summarized in Table 4.1.1.
Table 4.1.1 Special points in the Cr-O system
Melting of
Cr2O3 in
air, T (K)
Eutectic
T (K)
Eutectic
compo-
sition,
X(O)
Cr3O4
detected
Stability
range
of Cr3O4,
T (K)
Mono-
tectic
T (K) Reference
2257 -- -- -- -- -- Kanolt[4]
experimental
2317 -- -- -- -- -- Wilde and Rees[5]
experimental
2603 -- -- -- -- -- McNally et al.[6]
experimental
2543 ± 25 -- -- -- -- -- Bunting[7]
experimental
Page 55
Thermodynamic assessments
55
-- 1933 0.52 no -- 2083 Ol’shanskii and
Shlepov[2], experimental
-- 1918 0.523 no -- 2083 Johnson and Muan[12]
experimental
2571 1941 0.513 yes 1923 –
1978 --
Degterov and Pelton[39]
calculated
-- 1929 0.496 yes 1918 –
1974 2160
Kowalski and Spencer[40]
calculated
-- 1937 0.499 yes 1923 –
1978 2130
Taylor and Dinsdale[41]
calculated
-- 1938 ± 2 0.497 yes 1923 ± 2 –
1978 ± 3 2083
Toker et al.[13]
experimental
2539 1938 0.497 yes 1918 –
1973 2117 This work, calculated
Note: Itallicized data were used for optimization
The melting temperatures of eskolaite in air reported from Kanolt[4] and Wilde and Rees[5] can
be discarded as being too low. Mc Nally[6] measured a melting temperature of 2603 K in air
using an induction furnace. This value significantly deviates from the result of Bunting[7],
who measured T = 2543 ± 25 K also in air. Grube and Knabe[8] found that 1 wt.% Cr2O3
lowers the melting point of metallic Cr from T = 2163 K to between T = 2043 K and 2063 K.
Lam[9] reported the existence of molten chromium with oxygen impurities of 1400 ppm at
T = 2133 K. The monotectic reaction of Cr (bcc) metal and liquid was found at T = 2083 K by
Grube and Knabe[8] and by Ol’shanskii and Shlepov[2]. The question of the existence of a
crystalline Cr3O4 phase was discussed controversially by several authors. Investigations made
by Hilty et al.[10] and Hook and Adair[11] led them to postulate the existence of a crystalline
Cr3O4 phase in the Cr-Fe-O system. Concerning the pure Cr-O system, Ol’shanskii and
Shlepov[2] and Johnson and Muan[12] did not find Cr3O4 up to the eutectic temperature of
chromium oxide, whereas Toker et al.[13] concluded from microstructural observations and a
discontinuity in the slopes of the temperature-oxygen pressure curves for univariant equilibria
involving metallic Cr and various chromium oxide phases that a Cr3O4 phase exists in a
narrow temperature range between T = 1923 K and 1978 K. Microstructures of a quenched
Page 56
Thermodynamic assessments
56
chromium melt with maximum oxygen impurities of about 2930 ppm lately investigated by
Lam[9] document an inner Cr3O4 phase and an outer Cr2O3 phase in dispersed oxides in large
chromium grains and grain boundaries. This indicates that the first phase to crystallize on
solidification is Cr3O4 giving strong evidence for the stability of this phase. Thus in this study
the authors accept the findings of Toker et al.[13] and Lam[9].
Thermodynamic data:
Oxygen Potentials:
Grube and Flad[14] measured 2Olog( )p values for the Cr-Cr2O3 equilibrium between
T = 1053 K and 1573 K by both oxidizing Cr to Cr2O3 and reducing Cr2O3 to Cr in a flowing
H2-H2O atmosphere. At T ≥ 1573 K they were confronted with the loss of a quarter of Cr in
the case of oxidation; thus at these temperatures 2Olog( )p values were determined solely from
the reduction of Cr2O3. Novokhatskii and Lenev[15] studied the equilibrium of the reduction of
Cr2O3 to Cr with hydrogen from T=1493 K to 1893 K. These authors used a flow method
where thermal diffusion problems were suppressed by inserting corundum bushes into the
reaction tube. Appreciable sublimation of metallic chromium was not observed. Davies and
Smeltzer[16] determined 2Olog( )p values of Cr2O3 at T=1173 K, 1273 K, and 1373 K, using an
electrochemical cell with a calcia-zirconia electrolyte and a Fe/FeO reference electrode. Toker
et al.[13] measured 2
log( )Op values of Cr2O3 by equilibrating Cr and Cr2O3 in H2-CO2 mixtures
of known oxygen potentials at temperatures from T = 1773 K to 2098 K. Pehlke et al.[17] used
two separate series of emf measurements employing the solid oxide electrolyte galvanic cell
technique from T = 1148 K to 1548 K. The reversibility and accuracy of the yttria-doped
thoria electrolyte and the electrode was tested by measurements of a standard iron-chromium
alloy at 1326 K. The independent results of corrected cell potentials of the two measurement
series are excellent. The data are in close agreement with the gas-solid equilibrium
measurements by Jeannin et al.[18]. Disagreement between the emf results from Pehlke et
al.[17], Pugliese and Fitterer[19], and Tretjakow and Schmalzried[20] were assigned to possible
electronic conduction in the zirconia electrolyte used by the latter authors, as well as transport
of oxygen ions from the cathode to the Cr/Cr2O3 anode. Applying the same technique as
Pehlke et al.[17], Holzheid and O’Neill[21] noted a deviation from the well-established trend
from T = 900 K to 1300 K for high-temperature data caused by finite electronic conductivity
at elevated temperatures, causing transfer of oxygen through the cell, as well as the
importance of sufficient time to attain equilibrium, that is, days for T < 1100 K. The obtained
Page 57
Thermodynamic assessments
57
dissociation pressures of Cr2O3 are in agreement with average values derived from emf studies
using an yttria-doped thoria electrolyte worked out by Jacob[22] and a very high temperature
gas-mixing study of Toker et al.[13].
Heat Capacities, heat Contents, and entropies:
Anderson’s[23] calorimetric data set of Cp-values lacks detailed documentation of the
experimental procedure. Bruce and Cannell[24] applied a two-dimensional temperature wave
method using a single crystal of Cr2O3 to calculate specific heat in the temperature range
290.68 ≤ T ≤ 323.43 K, and fitted the data to the heat of diffusion equation that considers
some material properties employing a least-mean-squares fit. The accuracy of this study is
evident from excellent data reproduction by performing two runs in the entire temperature
range. Documentation of the experiments, data presentation, and fitting procedure are worked
out very carefully. Resulting Cp data correspond nicely to the most recent calorimetric results
from Klemme et al.[25]. The latter authors measured a consistent data set of heat capacities of
synthetic eskolaite from T = 1.5 K to 340 K with mean increments of 0.56 K. Uncertainties of
0.4 % for Cp (20 K < T < 200 K) and 0.7 % for Cp (T < 20 K) were estimated. For Cp(Cr2O3) =
120.37 J mol-1 K-1 at T = 298.15 K Chase et al.[26] relied on the calculated results from heat
content measurements performed by Kelley et al.[27]. The latter authors fitted their data
measured from T = 400 K to 1800 K by
2 1
298K 2 ° ° −− = + + +TbH H aT T cT d (4.1.1)
yielding
3 2 5 1
298K 28.53 1.10 10 3.736 10 9759° ° − −− = + × + × −TH H T T T (4.1.2)
Temperature derivation of Eq. 4.1.2 results in
3 5 228.53 2.20 10 3.736 10− −= + × − ×pC T T (4.1.3)
For K298° S (Cr2O3) Chase et al.[26] relied on the results from Anderson[23], who calculated
K298° S (Cr2O3) = 81.17 ± 0.84 J K-1mol-1 by a graphical method of plotting the heat capacity
against the logarithm of the temperature and modeling the heat capacity curves with Debye
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Thermodynamic assessments
58
functions. This procedure was critically documented by other authors, for example, Klemme
et al.[25]. Klemme et al.[25] recommend K298° S (Cr2O3) = 83.1 J K-1mol-1 by reevaluating emf
data from Holzheid and O’Neill[21], who calculated K298° S (Cr2O3) = 85.74 ± 1.3 J K-1 mol-1
from their measurements. Dellien et al.[28] adopted their K298° S (Cr2O3) value from Wagman et
al.[29].
Shirokov[30] estimated K298° S of a metastable CrO phase to be 46.86 J K-1 mol-1.
Enthalpies of Formation:
Roth and Wolf[31] found 298Kf,el°Δ H (Cr2O3) = –1125.8 ± 2.5 kJ mol-1 (el=elements) by
applying a calorimetric technique. Mah[32], using a bomb calorimetric combustion technique
at 1323 K and 30 atm oxygen pressure, calculated 298Kf,el°Δ H (Cr2O3) =–1140.98 ± 1.7 kJ mol-1
.
Some difficulty caused by moisture adsorption was encountered in weighing the combustion
products. This was circumvented by heating the combustion products to T = 1323 K. For the
calculation of 298Kf,el°Δ H (Cr2O3) the heat content data given by Kelley et al.[27] were used.
Ramsey et al.[33] used heat capacity and entropy data from tabulations of Coughlin[34] to
obtain 298Kf,el°Δ H (Cr2O3) = –1122.06 kJ mol-1. Navrotsky[35] cited Garrels and Christ[36] for
298Kf,el°Δ H (Cr2O3) = –1128.42 kJ mol-1. Chase et al.[26] evaluated 298Kf,el
°Δ H (Cr2O3) = –1134.7
± 8.4 kJ mol-1 from several earlier studies, while Dellien et al.[28] adopted 298Kf,el°Δ H (Cr2O3) =
–1139.72 kJ mol-1 from Wagman et al.[29]. Klemme et al.[25] recommended 298Kf,el°Δ H (Cr2O3)
= –1128.2 ± 0.4 kJ mol-1 by evaluating emf data from Holzheid and O’Neill[21].
Shirokov[30] estimated 298Kf,el°Δ H (CrO) = –305.4 kJ mol-1 for metastable CrO.
4.1.3 Previous assessments of the Cr-O system
Banik et al.[37] established a phase diagram for the Cr-O system based on a subregular
solution model that is in good agreement with experimental data obtained by Ol’shanskii and
Shlepov[2], thermodynamic data for Cr-Cr2O3 from Fromm and Gebhardt[38], and
thermodynamic estimates for CrO from Shirokov[30]. Degterov and Pelton[39] reassessed the
CrO-Cr2O3 subsystem for the molten slag database using a modified quasi-chemical model for
the liquid phase. Their calculated liquidus temperature of Cr2O3 in air is T = 2571.16 K,
which is in good agreement with an early finding by Bunting[7] who measured T = 2543
± 25 K. Kowalski and Spencer[40] used the associated solution model for the liquid phase
based on the experimental data used by Taylor and Dinsdale[41]. The latter authors proposed a
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Thermodynamic assessments
59
phase diagram in good agreement with the experimental data obtained by Toker[3], using the
same thermodynamic models as the authors use in this work, which are the two-sublattice
ionic model for the liquid and the compound energy model for the Cr2+xO3 phase. Taylor and
Dinsdale[41] fitted Cp data from Anderson[23] close to the antiferromagnetic to paramagnetic
transition and data from Chase et al.[26] at elevated temperatures as a sum of magnetic and
nonmagnetic contributions. Experimental information on phase relations for their assessment
was taken from Ol’shanskii and Shlepov[2], Toker[3], Kelley et al.[27], and Grube and Knabe[8].
The heat capacity of Cr3O4 was taken as 7/5 times the nonmagnetic value for Cr2O3 according
to Neumann and Kopp’s rule. Their calculated values for the enthalpy of formation and the
entropy of Cr3O4 are in agreement with an estimate done by Chipman[42].
Their optimization of one of the charged endpoints in their compound energy model for
eskolaite and the use of six interaction parameters to describe the liquid may lead to problems
on extrapolation to higher-order systems, especially as their miscibility gap does not close on
increasing temperature. The use of six parameters for the description of the Cr3O4 phase is
somewhat incommensurate with the scanty experimental information of this phase.
There is a large uncertainty concerning the exact melting point of Cr2O3, and only few
thermodynamic data of the Cr3O4 phase and the liquid phase exist. This is reflected by
significant variations of the position of the eutectics, the stability field of Cr3O4, and the
temperature of the monotectic reaction of Cr(bcc) and liquid between the assessments of the
Cr-O system.
4.1.4 Thermodynamic modeling
Solid phases:
The crystal structure of eskolaite is α-Al2O3 type, space group R3c . Eskolaite shows an
antiferromagnetic to paramagnetic transition at T = 305.5 K. The magnetic properties of
eskolaite can be described using a magnetic ordering model proposed by Inden[43], and
simplified by Hillert and Jarl[44]. In this model, a magnetic contribution to the Gibbs energy is
added to the nonmagnetic part of the Gibbs energy given as:
MAGmΔ = ln β τ( +1) ( )G RT f (4.1.4)
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60
where β is a parameter related to the total magnetic entropy, and τ = T/Tc. Tc is the critical
temperature for magnetic ordering. Tc and β are both dependent on the composition. The
magnetic parameter p equals 0.28.
The defect chemistry of Cr2+xO3 with the sublattice occupation (Cr2+,Cr3+)2 (Cr3+,Va)1 (O2-)3
can be modeled using experimental data from Matsui and Naito[45]. This means that reduction
is accomplished by the formation of interstitial Cr3+ and not by the formation of oxygen
vacancies, which is in agreement with Young et al.[46]. When modeling nonstoichiometry in
an oxide phase, it is important to submit the experimental data to a defect-chemistry analysis.
In the case of Cr2+xO3 modeled with interstitial Cr3+ the defect reaction reads
(g)•••
Cr O Cr O 2'2Cr Va 3O 3 2Cr 1 2Cr 1 4Va 9 4O 3 8O + + → + + + +x x x x x
i i i (4.1.5)
giving the equilibrium constant
3 2 ••• 1 2 1 4 9 4 3 8
Cr O O22 3
Cr O
'[Cr ] [Cr ] [Va ] [O ][Cr ] [Va ][O ]
=x x
i ir x x x
i
pK (4.1.6)
Assuming small defect concentrations all concentrations except Cr'[Cr ]and •••[Cr ]i are ~ 1 and
can be ignored. Due to charge neutrality the relation •••Cri'[Cr ] 3[Cr ]= must hold. Inserting this
into Eq. 4.1.6 gives the proportionalities ••• 3 16Oi 2
[Cr ] −∝ p and 3 16Cr O2'[Cr ] −∝ p . To explain their
experimental results Matsui and Naito[45] proposed a defect reaction that leads to the same
proportionality; however, their equation violates the fundamentals of defect chemistry and
must be rejected in favor of the defect reaction given above (Eqs. 4.1.5 and 4.1.6). The
following other interstitial defects could be assumed: ••Cri giving a slope of 1 4O2
−p , and
••••Cri giving a slope of 3 20O2
−p . Both are unlikely: the former because it is unlikely to get Cr4+
on reduction, the latter because of the large size of Cr2+. Assuming the defect reaction that
describes the formation of oxygen vacancies:
(g)••
Cr O Cr O 2'Cr 1 2O Cr 1 2Va 1 4O+ → + +x x (4.1.7)
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61
leads to a proportionality of •• 1 6O O2
[Va ] −∝ P and 1 6Cr O2'[Cr ] −∝ P . This slope does not correspond
to the experimental findings of Matsui and Naito[45]. Also the defects cannot explain the
electrical properties measured by Young et al.[46].
The low nonstoichiometry data from Matsui and Naito[45] show a different slope than their
higher nonstoichiometry data. In contrast to Matsui and Naito[45] who explain this assuming
that neutral Cr forms interstitially, the present authors believe that the different slopes are
caused by a competing defect reaction, for example charge disproportionation,
Cr3+ → Cr2+ + Cr4+, similar to the case of LaMnO3 perovskites[47]. The present authors didn’t
consider this by their defect chemistry model, as it would make the description quite complex.
Fig. 4.1.1 is a graphic representation of the model the authors use to describe the oxygen
nonstoichiometry of eskolaite, where each corner of the composition square represents a °G
parameter.
Fig. 4.1.1 Compound energy model for the Cr2+xO3 phase
The four corner compositions represent all possibilities to express the Cr2+xO3 phase
according to the above formula for the sublattice occupation. The corner Cr3+:Va:O2-
corresponds to stoichiometric Cr2O3. The three other corner compositions present charged
compounds. Only compounds along the neutral line can exist on their own. As the most
reasonable way to model reduction is to use the reduced neutral endpoint
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62
(Cr2+)2 (Cr3+2/3Va1/3)1 (O2-)3, labeled A in Fig. 4.1.1, one has to find functions of °G of three
charged corners expressed solely in terms of the neutral compositions. This is done by using
the two equations for the stoichiometric and the reduced endpoints, by choosing an arbitrary
reference, and by defining a reciprocal reaction giving four equations with which all °Gs at the
corners can be expressed.
The function to model the reduction then reads
° ° SER
2+ 3+ 2 Cr O CrCr (Cr Va )(O ) 2 32 2 3 1 3 32 3 (2 3ln 2 3+1 3ln1 3)°
− = + + + +G G G A BT RT (4.1.8)
The last term describes the configurational entropy due to mixing of Cr3+ and Va on the
interstitial site. °G of the 3+ charged endmember (Cr3+)2 (Cr3+)1 (O2-)3 is chosen as reference
and given the value °3+ 3+Cr :Cr
G . Then the reciprocal relation reads
° °
r3+ 3+ 2+ 3+ 2+ 3+Cr :Cr Cr :Va Cr :Va Cr :Cr° °+ = + = ΔG G G G G (4.1.9)
In order to avoid the inevitable formation of miscibility gaps if the energy of the reciprocal
relation is large we set this energy zero, which leads to
° ° ° °
3+ 3+ 2+ 3+ 2+ 3+Cr :Cr Cr :Va Cr :Va Cr :Cr0+ − − =G G G G (4.1.10)
This means that without introducing interaction parameters one gets an ideal description
between Cr2O3 and Cr2+xO3. The expressions for all °Gs at the corners resulting from Eq. 4.1.8
to 4.1.10 are listed in Table 4.1.2, pp.63-64.
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63
Table 4.1.2 Thermodynamic description of the
Cr-O System
Element
Element Reference Mass H298 - H0 S298
Cr Cr (bcc_A2) 51.996 4050.0 23.543
O 12 mol O2 15.999 4341.0 102.52
Liquid
2- 2+ 3+
2+ q-
3+ q-
3+ 2-
2+ 2-
2+ 3+ 2- q-p q
VaO Cr Cr
L SER [49]CrCr :Va
L SER [49]CrCr :Va
L SER SERCr OCr :O
L SER SERCr OCr :O
(Cr ,Cr ) (O ,Va )
2 , 2 3
GCR_L
2GCR_L GCR2O3_L 3GCR1O1_L
2 3 GCR2O3_L
2 2 2GCR1O1_
°
°
°
°
= + = +
− =
− = + −
− − =
− − =
p y qy q y y
G H
G H
G H H
G H H
2+ 2- q- 3+ 2- q-0 0
Cr :O ,Va Cr :O ,Va
L
121000= =L L
Solid Cr (bcc_A2)
1 3(Cr) (O,Va) bcc SER [49]Cr:Va Cr
bcc SER SER [49]Cr:O Cr O
0 bccCr:O,Va
GHSERCR
3 GHSERCR + 3GHSEROO + 243
7095420.4 311.5 0.008
°
°
− =
− − =
= −= = − = −c
G H
G H H T
Lp T β
CrO 1 1Cr O SER SER
Cr:O Cr O GCR1O1G H H° − − =
Cr2O3
2 33+ 2-
2 33+3+ 2-
2 33+2+ 2-
2+ 2
2+ 3+ 3+ 2-2 1 3
Cr O° SER SERCr OCr :Va:O
Cr O° SER SER [49]Cr OCr :Cr :O
Cr O° SER SER [49]Cr OCr :Cr :O
°Cr :Va:O
13
(Cr , Cr ) (Cr ,Va) (O )
2 -3 GCR2O3
3 3 GCR2O3 GHSERCR
3 3 GCRO0 GHSERCR 5.2923
− =
− − = +
− − = + −
G H H
G H H
G H H T
G 2 3-
Cr O SER SER [49]Cr O
233 3 GCRO0 GHSERCR 5.2923
0.28 308.6 3.0
− − = − −
= = =c
H H T
p T β
Cr3O4
3 4Cr O° SER SERCr:O Cr O3 4 GCR3O4 − − =G H H
Functions
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64
-3 2 -1
[49]
[49]
[49]23
GCR2O3 1164542 728.56 119.8 ln4.97 10 1050000
GCR1O1 0.5GCR2O3 0.5GHSEROO 255269 53.82GCR3O4 1.5GCR2O3 0.5GHSEROO 280045 93.76GCRO0 108305 GCR2O3 GHSERCR
GCR2O3_L GCR2O3 4390
= − + −− × +
= − + −= − + −
= + +
= +
T T TT T
TT
[49]
78 169GCR1O1_L 0.5GCR2O3 0.5GHSEROO 339673 121.4
−= − + −
TT
Note: All parameters are in SI units: J, mol, K, Pa: R = 8.31451 J mol-1 K-1.
Parameters for solid Cr, liquid Cr, and gaseous O are from Dinsdale[49]
In contrast to Taylor and Dinsdale[41], who needed 4 parameters to model the Cr2O3 phase and
had to arbitrarily equate the °G of (Cr2+)2 (Va)1 (O2-)3 to stoichiometric Cr2O3, the latter
constraint is not needed in the model, and one can reduce the number of parameters to only
two.
The oxygen solubility in solid Cr(bcc) can be described by an interstitial solution model of the
form (Cr)1(O,Va)3. For the optimization of model parameters, literature data from Caplan and
Fraser[48] are used. It was not possible to model the oxygen solubility using the
endmember °Cr:O G as this endmember turned out to be too stable and CrO3 appeared in the
stability diagram at high oxygen partial pressures. Therefore a large value is given to the
endmember °Cr:O G (in this case 0 was a large number) and the oxygen stability is modeled
with the temperature dependence of °Cr:O G and a regular interaction parameter 0
Cr:O,VaL that
must of course be negative.
The Cr3O4 phase is based on the eskolaite phase. Its heat capacity is given by Neumann and
Kopp’s rule. Metastable CrO is described in the same way.
The descriptions for solid and liquid chromium metal and gaseous O2 are from Dinsdale[49].
Ionic liquid:
The two-sublattice ionic liquid model[50,51] is selected to describe the ionic liquid. As the
experimental data on the liquid phase are scarce, the number of parameters is kept as low as
possible. The sublattice occupation (Cr3+,Cr2+)p(O2-,Vaq-)q is chosen. With this expression one
is able to obtain reasonable results for the liquid phase using the positive interaction
parameters, 2+ 2-0
Cr :O ,VaL and 3+ 2-0
Cr :O ,VaL that are required to give the miscibility gap. Fig. 4.1.2
(next page) is a graphic expression of the model, where each corner of the composition square
represents a °G parameter of the liquid phase.
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Thermodynamic assessments
65
Fig. 4.1.2 Two-sublattice ionic liquid model for the Cr-O system
The four corner compositions represent all possibilities to express the liquid phase according
to the above formula. The liquid composition changes along the hyperbolic curves in Fig.
4.1.2.
A special feature of the Cr-O system is the occurrence of a eutectic very close to the
composition of CrO. The eutectic temperature is mainly determined by the value of the corner
Cr2+:O2-.
One derives the °GL functions of the oxide compositions (Cr3+:O2-) and (Cr2+:O2-) from the
eskolaite phase. The °GL of liquid Cr is taken from Dinsdale[49]. In this model description of
the liquid phase metallic Cr-liquid can be described by both the corners Cr2+:Va and Cr3+:Va.
Cr3+:Va must be metastable compared to Cr2+:Va. One way of doing this would be to simply
say that Cr3+:Va equals Cr2+:Va plus a large positive term, for example +600000 as given
to 2+°
Cu :VaG by Hallstedt et al.[52] in his original assessment of the Cu-O system. This is
however problematic for reciprocal systems. If the reciprocal energy of the system is large
there will be a tendency to form miscibility gaps as pointed out by Hillert and Sundman[53].
Hallstedt and Gauckler[54] recently reoptimized the Cu-O liquid, obtaining the
parameter 2+°
Cu :VaG from the reciprocal relation and giving it a reciprocal energy of 0. This
considerably improved the description of the Cu-O liquid and removed the inverted
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66
miscibility gap found at high temperatures in the original assessment[52]. An identical strategy
is employed here. Thus metallic liquid is given by the corner 2+° L
Cr :VaG .The
parameter 3+° L
Cr :VaG is obtained by the reciprocal reaction given as
° L ° L ° L ° L
r r3+ 2+ 3+ 2- 2+ 2-Cr :Va Cr :Va Cr :O Cr :O = 2 + 3 ; 0− + Δ Δ =G G G G G G (4.1.11)
4.1.5 Optimization of parameters
The complete set of optimized thermodynamic parameters describing the Cr-O system is
given in Table 4.1.2 (pp. 63-64).
The optimization of the thermodynamic parameters was performed using the PARROT
module of the Thermo Calc[55] database system. In principle, PARROT can take into account
all sorts of thermodynamic and phase diagram data simultaneously. The program minimizes
the sum of squared errors between the calculated and experimentally determined phase
diagram and thermodynamic data. As the use of all the experimental data in a simultaneous
least square calculation often leads to divergence, the authors selectively adjusted the relative
weight of each experimental data point and excluded data that were inconsistent with the
majority of the data points during the optimization procedure.
The first parameters to be optimized were the Cp-parameters of Cr2O3. These parameters were
then kept fixed during the rest of the optimization. The data used were heat content data from
Kelley et al.[27] and Cp data from Klemme et al.[25] at T = 290 K and from T = 335 K to 338 K
with a low relative weight. The authors optimized Tc and β using Cp data from Klemme et
al.[25] close to the antiferromagnetic to paramagnetic transition temperature. To determine the
parameters describing the enthalpy and entropy of Cr2O3 2Olog( )p data from Jeannin et al.[18]
and Toker et al.[13], high temperature emf data from Holzheid and O’Neill [21], and, with low
relative weight, 298.16f,el°Δ H and 298.16
° S data from Holzheid and O’Neill[21] were used. In the
next step the authors optimized the nonstoichiometry of Cr2+xO3 using data from Matsui and
Naito[45]. They assessed Cr3O4 and the liquid simultaneously, using experimental phase
equilibria data from Toker et al.[13], experimental data on the liquidus at the oxygen poor side
from Toker et al.[13], and experimental data on the liquidus at the oxygen rich side of the
miscibility gap from Ol’shanskii and Shlepov[2]. The melting temperature of eskolaite in air
was taken from Bunting[7]. Finally the solubility of O in solid Cr was optimized using data
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Thermodynamic assessments
67
from Caplan and Fraser[48]. In Table 4.1.1 (p. 54-55) values that were used for our
optimization are written in italic letters.
4.1.6 Results and discussion
Phase diagram:
The calculated phase diagram with oxygen isobars is shown in Fig. 4.1.3.
Fig. 4.1.3 Calculated Cr-O phase diagram with oxygen isobars (Pa, logarithmic) given.
The gas phase was not included in the calculation
An enlargement of the phase diagram close to the CrO composition is presented in Fig. 4.1.4
(next page).
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Thermodynamic assessments
68
Fig. 4.1.4 Enlargement of the calculated Cr-O phase diagram close to the
CrO composition, with experimental data and oxygen isobars (Pa, logarithmic) included
The shape of the liquidus at the oxygen poor side of the miscibility gap resulting from the
authors’ optimization relying on a single experimental datum from Toker et al.[13] and an
earlier experiment from Ol’shanskii and Shlepov[2] is slightly deviating from former
optimizations. The calculated liquidus temperature of eskolaite in air is T = 2539 K, in good
agreement with the measurement from Bunting[7]. For the monotectic temperature of the
reaction of Cr (bcc) and liquid the present authors calculate T = 2117 K, and for the eutectic
one gets T=1938 K at a mole fraction of oxygen of 0.497. Cr3O4 is formed at T = 1918 K by
the eutectoid reaction 2 3 2 3 4Cr O Cr 1 2O Cr O+ + → . At a mole fraction of oxygen > 0.497 it
decomposes in a peritectic reaction at T = 1973 K forming Cr2O3 and liquid. Fig. 4.1.5 (next
page) shows the calculated oxygen potential phase diagram of the Cr-O system with
experimental 2Olog( )p data included.
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Thermodynamic assessments
69
Fig. 4.1.5 Calculated oxygen potential phase diagram of the Cr-O system,
with experimental2Olog( )p data as a function of temperature from different studies
The experimentally determined phase stabilities from Toker et al.[13] are particularly well
reproduced by the authors’ optimization. The shape and size of the miscibility gap is
speculative due to the lack of experimental data. The stability of Cr3O4 is shown in
the2Olog( )p versus temperature diagram in Fig. 4.1.6.
Fig. 4.1.6 Stability of Cr3O4 in the2Olog( )p versus temperature diagram
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The solubility of oxygen in Cr(bcc) is shown in Fig. 4.1.7.
Fig. 4.1.7 Calculated oxygen solubility in Cr(bcc)
with experimental data and oxygen isobars (Pa, logarithmic) included
For the maximum solubility of oxygen in Cr(bcc) one calculates 0.08 at.% at T=1938 K. If the
commonly used – however grubby – notation “Cr2O3-δ” is applied, the total charge of Cr is
given by 6+2δ. The maximum calculated δ = 0.098 at T = 1918 K. The cation
overstoichiometry resulting from the presented optimization might seem somewhat high, but
it results simply from the extrapolation of experimental data from Matsui and Naito[45] on
excess Cr as a function of 2Op down to the oxygen partial pressure at the Cr-Cr2O3
equilibrium following the proportionality given by the defect chemistry analysis in section
4.1.4. The comparison of the calculated nonstoichiometry in Cr2+xO3 with the experimental
data by Matsui and Naito[45] is given in Fig. 4.1.8 (next page).
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71
Fig. 4.1.8 Optimized nonstoichiometry of Cr2+xO3 with the only available experimental data
from Matsui and Naito[45] included. Optimization of a temperature dependence is represented
by dotted lines. Solid lines result from our accepted optimization without considering
temperature dependence. The low nonstoichiometry data show a different slope than the
higher nonstoichiometry data.
The solid lines correspond to the optimization that is accepted in this work. Obviously the
calculated results show a temperature dependence that is significantly stronger compared to
the experiments. Considering a temperature dependence for the reduced neutral endpoint of
the phase Cr2+xO3 gives values of GCRO0 202130 235 GCR2O3 2 3GHSERCR= − + + +T (dotted
lines in Fig. 4.1.8) and leads to the reduced neutral endpoint being too stable at low
temperatures. Therefore, and due to existing data at only three different temperatures from a
single author it was decided not to optimize a temperature dependence giving
GCRO0 108305 GCR2O3 2 3GHSERCR= + + . The data at low oxygen nonstoichiometries were
not used, as the introduction of an additional defect species would be required to reproduce
these.
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Thermodynamic assessments
72
Thermodynamic Data:
The heat capacities, Cp, of the solid Cr2O3 phase (Fig. 4.1.9) are well represented by our
assessment.
Fig. 4.1.9 Comparison of calculated heat capacities of Cr2O3 with experimental data
For the magnetic parameter β we calculate 3.0, and for Tc we get 308.6. For 298Kf,el°Δ H (Cr2O3)
we calculate –1123 kJ mol-1, which is in particularly good agreement with the data from
Ramsey et al.[33], and for 298K° S (Cr2O3) we get 85 J K-1mol-1, which is very close to the
results from Holzheid and O’Neill[21]. For 298Kf,el°Δ H (Cr3O4) we calculate –1402 kJ mol-1, and
for 298K° S (Cr3O4) we get 175 J K-1mol-1. These values for Cr3O4 deviate significantly from the
results of Taylor and Dinsdale[41] who calculated 298Kf°Δ H (Cr3O4) = –1447.685 kJ mol-1, and
298K° S (Cr3O4) = 150.555 J K-1 mol-1. For a metastable CrO phase we calculate
-1298Kf,el 306 kJ mol°Δ = −H , and -1 -1
298K 79 J K mol° = −S based on the estimates of Shirokov[30].
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Thermodynamic assessments
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4.1.7 Conclusions
With the presented reassessment of the Cr-O system the authors are able to excellently
describe available thermodynamic and phase diagram data with as few optimizing parameters
as possible. However, it must be kept in mind that experimental data on the liquid miscibility
gap are largely missing, and that a large variation of the measured melting points of eskolaite
exists.
References
1. S.P.S. Badwal, R. Deller, K. Foger, Y. Ramprakash, J.P. Zhang, Interaction between
chromia
forming alloy interconnects and air electrode of solid oxide fuel cells, Solid State Ionics,
1997, 99, pp. 297-310.
2. Y.I. Ol’shanskii, V.K. Shlepov, Sistema Cr-Cr2O3, Dokl. Akad. Nauk. SSSR, 1953, 91(3),
pp. 561-64.
3. N.Y. Toker, Equilibrium phase relations and thermodynamics for the systems Cr-O and
Fe-Cr-O in the temperature range 1500 to 1825 °C, Thesis, 1978, Pennsylvania State
University.
4. C.W. Kanolt, Melting points of some refractory oxides, J. Wash. Acad. Sci., 1913, 3, pp.
315-18.
5. W.T. Wilde, W.J. Rees, The ternary system MgO-Al2O3-Cr2O3, Brit. Ceram. Trans. J.,
1943, 42(7), pp. 123-55.
6. R.N. McNally, F.I. Peters, P.H. Ribbe, Laboratory furnace for studies in controlled
atmospheres; melting points of MgO in a N2 atmosphere and of Cr2O3 in N2 and in air
atmospheres, J. Am. Ceram. Soc., 1961, 44(10), pp. 491-93.
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1931, pp. 947-49.
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9. R.K.F. Lam, Melting and casting of high purity chromium with controlled oxygen content,
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Cr-O system, T. I. Min. Metall. Eng., 1955, 203(2), pp. 253-68.
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11. R.E. Hook, A.M. Adair, The formation and dissolution of chromium oxides in chromium,
T. Metall. Soc. Aime, 1964, 230(6), pp. 1278-83.
12. R.E. Johnson, A. Muan, Phase diagrams for the systems Si-O and Cr-O, J. Am. Ceram.
Soc., 1968, 51(8), pp. 430-33.
13. N.Y. Toker, L.S. Darken, A. Muan, Equilibrium phase relations and thermodynamics of
the Cr-O system in the temperature range of 1500 °C to 1825 °C, Metall. Trans. B, 1991,
22(2), pp. 225-32.
14. G. Grube, M. Flad, Affinity and enthalpy of the solid solution in the system Cr-Ni, Z.
Elektrochem., 1942, 48(7), pp. 377-89 (in German).
15. A. Novokhatskii, L.M. Lenev, Thermodynamic properties of Cr2O3 and FeCr2O4 at high
temperatures, Russ. J. Inorg. Chem., 1966, 11(9), pp. 1078-80.
16. H. Davies, W.W. Smeltzer, Oxygen and metal activities of the chromium–nickel–oxygen
system between 900° and 1100°C, J. Electrochem. Soc., 1974, 121(4), pp. 543-49.
17. R.D. Pehlke, F.N. Mazandarany, R.H. Radzilowski, Solid oxide electrolyte emf cell
determination of the standard free energy of Cr2O3 and applications to chromium–bearing
mineral systems, Geochim. Cosmochim. Ac., 1975, 39, pp. 833-45.
18. Y. Jeannin, C. Mannerskantz, F.D. Richardson, Activities in iron–chromium alloys, T.
Metall. Soc. Aime, 1963, 227(2), pp. 300-5.
19. L.A. Pugliese, G.R. Fitterer, Activities and phase boundaries in the Cr–Ni system using a
solid electrolyte technique, Metall. Trans., 1970, 1(7), pp. 1997-2002.
20. J.D. Tretjakow, H. Schmalzried, The thermodynamics of spinel phases (chromite, ferrite,
aluminate), Berich. Bunsen Gesell., 1965, 69(5), pp. 396-402 (in German).
21. A. Holzheid, H.S. O’Neill, The Cr-Cr2O3 oxygen buffer and the free energy of formation
of Cr2O3 from high-temperature electrochemical measurements, Geochim. Cosmochim.
Ac., 1995, 59(3), pp. 475-79.
22. K.T. Jacob, Potentiometric determination of the Gibbs free energy of formation of
cadmium and magnesium chromites, J. Electrochem. Soc., 1977, 124, pp. 1827-31.
23. C.T. Anderson, The heat capacities of chromium, chromic oxide, chromous chloride and
chromic chloride at low temperatures, J. Am. Ceram. Soc., 1937, 59, pp. 488-91.
24. R.H. Bruce, D.S. Cannell, Specific heat of Cr2O3 near the Neel temperature, Phys. Rev. B,
1977, 15(9), pp. 4451-59.
25. S. Klemme, H.S. O’Neill, W. Schnelle, E. Gmelin, The heat capacity of MgCr2O4,
FeCr2O4, and Cr2O3 at low temperatures and derived thermodynamic properties, Am.
Mineral., 2000, 85, pp. 1686-93.
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26. M.W. Chase, C.A. Davies, J.R. Jr. Downey, D.J. Flurip, R.A. McDonald, A.N. Syverud,
Janaf thermochemical tables - 3rd ed., J. Phys. Chem. Ref. Data, 1985, 14(Suppl. 1): pp.
940-42.
27. K.K. Kelley, F.S. Boericke, E.H. Huffman, W.M. Bangert, Thermodynamic properties of
carbides of chromium, Bur. Mines Tech. Paper, 1944, 662, 43 pp.
28. I. Dellien, F.M. Hall, L.G. Hepler, Chromium, molybdenum, and tungsten:
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29. D.D. Wagman, W.H. Evans, V.B. Parker, I. Halow, S.M. Bailey, R.H. Schumm, Selected
values of chemical thermodynamic properties. Tables for elements 35 through 53 in the
standard order of arrangement, NBS Tech. Notes, 1969, 270(4).
30. N.I. Shirokov, Thermodynamic properties of chromous oxide, Dokl. Akad. Nauk. SSSR,
Metal., 1973, 2, p. 102.
31. W.A. Roth, U. Wolf, The heat of formation of chromium oxide, Z. Elektrochem., 1940,
46, pp. 45-46 (in German).
32. D. Mah, Heats of formation of chromium oxide and cadmium oxide from combustion
calorimetry, J. Am. Chem. Soc., 1954, 76(13), pp. 3363-65.
33. J. N. Ramsey, D. Caplan, A.A. Burr, Thermodynamics of the oxidation of chromium, J.
Electrochem. Soc., 1956, 103(2), pp. 135-38.
34. J.P. Coughlin, Contributions to the data on theoretical metallurgy, Bur. Mines Bull., 1954,
542, 80 pp.
35. A. Navrotsky, Thermochemistry of chromium compounds, especially oxides at high
temperature, Geochim. Cosmochim. Ac., 1975, 39, pp. 819-32.
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p. 410.
37. G. Banik, T. Schmitt, P. Ettmayer, B. Lux, Thermodynamic consideration on the system
Cr-Cr2O3, Z. Metallkd., 1980, 71(10): pp. 644-45.
38. E. Fromm, E. Gebhardt: Gases and Carbon in Metals, Springer Verlag, Berlin,
Heidelberg, New York, 1976, pp. 521-34 (in German).
39. S. Degterov, A.D. Pelton, Critical evaluation and optimization of the thermodynamic
properties and phase diagrams of the CrO-Cr2O3, CrO-Cr2O3-Al2O3, and CrO-Cr2O3-CaO
systems, J. Phase Equilib., 1996, 17(6), pp. 476-87.
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40. M. Kowalski, P.J. Spencer, Thermodynamic reevaluation of the Cr-O, Fe-O and Ni-O
systems: Remodelling of the liquid, bcc and fcc phases, Calphad, 1995, 19(3), pp.
229-43.
41. J.R. Taylor, A.T. Dinsdale, A thermodynamic assessment of the Ni-O, Cr-O and Cr-Ni-O
systems using the ionic liquid and compound energy models, Z. Metallkd., 1990, 81(5),
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42. J. Chipman, Atomic interactions in molten alloy steels, J. Iron Steel Inst., 1955, 180, pp.
97-106.
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General treatment, Z. Metallkd., 1975, 66(10), pp. 577-82.
44. M. Hillert, M. Jarl, A model of alloying effects in ferromagnetic metals, Calphad, 1978,
2(3), pp. 227-38.
45. T. Matsui, K. Naito, Existence of hypostoichiometric chromium sesquioxide at low
oxygen partial pressures, J. Nucl. Mater., 1985, 136, pp. 78-82.
46. E.W.A. Young, J.H. Gerretson, J.H.W. de Witt, The oxygen partial-pressure dependence
of the defect structure of chromium(III)oxide, J. Electrochem. Soc., 1987, 134(9), pp.
2257-60.
47. A.N. Grundy, E. Povoden, T. Ivas, L.J. Gauckler, Calculation of defect chemistry using
the Calphad approach, Calphad, 2005, 30, pp. 33-41.
48. D. Caplan, M.J. Fraser, A.A. Burr: in Ductile Chromium, ASM, Cleveland, Ohio, 1957, p.
196.
49. A.T. Dinsdale, SGTE data for pure elements, Calphad, 1991, 15(4), pp. 317-425.
50. M. Hillert, B. Jansson, B. Sundman, J. Ågren, A two-sublattice model of molten solutions
with different tendency of ionization, Metall. Trans. A, 1985, 16A, pp. 261-66.
51. B. Sundman, Modification of the two-sublattice model for liquids, Calphad, 1991, 15, pp.
109-19.
52. B. Hallstedt, D. Risold, L.J. Gauckler, Thermodynamic assessment of the copper-oxygen
system, 1994, J. Phase Equilib., 1994, 15(5), pp. 483-99.
53. M. Hillert, B. Sundman, Predicting miscibility gaps in reciprocal liquids, Calphad, 2001,
25(4), pp. 599-605.
54. B. Hallstedt, L.J. Gauckler, Revision of the thermodynamic descriptions of the Cu-O, Ag-
O, Ag-Cu-O, Bi-Sr-O, Bi-Cu-O, Sr-Cu-O, Ca-Cu-O and Sr-Ca-Cu-O systems, Calphad,
2003, 27(2), pp. 177-91.
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55. B. Sundman, B. Jansson, J.O. Andersson, The Thermo-Calc databank system, Calphad,
1985, 9(2), pp. 153-90.
4.2 Thermodynamic assessment of the Mn-Cr-O system for SOFC
materials
E. Povoden, A.N. Grundy, and L.J. Gauckler
Int. J. Mater. Res., 2006, 97, pp. 569-78.
By application of the CALPHAD method, a consistent set of thermodynamic model
parameters is optimized for the Cr-Mn-O system based on experimental data. Chromium
manganese spinel MnyCr3-yO4 and its tetragonally distorted polymorph are described using the
compound energy model, and the liquid is described using the two-sublattice model for ionic
liquids. Also solid solutions of the phases (Cr1-yMny)2+xO3, Mn2-yCryO3, and (Mn1-yCry)1-xO are
considered. Relevance for solid oxide fuel cells is discussed.
4.2.1 Introduction
For the planar design of SOFC the use of heat-resistant high chromium alloys has been
promoted as a suitable alternative to earth alkaline doped LaCrO3 ceramic interconnect
materials[1,2]. However, mobilization predominantly via the gas phase[3] of Cr originating from
the alloy interconnect leads to the formation of Cr2+xO3 (eskolaite) and chromium manganese
spinel MnyCr3-yO4 which block catalytically active sites as well as pores, thus substantially
diminishing the triple phase boundary area for the normal oxygen reduction reaction at the
cathode/electrolyte interface[4]. Simner et al.[5] observed that the formation of chromium
manganese spinel layers on top of a Cr2O3 oxide scale on the surface of a Mn-containing
ferritic stainless steel (Crofer22 APU) interconnect with 76.6 wt.% Fe, 22.8 wt.% Cr, and
0.45 wt.% Mn resulted in an improvement of short-term SOFC operation. The processes by
which these protective oxide scales reduce the chromium poisoning and their effect on cell
degradation during long-term SOFC operation are not well known yet. We are contributing to
the understanding of the underlying thermodynamics of these processes by assessing the Mn-
Cr-O system using the CALPHAD approach.
The thermodynamic data of the pure elements are taken from Dinsdale[6], and the data for the
Mn-O, Cr-O, and Mn-Cr binaries from Grundy et al.[7], Povoden et al.[8], and Lee [9]
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Thermodynamic assessments
78
respectively. No new ternary phases are found in the Mn-Cr-O system, however all the binary
oxides except pyrolusite (prl), MnO2, show varying degrees of mutual solid solubility.
The most prominent oxide phase in the Mn-Cr-O system is cubic chromium manganese spinel
with the formula MnyCr3-yO4. Normal spinel is given by the formula [A2+](B3+)2O4, whereas
spinel of the formula [B3+](A2+B3+)O4 with half of B on the tetrahedral sites – marked with
angular brackets in the above formulas – is called inverse spinel. In the case of cubic
MnyCr3-yO4 both the trivalent cations of manganese and chromium show a remarkable
preference to fill the octahedral sites marked with round brackets in above formulas[10]. Spinel
containing a large amount of Mn3+ becomes tetragonally distorted on lowering the
temperature as a consequence of the macroscopic Jahn-Teller effect that is caused by the
distortion of the octahedral sites occupied by Mn3+[11].
In this work we use the following abbreviations: β-spl for cubic chromium manganese spinel
solid solution, α-spl for tetragonally distorted polymorph spinel solid solution, β-hsm (β-
hausmannite) for the cubic and α-hsm (α-hausmannite) for the tetragonally distorted Mn3O4
endmember of the spinel solid solution, bxb for Mn2O3 (bixbyite) with dissolved Cr, esk for
Cr2+xO3 (eskolaite) with dissolved Mn, mgs for Mn1-xO (manganosite) with dissolved Cr, bcc
for chromium manganese alloy with bcc A2 structure, and liq for the liquid phase.
4.2.2 Experimental
Phase diagram data:
Our calculated phase diagram of the MnOx-Cr2O3 system in air is shown in Figs. 4.2.1, 4.2.2
(p. 79), and 4.2.3 (p. 80). Fig. 4.2.4 (p. 80) shows the calculated phase diagram at
2
-4O 1×10 Pa=p .
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Thermodynamic assessments
79
Fig. 4.2.1 Calculated pseudo-binary phase diagram of the system MnOx-Cr2O3 in air. The gas
phase was not included in the calculation.
Fig. 4.2.2 Calculated pseudo-binary phase diagram of the system MnOx-Cr2O3 in air, with
experimental data. The gas phase was not included in the calculation.
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Thermodynamic assessments
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Fig. 4.2.3 Mn rich part of the calculated pseudo-binary phase diagram
of the system MnOx-Cr2O3 in air, with experimental data.
Fig. 4.2.4 Calculated pseudo-binary phase diagram of the system MnOx-Cr2O3 under strongly
reducing conditions (2
-4O 1×10 Pa=P ), showing the expanded stability field of β-spl + mgs.
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81
Speidel and Muan[12] present a phase diagram of the MnOx-Cr2O3 system in air in the
temperature range 873 K to 2253 K resulting from the determination of phase equilibria using
quenching techniques and X-ray and microscopic examination (Fig. 4.2.2, p. 79).
They find β-spl + α-spl + bxb coexisting in equilibrium at T = 1183 ± 5 K, and β-spl + esk +
liq in equilibrium at T = 2243 ± 20 K. They estimate a minimum temperature of T = 773 K for
the stability of β-spl. The Mn solubility in (Cr2-yMny)1+xO3 reported from Speidel and Muan[12]
is significantly higher than it is found by Golikov et al.[13] and Pollert et al.[14].
Golikov et al.[13] studied the MnOx-Cr2O3 system using quenching techniques and high
temperature X-ray diffractometry in air in the temperature range from T = 973 K to 1673 K.
Their resulting phase diagram is in considerable disagreement with the findings of Speidel
and Muan[12]. They report a minimum temperature of β-spl stability of T = 973 K and lower
solubility of Cr in tetragonally distorted MnyCr3-yO4 and of Cr in Mn2-yCryO3. They consider
the solubility limit of Mn in (Cr1-yMny)2+xO3 to be negligible.
Pollert et al.[14,15] studied phase stabilities in the MnOx-Cr2O3 system in the temperature range
from T = 1100 K to 1620 K in air by means of X-ray measurement of annealed samples. Their
data are shown in Figs. 4.2.2, p. 79 and 4.2.3, p. 80.
The solubility limit of Cr in Mn2-yCryO3 is measured by these authors to be y = 0.14 at T =
1105 K in air. This value is in agreement with the result from Geller and Espinosa[16], but it is
lower than the findings from Speidel and Muan[12]. Pollert et al.[14] report a solubility limit of
y = 1.42 at oxygen partial pressure >> 20000 Pa. From the absence of changes of the lattice
parameters of esk in equilibrium with β-spl annealed at T = 1105 K and 1620 K in air
compared to pure Cr2O3 they conclude that the solubility of Mn in (Cr2-yMny)1+xO3 is low and
does not depend significantly on temperature.
Tanahashi et al.[17] investigated the compositions of coexisting β-spl + mgs and β-spl + esk
from 2
-6O 2×10=p to 2 2×10 Pa at T = 1873 K thus determining the range of solid solubility of
β-spl by quenching techniques under controlled CO-CO2 atmosphere (Fig. 4.2.5, next page).
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Thermodynamic assessments
82
Fig. 4.2.5 Cr contents of β-spl in equilibrium with mgs, β-spl in equilibrium with esk, esk in
equilibrium with β-spl, and mgs in equilibrium with β-spl in the pseudo-binary MnOx-Cr2O3
system as a function of oxygen partial pressures at T = 1073 K, 1473 K, and 1873 K.
Experimental data are included.
Phase relations were verified using X-ray diffraction. In order to identify the equilibrium
compositions, each phase in the quenched specimens was subjected to electron probe
microanalysis (EPMA). They found increasing Mn solubility in cubic MnyCr3-yO4 at oxygen
partial pressure higher than -22 10 Pa× , and significantly increasing Cr solubility in cubic
MnyCr3-yO4 with decreasing oxygen partial pressure (Fig. 4.2.5). The compositions of β-spl
are located on a line connecting MnCr2O4 with β-hsm in the ternary plot. From this result
Tanahashi et al.[17] conclude that Mn is dissolved in cubic MnyCr3-yO4 in the form of Mn3O4.
They report small solubility of Mn in (Cr1-yMny)2+xO3 at 2
-6O 2×10=p , which increases slightly
with increasing oxygen partial pressure. They found almost unchanging solubility of Cr in
(Mn1-yCry)1-xO from 2
-6O 2×10=p to 22 10 Pa× at T = 1873 K. As the compositions of mgs
solid solution are located on the line connecting Mn1-xO with CrO in the ternary phase
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Thermodynamic assessments
83
diagram, these authors conclude that chromium oxide dissolves in (Mn1-yCry)1-xO in the form
of CrO.
Bobov et al.[18] investigated the composition changes of the two phase equilibrium β-spl +
mgs at T = 1073 K, 1173 K, and 1273 ± 5 K in the oxygen partial pressure range from 0.1 to
10-13 Pa (Fig. 4.2.5, p. 82).
For the invariant three phase equilibrium mgs + β-spl + bcc Ranganathan and Hajra[19]
measured the Mn content in bcc to be 25.2 cat.% at T = 1323 K performing an isopiestic
experiment (Fig. 4.2.6).
Fig. 4.2.6 Ternary phase diagram of the system Cr-Mn-O with stoichiometric single phase
equilibria (points), single solid solution phase equilibria (heavy lines), two-phase fields and
three-phase fields. Dotted lines are tie lines. Three-phase field boundaries are denoted with
thin solid lines. Also the experimental result on the three phase equilibrium MnO + MnCr2O4
+ bcc from Ranganathan[19] is plotted.
There are no data on oxygen nonstoichiometry of MnyCr3-yO4.
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Thermodynamic assessments
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Holba et al.[11] investigated the martensitic α-spl → β-spl transition temperatures, enthalpies
and entropies of MnyCr3-yO4 samples annealed at T = 1723 K using X-ray analysis and DTA
measurement. With decreasing Mn-content the temperature for the transition decreases (Fig.
4.2.2, p. 79). Samples with y < 1.8 do not show Jahn–Teller distortion at room temperatures,
and remain β-spl. Giving α-spl the formula [Mn2+](Mn3+,Cr3+)2O4 this corresponds to a
minimum concentration of [Mn3+] = 0.4 for the formation of α-spl.
Thermodynamic data:
Cubic spinel (β-spl):
Only values for the standard Gibbs energy of formation of β-spl of the composition MnCr2O4
are published. Tanahashi et al.[20] derive 2 4
β-splMnCr Of
°Δ G = –958 ± 8 kJ mol-1 from liquid Mn,
solid Cr and oxygen at T = 1873 K in the 2Op range from -62×10 to -4 1.5×10 Pa from the
standard Gibbs free energy changes of the reactions
Mn (in molten Fe) + 2 Cr (in molten Fe) +2 O2(g) = MnCr2O4 (4.2.1)
and
Mn (in molten Cu) + 2 Cr (s) + 2O2(g) = MnCr2O4 (4.2.2)
Using compiled °MnOfΔ G and
2 3
°Cr OfΔ G [21] they calculate
2 4
β-splMnCr Of
°Δ G from its oxides to be
–59 ± 8 kJ mol-1. We recalculate this value using the most recently assessed °MnOfΔ G [7] and
2 3
°Cr OfΔ G [8] values at T = 1873 K giving
2 4
β-splMnCr Of
°Δ G = –66 ± 8 kJ mol-1. Tsai and Muan[22]
experimentally determined compositions of coexisting MnyCr3-yO4 - MnyAl3-yO4 solid
solutions formed from Cr2O3-Al2O3 mixtures at T = 1873 K. From these data and the activities
of CrO1.5 in Mn0.5AlO2 and AlO1.5 in Mn0.5CrO2 obtained from a previous study[23] they derive
ΔG of the reaction
CrO1.5 + Mn0.5AlO2 = AlO1.5 + Mn0.5CrO2 (4.2.3)
to be –10 kJ mol-1 at T = 1873 K, which is equivalent to fΔ G of 2 4 2 4
β-splMnCr Of f MnAl O )1 2(Δ − ΔG G .
This means that the Gibbs energy of formation of β-spl of the composition MnCr2O4 from its
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Thermodynamic assessments
85
oxides using this calculation technique depends on the value of 2 4f MnAl O
°Δ G . Tsai and Muan[22]
chose the value determined by Lenev and Novokhatskiy[24], 2 4f MnAl O
°Δ G = –32.6 kJ mol-1
giving 2 4
β-splMnCr Of
°Δ G = –52.6 kJ mol-1 at T = 1873 K. Using other values for 2 4f MnAl O
°Δ G reported
in the literature[25-27] leads to deviating 2 4
β-splMnCr Of
°Δ G of –34.4 ± 10 kJ mol-1, –46.1 kJ mol-1, and
–36.1 kJ mol-1. Biggers[28] by using the same technique as Tsai and Muan [22] in the CoO-
MnO-Cr2O3 system found 2 4
β-splMnCr Of
°Δ G = –59.0 kJ mol-1 at T=1523 K.
The spread of 2 4
β-splMnCr Of
°Δ G values resulting from different studies and our recalculations is
shown in Fig. 4.2.7.
Fig. 4.2.7 Calculated Gibbs energy of formation of β-spl of the composition MnCr2O4 as a
function of temperature, with experimental data and error bars. Filled symbols correspond to
originally reported literature data, unfilled symbols correspond to recalculated values.
Tetragonally distorted spinel (α-spl):
Pollert et al.[15] present thermodynamic data on the transition of α-spl to β-spl. According to
these authors the transition of pure α-hsm to β-hsm takes place at T=1445 K.
ΔΗ α β = 18810 J mol-1, and ΔS α β = 13 J K-1 mol-1.
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Thermodynamic assessments
86
4.2.3 Thermodynamic modeling
Cubic spinel (β-spl):
There is experimental evidence on the presence of Cr2+ in β-spl as the Cr endmember of β-spl
was found to be a stable phase in a small temperature range[29,30]. As the degree of inversity of
β-spl is very low[10], β-spl can therefore be described by the simple formula
[Mn2+,Cr2+](Cr3+,Mn3+)2O4 using the compound energy model[31–33].
Lu et al.[34] measured the electrical conductivity of β-spl. They propose small polaron hopping
between Mn3+ and Mn4+ on the octahedral sites as mechanism for the electrical conductivity.
To maintain electroneutrality Mn2+ is formed on the octahedral sites resulting in a charge
disproportionation reaction. Considering these findings an alternative description of β-spl
would read [Mn2+,Cr2+](Cr3+,Mn2+,Mn3+,Mn4+)2O4. However there is no experimental data
quantifying the amount of Mn4+ in β-spl, so we stick to the less complex description without
Mn2+ and Mn4+ on the octahedral sites. In our description we further go along with the
presumption that the amount of oxygen vacancies may be neglected.
All endmembers of our model β-spl are neutral. In our CALPHAD assessment the °G values
of all compounds are given relative to the enthalpy of selected reference states for the
elements at T = 298.15 K and p = 105 Pa[6]. This state is denoted SER (Stable Element
Reference). The Gibbs energies of the endmembers [Mn2+](Mn3+)2O4 that corresponds to
β-hsm, and [Cr2+](Cr3+)2O4 that corresponds to Cr3O4 are taken from the assessed binaries[7,8].
The Gibbs energy of the endmember of the formula [Mn2+](Cr3+)2O4 is given by the
expression
3 4
2+ 3+ 2+ 3+ 2+ 3+2 4 2 4 2 4
Cr Oβ-spl β-hsm β-spl β-spl° ° °[Mn ](Cr ) O [Cr ](Cr ) O [Mn ](Mn ) O= 2 3 1 3+ + +G G G A B T (4.2.4)
This endmember is considerably more stable than the endmember of the formula
[Cr2+](Mn3+)2O4. We define this last endmember using a reciprocal relation
3 4
2+ 3+ 2+ 3+ 2+ 3+ 2+ 3+2 4 2 4 2 4 2 4
Cr Oβ-spl β-hsm β-spl° ° ° °[Cr ](Mn ) O [Cr ](Cr ) O [Mn ](Mn ) O [Mn ](Cr ) O1 3= + −G G G G (4.2.5)
The Gibbs energy of the reciprocal reaction is taken to be zero. Thus the endmember
2+ 3+2 4
β-spl°[Cr ](Mn ) OG becomes less stable the more stable 2+ 3+
2 4
β-spl°[Mn ](Cr ) OG becomes.
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Thermodynamic assessments
87
Tetragonally distorted spinel (α-spl):
The transformation of β-spl to α-spl is due to the Jahn-Teller distortion of the octahedral sites
occupied by trivalent Mn ions leading to the tetragonal structure of α-spl[11,15].
Experiments[11,14,15,34] show that α-spl is stabilized at high Mn contents, and the Cr solubility
in tetragonally distorted MnyCr3-yO4 does not extend beyond MnCr2O4. It is very unlikely that
trivalent cations are incorporated into the tetrahedral sites of α-spl, as the degree of inversity
is increasing with higher temperature, whereas for ordering due to Jahn–Teller distortion the
opposite holds. Due to these considerations we may write [Mn2+](Cr3+,Mn3+)2O4 to describe
α-spl. Hence, the two endmembers of α-spl read [Mn2+](Mn3+)2O4 and [Mn2+](Cr3+)2O4. The
Gibbs energy of [Mn2+](Mn3+)2O4 is equal to α-hsm. The Gibbs energy of [Mn2+](Cr3+)2O4 is
given by
3 4
2+ 3+ 2+ 3+ 2+ 3+2 4 2 4 2 4
Cr Oα-spl α-spl α-spl° ° ° α-hsm[Cr ](Mn ) O [Cr ](Cr ) O [Mn ](Mn ) O= 2 3 1 3+ + +G G G A B T (4.2.6)
Bixbyite (bxb):
Geller and Espinosa[16] postulate the incorporation of Cr into Mn2-yCryO3 by a simple
substitution mechanism between Cr3+ and Mn3+. This is a reasonable assumption as the radii
of these ions are very similar[35]. The incorporation of chromium of valencies other than three
is mentioned nowhere in literature. Thus we may describe bxb as (Mn3+,Cr3+)2(O2-)3. The
Gibbs energy of the endmember (Mn3+)2(O2-)3 is taken from Grundy et al.[7], and the Gibbs
energy of (Cr3+)2(O2-)3 is given by
3+ 3+ 2-2 3 2 1 3
° bxb ° esk bxb(Cr ) O (Cr ) (Va) (O )= +G G A (4.2.7)
The experimental data could be reproduced without the optimization of a temperature
dependent parameter.
Manganosite (mgs):
Based on the proposed incorporation of Cr into (Mn1-yCry)1-xO in the form of CrO[15] we tested
a description of mgs given by (Mn2+,Mn3+,Cr2+,Va)(O2-). Using this description the solubility
of Cr in function of oxygen partial pressure experimentally determined by Tanahashi[17] could
not be reproduced correctly. (Mn2+,Mn3+,Cr3+,Va)(O2-) leads to far more satisfactory
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Thermodynamic assessments
88
reproduction of these data. With this description we are in agreement with O’Keefe and
Valigi[36] who observe a decrease in the lattice parameter of mgs compared to undoped
Mn1-xO providing strong support for the assumption that it is Cr3+ that is substituting the much
larger Mn2+ ion and which is forcing the lattice to contract. These experiments also provide
evidence against Cr being incorporated interstitially. The model description of mgs is shown
in Fig. 4.2.8.
Fig. 4.2.8 Geometrical representation of the mgs phase described
using the compound energy model.
The Gibbs energy of the neutral endpoint ( )3+2/3 1/3Cr Va O is given by
3+ (Va )O(Cr )O 11
mgs mgs° °2 3 + 1 3 (1 3ln1 3 2 3ln 2 3)+ +G G RT and based on the Gibbs energy of 13 mole of
esk. Using O(Va)O 21
mgs° ° Gas12= G G the following expression for the parameter
3+(Cr )O1
mgs°G is obtained
3+ 3+ 2- O2(Cr )O (Cr ) (Va) (O )1 2 1 3
mgs mgs° ° esk ° Gas= 1 2 1 3 3 2 (1 3ln1 3 2 3ln 2 3)− − + +G G G RT A (4.2.8)
The Gibbs energies of the three other endmembers are taken from Grundy et al.[7].
Eskolaite (esk):
Pollert et al.[14] postulate the incorporation of trivalent Mn ions into (Cr1-yMny)2+xO3.
Agreeing with these authors we model the solubility of Mn by
(Cr3+,Cr2+,Mn3+)2(Cr3+,Va)1(O2-)3. The Gibbs energy of (Mn3+)2(Cr3+)1(O2-)3 is given by
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89
3+ 3+ 3+ 2-(Mn ) (Cr ) O (Mn ) (O )2 1 3 2 3
° esk ° bxb ° SER eskCr= + +G G G A (4.2.9)
and the Gibbs energy of (Mn3+)2(Va)1(O2-)3 by
3+ 3+ 2-(Mn ) (Va) O (Mn ) (O )2 1 3 2 3
° esk ° bxb esk= +G G A (4.2.10)
We take the Gibbs energies of the other endmembers from Povoden et al.[8].
Cr-Mn alloys:
We describe the oxygen solubility in bcc by an interstitial solution model of the form
(Cr,Mn)1(O,Va)3. Experimental data on the oxygen solubility in pure bcc A2 chromium
metal[37] were used for the description of (Cr)1(O,Va)3[8]. No data are reported for the oxygen
solubility in pure bcc A2 manganese metal. Assuming low oxygen solubility in bcc
manganese metal we give a large value to the endmemberMn:O
° bcc G .
The descriptions of further alloy phases are taken from[9].
Liquid:
We model the liquid phase as (Cr3+,Cr2+, Mn3+,Mn2+)p(O2-,Vaq-)q using the two-sublattice
model for ionic liquids [38,39]. The liquidus temperature is optimized using the interaction
parameter3+ 3+ 2-Cr ,Mn :O
liq0L .The binary interaction parameters are taken from Grundy et al.[7],
Povoden et al.[8], and Lee[9].
4.2.4 Optimization of parameters
The complete set of optimized thermodynamic parameters describing the Mn-Cr-O system is
given in Table 4.2.1 (pp. 90-92).
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Thermodynamic assessments
90
Table 4.2.1 Thermodynamic description of the
Cr-Mn-O system a)
Element
Element Reference Mass H298 - H0 S298
Cr BCC_A2 51.996 4050.0 23.543
Mn CBCC_A12 54.938 4996.0 32.008
O ½ mol O2 15.999 4341.0 102.52
Liquid (liq)
2- 2+ 2+ 3+ 3+
2+ q-
3+ q-
3+ 2-
2+ 3+ 2+ 3+ 2- q-p q
VaO Cr Mn Cr Mn
liq SER [9]CrCr :Va
liq SER [9] [9]CrCr :Va
liq SER SER [9]Cr OCr :O
(Cr ,Cr ,Mn ,Mn ) (O ,Va )
2 , 2 2 3 3
GCR_L
2GCR_L GCR2O3_L 3GCR1O1_L
2 3 GCR2O3_L
°
°
°
°
= + = + + +
− =
− = + −
− − =
p y qy q y y y y
G H
G H
G H H
G 2+ 2-
2+ q-
3+ q-
3+ 2-
2+ 2-
liq SER SER [9]Cr OCr :O
liq SER [7]MnMn :Va
liq SER [7] [8] [8]MnMn :Va
liq SER SER [8]Mn OMn :O
liq SER SERMn OMn :O
2 2 2GCR1O1_L
GMN_L
2GMN_L GMN2O3_L 3GMN1O1_L
2 3 GMN2O3_L
2 2 2GMN1O
°
°
°
°
− − =
− =
− = + −
− − =
− − =
H H
G H
G H
G H H
G H H
2+ 2- q-
2+ 2- q-
2+ 2- q-
2+ 3+ 2- q-
2+ 2+ q-
2+ 2+ q-
3+ 3+
[8]
0 liq [9]Cr :O ,Va
0 liq [8]Mn :O ,Va
1 liq [8]Mn :O ,Va
0 liq [8]Mn ,Mn :O ,Va
0 liqCr ,Mn :Va
1 liqCr ,Mn :Va
0Cr ,Mn
1_L
121000
129519
45459
33859
15009 13.6587
504 0.9479
=
=
= −
= −
= − +
= +
L
L
L
L
L T
L T
L 2-liq
:O188487.6 = −
Bcc A2 alloy (bcc)
1 3(Mn,Cr) (Va,O)
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91
bcc SER [7]Cr:Va Crbcc SER [7]Mn:Va Mnbcc SER SER [7] [7]Cr:O Cr Obcc SER SER [7] [7]Mn:O Mn O
0 bcc [10]Cr,Mn:Va
1Cr,Mn
GHSERCR
GHSERMN
3 GHSERCR + 3GHSEROO + 243
3 GHSERMN + 3GHSEROO
20328 18.7339
°
°
°
°
− =
− =
− − =
− − =
= − +
G H
G H
G H H T
G H H
L T
Lbcc [10]:Va
0 bcc [9]Cr:O,Va
bcc 2c Cr Mn Cr Mn Cr Mn
4 6 8 [10]Cr Mn Cr Mn Cr Mn
bccCr Mn Cr Mn
9162 4.4183
7095420.4
311.5 580 [ 1325 1133( )
10294( ) 26706( ) 28.117( ) ]
0.008 0.27 [0.48
= − +
= −=
= − − + − − −
− − + − − −
= − − +
T
LpT y y y y y y
y y y y y y
y y y yβ 2Cr Mn
4 [10]Cr Mn
643 0.72035( )
1.93265( ) ]
− −
− −
y y
y y
Manganosite (mgs)
2+ 2-
3+ 2-
2-3+
2-3+2+
2+ 3+ 3+ 2-1 1
° mgs SER SER [8]Mn OMn :O
° mgs SER SER [9]Cr OCr :O
° mgs SER SER [8]Mn OMn :O
0 mgsMn ,Mn :O
(Mn ,Mn , Cr ,Va) (O )
GMN1O1
0.5GCR2O3 71549.3 7.93845
GMN1O1 21883.5213 22.1853365
42
− − =
− − = + −
− − = − −
= −
G H H
G H H T
G H H T
L
3+2+ 2-
[8]
1 mgs [8]Mn ,Mn :O
104.8766
46513.1533=L
Bixbyite (bxb)
2-3+
3+ 2-
3+ 3+ 2-2 3
° bxb SER SER [8]Mn OMn :O
° bxb SER SER [9]Cr OCr :O
(Mn ,Cr ) (O )
2 3 GMN2O3
2 3 GCR2O3 3459
− − =
− − = +
G H H
G H H
Eskolaite (esk)
3+ 2-
3+3+ 2-
3+2+ 2-
2+
2+ 3+ 3+ 3+ 2-2 1 3
° esk SER SER [9]Cr OCr :Va:O
° esk SER SER [9] [7]Cr OCr :Cr :O
° esk SER SER [9] [7]Cr OCr :Cr :O
°Cr
13
(Cr , Cr ,Mn ) (Cr ,Va) (O )
2 3 GCR2O3
3 3 GCR2O3 GHSERCR
3 3 GCRO0 GHSERCR 5.2923
− − =
− − = +
− − = + −
G H H
G H H
G H H T
G 2-
3+ 2-3+
3+ 2-
esk SER SER [9] [7]Cr O:Va:O
° esk SER SER SER [8] [7]Mn Cr OMn :Cr :O
° esk SER SER [8]Mn OMn :Va:O
[9]
232 3 GCRO0 GHSERCR 5.2923
2 3 GMN2O3 GHSERCR 39503
2 3 GMN2O3 39503
Magnetic contribution0.28
− − = − −
− − − = + +
− − = +
=
H H T
G H H H
G H H
pT 3+ 3+ 2- 3+ 3+ 2-
3+ 2- 3+ 2-
2+ 3+ 2- 2+ 3+ 2-
2+ 2-
esk esk esk eskc Cr :Cr :O Cr :Cr :Oesk esk esk esk
c Cr :Va:O Cr :Va:O
esk esk esk eskc Cr :Cr :O Cr :Cr :Oesk esk
c Cr :Va:O
308.6 3
308.6 3
308.6 3
308.6
= =
= =
= =
=
y y
T y y
T y y
T y
β
β
β
2+ 2-esk esk
Cr :Va:O 3= yβ
Cubic spinel (β-spl)
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92
2-3+2+
3+2+ 2-
3+2+ 2-
3+2+ 2-
2+ 2+ 3+ 3+ 2-1 2 4
° β-spl SER SER SERMn Cr OMn :Cr :O
° β-spl SER SER [9]Cr OCr :Cr :O
° β-spl SER SER [8]Mn OMn :Mn :O
° β-spl SERCrCr :Mn :O
(Mn ,Cr ) (Cr ,Mn ) (O )
2 4 GSPINEL
3 4 GCR3O4
3 4 GMN3O4B
− − − =
− − =
− − =
− −
G H H H
G H H
G H H
G H SER SER [8]Mn O2 4 GCR3O4+GMN3O4B -GSPINEL− =H H
Tetragonally distorted spinel (α-spl)
3+2+ 2-
3+2+ 2-
2+ 3+ 3+ 2-1 2 4
° α-spl SER SER SERMn Cr OMn :Cr :O
° α-spl SER SER [8]Mn OMn :Mn :O
(Mn ) (Cr ,Mn ) (O )
2 4 GTSPINEL
3 4 GMN3O4
− − − =
− − =
G H H H
G H H
Functions [8]
[8]
2 13 3
2 13 3
GSPINEL GCR3O4+ GMN3O4B
210795.5+61.69GTSPINEL GCR3O4+ GMN3O4
200941.9+75.1
=
−=
−
T
T
a) Note: All parameters are in SI units: J, mol, K, Pa: R = 8.31451 J mol-1 K-1.
The optimization of the thermodynamic parameters is performed using the PARROT module
of the Thermo Calc[40] database system. PARROT takes into account all sorts of
thermodynamic and phase diagram data simultaneously. The program minimizes the sum of
squared errors between the experimentally determined phase diagram and thermodynamic
data and the corresponding calculated data. As the use of all the experimental data in a
simultaneous least square calculation often leads to divergence, we selectively adjust the
relative weight of each experimental data point and exclude data that are inconsistent with the
majority of the data points during the optimization procedure.
To optimize the parameters Aβ-spl and Bβ-spl in Eq. 4.2.4 we use the 2 4
β-splMnCr Of
°Δ G value derived
from Tsai and Muan[23] using 2 4f MnAl O
°Δ G from Kim and McLean[25] and the composition of
bcc in equilibrium with β-spl and mgs reported by Ranganathan and Hajra[19]. Further the
melting temperature of β-spl in air found by Speidel and Muan[12] is used to optimize Aβ-spl
and Bβ-spl in Eq. 4.2.4 and 3+ 3+ 2-liq0Cr ,Mn :OL . The temperature found from Speidel and Muan[12] for
the two phase equilibrium of Mn rich β-spl (Mn = 94.7 cat.%) and α-spl is used to optimize
Aβ-spl and Bβ-spl in Eq. 4.2.4 and Aα-spl and Bα-spl in Eq. 4.2.4. All these data are given a high
weight.
Further we use – with lower weights – the temperature of the two phase equilibrium β-spl +
liq at X(Cr) = 0.105 from Speidel and Muan[12] to optimize Aβ-spl and Bβ-spl in Eq. 4.2.4 and
3+ 3+ 2-Cr ,Mn :O
liq0L , and we use data on the solubility of Cr in MnyCr3-yO4 at T=1873 K under varying
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Thermodynamic assessments
93
oxygen partial pressures from Tanahashi et al.[17] shown in Fig. 4.2.5, p. 82, and data from
Pollert et al.[14] on the two phase equilibrium β-spl + bxb in air (Fig. 4.2.3, p. 80) to optimize
Aβ-spl and Bβ-spl in Eq. 4.2.4. Temperature data from Speidel and Muan[12] and Pollert et al.[14]
on the phase equilibria α-spl + β-spl and α-spl + β-spl + bxb are used to optimize Aβ-spl and
Bβ-spl in Eq. 4.2.4, and Aα-spl and Bα-spl in Eq. 4.2.6. We use data from Holba et al.[11] on the
temperature dependence of the diffusionless transformation of α-spl to β-spl shown in Fig.
4.2.2, p. 79 to optimize Aβ-spl and Bβ-spl in Eq. 4.2.4, and Aα-spl and Bα-spl in Eq. 4.2.6. Abxb in
Eq. 4.2.7 is optimized using data on the solubility of Cr in Mn2-yCryO3 from Pollert[14], for
Amgs in Eq. 4.2.8 data on the solubility of Cr in (Mn1-yCry)1-xO from Tanahashi et al.[17] are
used (Fig. 4.2.5, p. 82), and for Aesk in Eq. 4.2.9 and 4.2.10 data on the solubility of Mn in
(Cr1-yMny)2+xO3 from Pollert et al.[14] shown in Fig. 4.2.2, p. 79 and Fig. 4.2.5, p. 82 are used.
4.2.5 Results
Phase diagram data:
The calculated phase diagram of the pseudo-binary system MnOx-Cr2O3 in air is shown in
Figs. 4.2.1 and 4.2.2, p. 79. In Fig. 4.2.3, p. 80 the Mn rich part of the diagram is shown in
detail. β-spl is stable in a large temperature range from T = 513 K to 2243 K and from X(Cr) =
0 to X(Cr) = 0.67 in air. β-spl and esk coexist from X(Cr) = 0.66 to 0.992 at 1203 K in air. The
maximum Mn solubility in (Cr1-yMny)2+xO3 is 0.2 cat.% at 2243 K in air. Single phase α-spl is
stable in a small T–X(Cr) range from T = 1153 K to 1441 K and X(Cr) = 0 to 0.054 in air. α-
spl coexists with β-spl from X(Cr) = 0 at T = 1441 K to X(Cr) = 0.175 at T = 1156 K. The
dotted line in Fig. 4.2.2, p. 79 shows the temperature dependence of the diffusionless
transformation of α-spl to β-spl. bxb is stable from T = 694 K to 1154 K in air. The maximum
Cr solubility in Mn2-yCryO3 is 23 cat.% at T = 668 K in air. The two-phase field bxb + α-spl is
only found in a very small area at about 1150 K. prl coexists with esk at T < 513 K in air.
From T = 513 K to 668 K and maximum X(Cr) = 0.65 prl and β-spl coexist in air. prl + bxb is
stable in a small area from T = 668 K to 694 K and X(Cr) = 0 to 0.23 in air.
mgs is not stable in air. At 2Op = 400 Pa it starts to form in equilibrium with β-spl in a small
area at the Mn-rich side of the MnOx-Cr2O3 system around T = 1840 K. This two-phase field
expands under more reducing conditions which can be seen in the calculated phase diagram of
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Thermodynamic assessments
94
the pseudo-binary MnOx-Cr2O3 system at an oxygen partial pressure of -4 1×10 Pa in Fig. 4.2.4,
p. 80.
In Fig. 4.2.5, p. 82 experimental and calculated solubility data of Cr in mgs + β-spl, and Mn
in esk + β-spl are presented. Experimental data from Tanahashi et al.[17] on the solubility of
Cr in the phases of the two phase equilibria mgs + β-spl and esk + β-spl at 1873 K, and from
Bobov et al.[18] on the solubility of Cr in the phases of the two phase equilibria mgs + β-spl at
T = 1073 K, 1173 K, and 1273 K in function of 2Olog( )p are compared to the calculated
results from this work. The data from Bobov et al.[18] were not used for the optimization.
In the isothermal phase diagram of the Mn-Cr-O system at T = 1323 K of Fig. 4.2.6, p. 83 the
stable alloy phases of the system are plotted in addition to the oxides based on the assessment
of the binary Cr-Mn system from Lee[9].
Isothermal sections of the Cr2O3-MnO-MnO2 system at different temperatures are plotted in
Fig. 4.2.9 (next page).
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Thermodynamic assessments
95
Fig. 4.2.9 Isothermal sections of the ternary system Cr2O3-MnO-MnO2 showing oxide and
liquid evolution as a function of temperature and composition. Stoichiometric single phase
equilibria are points, and single solid solution phase equilibria are heavy lines. Dotted lines
are tielines. Three-phase field boundaries are denoted with thin lines.
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Thermodynamic assessments
96
Thermodynamic data:
The calculated enthalpy, entropy and Gibbs energy of formation of β-spl of the composition
MnCr2O4 from the elements is 2 4
β-splMnCr Of
°Δ H = –1599421 J mol-1, 2 4
β-splMnCr O
°S = 116 J mol-1 K-1, and
2 4
β-splMnCr Of
°Δ G = –1634017 J mol-1 at T = 298.15 K. The calculated temperature dependence of the
Gibbs energy of formation of of β-spl of the composition MnCr2O4 from the oxides MnO and
Cr2O3 is shown in Fig. 4.2.7, p. 85. At T = 1873 K we get 2 4
β-splMnCr Of
°Δ G = –34388 J mol-1. In the
temperature range from 1050 to 1800 K 2 4
β-splMnCr Of
°Δ G from the oxides is given by the term
–89167 + 29.338 T with an error of ± 0.21 %.
For α-spl of the composition MnCr2O4 we calculate α-splf
°Δ H = –1596517 J mol-1,
α-spl°S = 98 J mol-1K-1, and fα-spl°Δ G = –1625681 J mol-1 at T = 298.15 K.
4.2.6 Discussion
Phase diagram data:
Our assessed phase diagram is in rough agreement with the findings from Speidel and
Muan[12]. Large deviations of our calculated phase diagram from the phase diagram presented
by these authors concern the stability of the liquid and phase stabilities at low temperatures.
For both cases Speidel and Muan[12] mention the speculative character of their phase diagram
due to the lack of experimental data.
Our assessed phase diagram is in excellent agreement with the findings of Pollert et al.[14,15]
and Ranganathan et al.[19] as shown in Figs. 4.2.2 (p. 79), 4.2.3 (p. 80), and Fig. 4.2.6 (p. 83).
Our calculated T0 line for the diffusionless transformation of α-spl → β-spl is in perfect
agreement with experiments by Holba et al.[11] (Fig. 4.2.2, p. 79). The calculated dependence
of β-spl solid solubility on oxygen partial pressures shown in Fig. 4.2.5, p. 82 agrees well
with the results from Tanahashi et al.[17]. The results from Bobov et al.[18] on the other hand
cannot be reproduced.
Fig. 4.2.9 (p. 95) represents the phase relations of the oxides and the evolution of liquid
formation. The three-phase regions prl + esk + bxb and bxb + esk + β-spl, and the two-phase
fields prl + bxb, β-spl + bxb, and mgs + β-spl dominate the system in a wide temperature
range from T=1200 K to 1900 K (Figs. 4.2.9 a to c). At T=1700 K α-spl is no longer stable
and the three-phase regions mgs + α-spl + β-spl and bxb + α-spl + β-spl (Fig. 4.2.9 a)
disappear. At this temperature small oxygen nonstoichiometry of esk is apparent. The oxygen
nonstoichiometry of mgs is yet insignificant (Fig. 4.2.9 b), but it increases at elevated
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Thermodynamic assessments
97
temperatures becoming apparent at T = 2000 K (Fig. 4.2.9 d). At T = 1900 K phase relations
become more complex due to incipient melting (Fig. 4.2.9 c). At T = 1900 K liquid is formed
at the Mn-rich side of the system, and the-three phase fields bxb + β-spl + liq and mgs + β-spl
+ liq emerge
(Fig. 4.2.9 c). Even more three phase regions due to increasing liquid formation start to exist
at T = 2000 K (Fig. 4.2.9 d). At T = 2400 K the only remaining stable solid phases are esk and
prl (Fig. 4.2.9 f).
Thermodynamic data:
Our calculated 2 4
β-splMnCr Of
°Δ G value at T = 1873 K is in agreement with the 2 4
β-splMnCr Of
°Δ G value
derived from Tsai and Muan[22] using 2 4
splf MnAl O
°Δ G from Kim and McLean[25].
Our assessed ΔHα β and ΔSα β values for the transition of α-hsm to β-hsm compare
favorably with the values reported by Holba et al.[12]. The calculated ΔHα β and ΔSα β values
for the transformation of α-spl to β-spl are very small, indicating that only very little energy is
needed for the transformation to take place.
4.2.7 Applications on SOFC
Due to the large stability range of β-spl and esk in air it is not realistic to prevent the
formation of these unwanted phases under oxidizing conditions at the cathode side of SOFC
operated with high Cr alloy interconnects and LSM cathode.
The composition of Crofer22 APU alloy is close to the Cr-corner of the Mn-Cr-O phase
diagram. In a thermodynamic view the formation of β-sp with the composition MnCr2O4
(Point A in Fig. 4.2.6, p. 84) on Crofer22 APU alloy is expected under SOFC operating
conditions. Hence, the formation of a protective Cr2O3 single phase layer followed by a
chromium manganese spinel on Mn bearing interconnects as it is observed by Simner et al.[5]
must be kinetically controlled. The occurrence of other Cr-Mn phases in the protective scales
formed during thermal exposure of Crofer 22 APU interconnects is not expected
thermodynamically. This is obvious from Fig. 4.2.6, p. 83.
Recently Qu et al.[42] found that the electrical conductivity of chromium manganese spinel
increases with increasing Mn-content. The problem of the application of synthesized Mn-rich
α-spl on the interconnect for the purpose of combining a decrease of Cr evaporation with
enhanced electrical conductivity is that α-spl will with time tend towards its stable
composition of MnCr2O4, which is at point A in Fig. 4.2.6, p. 83 associated with decreasing
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Thermodynamic assessments
98
electrical conductivity. Also α-spl will then transform to β-spl and on thermal cycling of the
SOFC back to α-spl leading to mechanical stresses that might result in the appearance of
cracks.
4.2.8 Conclusions
Due to the lack of inversity and oxygen nonstoichiometry of spinel we chose a model
description of β-spl and α-spl without the introduction of vacancies into the spinel structure.
All features of the system are well described with the optimization of only 8 additional
optimization parameters.
There is a surprising lack of thermodynamic data on β-spl, and the only available
2 4
β-splMnCr Of
°Δ G values are spread over a range of 31 kJ mol-1. Recalculating old experiments using
new thermodynamic data together with phase diagram data we achieved a description, which
is very close to the experimental findings of several authors, and we present well-founded
Δf°H, °S, and Δf
°G data for β-spl and α-spl.
Our Thermo Calc[40] dataset resulting from the presented CALPHAD modeling of the Mn-Cr-
O system allows the calculation of phase stabilities, compositions and transformations of
unwanted MnxCr3-xO4 spinel solid solution and eskolaite phases in solid oxide fuel cells under
any desired temperature and oxygen partial pressure conditions.
References
1. K. Hilpert, W.J. Quadakkers, L. Singheiser, in: W. Vielstich, A. Lamm, H.A. Gasteiger
(Eds.), Handbook of Fuel Cells – Fundamentals, Technology and Applications, John
Wiley & Sons, Chichester, 2003, p. 1037.
2. J.W. Fergus, Lanthanum chromite-based materials for solid oxide fuel cell interconnects,
Solid State Ionics, 2004, 171, pp. 1-15.
3. D. Das, M. Miller, H. Nickel, K. Hilpert, in: U. Bossel (Ed.), First European Solid Oxide
Fuel Cell Forum Proceedings, Vol. 2, Druckerei J. Kinzel, Göttingen, 1994, p. 703.
4. S.P.S. Badwal, R. Deller, K. Foger, Y. Ramprakash, J.P. Zhang, Interaction between
chromia forming alloy interconnects and air electrode of solid oxide fuel cells, Solid State
Ionics, 1997, 99, pp. 297-310.
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99
5. S.P. Simner, M.D. Anderson, G.-G. Xia, Z. Yang, L.R. Pederson, J.W. Stevenson, SOFC
performance with Fe-Cr-Mn alloy interconnect, J. Electrochem. Soc., 2005, 152, pp.
A740-45.
6. A. T. Dinsdale, SGTE Data for Pure Elements, Calphad, 1991, 15(4), pp. 317-425.
7. A.N. Grundy, B. Hallstedt, L.J. Gauckler, Assessment of the Mn-O system, J. Phase
Equilib., 2003, 24, pp. 21-39.
8. E. Povoden, A.N. Grundy, L.J. Gauckler, Thermodynamic reassessment of the Cr-O
system in the framework of solid oxide fuel cell (SOFC) research, J. Phase Equilib. Diff.,
2006, 27, pp. 353-62.
9. B-J. Lee, A thermodynamic evaluation of the Cr-Mn and Fe-Cr-Mn systems, Metall.
Trans., 1993, A 24, pp. 1919-1933.
10. J.M. Hastings, L.M. Corliss, Magnetic structure of manganese chromite, Phys. Rev., 1962,
126, pp. 556-65.
11. P. Holba, M. Nevřiva, E. Pollert, Tetragonal distortion of spinel solid-solutions MnCr2O4-
Mn3O4, Mater. Res. Bull., 1975, 10, pp. 853-60.
12. D.H. Speidel, A. Muan, The system manganese oxide-Cr2O3 in air, J. Am. Ceram. Soc.,
1963, 46, pp. 577-78.
13. Y.V. Golikov, V.F. Balakirev, Phase equilibrium diagram of the system Mn-Cr-O, J. Solid
State Chem., 1987, 71, pp. 562-65.
14. E. Pollert, M. Nevriva, J. Novak, Phase diagram of the Mn2O3-Cr2O3 system in air, Mater.
Res. Bull., 1980, 15, pp. 1453-56.
15. E. Pollert, M. Nevriva, J. Novak, Miscibility gap of MnxCr3-xO4 spinels, J. Phys. Chem.
Solids, 1977, 38, pp. 1145-47.
16. S. Geller, G.P. Espinosa, Magnetic and crystallographic transitions in Sc3+, Cr3+, and Ga3+
substituted Mn2O3, Phys. Rev., 1970, B 1, pp. 3763-69.
17. M. Tanahashi, N. Furuta, C. Yamauchi, T. Fujisawa, Phase equilibria of the MnO-SiO2-
CrOx system at 1873 K under controlled oxygen partial pressure, ISIJ Int., 2001, 41, pp.
1309-1315.
18. A.P. Bobov, A.G. Zalazinsky, V.F. Balakirev, Y.V. Golikov, G.I. Chufarov, Peculiarities
of phase-diagram in the reduction of Me0.25Mn2.75O4 solid-solutions, Zh. Fiz. Khim., 1984,
58, pp. 750-751 (in Russian).
19. S. Ranganathan, J.P. Hajra, Alloy oxide equilibria in the Cr-Mn-O system, Bull. Mater.
Sci., 1987, 9, pp. 149-58.
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20. M. Tanahashi, N. Furuta, T. Taniguchi, C. Yamauchi, T. Fujisawa, Standard Gibbs free
energy of formation of MnO-saturated MnO.Cr2O3 solid solution at 1873 K, ISIJ Int.,
2003, 43, pp. 7-13.
21. I. Barin: Thermochemical Data of Pure Substances, 2nd Ed., Parts I and II, VCH
Verlagsgesellschaft mbH, Weinheim, 1993.
22. H.T. Tsai, A. Muan, Activity composition relations in FeCr2O4-FeAl2O4 and MnCr2O4-
MnAl2O4 solid-solutions at 1500°C and 1600 °C, J. Am. Ceram. Soc., 1992, 75, pp.
1407-11.
23. H.T. Tsai, A. Muan, Activity composition relations in refractory oxide solid-solutions at
high-temperatures – the system Cr2O3-Al2O3, J. Am. Ceram. Soc., 1992, 75, pp. 1412-15.
24. L.M. Lenev, I.A. Novokhatskiy, Phase diagram of system MnO-Al2O3 and
thermodynamic properties of MnAl2O4, Izv. Akad. Nauk SSSR, Met., 1966, 3, pp. 73- (in
Russian).
25. C.K. Kim, A. McLean, Thermodynamics of iron-manganese aluminate spinel inclusions
in steel, Metall. Trans. B, 1979, 10B, pp. 575-84.
26. K.T. Jacob, Revision of thermodynamic data on MnO-Al2O3 melts, Can. Metall. Q., 1981,
20, pp. 89-92.
27. S. Dimitrov, A. Weyl, D. Janke, Control of the manganese-oxygen reaction in pure iron
melts, Steel Res., 1995, 66, pp. 87-92.
28. J.V. Biggers: Ph.D. Thesis, Pennsylvania State University, University Park, PA, 1966.
29. N.Y. Toker, L.S. Darken, A. Muan, Equilibrium phase-relations and thermodynamics of
the Cr-O system in the temperature-range of 1500°C to 1825°C, Metall. Trans. B, 1991,
22, pp. 225-232.
30. R.K.F. Lam: United States Patent 6039788, 2000.
31. J.-O. Andersson, A.F. Guillermet, M. Hillert, B. Jansson, B. Sundman, A Compound-
Energy Model of Ordering in a Phase with Sites of Different Coordination Numbers, Acta
Metall., 1986, 34, pp. 437-445.
32. M. Hillert, B. Jansson, B. Sundman, Application of the Compound-Energy Model to
Oxide Systems, Z. Metallkd., 1988, 79(2), pp. 81-87.
33. M. Hillert, The Compound Energy Formalism, J. Alloy. Cmpd., 2001, 320, pp. 161-76.
34. Z. Lu, J. Zhu, E.A. Payzant, M.P. Paranthaman, Electrical conductivity of the manganese
chromite spinel solid solution, J. Am. Ceram. Soc., 2005, 88, pp. 1050-53.
35. R.D. Shannon, Revised effective ionic-radii and systematic studies of interatomic
distances in halides and chalcogenides, Acta Crystallogr., 1976, A 32, pp. 751-67.
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36. M. O’Keefe, M. Valigi, The electrical properties and defect structure of pure and
chromium-doped MnO, J. Phys. Chem. Solids, 1970, 31, pp. 947-962.
37. D. Caplan, M.J. Fraser, A.A. Burr, in: Ductile Chromium, ASM, Cleveland, Ohio, 1957,
p. 196.
38. M. Hillert, B. Jansson, B. Sundman, J. Ågren, A Two-Sublattice Model of Molten
Solutions with Different Tendency of Ionization, Metall. Trans. A, 1985, 16A, pp. 261-66.
39. B. Sundman, Modification of the Two-sublattice Model for Liquids, Calphad, 1991, 15,
pp. 109-19.
40. B. Sundman, B. Jansson, J.-O. Andersson, The Thermo-Calc Databank System, Calphad,
1985, 9(2), pp. 153-90.
41. V.M. Eremenko, G.M. Lukashenko, V.R. Sidorko, Thermodynamic properties of alloys of
manganese with transition elements of fourth period (Cr Fe Co Ni) and with copper, Russ.
J. Phys. Chem., 1968, 42, pp. 343-.
42. W. Qu, L. Jian, J.M. Hill, D.G. Ivey, Electrical and microstructural characterization of
spinel phases as potential coatings for SOFC metallic interconnects, J. Power sources,
2006, 153, pp. 114-24.
4.3 Thermodynamic assessment of the La-Cr-O system
E. Povoden, M. Chen , A.N. Grundy, T. Ivas, and L.J. Gauckler
J. Phase Equilib. Diff. (accepted)
The La-Cr and the La-Cr-O systems are assessed using the Calphad approach. The calculated
La-Cr phase diagram as well as LaO1.5-CrO1.5 phase diagrams in pure oxygen, air, and under
reducing conditions are presented. Phase equilibria of the La-Cr-O system are calculated at T
= 1273 K as a function of oxygen partial pressure.
In the La-Cr system reported solubility of lanthanum in bcc chromium is considered in the
modeling.
In the La-Cr-O system the Gibbs energy functions of La2CrO6, La2(CrO4)3, and perovskite-
structured LaCrO3 are presented, and oxygen solubilities in bcc and fcc metals are modeled.
Emphasis is placed on a detailed description of the perovskite phase: the orthorhombic to
rhombohedral transformation and the contribution to the Gibbs energy due to a magnetic
order-disorder transition are considered in the model. The following standard data of
Page 102
Thermodynamic assessments
102
stoichiometric perovskite are calculated: -13298 Kf,oxides (LaCrO ) 73.7 kJ mol° = −Δ H ,
and -1 -1298 K 3 (LaCrO ) 109.2 J mol K° =S . The Gibbs energy of formation from the
oxides, 3f,oxides (LaCrO )Δ =G –72.403–0.0034 T (kJ mol-1) (T = 1273 K to 2673 K) is calculated.
The decomposition of the perovskite phase by the reaction
3 2 3 21 3LaCrO La O Cr + O (g)2 4
→ + ↑ is calculated as a function of temperature and oxygen partial
pressure: at 1273 K the oxygen partial pressure of the decomposition,2O (decomp)p = 10-20.97 Pa.
Cation nonstoichiometry of
La1-xCrO3 perovskite is described using the compound energy formalism (CEF), and the
model is submitted to a defect chemistry analysis.
The liquid phase is modeled using the two-sublattice model for ionic liquids.
4.3.1 Introduction
In SOFC, the thermodynamic stability of the cathode is particularly important for efficient
long-term operation. Sr-doped lanthanum manganites (LSM) with the perovskite structure are
used as cathode materials in SOFC. Diffusion of chromium from the metallic interconnect
with high chromium content into the cathode leads to the formation of Mn(Cr,Mn)2O4 spinel
and Cr2O3 along with a severe cell voltage decrease[1-4]. As the thermal expansions of
LaCrO3-based interconnect and conventional perovskite cathode materials are similar, and Cr-
diffusion into the cathode from LaCrO3-based interconnects is significantly lower than from
Cr-containing metallic interconnects, recently Sr-, V-doped[5] and Zn-doped[6] La1-xCaxCrO3-δ
have been considered as promising alternative interconnect materials for SOFC. Furthermore
earth alkaline-containing LaCrO3 has been proposed as a cathode material in a recent study by
Jiang et al[7].
The presented thermodynamic assessment of the La-Cr-O system is laying the grounding for
extensions to the thermodynamic La-Sr-Mn-Cr-O oxide database that is required to
understand the thermodynamics of SOFC degradation by chromium. It is also a starting point
for extensions to thermodynamic databases with additional components serving as dopants in
LaCrO3 for SOFC interconnect and cathode applications.
The assessment of the La-Cr-O system using the Calphad approach is based on the recently
reassessed La-O[8] and Cr-O subsystems[9]. The lattice stabilities of elements are adopted from
Dinsdale[10]. All available experimental phase diagram, thermodynamic, and structure-
chemical data are critically assessed, aiming on minimizing the squared errors between
Page 103
Thermodynamic assessments
103
experiments and calculation during the optimization of model parameters using the PARROT
module of the Thermocalc[11] software.
4.3.2 Literature review of the La-Cr system
The La-Cr system has a eutectic at T = 1138 K[12,13] and 3.4 at.% Cr[13] and a monotectic at
T = 1983 K[12] or T = 2103 K[14] and 96 at.%[12] or 99.1 at.%[14] Cr, as well as a large liquid-
liquid miscibility gap[12,13]. No intermetallic phases were found in the La-Cr system[12,13].
Berezutskii et al.[15] determined the partial enthalpy of mixing in La-Cr liquid with infinite
dilution of Cr, CrΔH at T = 1700 K using high-temperature calorimetry.
As small additions of rare-earth metals essentially increase the high-temperature corrosion
resistance of chromium[16], modeling of the La-solubility in bcc-structured Cr, denoted as
ssαCr , is of technological interest. Small solubility of La in ssαCr was reported[12,14,17], whereas
Cr is almost insoluble in La[13]. The solubility of La in ssαCr was determined in investigations
by Savitskii et al.[12] from T = 1073 K up to the melting of Cr using metallographic and micro-
hardness techniques to be 2.5 at.% at 1983 K. Svechnikov et al.[14] reported a La solubility of
0.68 at.% at T = 2103 K, and Epstein et al.[17] found La < 0.04 at.% in ssαCr at T = 1533 K. The
solubility of La in ssαCr decreases towards lower temperatures.
4.3.3 Literature review of the La-Cr-O system
In the LaO1.5- CrO1.5 system two eutectics were found at 19 at.% Cr2O3 (T = 2243 K)[18] or 12
at.% Cr2O3 (T = 2323±20 K)[19], and at 84 at.% Cr2O3 (T = 2248 K)[18] or 80 at.% Cr2O3 (T =
2473±20 K)[19] in argon atmosphere on either side of the congruently melting perovskite-
structured lanthanum chromite[18-20] (in this study oxides containing Cr(III) and Cr with
higher valencies than three are denoted as chromite and chromate respectively). The melting
temperature of lanthanum chromite in air, Tm(air) = 2773 K was determined by Foëx[21] and
by Coutures[20] using a thermal analysis technique described in more detail in earlier
publications.[22-24] The melting temperature was measured with optical pyrometers. Tm(argon)
= 2703 K was reported by Tresvjatskiy et al.[18], but in the graphic presentation of the phase
diagram in the same paper Tm(argon) ≈ 2600 K, and the exact value of the oxygen partial
pressure was not specified. Experimentally determined special points in the LaO1.5-CrO1.5
quasibinary system reveal a considerable spread. This is not surprising as experiments are
complicated due to the high investigation temperatures and evaporation of predominantly
Cr[25,26]. Furthermore deviations between the data from Tresvjatskiy et al.[18] and Berjoan[19]
Page 104
Thermodynamic assessments
104
may partly originate from differences of the oxygen partial pressure, which in both studies
was not exactly specified. The peritectic phase diagram proposed by Cassedanne[27] is in gross
conflict with the phase diagram data from the other groups.
Experimental oxygen solubilities in pure Cr and La were considered in thermodynamic
assessments by Povoden et al.[9] and Grundy et al. [28], whereas experiments on oxygen
solubilities in ssαCr are missing.
Lanthanum chromates:
The following lanthanum chromates were documented: Berjoan[19] reported that orthorhombic
La2CrO6 forms at T > 923 K. Using differential scanning calorimetry (DSC) he determined
the enthalpy change of the reaction
2 3 2 3 2 62(g)32La O Cr O O 2La CrO2
+ + → (4.3.1)
at T=1055 K and 2Op =83000 Pa to be −151±8 kJ mol-1.
The enthalpy of formation of La2(CrO4)3 from the elements at T = 298 K was proposed by
Tsyrenova et al.[29] to be −3961±11.7 kJ mol-1. La2(CrO4)3 decomposes by
890 1030 K
2 4 3 3 2 3 2(g)La (CrO ) 2LaCrO 0.5Cr O 2.25O−⎯⎯⎯⎯⎯→ + + ↑ (4.3.2)
An enthalpy change of 231 kJ mol-1 was determined for this reaction at the average
temperature of T = 960 K.[30]
LaCrO4 has been interpreted as a mixed-valent intermediate decomposition product of
La2(CrO4)3[30,31].
Stoichiometries and thermal stability ranges of lanthanum chromates with complex formulae
were reported by Berjoan et al.[32]. However these were in significant disagreement with later
results obtained by the same author[19].
The perovskite phase:
Existing experimental data of lanthanum chromite perovskite structure[33-45],
thermodynamics[30,33-35,43,46-53], phase stability[54], and nonstoichiometry[55-56] along with the
investigation techniques used are listed in Table 4.3.1 (next page).
Page 105
Thermodynamic assessments
105
Table 4.3.1 Calculated and experimental thermodynamic data of La-Cr oxides
1298
[30]
[30]
Enthalpy increments , (kJmol )1090 K
98.19, this work, calculated94.4 HT (high temperature) - calorimetry
1350 K133.05 this work, calculated139.2 HT - calorimetryActivit
−−=
=
KH HT
T
2 3
2 3
2 3 34
Cr O
4 5[53]Cr O
2 6
2 3 2 3
y of Cr O in LaCrO
2100 1.11 10 this work, calculated
2100 1.1 10 1.1 10 Knudsen mass spectrometry
La CrOEnthalpy of the formation reactionLa O + 0.5Cr O +1.5O
−
− −
= = ×
= = × ± ×
T K a
T K a
298K
298K
298K
2(g) 2 6
1f,oxides
-1 -1
2 4 3
1f,elements
f,ele
La CrO
73.0 kJmol this work, calculated
330 Jmol K this work, calculated
La (CrO )
3845 kJmol this work, calculated
2 6
2 6
42 3
La CrO
La CrO
La (CrO )
° −
°
° −
→
Δ = −
=
Δ = −
Δ
H
S
H
298K
298K
298K
1 [29]ments
1 1
2 3 2 3 2(g) 2 4 3
f,oxides
3961 11.7 kJmol , calculated
516 Jmol K this work, calculated
Enthalpy of the formation reactionLa O +1.5Cr O + 2.25O La (CrO )
42 3
42 3
2
La (CrO )
La (CrO )
La (CrO
° −
° − −
°
= − ±
=
→
Δ
H
S
H
298K
1
2 4 3 3 2 3 2(g)
1[30]
372 kJmol this work, calculated
Enthalpy of the dissociation reactionLa (CrO ) 2LaCrO + 0.5Cr O + 2.25O
231 kJmol and this work, fitted
4 3
42 3
)
La (CrO )
−
−
= −
→
Δ =H
298K
298K
975K
3
-1f,elements
-1f,oxides
-1f,oxides
Rhombohedral LaCrOStandard enthalpy
1368.2 kJmol this work, calculated
73.7 kJmol this work, calculated
62.35 kJmol this w
3
3
3
LaCrO
LaCrO
LaCrO
°
°
°
Δ = −
Δ = −
Δ = −
H
H
H
1078K
298K
-1 [46]f,oxides 2 3
-1 -1
ork, calculated
73.06 ± 2.79 kJmol Drop solution calorimetry in 2PbO× B O
Standard entropy
109.2 Jmol K this work, calculated
Gibbs energy of formation by 3 L4
3
3
LaCrO
LaCrO
°
°
Δ = −
=
H
S
2 3 2 3 3
1
1[49]
1[52] 2
1a O Cr O LaCrO 2
1273 K 76.75 kJmol this work, calculated1273 K 30.1 1.5 kJmol solid oxide electrolyte - emf 1273 K 42.29 0.38 kJmol CaF - based emf
° −
° −
° −
+ →
= Δ = −= Δ = − ±= Δ = − ±
=
T GT GT G
T 1
1[53]
1
2100 K 79.52 kJmol this work, calculated2100 K 78.9 1.1 kJmol Knudsen mass spectrometry
72.403 0.0034 (kJmol ), 1273 - 2673 K this work, calculated44.45 0.002115
° −
° −
° −
°
Δ = −= Δ = − ±
Δ = − −Δ = − +
GT G
G TG 1 [50]
21 [51]
2
0.4(kJmol ), 855 -1073 K CaF - based emf
94.758 0.08530 (kJmol ), 700 -885 K CaF - based emf
−
° −
±
Δ = − +
T
G T
Page 106
Thermodynamic assessments
106
Crystal and magnetic structure: LaCrO3 is orthorhombic (o-prv) at room temperature and
transforms to rhombohedral structure (r-prv) at higher temperatures[20,33-42]. The temperatures,
enthalpy and entropy changes of this first-order[44] transition taken from the literature are
listed in Table 4.3.2 along with the investigation techniques used.
Table 4.3.2 Calculated and experimental data of the orthorhombic to rhombohedral
transition of LaCrO3
The reported transformation temperatures lie between T = 503 K and 583 K. The determined
enthalpy and entropy changes vary from 277 J mol-1 to 502.08 J mol-1 and 0.5 J mol-1 to
[33]
[34] a)
[35] a)
Transition temperature (K)540, this work, calculated503 583 adiabatic calorimetry544 1 DTA, DSC, thermogravimetry, dilatometry536 adiabatic shield calorimetry, HT - XRD (air and vacuu
−±
[36]
[37]
[38] a)
[38] a)
[39]
[20]
[40] a)
[40] a)
m)563 5 DTA, dilatometry, HT - XRD, HT - microscopy, HT - x - ray photography550 HT - XRD528 533 HT - XRD533 3 DTA543 XRD533 HT - XRD540 2 HT - XRD, DSC533 5 HT - XRD, dilatomet
±
−±
±±
[41]
[41]
[41]
[42] a)
[42] a)
[43]
ry545 heating, DSC535 cooling, DSC550 HT - XRD523 starting transition, simultaneous DSC - XRD541 completed transition, simultaneous DSC - XRD533 estimated from neutron powder d
[44]
1
[33]
[34] a)
[3
iffraction509 DSC, XRD
Enthalpy change of transition (Jmol )340, this work, calculated502.08 41.84 at 503 583 K calculated from adiabatic calorimetry277 at 544 1 K DSC403.25 at 536 K
−
± −±
5] a)
[40] a)
[41]
[44]
-1 1
calculated from adiabatic shield calorimetry340 (10 - 40) at 533 5 DSC380 at 550 K DSC310 at 509 K DSC
Entropy change of transition (Jmol K )0.63, this work, calculated0.96 at 503
−
± ±
− [33]
[34] a)
[35] a)
a) used for optimization
583K calculated from adiabatic calorimetry0.5 calculated from DSC0.75 calculated from adiabatic shield calorimetry
Page 107
Thermodynamic assessments
107
0.96 J mol-1 K-1. A transformation from rhombohedral to cubic structure at a temperature close
to T = 1300 K was reported by Ruiz et al.[37] and Momin et al.[41], whereas Coutures et al.[20]
reported T = 1923 K using high-temperature x-ray diffraction (HT-XRD), in agreement with
Berjoan[19] (T = 1923 ± 20 K) using dilatometry. Berjoan[19] further reported prevailing of the
cubic structure at T = 2173 K. On the other hand Geller and Raccah[38] as well as Höfer and
Kock[34] did not observe the rhombohedral to cubic transition up to T = 1873 K and
T = 1823 K respectively using differential thermal analysis (DTA).
A magnetic order-disorder transition was documented to occur at T ≈ 287 K[35], 289 K[45], or
295 K[46].
Enthalpy of formation: Cheng and Navrotsky[47] determined the enthalpy of formation of
LaCrO3 by oxide melt solution calorimetry at T = 1078 K.
Heat capacity and enthalpy increment data: the heat capacities of LaCrO3 were measured by
Korobeinikova and Reznitskii[33] from T = 340 K to 900 K using adiabatic calorimetry, Höfer
and Kock[34] (480 to 610 K) and Satoh et al.[45] (150 to 450 K) using DSC, Satoh et al.[45] (T =
77 K to 280 K) using alternating current calorimetry, Sakai et al.[35] (T=100 K to 1000 K)
using laser-flash calorimetry, and Sakai and Stølen[43] (T = 272 K to 1000 K) using adiabatic
shield calorimetry. Enthalpy increments of LaCrO3 at T = 1090 K and 1350 K were measured
by Suponitskii[30] using a high-temperature heat-conducting calorimeter.
Gibbs energy of formation: in order to obtain the Gibbs energy of formation of LaCrO3, Chen
et al.[49] measured electromotive force (emf) of the solid oxide galvanic cell Pt/Cr, La2O3,
LaCrO3/MgO-stabilized ZrO2/Cr2O3, Cr/Pt at 1273 K. Azad et al.[50], Chen et al.[51], and
Dudek et al.[52] measured emf of Pt, O2/La2O3, LaF3/CaF2/LaF3, LaCrO3, Cr2O3/O2, Pt in pure
oxygen from T = 855 K to 1073 K, T = 700 to 885 K, and T = 1273 K respectively. Peck et
al.[53] derived the Gibbs energy of formation of LaCrO3 from the determination of the
thermodynamic activity of Cr2O3 in LaCrO3 for the Cr2O3-poor phase boundary of LaCrO3 in
the temperature range from T = 1887 K to 2333 K using Knudsen effusion mass spectrometry.
Chemical stability: Nakamura et al.[54] reported no weight loss of lanthanum chromite at
T=1273 K from pure oxygen to 2Op =10-16.1 Pa using thermogravimetry combined with X-ray
diffraction (XRD). This means that the perovskite phase does not decompose within this
oxygen partial pressure range, and its oxgen nonstoichiometry is negligible.
Cation nonstoichiometry and defect chemistry: Maximum excess Cr in single-phase La1-xCrO3
of 0.38 cat.% in furnace-cooled LaCrO3 annealed at T = 1773 K in air was reported from
Khattak and Cox[55]. Single phase lanthanum chromite with 0.76 cat.% to 1.28 cat.% excess
Page 108
Thermodynamic assessments
108
Cr was prepared at T = 1773 K in a pure oxygen atmosphere[56]. Iliev et al.[56] observed an
intensity decrease of the high frequency band in a Raman spectrum of lanthanum chromite
measured after annealing the phase in vacuum at T = 1273 K. This feature was assigned to a
reduced number of Cr4+ due to partial removal of oxygen during the annealing of the
originally lanthanum-deficient perovskite phase.
Interpretations of the defect chemistry of the perovskite phase were made from electrical
conductivity measurements: the electrical conduction in lanthanum chromite is almost purely
electronic[37,57], affirming the lack of oxygen vacancies in the structure, in line with the results
from thermogravimetry[54]. Ruiz et al.[37] reported that the ionic transport number in
lanthanum chromite is less than 0.05 % up to T = 1250 K. Akashi et al.[58] measured the
isothermal electrical conductivity of an equilibrated La1-xCrO3-Cr2O3 mixture with 5 vol.%
excess Cr2O3 from T = 1573 K to 1673 K from 2
3O 1.0 10 Pa= ×p to
2
4O 2.0 10 Pa= ×p . They
observed an extraordinarily slow equilibration of the samples: More than four months were
required to measure the electrical conductivity at equilibrium state. The conductivity was
proportional to 2
3 16Op , the same as reported in an earlier study[25]. On the other hand a slope
of 2
1 4Op from T=700 K to 1300 K and purely intrinsic conductivity > 1600 K stated by
Shvaiko-Shvaikovskii et al.[57] is inconsistent with the findings from Akashi et al.[58] Shvaiko-
Shvaikovskii et al.[57] deduced n-type conductivity from measurements of transport number,
resistivity and thermo-emf at 2O 1Pa=p and
2
2O 10 Pap = , the electrical conductivity being
proportional to 2
3 8O
−p . The transition from reduced to stoichiometric chromite was
accompanied by a decrease of about 0.1% in weight, thus the presence of interstitial Cr in
reduced chromite was proposed. However n-type conductivity was not approved by any
further study.
Several groups[58,59] agree that the electrical neutrality is maintained by holes and lanthanum
vacancies, and that the carrier is the hole in lanthanum chromite[25,58-60]. Akashi et al.[58]
reported that concentrations of lanthanum vacancies and holes slightly increase from T = 1550
K to 1700 K. In contrast to the other authors Shvaiko-Shvaikovskii et al.[57] and
Meadowcroft[25] proposed the occurrence of chromium vacancies instead of lanthanum
vacancies.
Page 109
Thermodynamic assessments
109
4.3.4 Thermodynamic modeling and optimization
Metal phases:
In order to account for the solubility of La in ssαCr , the zeroth-order, composition-
independent interaction parameter[61] 0 bccCr,La:VaL was given a positive value. We chose the
solubility values from Svechnikov et al.[14] for its optimization, as these data are more
comparable to solubilities in other rare earths-transition elements systems.
Povoden et al.[9] described the solubility of oxygen in Cr(bcc) using the model Cr(Va,O)3. For
the reasons discussed recently[62], we reassess the oxygen-solubility in Cr(bcc) using the
model (Cr)(O,Va)1.5, and ssαCr is then given by the two-sublattice description
(La,Cr)(Va,O)1.5. The Gibbs energy of the end-member (Cr)(O)1.5 is defined as
[10] [10]3 32 41.5 2
gasSER SER(Cr)(O) Cr O Cr(bcc) O
° ° °− − = + + +G H H G G A BT (4.3.3)
SERxH is the standard enthalpy of the stable state of element x at 298.15 K and 105 Pa.[10] A and
B are adjustable parameters; using the PARROT module of the Thermocalc software[11] A was
given the fix value 0 for the reasons discussed in an earlier paper[9], and B and a regular
interaction parameter 0Cr:O,VaL were optimized with the same experimental data[9]. Due to the
lack of experimental data the oxygen solubility in ssαCr was modeled as an ideal extension of
the oxygen solubilities in pure La and Cr.
Solid oxides:
Lanthanum chromates:
The Gibbs energy function of La2CrO6 was based on the sum of the Gibbs energy functions of
La2O3, Cr2O3, and O2 in proper stoichiometries and A + BT parameters that were fitted to the
enthalpy of formation from the oxides, Eq. 4.3.1 as well as thermal stability data. The thermal
stability of La2CrO6 is slightly influenced by the thermodynamics of the intermediate, mixed-
valent chromates mentioned above. In order to refine the model parameters of La2CrO6, it was
thus necessary to consider these mixed-valent chromates in a provisional version of the
thermodynamic La-Cr-O database in spite of their arguable stoichiometries, and to optimize
their model parameters with phase diagram data[19,32]. The formation of chromates that contain
mixed Cr valences may be explained by gradual reduction of Cr6+ in La2CrO6 as the
temperature increases. These chromates can be interpreted as intermediate products in the
Page 110
Thermodynamic assessments
110
scope of a sluggish decomposition of La2CrO6, which starts at T = 1153 K[19,32] and is
completed at T = 1473 K[32] or 1523 K[19]. The simplified decomposition reaction reads
2 6 2 3 1- 3 21.5- (1.5 )1+La CrO La O La CrO O (g)
2 2[19,32]mixed-valent chromates⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ + + ↑x
xx (4.3.4)
Slight differences of the oxygen partial pressure during experiments may be reflected by a
variable extent of Cr-reduction, and consequently ambiguous stoichiometries of mixed-valent
intermediate chromates. These lanthanum chromates with conflicting stoichiometries[19,32] are
not included in the presented thermodynamic database.
The Gibbs energy function of La2(CrO4)3 was formulated using the same strategy as for
La2CrO6. The model parameters were fitted to the experimental enthalpy and temperature of
decomposition[30]. The enthalpy of formation from the elements[29] was not used as it is a
calculated value.
We go along with the interpretation of LaCrO4 being an intermediate reaction product during
the decomposition of La2(CrO4)3 by Eq. 4.3.2 and do not include this phase in the modeling.
The perovskite phase:
The following denotations are used in this section: the superscript prv is written if the
regarding Gibbs energy expression is the same for both orthorhombic and rhombohedral
perovskite. The superscripts o-prv and r-prv stand for Gibbs energy expressions that have
different values for orthorhombic and rhombohedral perovskite. GRPRV denotes the Gibbs
energy function for stoichiometric rhombohedral perovskite. GVCR4O and GLCR4O stand
for the Gibbs energy functions of the completely oxidized neutral endmember. GVCR4O and
GLCR4O are set equal for orthorhombic and rhombohedral perovskite.
Stoichiometric perovskite: The Gibbs energy function of stoichiometric rhombohedral
LaCrO3 with the sublattice formula (La3+)(Cr3+)(O2-), 3
r-prvLaCrO
°G is given by
[9] [8]
3 GRPRV1 1 ln2 2
3+ 3+ 23
2 3 2 3
r-prv SER SER SERLaLaCrO Cr O La :Cr :O
magCr O La O
−° °
− − −
° °
= =
= + + + + +
G H H H G
G G G A BT CT T (4.3.5)
The parameters A, B, and C are optimized using the enthalpy of formation from Cheng and
Navrotsky[47], activity-data of Cr2O3 in LaCrO3 from Peck et al.[53], heat capacity-data
obtained by adiabatic calorimetry from Sakai and Stølen,[35] and enthalpy increment-data
Page 111
Thermodynamic assessments
111
measured at high temperatures[30]. A phase diagram with congruent melting of lanthanum
chromite and two eutectics[18,19] cannot be reproduced by using the emf-experiments[49-52].
Thus these data were excluded from the optimization.
A+BT parameters of the low-temperature orthorhombic perovskite phase were optimized with
those temperatures[34,35,38,40,42], enthalpies[34,35,40] and entropies[34,35] of transition having been
obtained by combined investigation techniques and being internally most consistent. The
rhombohedral to cubic transformation at high temperatures is not considered in the model, as
there is no existing thermodynamic data for this transition.
Cation-nonstoichiometric perovskite: To choose a proper model for nonstoichiometric
perovskite the following considerations are made: the formation of interstitial Cr in lanthanum
chromite proposed by Shvaiko-Shvaikovskii et al.[57] is unlikely due to the densely-packed
perovskite structure, and oxygen nonstoichiometry can be excluded from thermogravimetry[54]
and electrical conductivity[37,58] measurements. Thus the defects in n-type conducting[57]
lanthanum chromite are ambiguous and were not considered in the model.
B-site vacancies are energetically less favored than A-site vacancies in the perovskite
structure[63,64]. This means that the simplest sublattice model to describe cation
nonstoichiometric La1-xCrO3 reads (La3+,Va)(Cr3+,Cr4+)(O2-)3. While this model results in a
satisfying reproduction of experimental data, irreconcilable trouble is encountered at the
extension to the LaO1.5-MnO1.5-CrO1.5 system required for SOFC applications due to
diversities between the model descriptions of lanthanum chromite and lanthanum
manganite[65]. These are solved by allowing Va on the B-site and the anion sublattice of
lanthanum chromite just like in lanthanum manganite[65] leading to the appropriate sublattice
formula (La3+,Va)(Cr3+,Cr4+,Va)(O2-,Va)3. The optimization of selective model parameters
listed in Table 4.3.3 (pp. 112-114) resulted in negligible concentrations of Va on the B-site
and the anion sublattice, and the perovskite formula essentially remains La1-xCrO3.
Page 112
Thermodynamic assessments
112
Table 4.3.3 Model descriptions and Gibbs energy functionsa)
3+ 2+ 3+ 2- q-p q
[8]
[8]
[10]
(La ,Cr ,Cr ) (O ,Va )
2 , 3 2 3
GLALIQ
2 3 GLA2O3LIQ
GCRLIQ
2- 3+ 2+ 3+
q-3+
3+ 2-
q-2+
q-3+
VaO La Cr Crliq SER
LaLa :Valiq SER SER
La OLa :Oliq SER
CrCr :Valiq SER
CrCr :Va
p q°
°
°
°
= + = + +
− =
− − =
− =
−
y qy y y y
G H
G H H
G H
G H
Liquid (liq)
[10] [9] [9]
[9]
[9]
[9]
2GCRLIQ GCR2O3_L 3GCR1O1_L
2 5GCROLIQ 179638 79.923
2 2GCR1O1_L
Interaction terms
121000
3+ 2-
2+ 2-
q- q-2+ 2- 3+ 2-
2+
liq SER SERCr OCr :O
liq SER SERCr OCr :O
liq liqCr :O ,Va Cr :O ,Va
Cr
3
2
°
°
= − −
− − = − +
− − =
= =
G H H T
G H H
L L
L
1.5
[10]
61397 5.23 (65393 23 )( )
101850 39016( )
101850 39016( )
(La,Cr)(Va,O)
GHSERCR
q-3+ 2+ 3+
2+ 3+ 2- 2+ 3+
3+ 3+ 2- 3+ 3+
liq,La :Va Cr La
liqCr ,La :O Cr LaliqCr ,La :O Cr La
bcc SERFeCr:Va
La
°
°
= − + − −
= − − −
= − − −
− =
T T y y
L y y
L y y
G H
G
Bcc A2 phase
[10]
[10] [10]2(g)
[10] [10] [28]2(g)
GLABCC3 3GHSERCR (O ) 113.177552 43 3GLABCC (O ) 855000 142.52 4
355151.422
8350
bcc SER:Va La
bcc SER SERCr:O Cr O
bcc SER SERLaLa:O O
bccCr:Va,ObccCr,La:Va
° °
° °
− =
− − = + +
− − = + − +
= −
=
H
G H H G T
G H H G T
L
L[9]
[9]
[9]
0
0.4
311.5
0.008
bccc Crbcc
Cr
=
= −
= −
p
T y
yβ
Page 113
Thermodynamic assessments
113
3+ 4+ 3+ 2-3(La ,Va)(Cr ,Cr ,Va)(O ,Va)
3 GOPRV
3 GRPRV
3 5 6
3+3+ 2-
3+3+ 2-
4+3+ 2-
mag
mag
o-prv SER SER SERLa Cr OLa :Cr :O
r-prv SER SER SERLa Cr OLa :Cr :O
o-prv SER SER SERLa Cr OLa :Cr :O
°
°
°
− − − = +
− − − = +
− − − =
x
G H H H G
G H H H G
G H H H
1- 3La CrO perovskite
[72]
[72] [72]
[72]
[72] [72]
[10]2(g)
GS4O
GOPRV GS3V 1 6GS4V
3 5 6GS4O
GRPRV GS3V 1 6GS4V
GOPRV 1.5 (O )3+ 3+
3+ 3+
4+3+ 2-
mag
mag
o-prvmagLa :Cr :Va
r-pLa :Cr :Va
r-prv SER SER SERLa Cr OLa :Cr :O
SER SERLa Cr
°
° °
°
+ − + +
− − − =
+ − + +
− − = − +
G
G H H H
G
G H H G G
G [10]2(g)
[72] [72] [72]
[10]2(g)
[72] [72] [72]
GRPRV 1.5 (O )
5 6GS4O GS3V 1 6GS4V
GOPRV 1.5 (O )
5 6GS4O GS3V 1 6GS4V
3+ 4+
3+ 4+
rvmag
o-prvLa :Cr :Va
mag
r-prvLa :Cr :Va
SER SERLa CrSER SERLa Cr
SER SERLa Cr
°
°
°
°
− − = − +
− − = − +
+ − +
− − = − +
H H G G
G H H
G G
G H H[10]
2(g)
[65] [10]2(g)
[65]
GRPRV 1.5 (O )
3 GOPRV 1.5GVCR4O
0.5GVVV 2GLCR4O 0.75 (O ) 1.41263
3 GRPRV 1.5GVCR4O
0.5GVVV 2GLCR4O 0.7
3+ 2-
3+ 2-
mag
mag
o-prv SER SERCr OVa:Cr :O
r-prv SER SERCr OVa:Cr :O
°
°
°
°
+ − +
− − = +
+ − + − +
− − = +
+ − +
G G
G H H
G T G
G H H[10]
2(g)
[65] [10]2(g)
[65] [10]2(g)
5 (O ) 1.41263
GOPRV 1.5GVCR4O
0.5GVVV 2GLCR4O 0.75 (O ) 1.41263
GRPRV 1.5GVCR4O
0.5GVVV 2GLCR4O 0.75 (O ) 1
3+
3+
mag
mag
o-prv SERCrVa:Cr :Va
r-prv SERCrVa:Cr :Va
°
°
°
°
°
− +
− = +
+ − − − +
− = +
+ − − −
G T G
G H
G T G
G H
G
[65] [10]2(g)
.41263
3 3
2GVCR4O 1 3GVVV 4 3GLCR4O 0.5 (O ) 4.35056
2GVCR4O 1 3GV
4+ 4+2- 2-
4+ 4+
mag
mag
o-prv SER SER r-prv SER SERCr O Cr OVa:Cr :O Va:Cr :O
o-prv SER r-prv SERCr CrVa:Cr :Va Va:Cr :Va
° °
°
° °
+
− − = − − =
= + − + + +
− = − =
= +
T G
G H H G H H
G T G
G H G H[65] [10]
2(g)
3+
VV 4 3GLCR4O (O ) 4.35056
Interaction term250000
Magnetic contribution 291.35 0.894
= La
3+ 3+ 2- 3+ 4+ 2-
mag
prv prvLa :Cr ,Va:O La :Cr ,Va:O
o-prv r-prv o-prv r-prv prvc c i:j:k i:j:k
i
°− − + +
= =
= = = =
G T G
L L
T T y yβ β
4+ 3+
-2
2 6
3+ 6+ 2-2 6
2 4 3
3+ 6+ 2-2 3 12
,Va= Cr ,Cr= O Va
La CrO
(La ) (Cr )(O )
2 6 GLA2CRO6
La (CrO )
(La ) (Cr ) (O )
2 3 12 GLA2C
2 66+3+ 2-
42 36+3+ 2-
(
La CrO SER SER SERLa Cr OLa :Cr :O
La CrO ) SER SER SERLa Cr OLa :Cr :O
jk ,
°
°
− − − =
− − − =
G H H H
G H H H
La -Chromates
R3O12
Page 114
Thermodynamic assessments
114
[8] [9]
[8] [9]
Perovskite
Stoichiometric orthorhombic perovskiteGOPRV 0.5GLA2O3A 0.5GCR2O3 73931 3.01 0.68 lnStoichiometric rhombohedral perovskiteGRPRV 0.5GLA2O3A 0.5GCR2O3 73591 2.38 0.68 ln
= + − + −
= + − + −
T T T
T T
Functions
[72] 2 1
[9] [10]2(g)
[72] 2 1
Neutral nonstoichiometric perovskite endmembersGS4O = 597648 213.38 47.56 ln( ) 0.00307 190000
0.5GCR2O3 0.25 (O )
GS3O = 472704 191.7186 47.56 ln( ) 0.00307 1900000.5GCR
−
°
−
− + − − ++ +
− + − − ++
T
T T T T TG
T T T T T[9]
[9] [10]2(g)
[8] [9] [10]2(g)
[72]
[72] 2 1
2O3GVCR4O = 0.5GCR2O3 0.25 (O ) 291802 250
GLCR4O =1 3GLA2O3A 0.5GCR2O3 0.25 (O ) 200000
Perovskite referenceGS4V 607870 268.9 47.56 ln( ) 0.00307 190000
0.5GCR2O
°
°
−
+ − −
+ + −
= − + − − ++
G T
G
T T T T T[10]
2(g)
2 6[8] [9] [10]
2(g)
2 4 3
[8] [9] [10]2(g)
a) All parameters are in SI units : J,
3 1.25 (O )
La CrO
GLA2CRO6 = GLA2O3A 0.5GCR2O3 0.75 (O ) 72615 4.5
La (CrO )
GLA2CR3O12 = GLA2O3A 1.5GCR2O3 2.25 (O ) 371557 205
°
°
°
−
+ + − −
+ + − +
G
G T
G T
1 1mol, K. = 8.31451 Jmol K− −R
Using the compound energy formalism (CEF)[66-68] the molar Gibbs energy of La1-xCrO3 reads
: : ln ln lnprv ° E prvm m mag
° ⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠
= + + + + +∑∑∑ ∑ ∑ ∑i j i i j jk i j k k ki j k i j k
G y y y G RT y y y y y y G G (4.3.6)
where yi is the site fraction of Va and La3+ on the A-sublattice, yj is the site fraction of Cr3+,
Cr4+ and Va on the B-sublattice, and yk is the site fraction of O2- and Va on the anion
sublattice of the perovskite A1-xBO3. R = 8.31451 J mol-1 K-1. The third-last term accounts for
the configurational entropy of mixing. The second-last term describes the excess Gibbs
energy of mixing due to interactions of ions in the mixture. These are accounted for by the
Page 115
Thermodynamic assessments
115
optimization of interaction parameters. The last term designates the magnetic contribution to
the Gibbs energy. For the magnetic part of the Gibbs energy a magnetic ordering-model
proposed by Inden[69] and simplified by Hillert and Jarl[70] was used. A short summary of this
model can be found in Chen et al.[71] The magnetic parameters Tc and β were fitted to the pC -
data around the magnetic transition temperature from Sakai and Stølen[35].
Fig. 4.3.1 is a visualization of the Cr-containing part of the model the authors use to describe
the cation nonstoichiometry of lanthanum chromite.
Fig. 4.3.1 Representation of the Cr-containing part of the model for nonstoichiometric
lanthanum chromite. The thin lines margin the neutral plane. The neutral compounds used for
the optimization are marked by the black spots.
The parameters of the compound energy formalism are the Gibbs energies of the not
necessarily neutral 12 end-member compounds : :°
i j kG , with the 8 Cr-containing compounds
being the corners of the cube. Only compounds inside the neutral plane can exist on their
own.
3+ 4+ 2-3
prv(La )(Cr )(O )
°G and 3+ 4+3
prv(La )(Cr )(Va)
°G are given in Table 4.3.3 (pp. 112-114). These endmembers of
nonstoichiometric perovskite have been fixed firmly by a sufficient number of consistent
experiments in the LaO1.5-SrO-CrO1.5 system [72]. Thus the authors
adopted 3+ 4+ 2-3
prv(La )(Cr )(O )
°G and 3+ 4+3
prv(La )(Cr )(Va)
°G from Povoden et al.[72].
Page 116
Thermodynamic assessments
116
The neutral Cr4+ -containing endmembers
[9] [10]
2 1 2 2 1 12 3 ln ln3 3 3 3 3 3
1 1GVCR4O2 4
4+4+ 22
2 3 2
prv SER SERVaCrO Cr O Va:Cr :VaVa:Cr :O
gasmagCr O O
−° ° °
− −
° °
⎛ ⎞⎜ ⎟⎝ ⎠
= + + +
= = + + + +
G H H G G RT
G G G A BT (4.3.7)
and
[9] [8] [10]
2 2 1 2 2 1 13 ln ln3 3 3 3 3 3 3
1 1 1GLCR4O2 3 4
3+ 4+ 2 4+ 22 3 3
2 3 2 3 2
prv SER SER SERLaLa CrO Cr O La :Cr :O Va:Cr :O
gasmagCr O La O O
− −° ° °
− − −
° ° °
⎛ ⎞⎜ ⎟⎝ ⎠
= + + +
= = + + + +
G H H H G G RT
G G G G A (4.3.8)
and reciprocal relations which were set zero in analogy to Grundy et al.[65] were used to obtain
3+ 2-3
prv(Va)(Cr )(O )
°G , 4+ 2-3
prv(Va)(Cr )(O )
°G , 3+3
prv(Va)(Cr )(Va)
°G , and 4+3
prv(Va)(Cr )(Va)
°G . The configurational entropy-
term in Eq. 4.3.7 describes random mixing of O2- with Va on the anion sublattice. In Eq. 4.3.8
it describes random mixing of La3+ and Va on the A-site.
The parameters A and B of Eq. 4.3.7 and A of Eq. 4.3.8 are optimized using experimental data
of excess Cr in perovskite[56]. Furthermore the temperature dependence of lanthanum
vancancy and hole concentrations from Akashi et al.[58] was considered in the optimization.
As cation diffusion in La1-xCrO3 is extremely slow even at high temperatures, the Cr-
overstoichiometry in a furnace-cooled specimen reported by Khattak and Cox[55] does most
likely not represent the overstoichiometry at an intermediate temperature and was not used for
the optimization.
3+ 3+3
prv(La )(Cr )(Va)
°G results from a reciprocal relation which was set zero in analogy to Grundy et
al.[65]:
[10]2(g)
3 (O )23+ 3+3 3
o-prv,r-prv SER SER o-prv,r-prvLaLaCrVa Cr LaCrOLa :Cr :Va
° ° °− − = = −G H H G G G (4.3.9)
Using Eqs. 4.3.5 to 4.3.8 and adopting the Gibbs energies of the remaining endmembers
3+ 2-3
prv(La )(Va)(O )
°G , 3+3
prv(La )(Va)(Va)
°G , 2-3
prv(Va)(Va)(O )
°G , and3
prv(Va)(Va)(Va)
°G from Grundy et al.[65], the 12
endmembers of the compound energy formalism of the perovskite phase are defined. The
Page 117
Thermodynamic assessments
117
introduction of positive interaction parameters 3+ 3+ 2-prv0La ,Va:Cr :OL and 3+ 4+ 2-
prv0La ,Va:Cr :OL that were given
the same values circumvents too high Cr4+ contents at low temperatures that would be in
conflict with the experiments.
The liquid phase:
The two-sublattice model for ionic liquids[73,74] was used for the description of the liquid
phase of the La-Cr-O system. It was based on the liquid descriptions of the binary
subsystems. The chromium species considered in the liquid are Cr2+ and Cr3+. Higher
oxidation states are unlikely to exist in the liquid at normal oxygen partial pressures. The
liquid is thus given by the model description (La3+,Cr2+,Cr3+)p(O2-,Vaq-)q. The experimentally
determined temperatures and liquid compositions[13,14] at the eutectic and monotectic in the
metallic La-Cr system and the partial enthalpy of mixing of Cr, CrΔH [15] in La-Cr liquid were
used to optimize the temperature-dependent regular 02+ 3+
liqCr ,La :VaL and subregular 1
2+ 3+liqCr ,La :VaL
interaction parameters to account for interactions between La and Cr. Furthermore the two
regular interaction parameters 03+ 3+ 2-
liqCr ,La :OL = 0
2+ 3+ 2-liqCr ,La :OL and the two subregular 1
3+ 3+ 2-liqCr ,La :OL =
12+ 3+ 2-
liqCr ,La :O
L were optimized. It was assumed that the interactions between Cr2+-La3+ and
Cr3+-La3+ are of the same order of magnitude in the oxide melt, thus the two regular
interaction parameters were set equal to each other, as were the two sub-regular interaction
parameters. Using the following data for their optimization led to the lowest error between
experiments and calculation: the composition and temperature of the eutectic at the La-rich
side and the composition of the eutectic at the Cr-rich side in the oxide LaO1.5- CrO1.5 system
from Tresvjatskiy et al.[18], the temperature of the eutectic at the Cr-rich side from Berjoan[19],
and the congruent melting temperature of the perovskite phase from Coutures et al.[20] and
Foëx[21]. Berjoan[32] and Tresvjatskiy et al.[18] did not specify the value of the prevailing
oxygen partial pressure during their phase diagram experiments conducted in an argon
atmosphere. As a value of the oxygen partial pressure is required for the optimization, we
defined 2Op = 1 Pa.
4.3.5 Results and Discussion
The La-Cr system:
The calculated phase diagram of the La-Cr system is presented in Fig. 4.3.2 (next page),
together with experimental phase diagram data[12,13,14,17].
Page 118
Thermodynamic assessments
118
Fig. 4.3.2 Calculated phase diagram of the La-Cr system with data
from the literature included (symbols).
The positive value of 0 bccCr,La:VaL used to model the bcc phase results in a large miscibility gap
between the La-rich and Cr-rich metals, which is tantamount to a small solubility of La in
ssαCr in agreement with the experiments[14,17]. The model description of the bcc phase results
in a tiny solubility of Cr in La(bcc), denoted as ssLaγ , of -32 10× at.% at 1134 K, the lowest
temperature of stable ssLaγ , which further decreases as a function of increasing temperature.
The calculated enthalpies of mixing are shown in Fig. 4.3.3 (next page) together with the
experimentally determined value[15] that is well reproduced by the calculation.
Page 119
Thermodynamic assessments
119
Fig. 4.3.3 Calculated partial enthalpies of mixing of La and Cr in La-Cr liquid, and integral
enthalpies of mixing as a function of composition, with the experiment from Berezutskii et
al.[15] at T = 1700 K included (symbol with error-bar).
Considerable deviations of the calculated liquidus from experiments at the Cr-rich side of the
system can be ascribed to the problem of two different melting temperatures for Cr cited in
the literature, which are T = 2180 K and 2130 K. The higher value was favored by
Dinsdale[10] and is adopted in this study, whereas the lower melting temperature was chosen
by Savitskii et al.[12] and Svechnikov et al.[14].
A satisfying reproduction of the experimental data was obtained by considering a moderate
temperature dependence of 02+ 3+
liqCr ,La :Va
L and 12+ 3+
liqCr ,La :Va
L . This is unfortunately associated with
an inverse liquid-liquid miscibility gap with a minimum at X(Cr) = 0.25 and T ≈ 5000 K that
is of course unphysical.
The La-Cr-O system:
Phase equilibria:
Calculated LaO1.5- CrO1.5 phase diagrams in pure oxygen at2Op =105 Pa, in air at
Page 120
Thermodynamic assessments
120
2Op = 21278 Pa, and under reducing conditions at 2Op = 1 Pa representing the typical oxygen
partial pressure in argon atmosphere are shown in Fig. 4.3.4 together with experimental
data[18-21].
Fig. 4.3.4 Calculated phase diagrams of the LaO1.5-CrO1.5 system in pure oxygen, air
atmosphere, and under reducing conditions representing argon atmosphere at 2Op = 1 Pa with
experimental data included (symbols).
Excess Cr in lanthanum chromite is favored at high oxygen partial pressures. A decrease of
Cr4+ during annealing of an originally lanthanum-deficient perovskite phase under reducing
conditions is predicted by the model, reflected by the disappearance of Cr overstoichiometry.
This is in line with the interpretations of Raman spectra from Iliev et al.[56] Be it that the
reported thermodynamic data of La2CrO6[19] and La2(CrO4)3
[30] are correct, lanthanum
chromite is expected to be metastable at room temperature, and orthorhombic perovskite is
stable only at2Op ≤102 Pa. La2CrO6 is stable within a wide temperature-range in pure oxygen,
whereas it does not form in air and argon atmosphere.
Due to the ambiguous oxygen partial pressure of phase diagram experiments[18,19] and the
conflicting data on the melting temperature of lanthanum chromite in argon atmosphere[18] the
presented liquid description is rather tentative. Under oxidizing conditions Cr3+ is favored
over Cr2+ in the liquid. Analogous to Fe in the La-Fe-O system[62] this oxidation of Cr2+ to
Cr3+ governs shifts of eutectic compositions and temperatures and the increase of the melting
temperature of the perovskite phase on increasing the oxygen partial pressure. On the other
hand a significant amount of Cr3+ in the ionic liquid is reduced to Cr2+ under reducing
conditions, and the liquid stability increases considerably at the Cr-rich part of the system
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Thermodynamic assessments
121
leading to a considerably lowered eutectic temperature. The liquid description using the two-
sublattice model for ionic liquids also resulted in a significantly larger decrease of the melting
temperature of lanthanum chromite at 2Op ≈ 1 Pa than the given values in argon
atmosphere[18]. Despite this discrepancy we did not go for an alternative liquid model for the
sake of consistency with our previously assessed systems.
In Fig. 4.3.5 calculated phase equilibria of the La-Cr-O system at T = 1273 K are shown as a
function of oxygen partial pressure.
Fig. 4.3.5 Calculated phase equilibria of the La-Cr-O system at T = 1273 K
as a function of oxygen partial pressure.
It is obvious that no mutual solubilities of La and Cr in bcc metal in equilibrium with oxides
are expected. The same oxygen solubility in Cr as in the assessment by Povoden et al.[9] was
obtained using the new model description (Cr)(O,Va)1.5. At 2Op = 10-34.04 Pa metallic liquid
forms at the lanthanum-rich side of the phase diagram.
Thermodynamic data:
Calculated thermodynamic data of solid oxides are listed together with experimental data
from the literature in Table 4.3.1 (p. 105). Calculated and experimental data on the
orthorhombic to rhombohedral transition of LaCrO3 are listed in Table 4.3.2 (p. 106). Table
4.3.3 (pp. 105-107) is a compilation of the Gibbs energy functions and model descriptions of
the phases in the La-Cr-O system obtained in this study.
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Thermodynamic assessments
122
Lanthanum chromates: Testing an optimization of model parameters of La2(CrO4)3 by using
all available thermodynamic data[29,31] resulted in gross disagreement between optimized and
reported values. The considerable error might be explained by experimental difficulties to
reach equilibrium at the low investigation temperatures, and/or by significant deviations
between the thermodynamic standard data used for the calculation of the enthalpy of
formation from the elements[29] and assessed values[8-10]. Anyway the model parameters were
fitted to the experimental data[30], whereas the calculated standard enthalpy of formation from
the elements[29] was rejected, bearing in mind the high degree of uncertainty of the resulting
description. The perovskite phase: the calculated heat capacities of LaCrO3 are compared with
experiments from the literature in Fig. 4.3.6.
Fig. 4.3.6 Calculated heat capacities of LaCrO3 (solid curve) as a function of T with
experimental data included (symbols). The dashed line marks the temperature of the o-prv ↔
r-prv transition.
The calculated pC -curve extrapolates well to high temperatures. The use of pC -data from
Sakai and Stølen[35] along with enthalpy increment-data from Suponitskii[30] to optimize the
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Thermodynamic assessments
123
parameter CTlnT of the Gibbs energy of stoichiometric perovskite resulted in the lowest error
between experiments and calculation. As CTlnT was set equal for o-prv and r-prv, their pC is
the same. The experimentally determined pC -peak around 545 K caused by the first-order
transition o-prv ↔ r-prv is in fact a discontinuity which cannot be implemented in the model.
The calculated transition temperature of T = 540 K is shown by the broken line in Fig. 4.3.6.
The calculated pC -peak at T = 290 K reflects the temperature of the magnetic order-disorder
transition, the transition temperature being in agreement with the experiments. Two values for
the magnetic parameter p are possible depending on the crystal structure, p=0.28 and p=0.4,
whereby the proper p-value for structures other than bcc, fcc, and hcp is not available in the
literature. The pC -anomaly is equally well reproduced by the model[69,70] using p = 0.28 or p
= 0.4. For the sake of compatibility with the recent assessment of the La-Fe-O system[62] we
chose p = 0.28. Experimental enthalpy increments[30] are well reproduced by the calculation
(see Table 4.3.1, p. 105). Due to the consistency between both groups of calorimetric
experiments[30,35] the term CTlnT is fixed firmly. A small peak which was found around 855 K
can be explained most likely by the decomposition of an undetected impurity phase[35].
The calculated Gibbs energies of the formation of LaCrO3 from the oxides
2 3 2 3 31 1La O + Cr O LaCrO2 2 → (4.3.10)
are listed as a function of temperature together with data from the literature [49-53] in Table
4.3.1, p. 105. The resulting Gibbs energies of formation from emf-measurements are
remarkably less negative than the Gibbs energies of formation derived from Knudsen mass
spectrometry[53]. Only the use of the latter data for the optimization resulted in the proper
phase diagram with congruent melting of the perovskite phase and two eutectics. It needs to
be clarified why all of the emf-measurements are problematic: Azad et al.[50] stated that the
Gibbs energy of formation of LaCrO3 cannot be studied properly using the solid oxide
electrolyte method due to experimental difficulties in measuring the low oxygen potentials
encountered in a mixture of coexisting LaCrO3-La2O3-Cr. Yet it is obvious that the CaF2-
based emf-technique is neither suitable for the determination of thermodynamic data of
lanthanum chromite, as it unavoidably leads to emf that are too low. A possible explanation is
found in a study by Akila and Jacob[75]: Fine precipitates of CaO can form on the surface of
CaF2 in water- or oxygen-containing atmosphere. In this case the emf depends on the activity
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Thermodynamic assessments
124
of CaO at the electrode/electrolyte interface, and changing activity of CaO at the
electrode/electrolyte interface can alter the chemical potential of fluorine at this electrode and
thus the emf across the electrolyte.
Chemical stability of the perovskite phase:
The calculated oxygen partial pressure for the decomposition of lanthanum chromite by the
reaction
3 2 3 21 3LaCrO La O αCr + O (g)2 4
→ + ↑ (4.3.11)
is2Op = 10-20.97 at 1273 K. The calculated decomposition of the perovskite phase by Eq. 4.3.11
is plotted as a function of temperature and oxygen partial pressure in Fig. 4.3.7.
Fig. 4.3.7 Calculated decomposition of lanthanum chromite
as a function of temperature and oxygen partial pressure.
Defect chemistry of the perovskite phase:
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Thermodynamic assessments
125
Applying a defect chemistry analysis of La1-xCrO3 in equilibrium with Cr2O3 the following
defect reaction for its oxidation can be written in the sublattice form, if Cr[Va ]′′′ and ••O[Va ]are
assumed to be negligible according to Akashi et al.[58]:
3+ 3+ 2- 3+ 4+ 2-3 2 2 3 1 3 3(g)
1(La )(Cr )(O ) O (La Va )(Cr )(O )4
+ → (4.3.12)
Using Kröger-Vink notation this defect reaction reads
x x x x xLa La LaCr O 2 Cr O(g)
1 2 1La +Cr +3O O La + Va + Cr +3O4 3 3
•′′′+ → (4.3.13)
and the equilibrium constant of the oxidation reaction is
2
1 3 x 2 3 x 3La La Cr O
x x x 3 1 4La Cr O
[Va ] [La ] [Cr ][O ]= [La ][Cr ][O ]
•′′′ox
OK
p (4.3.14)
For small oxidation extent xLa[La ] , x
Cr[Cr ] , and xO[O ]can be considered to be ~ 1, and charge
neutrality is maintained by
La1[Va ]=3
′′′ Cr[Cr ]• (4.3.15)
Substituting this into Eq. 4.3.14 gives the proportionalities 3
16La Cr O2
[Va ], [Cr ]•′′′ ∝ P .
The concentrations of the defects , , ,La Va Cr and Crx x La La Cr Cr
•′′′ in La1-xCrO3 correspond to the site
fractions A 3+prv
Lay , Aprv
Vay , B 3+prv
Cry , and B 4+prv
Cry in the compound energy formalism. A 3+prv
Lay , Aprv
Vay , B 3+prv
Cry ,
B 4+prv
Cry and the tiny fractions Bprv
Vay and Oprv
Vay are plotted logarithmically as a function of
2Olog p at T = 1073 K and 1673 K in Fig. 4.3.8 (next page) for lanthanum chromite in
equilibrium with Cr2O3. The line for A 3+prv
Lay at 1073 K cannot be seen as it is very close to 1.
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Thermodynamic assessments
126
Fig. 4.3.8 Calculated site fractions of species in La1-xCrO3 in thermodynamic equilibrium
with Cr2O3 logarithmically plotted at T = 1073 K and 1673 K as a function of 2Op . The slope
of 3/16 of the calculated defect concentrations is indicated in the triangle.
At T=1073 K a constant slope of 3/16 of the defect concentrations La Cr[Va ] and [Cr ]•′′′ shown in
the triangle, is calculated from very high to very low oxygen partial pressures. This slope is
fixed by the defect reaction Eq. 4.3.12. At T = 1673 K the slope of 3/16 of La Cr[Va ] and [Cr ]•′′′ is
reproduced by the calculated slope using the compound energy formalism at 105 Pa >2Op >
10-8 Pa; hence oxidation of LaCrO3 to La1-xCrO3 governs the electrical conductivity of
perovskite with fixed activity of Cr2O3 at unity between2Op = 105 Pa and 10-8 Pa at this
temperature. The calculated slopes of La Cr[Va ] and [Cr ]•′′′ are equal to the slope of the electrical
conductivity from 1573 to 1673 K between 2
3O 1.0 10 Pa= ×p and
2
4O 2.0 10 Pa= ×p determined
by Akashi et al.[58]. The conflicting data from Shvaiko-Shvaikovskii et al.[57] may be
explained by problems of reaching equilibrium due to extraordinarily slow cation diffusion in
lanthanum chromite. In Fig. 4.3.9 (next page) the calculated slopes of Va and Cr La Cr•′′′ are
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Thermodynamic assessments
127
compared with slopes of La Cr[Va ] and [Cr ]•′′′ determined by Akashi et al.[58] as a function of
reciprocal temperatures.
Fig. 4.3.9 Calculated defect concentrations in La1-xCrO3 in thermodynamic equilibrium with
Cr2O3 (solid lines) logarithmically plotted as a function of reciprocal temperature along with
the data from Akashi et al.[58] derived from electrical conductivity measurements (symbols
with error-bars, broken lines).
The calculated concentrations agree well with the data derived from electrical conductivity
measurements[58]. The calculated amount of La Cr[Va ] relative to [Cr ]•′′′ is fixed by the criterion for
charge neutrality, Eq. 4.3.15, as calculated Cr[Va ]′′′ and ••O[Va ] are very small. The calculated
relative defect concentrations are in line with those proposed by Akashi et al.[58].
The presented defect chemistry calculations are still rather tentative, as the temperature and
oxygen partial pressure dependence of excess Cr in La1-xCrO3 has not been investigated
systematically so far.
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Thermodynamic assessments
128
4.3.6 Conclusions
Model parameters of the presented thermodynamic La-Cr-O database were optimized with
assessed thermodynamic and phase diagram data.
The thermodynamic descriptions of lanthanum chromates and the liquid phase are rather
tentative due to humble or sketchy experimental information.
The thermodynamic modeling of lanthanum chromite was based on experimental
thermodynamic data reported by Peck et al.[53] and Cheng and Navrotsky[46], as the use of
these data for the optimization of model parameters resulted in a proper reproduction of the
phase equilibria derived from experiments. The orthorhombic to rhombohedral transition in
lanthanum chromite and the magnetic order-disorder transformation are well reproduced by
the model.
Using the new database the stability limits of lanthanum chromite in function of temperature
and oxygen partial pressure can be quantified.
The proposed existence of lanthanum vacancies and holes to maintain charge neutrality in
lanthanum chromite with excess Cr is reproduced by the model, and the calculated slopes of
defect concentrations in function of oxygen partial pressure and temperature are in line with
the slopes derived from electrical conductivity measurements. However the amounts of excess
Cr in La1-xCrO3 used for the optimization of the cation nonstoichiometry are preliminary, and
further work on the temperature dependence of excess Cr as a function of temperature and
oxygen partial pressure would allow a more accurate quantification of the defect chemistry of
lanthanum chromite.
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63. C.N.R. Rao, J. Gopalakrishnan, K. Vidyasagar, Superstructures, Ordered Defects &
Nonstoichiometry in Metal Oxides of Perovskite & Related Structures, Indian J. Chem.,
1984, 23A, pp. 265-84.
64. L.G. Tejuca, J.L.G. Fierro, Structure and Reactivity of Perovskite-Type Oxides, Advances
in Catalysis, 1989, 36, pp. 243-.
65. A.N. Grundy, E. Povoden, T. Ivas, L.J. Gauckler, Calculation of Defect Chemistry Using
the CALPHAD Approach, Calphad, 2006, 30, pp. 33-41.
66. J.-O. Andersson, A.F. Guillermet, M. Hillert, B. Jansson, B. Sundman, A Compound-
Energy Model of Ordering in a Phase with Sites of Different Coordination Numbers, Acta
Metall., 1986, 34, pp. 437-45.
67. M. Hillert, B. Jansson, B. Sundman, Application of the Compound-Energy Model to
Oxide Systems, Z. Metallkd., 1988, 79(2), pp. 81-87.
68. M. Hillert, The Compound Energy Formalism, J. Alloy. Cmpd., 2001, 320, p 161-76.
69. G. Inden, Determination of Chemical and Magnetic Interchange Energies in BCC Alloys.
I. General Treatment, Z. Metallkd., 1975, 66(10), pp. 577-82.
70. M. Hillert, M. Jarl, A Model of Alloying Effects in Ferromagnetic Metals, Calphad, 1978,
2(3), p 227-38.
71. M. Chen, B. Hallstedt, L.J. Gauckler, Thermodynamic Assessment of the Co-O System, J.
Phase Equilib., 2003, 24(3), pp. 212-27.
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Thermodynamic assessments
134
72. E. Povoden, M. Chen, A.N. Grundy, L.J. Gauckler, Thermodynamic La-Sr-Mn-Cr-O
oxide database for solid oxide fuel cell applications, submitted to Scripta Mater.
73. M. Hillert, B. Jansson, B. Sundman, J. Ågren, A Two-Sublattice Model of Molten
Solutions with Different Tendency of Ionization, Metall. Trans. A, 1985, 16A, pp. 261-66.
74. B. Sundman, Modification of the Two-sublattice Model for Liquids, Calphad, 1991, 15,
pp. 109-19.
75. R. Akila, K.T. Jacob, The Mobility of Oxygen Ions in CaF2, J. Appl. Electrochem., 1990,
20, pp. 294-300.
4.4 Thermodynamic La-Sr-Mn-Cr-O oxide database for SOFC
applications
E. Povoden, M. Chen, A.N. Grundy, and L.J. Gauckler
to be submitted
The thermodynamic La-Sr-Mn-Cr-O oxide database is obtained as an extension of
thermodynamic assessments of oxide subsystems using the Calphad approach. Gibbs energy
functions of SrCrO4, Sr2.67Cr2O8, Sr2CrO4, and SrCr2O4 are presented. Experimental solid
solubilities and nonstoichiometries in La1-xSrxCrO3-δ and LaMn1-xCrxO3-δ are reproduced by
the model.
4.4.1 Introduction
Sr-doped lanthanum manganite (LSM) with the perovskite structure ABO3-δ is used as
cathode materials in SOFC. However diffusion of chromium from the metallic interconnects
into the cathode leads to a severe cell voltage decrease that was linked to the formation of Cr-
containing phases[1,2]. A thermodynamic La-Sr-Mn-Cr-O oxide database is highly desirable
for the development of endurable SOFC: thermodynamic calculations set an important base
for the optimization of cathodes aiming to avoid long-term degradation due to chromium
poisoning. The database should meet the demand to calculate stable and metastable phase
equilibria, thermodynamic driving forces and activities, as well as defect concentrations of the
cathode contaminated by Cr at different temperatures and oxygen partial pressures. These
requirements are conformed by using the CALPHAD approach. For the construction of the
Page 135
Thermodynamic assessments
135
La-Sr-Mn-Cr-O oxide database La-Mn-Cr-O oxide and La-Sr-Cr-O oxide systems are
assessed. Sr-Mn-Cr-O oxide is treated as ideal extension from the subsystems.
4.4.2 Assessment of data from the literature
Previous assessments of the La-O, Cr-O, and La-Cr-O databases are adopted[3-5], and the La-
Sr-Mn-O oxide database is taken from Grundy et al.[6] with a slight modification: Grundy et
al.[6] allowed Mn3+ on the A-site of LSM to reproduce experimental oxygen
nonstoichiometries under low oxygen partial pressures. Due to large differences between the
ionic radii of La3+ and Mn3+ and possible coordination numbers (1.5 Å for 12-fold
coordinated La3+, 0.785 Å for at maximum 6-fold coordinated Mn3+)[7] we omit Mn3+ on the
A-site. Calculation of the oxygen nonstoichiometry of perovskite + MnO instead of
metastable single phase perovskite[6] leads to a good agreement between experimental and
calculated nonstoichiometries.
No quaternary phases or solid solutions were found in the Sr-Mn-Cr-O oxide system[8].
Sr-Cr-O oxide:
Thermodynamic functions for Sr-Cr-oxides in the SSUB database[9] are based on estimates[10].
We propose optimized thermodynamic functions for oxide phases of the Sr-Cr-O oxide
system resulting from the assessment of all available experimental data: agreement exists
between Gibbs energies of formation of SrCrO4 determined by emf technique using a Y2O3
stabilized ZrO2 electrolyte[11,12], whereas emf measurements using CaF2-based emf-
technique[13] led to conflicting results likely caused by competing reactions[14]. Differences
concern the reported stabilities of further compounds[11,12,15-19]: for the stabilities of SrCr2O4
and Sr2CrO4 we trust the accurate study of Jacob[11], which is in agreement with Negas and
Roth[15]. On the other hand the conflicting phase equilibria presented by Kisil[16] lack
experimental details. Sr3Cr2O7[12] was approved as high pressure phase only[17]. The
stoichiometry of a phase defined as Sr3Cr2O8[15] was later corrected to be essentially
Sr2.67Cr2O8 by using microprobe analysis[18], in agreement with Hartl and Braungart[19].
La-Sr-Cr-O oxide:
In the La-Sr-Cr-O oxide and La-Mn-Cr-O oxide systems no quaternary stoichiometric
compounds were reported. Phase equilibria in the La-Sr-Cr-O oxide system in air at 1223 K
and under vacuum at 1873 K were determined by using solid state technique[18]. Limited
solution of Sr in La1-xSrxCrO3-δ perovskite[18] was confirmed by a later investigation[20]. The
Page 136
Thermodynamic assessments
136
existence of several Ruddlesden-Popper phases is restricted to reducing conditions; solely
Sr(La,Sr)CrO4 showed reproducible stoichiometry[18]. In contrast to Peck et al.[18] it was
proposed earlier that Sr(La,Sr)CrO4 were stable in air[10]. The exact temperature and oxygen
partial pressure range of Sr(La,Sr)CrO4 is ambiguous, thermodynamic data are missing, and
the solubility of Cr is unknown. Thus its extension to the quinary database would not be
reliable. As Ruddlesden-Popper phases have not been reported to form during SOFC
operation with LSM cathodes, Sr(La,Sr)CrO4 is omitted in the modeling. Myoshi et al.[20]
investigated the single phase region of La1-xSrxCrO3 with x = 0.1, 0.2, and 0.3 as a function of
temperature and oxygen partial pressure using XRD analysis. Peck et al.[21] determined the
Gibbs energy of formation of La1-xSrxCrO3 with x = 0.1, 0.2, and 0.3 using Knudsen mass
spectrometry. Cheng and Navrotsky[22] measured enthalpies of formation of La1-xSrxCrO3-δ
with x = 0.1, 0.2. and 0.3, and δ = 0, −0.04, −0.09, and −0.11 using drop calorimetry at
T = 1080 K. Positive δ in the perovskite formula reflects oxygen deficiency, whereas negative
δ essentially stands for cation nonstoichiometriy. Nonstoichiometry data for La1-xSrxCrO3-δ
with x=0.1, 0.2. and 0.3 at T = 1273K, 1373 K, 1473K, and 1573 K[23], and La0.8Sr0.2CrO3-δ at
1273 K[24] were measured as a function of oxygen partial pressure using thermogravimetry.
Cr4+ and oxygen vacancies are regarded as the major defects[23,24].
La-Mn-Cr-O oxide:
In the La-Mn-Cr-O oxide system no quaternary stoichiometric compounds were reported. An
isothermal section of the La-Mn-Cr-O oxide system at 1073 K in air and pure oxygen has
been published without further commenting of experimental evidences[25]. Complete solid
solution between the LaMnO3 and the LaCrO3 perovskites was affirmed[8].
δ of LaMn0.9Cr0.1O3-δ was measured using thermogravimetry[26].
La-Sr-Mn-Cr-O oxide:
In the La-Sr-Mn-Cr-O oxide system complete solid solubility of Mn and Cr is reported for
La1-xSrxMn1-yCryO3-δ perovskite[8]. Plint et al.[27] concluded from the similarity between X-ray
absorbtion spectra of Cr K of LaCrO3 and La1-xSrxMn0.5Cr0.5O3-δ with x = 0.2, 0.25, and 0.3 at
T = 1173 K that Cr4+ were absent in the latter. Perovskite+MnCr2O4 spinel equilibrium of a
powdered mixture of La0.8Sr0.2MnO3 and Cr2O3 at 1073 K was reported after 1000 h of heat
treatment in air[28].
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Thermodynamic assessments
137
The perovskite phase:
Magnetic and structural transitions of La1-xSrxCrO3-δ [29−35], LaMn1-xCrxO3-δ [26,36−40], and
La1-xSrxMn1-yCryO3-δ [8,41] were reported. Transitions of LaMn1-xCrxO3-δ are complex as they
depend on temperature, composition and oxygen partial pressure. Consistency among
transition data for La1-xSrxCrO3-δ and LaMn1-xCrxO3-δ prevails, whereas diversities exist
regarding the transitions in La1-xSrxMn1-yCryO3-δ . Thus, in terms of the applicability of the
new database for SOFC the authors omit structural transitions in the modeling. Magnetic
transitions have been well reproduced by an ordering-model[42,43] for LaCrO3[5]. However we
did not obtain satisfying results in higher-order perovskites, most likely due to interactions
that cannot be reproduced by the model. As the magnetic transitions are low temperature
features, their modeling was omitted without consequences for the applicability of the
database for SOFC.
4.4.3 Modeling and optimization
Sr-Cr-O oxide:
The sublattice models (Sr2+)(Cr6+)(O2-)4 and (Sr2+)(Cr3+)2(O2-)4 are employed for the
descriptions of SrCrO4 and SrCr2O4. (Sr2+)8/3(Va)1/3(Cr6+)2/3(O2-)8/3(Cr5+)4/3(O2-)16/3 and
(Sr2+)(O2-)1(Sr2+)(Cr4+)(O2-)3 were chosen for Sr2.67Cr2O8 following the proposed formula[19]
and for the Ruddlesden-Popper phase Sr2CrO4, accounting for the structural feature of
alternating rocksalt- and perovskite layers of the latter. Gibbs energy functions of Sr-Cr-
oxides were formulated as
[44] [4] [45]12
y z 2 3 2
gasSER SER SER(Sr) (Cr) (O) Sr Cr O SrO Cr O O
° ° ° °− − − = + + + +x y z xG H H H x G y G v G A BT (4.4.1)
v = 0.75, 0, 7/6, and 0.25 for SrCrO4, SrCr2O4, Sr2.67Cr2O8, and Sr2CrO4 respectively. SERaH is
the standard enthalpy of the stable state of element a at 298.15 K and 105 Pa[45]. A and B are
adjustable parameters; their optimization with the following experimental phase diagram and
thermodynamic data using the PARROT module of the Thermocalc software[46] resulted in
the lowest error between model and experiments: Gibbs energies of formation of SrCrO4[11,12]
and phase stabilities of SrCr2O4 and Sr2CrO4 investigated by equilibration experiments of
different mixed oxide compositions under controlled atmospheres[11], and the equilibrium
Sr2.67Cr2O8+SrCrO4+Cr2O3 as a function of temperature and oxygen partial pressure[11,12]. All
Page 138
Thermodynamic assessments
138
reported phase equilibria[11] are correctly reproduced by the model. Optimized parameters and
calculated and experimental thermodynamic data are listed in Table 4.4.1 and 4.4.2.
Table 4.4.1 Optimized model parameters
SrCrO4 SrCrO4
Sr2CrO4 Sr2CrO4
SrCr2O4 SrCr2O4
Sr2.67Cr2O8 Sr2.67Cr2O8
1 3
Sr - Cr oxides273771 J; 131.6 J145000 J; 50 J
98000 J; 95.5 J508507 J; 219 J
La Sr CrO5 6GS4O GS3V 1 6G3+ 4+La :Cr :Va
− −
°
= − == − == = −
= − =
= − +x x
A BA BA BA B
Gδ
[5] [45]
[5]
S4V GRPRV 1.5
5 6GS4O GS3V 1 6GS4V GRPRV
GS3V 1 6GS4O 1 6GS4V
GS3V 5 6GS4O 5 6GS4V
2
3+ 4+ 2-
2+ 3+ 2-
2+ 3+
gasO
La :Cr :O
Sr :Cr :O
Sr :Cr :Va
°
°
°
°
+ −
= − + +
= + −
= − +
G
G
G
G
Table 4.4.2 Calculated and experimental thermodynamic data
2
2 3 2 4-1
-1 [12]
-1 [10]
2.67 2 8 4 2 3
SrO +1 2Cr O + 3 4O SrCrO
273.774 0.13152 kJmol this work, calc.213.050 0.106904 kJmol ,851 1116 K273.825 0.2 0.13157 kJmol ,950 1280 K
Sr Cr O SrCrO Cr O
265.859
°
°
°
=
Δ = − +Δ = − + −Δ = − ± + −
+ +
Δ = −O
G TG TG T
μ2
2
-1
-1 [11]
-1 [10]
2 3 2 3 2 2 1 3
0.15832 kJmol this work, calc.262.340 0.15553 kJmol ,1073 1473 K276.767 0.166 kJmol ,1080 1380 K
(1 ) 2La O SrO 1 2Cr O 4O 2 La Sr CrO
0.1, 0, 2000 K, 93− −
°
+Δ = − + −Δ = − + −
− + + + − =
= = = Δ = −
O
O
x x
TT
Tx x x O
x T Gδ
μμ
δδ -1
-1[20]
.3 kJmol this work, calc.85.7 kJmol°Δ = −G
-1
-1[20]
-1
0.2, 0, 2000 K, 102.4 kJmol this work, calc. 88.7 kJmol
0.3, 0, 2000 K, 109.4 kJmol this work, calc.
°
°
°
= = = Δ = −Δ = −
= = = Δ = −
x T GG
x T G
δ
δ-1[20]
-1
-1[21]
-1
93.5 kJmol0.1, 0, 298 K, 65.2 kJmol this work, calc.
67.88 kJmol0.1, 0.04, 298 K, 55.1 kJmol this
°
°
°
°
Δ = −= = = Δ = −
Δ = −= = = Δ = −
Gx T H
Hx T H
δ
δ-1[21]
-1
° -1[21]
work, calc. 59.15 kJmol
0.2, 0, 298 K, 56.8 kJmol this work, calc. Δ H = 50.54 kJmol
0.2,
°
°
Δ = −= = = Δ = −
−=
Hx T H
x
δ
δ -1
-1[21]
-1
0.09, 298 K, 34.0 kJmol this work, calc. 34.76 kJmol
0.3, 0, 298 K, 48.3 kJmol this work, calc.
°
°
°
= = Δ = −Δ = −
= = = Δ = −
T HH
x T Hδ-1[21]
-1
-1[21]
36.72 kJmol0.3, 0.11, 298 K, 20.6 kJmol this work, calc.
20.48 kJmol
°
°
°
Δ = −= = = Δ = −
Δ = −
Hx T H
Hδ
Page 139
Thermodynamic assessments
139
The perovskite phase:
It is essential for a consistent description of the perovskite phase that defects that occur in the
structure in low-order systems remain on the same sites at the extension to higher order; this
is achieved by using the same model. We adopt the description (A,Va)(B,Va)(O-2,Va)3 with
A, B = cations and Va = vacancies[6] using the compound energy formalism[47]. The molar
Gibbs energy of the perovskite phase then reads
: : ln ln 3 lnprv ° E prvm m
° ⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠
= + + + +∑∑∑ ∑ ∑ ∑i j i i j jk i j k k ki j k i j k
G y y y G RT y y y y y y G (4.4.2)
where yi is the site fraction of each cation and Va on the A-sublattice, yj is the site fraction of
each cation and Va on the B-sublattice, and yk is the site fraction of O2- and Va on the anion
sublattice. R = 8.31451 J mol-1 K-1. The second-last term accounts for the configurational
entropy of mixing. The last term describes the excess Gibbs energy of mixing. It can be
accounted for by introducing interaction parameters. The parameters of the compound energy
formalism are the Gibbs energies of the end-member compounds : :°
i j kG . Typical compositions
of Sr-doped lanthanum manganites used for SOFC cathodes, e.g. La0.8Sr0.2MnO3-δ are
rhombohedral at SOFC operating temperatures (T=1073 K to 1273 K), and small amounts of
Cr brought into the cathode unlikely lead to a change of the structure. Thus it is reliable to
take the Gibbs energies of the compounds of rhombohedral perovskite from [5] for the model.
Using the above model and the proposed defect chemistry[22-24] the sublattice formula for
La1-xSrxCrO3-δ reads (La3+,Sr2+,Va)(Cr3+,Cr4+,Va)(O2-,Va)3. The molar Gibbs energy °G of
La1-xSrxCrO3-δ is uniquely defined as follows: °Gs of the endmembers (La3+)(Cr3+)(O2-)3,
(La3+)(Cr3+)(Va)3, (La3+)(Va)(O2-)3, (La3+)(Va)(Va)3, (Sr2+)(Va)(O2-)3, (Sr2+)(Va)(Va)3,
(Va)(Va)(O2-)3, and (Va)(Va)(Va)3 and ternary interaction parameters are adopted[5,6,48],
°G(Sr2+)(Cr4+)(Va)3
[44] [4] [45]:
1 5GS4V2 42+ 4+3 2 3 2
gasSER SERSrCrVa Sr Cr SrO Cr O OSr :Cr Va
° ° ° ° °− − = = = + −G H H G G G G (4.4.3)
is chosen as reference, and A and B parameters of °G of two neutral compounds
Page 140
Thermodynamic assessments
140
[44] [4] [45]
3 GS4O1 12 4
2+ 4+ 23
2 3 2
SER SER SERSrCrO Sr Cr O Sr :Cr :O
gasSrO Cr O O
−° °
− − −
° ° °
= =
= + + + +
G H H H G
G G G A BT (4.4.4)
[44] [4]
2.5 GS3V5 1 5 5 1 1 1ln ln6 6 6 6 6 6 2
2.5 0.5
2+ 3+ 2 2+ 3+ 2 3
SER SER SERSrCrO Va Sr Cr O
SrO Cr OSr :Cr :O Sr :Cr :Va−
°− − −
° ° ° °⎛ ⎞⎜ ⎟⎝ ⎠
=
= + + + = + + +
G H H H
G G RT G G A BT (4.4.5)
are optimized with all available experimental data of the perovskite phase. Eq. 4.4.4 denotes
°G (Sr2+)(Cr4+)(O2-)3, with A = 27027 and B = −69.6. A = 136453 and B = −91.2 for
2.5 0.5SrCrO Va°G in Eq. 4.4.5. °Gs of the remaining endmembers (La3+)(Cr4+)(Va)3,
(La3+)(Cr4+)(O2-)3, (Sr2+)(Cr3+)(O2-)3, and (Sr2+)(Cr3+)(Va)3 are obtained by conversions of
reciprocal equations that are set zero[48] and are listed in Table 4.4.1 (p. 138).
Though structure-chemical information of site occupancies in LaMn1-xCrxO3-δ perovskite is
missing, it is reliable to allow Cr4+ on the B-site: as Cr4+ exists in nonstoichiometric
lanthanum chromite perovskite[5], it is expected that it is not removed from the structure if the
phase is doped. Thus for LaMn1-xCrxO3-δ we propose the sublattice formula
(La3+,Va)(Mn2+,Mn3+,Mn4+,Cr3+,Cr4+,Va)(O2-,Va)3. All endmember compounds have been
defined in the assessed subsystems. The regular interaction parameter 0L(La3+:Cr3+,Mn3+:O2-)
accounting for interactions between Cr and Mn cations is fitted to experimental
nonstoichiometries[26]; 0L(La3+:Cr3+,Mn3+:O2-) = +9421 J.
The sublattice formula of the quinary perovskite reads
(La3+,Sr2+,Va)(Mn2+,Mn3+,Mn4+,Cr3+,Cr4+,Va)(O2-,Va)3. All endmembers have been defined in
the assessed subsystems.
4.4.4 Results and discussion
The reproduction of experimentally determined Gibbs energies[21] and enthalpies of
formation[22], solid solubilities[18,20], and nonstoichiometries[23,24] of La1-xSrxCrO3-δ, and phase
equilibria in the La-Sr-Cr-O oxide system by the modeling is satisfying as shown in Table
4.4.2 (p. 138), and in Figs. 4.4.1 and 4.4.2 (next page).
Page 141
Thermodynamic assessments
141
Fig. 4.4.1 LaO1.5-SrO-CrO1.5 system calculated at T = 1223 K in air atmosphere (solid lines)
with experimental data[17] included (symbols). prv = La1-xSrxCrO3-δ. Calculated phase
equilibria are the same as in[17]. Filled circles, blank circles, and circles with crosses denote
single phase, two phase, and three phase equilibria.
Page 142
Thermodynamic assessments
142
Fig. 4.4.2, p. 141 Calculated (lines) and experimental (symbols)[22,23] nonstoichiometries of
La1-xSrxCrO3-δ at different temperatures for x = 0.1, 0.2, 0.25, and 0.3 as a function of oxygen
partial pressure.
The calculated isothermal section of the La-Mn-Cr-O oxide system at T = 1273 K in air is
presented in Fig. 4.4.3.
Fig. 4.4.3 LaO1.5-MnOx-CrO1.5 system calculated at T = 1273 K in air atmosphere. α-spl =
tetragonally distorted Cr-Mn-spinel, β-spl = cubic Cr-Mn-spinel, prv = LaMn1-xCrxO3-δ.
The calculated nonstoichiometries of La1-xSrxCrO3-δ are in good agreement with the
experimental values at higher temperatures, as shown in Fig. 4.4.4 (next page). However it
was not possible to reproduce the nonstoichiometries at T = 1073 K and 973 K. Deducing
from the change of δ from T = 1273 K to 1173 K the measured increase of δ from T = 1173 K
to
1073 K might be too small, possibly caused by equilibration difficulties due to slow diffusion.
Page 143
Thermodynamic assessments
143
Fig. 4.4.4 Calculated (lines) and experimental (symbols)[27] nonstoichiometries of
LaMn0.9Cr0.1O3-δ at different temperatures as a function of oxygen partial pressure.
To approximate the absence of Cr4+[27] in quinary perovskite, it would be necessary to give
large positive values to the regular interaction parameters 0L(Sr2+:Cr3+,Mn3+:O2-) and 0L(Sr2+:Cr4+,Mn3+:O2-). Experimentally determined nonstoichiometry of LaCrO3 indicates the
existence of some Cr4+, and the conclusion of missing Cr4+[27] is not based on a direct
chemical analysis of Cr valencies. We believe that complete removal of Cr4+ from the
perovskite structure is unlikely. Thus we stick to a model without interaction parameters.
Experimental findings[8,28] are in line with our calculations.
4.4.5 Conclusions
The thermodynamic La-Sr-Mn-Cr-O oxide database has been obtained by combining
thermodynamic assessments of oxide subsystems. We propose the model
(La3+,Sr2+,Va)(Mn2+,Mn3+,Mn4+,Cr3+,Cr4+,Va)(O2-,Va)3 for the quinary perovskite phase.
Optimized by experiments in pseudoternary and pseudoquaternary oxide subsystems, this
model allows the quantitative calculation of defects as a function of composition, temperature,
and oxygen partial pressure. The new database is adapted for quantitative calculations of
Page 144
Thermodynamic assessments
144
phase equilibria and defect chemistry in a Sr-doped lanthanum manganite SOFC cathode
poisoned by chromium.
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Thermodynamic calculations of impacts of chromium on LSM cathodes
148
5 Thermodynamic calculations of impacts of chromium on Sr-
doped lanthanum manganite (LSM) cathodes for solid oxide
fuel cells (SOFC)
E. Povoden, T. Ivas, M. Chen, and L.J. Gauckler, to be submitted
A new thermodynamic database is used for thermodynamic equilibrium calculations in a Sr-
doped lanthanum manganite cathode (LSM) affected by chromium at typical operation
temperatures of 1073 K and 1273 K as a function of oxygen partial pressure. From the results
of these calculations it is concluded that the processes of chromium poisoning of solid oxide
fuel cells (SOFC) are partly explicable by thermodynamics, and partly they occur under
kinetic control: at the cathode/electrolyte interface of a Cr-“poisoned” cell Cr-Mn spinel
exists in thermodynamic equilibrium with LSM, whereas Cr2O3 is metastable. The spinel
formation goes along with increasing Mn2+ in LSM under decreasing oxygen partial
pressures.
From the thermodynamic calculations structural chemical changes in the cathode perovskite
caused by the interaction with chromium can be predicted: it is shown that the interaction of
chromium with the LSM cathode leads to a change of the defect chemistry of the perovskite
phase. In particular the concentrations of cation and oxygen vacancies are smaller than in an
LSM without chromium under decreased oxygen partial pressure at 1273 K. This has
consequences for the electrochemical properties of the cell: the electronic conductivity of the
cathode will decrease, and the contribution of a vacancy mechanism for the oxygen diffusion
in LSM is thermodynamically hampered in the presence of chromium at high temperature and
high current loads.
Even though the chromium problem cannot be solved satisfactorily by varying the cathode
composition or the SOFC operating conditions, the deterioration of the cell performance is
expected to be less pronounced when the cell is operated at lower temperatures and current
loads. Proper strategies to prevent the problem of chromium “poisoning” are proposed.
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Thermodynamic calculations of impacts of Cr on LSM cathodes
149
5.1 Introduction
Chromium-containing metallic interconnects are commonly used in planar-design solid oxide
fuel cells (SOFC) due to their high oxidation resistance, thermal stability, mechanical
strength, good electronic and negligible ionic conductivity, as well as low fabrication costs.
However high-valent gaseous Cr-oxide and chromium-oxyhydroxides can diffuse under fuel-
cell operation conditions from the interconnect into the cathode up to the cathode-electrolyte
interface, where they cause the degradation of the cell by detrimentally affecting the O2-
adsorbtion, -reduction, and -diffusion process[1]. In the last decade a lot of efforts were made
to elucidate the degradation mechanisms, though partly with conflicting results.
Consequences of Cr poisoning have been investigated specifically in (La1-xSrx)MnO3-δ (LSM)
perovskite-structured cathodes. For the mechanism of chromium poisoning two models have
been proposed: 1) reduction of gaseous CrO3(g) in dry atmosphere or chromium
oxyhydroxide(g) in wet atmosphere under polarization[2-6] and 2) chemical dissociation of Cr-
species on the LSM surface[7-14].
Ad 1) In an LSM cathode the reduction of CrO3(g) is expected to be localized at the triple
phase boundary, where the reaction partners for the reduction, electron-donating LSM and
oxygen-accepting yttrium-stabilized zirconia (YSZ) are available[15]. This reduction reaction
would compete with the oxygen reduction and lead to blocking of the active sites at the triple
phase boundary (TPB).
Ad 2) In contrast to 1) it was proposed that gaseous Cr-species would be chemically
dissociated to LSM under the polarization of the cell. This affinity would be linked to the
creation of free Mn2+ on the surface of LSM due to the oxygen partial pressure gradient
caused by the polarization. Mn2+ would serve as agent for the formation of Cr-Mn-O nuclei
that would be able to migrate to the triple phase boundary and further into the electrolyte.
Consequently Cr-Mn spinel and Cr2O3(s) would form, associated to these nuclei. The chemical
dissociation approach is coherently based on the interpretation of a large number of
impedance spectra.
Both groups of researchers agree that without polarization Cr is randomly deposited inside the
cathode, and no Cr2O3(s) is formed. On the other hand the electrochemical reduction of CrO3(g)
was rejected by the authors favoring the chemical dissociation approach.
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Thermodynamic calculations of impacts of Cr on LSM cathodes
150
In the critical assessment in chapter 1.3.6 it was concluded that doubtless reasons to reject the
reduction approach do not exist. One critical point concerns the extension of dense Cr2O3-
layers into the YSZ electrolyte[6]: this phenomenon can be explained best by continuous
feeding of an initial Cr2O3-layer with CrO3(g), the latter becoming reduced at a new TPB
consisting of YSZ and electron-donating Cr2O3(s). On the other hand this process cannot be
explained satisfactorily by using the chemical dissociation approach.
Even though particularly the early stages of chromium “poisoning” occur in thermodynamic
non-equilibrium, the system SOFC develops towards thermodynamic equilibrium by time.
This is reflected by a flattening of the curves that reflect the performance deterioration as a
function of time, such as the curves of voltage drop and overpotential loss. Thus
thermodynamic calculations allow interpretations of the phase equilibria that result from the
interactions between LSM and chromium, as well as changes of the phase chemistry that are
associated with the chromium contamination of LSM cathodes.
5.2 Method
The La-Sr-Mn-Cr-O oxide database is used for the following thermodynamic calculations:
phase equilibria in Cr-contaminated LSM (in the following denoted as LSM(Cr)), phase
compositions of LSM(Cr) and Cr-Mn spinel, defect concentrations of LSM(Cr), as well as
driving forces for the formation of Cr2O3 were calculated with the poly-module of the
ThermoCalc software[16].
The following model descriptions were used: for the Cr-contaminated cathode perovskite with
the general formula ABO3 a proper sublattice description reads
(La3+,Sr2+,Va)(Mn4+,Mn3+,Mn2+,Cr4+,Cr3+,Va)(O2-,Va)3, for tetragonally distorted spinel
(Mn2+)(Mn3+,Cr3+)2(O2-)4 was chosen[17], for cubic spinel, AB2O4,
(Mn2+,Cr2+)(Mn3+,Cr3+)2(O2-)4 was used[18], and for Cr2O3 (Cr2+,Cr3+)2(Cr3+,Va)(O2-)3 was
taken[18]. Uptake of Cr in LSM is expected, as a complete solid solubility of Cr in LSM has
been shown experimentally[19].
For proper thermodynamic calculations of phase equilibria thermodynamic conditions need to
be set that reflect the conditions of the chromium contamination of SOFC: the bulk pressure
(room pressure, 101325 Pa), the operation temperature (typically from T = 1073 K to
1273 K), the oxygen partial pressure, the cathode composition, and the amount of chromium.
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Thermodynamic calculations of impacts of Cr on LSM cathodes
151
The oxygen partial pressure at the interconnect-cathode interface is air. Under current load it
is expected that the oxygen partial pressure will strongly decrease close to the cathode-
electrolyte interface in the triple phase boundary (TPB) region where the oxygen reduction in
LSM takes place: the oxygen partial pressure at the cathode-electrolyte interface, 2O (i)
p can be
approximated from the measured cell voltage of a Pt/LSM/YSZ/Ni-Cermet/Pt solid oxide cell
and the fuel composition by using the equation for the overall electromotive force E of the
cell:
2
2
O
Oln
4(i)
(an)
=pRTE
F p (5.2.1)
R = 8.31451 J mol-1 K-1, F = 96485.309 C mol-1 and 2O (an)
p is given by the ratio of H2-H2O in
the fuel. From a measured cell voltage of 0.7 V[2] at T = 1173 K (fuel: 97 vol.% H2, 3 vol.%
H2O) and a high current load of 300 mA cm-2 a strong decrease of the oxygen partial pressure
at the oxygen reduction sites is expected, 2O (i)
p ≈ 0.01 Pa. As we are interested in the
influences of chromium throughout a cathode under realistic operation conditions of SOFC,
results of the thermodynamic calculations are presented for 2Op ≤ 21278 Pa ≥ 0.01 Pa.
Several LSM cathode compositions can be found in the literature. Part of them is cation
stoichiometric, and part of them has excess Mn that is known to prevent unwanted formation
of electrochemically isolating zirconate at the cathode/electrolyte interface. In this study two
cathode compositions are used for the thermodynamic calculations:
La0.9Sr0.1MnO3-δ and (La0.8Sr0.2)0.9MnO3-δ. The sublattice model for this perovskite phase[20]
allows the formation of vacancies on each site and changing valencies of Mn as a function of
temperature and oxygen partial pressure.
The amount of chromium in the system is defined by the partial pressure of the Cr-gas phase:
exp⎛ ⎞= ⎜ ⎟⎝ ⎠
CrCr
RTp μ
(5.2.2)
This means that by knowing the partial pressure of the Cr-gas phase in the TPB region, it is
possible to calculate the thermodynamics of the chromium contamination. The problem is that
the definite amount of gas that contributes to the degradation phenomena is not known
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Thermodynamic calculations of impacts of Cr on LSM cathodes
152
exactly, as only a fraction of the Cr-gas that evaporates from the Cr2O3 scale on the Cr-alloy
interconnect interacts with LSM or is reduced. Fortunately the amount of deposited Cr in a
degraded LSM cathode has been analyzed as a function of distance from the cathode/YSZ
electrolyte interface[21], and the combined data of X(Cr) and the oxygen partial pressure at the
TPB fix the chemical potential of Cr. The amount of deposited Cr close to the LSM(Cr)/YSZ
interface was about 3 wt.% after a long cell test of 300 h at T = 1073 K. If one assumes that
the 2Op under the test conditions was 1 Pa at the the LSM(Cr)/YSZ interface (normal cell
performance), the chemical potential of the Cr-gas phase can be calculated. Even though it is
clear that the chemical potential of Cr will change if the amount of evaporated Cr from
different interconnect materials is different, the Cr-gas reservoir is assumed to be in a
saturated state due to “unlimited” supply from the interconnect during the cell performance,
and thus its chemical potential is fixed in the thermodynamic calculations. This simplification
is reasonable, as in all investigated cell tests with LSM and Cr-alloy interconnects the
degradation was similar, so that changing chromium amounts due to different interconnect
alloys are obviously not detrimental for the cell degradation.
H2O (operation of SOFC in humid air) is not considered in the calculations, as neither
hydroxides nor solubilities of hydrogen or OH− were included in the La-Sr-Mn-Cr-O oxide
database.
5.3 Results
5.3.1 Thermodynamic calulcations of La0.9Sr0.1MnO3 contaminated by chromium
Fig. 5.3.1 (next page) shows phase fractions in Cr-“poisoned” La0.9Sr0.1MnO3-δ at constant
chemical potential of CrO3, μ(CrO3) = −300000 J mol-1 referred to 100000 Pa of CrO3(g) as a
function of oxygen partial pressure at T = 1273 K and 1073 K, and in Figs. 5.3.2 (next page)
and 5.3.3 (p. 153) phase equilibria are indicated: the cathode remains single phase at 2Op >
102.75 Pa. By decreasing the oxygen partial pressure, tetragonally distorted Mn3O4 spinel
(t-sp), the manganese endmember of the Cr-Mn spinel solid solution phase forms.
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Thermodynamic calculations of impacts of Cr on LSM cathodes
153
Fig. 5.3.1 phase fractions in Cr-“poisoned” La0.9Sr0.1MnO3-δ as a function of oxygen partial
pressure at T=1273 K and 1073 K at μ(CrO3) = −300000 J mol-1
Fig. 5.3.2 Phase equilibria in Cr-“poisoned” La0.9Sr0.1MnO3-δ and defect concentrations of
La0.9Sr0.1(Mn,Cr)O3-δ as a function of oxygen partial pressure at T = 1273 K and
μ(CrO3) = −300000 J mol-1. A, B, and C denote sublattices of the perovskite phase, with A
and B standing for the cation sublattices and C standing for the oxygen sublattice. Vertical
lines indicate boundaries between different phase equilibria
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Thermodynamic calculations of impacts of Cr on LSM cathodes
154
Fig. 5.3.3 Phase equilibria in Cr-“poisoned” La0.9Sr0.1MnO3-δ and defect concentrations of
La0.9Sr0.1(Mn,Cr)O3-δ as a function of oxygen partial pressure at T = 1073 K and
μ(CrO3)= −300000 J mol-1. The vertical line indicates the boundary between phase equilibria
At T = 1273 K (Figs. 5.3.1, p. 153 and 5.3.2, p. 153), tetragonally distorted spinel remains
stable to 2Op = 10-0.4 Pa. At lower
2Op cubic Mn-Cr spinel forms. At 1073 K (Figs. 5.3.1, p.
152 and 5.3.3), tetragonally distorted spinel remains stable to 2Op = 100.75 Pa, followed by the
formation of cubic spinel at lower 2Op . This means that by decreasing the oxygen partial
pressure from 2Op = 104.3, the pressure of air, to 10-1.5 Pa, the amount of spinel in the
contaminated cell increases. At 1073 K Cr-Mn spinel formation is less pronounced, and Cr-
Mn spinel formation starts at lower 2Op than at 1273 K.
To find out about the structural chemical changes in the cathode perovskite caused by reaction
with chromium, the fractions of species in a specific sublattice (site fractions) are calculated at
T=1273 K and 1073 K (plots in Figs. 5.3.2, p. 152 and 5.3.3) as a function of 2Op . The results
are compared with the calculated site fractions in a cathode with a very small chemical
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Thermodynamic calculations of impacts of Cr on LSM cathodes
155
potential of Cr, μ(CrO3) = −106 J mol-1 that means with practically no Cr (Figs. 5.3.4 to
5.3.5).
Fig. 5.3.4 Defect concentrations in La0.9Sr0.1MnO3-δ
as a function of oxygen partial pressure at T=1273 K.
Fig. 5.3.5 Defect concentrations in La0.9Sr0.1MnO3-δ
as a function of oxygen partial pressure at T = 1073 K.
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Thermodynamic calculations of impacts of Cr on LSM cathodes
156
In general defect concentrations of the Cr-contaminated LSM differ from the defect
concentrations in LSM without Cr at a high temperature of 1273 K: with Cr the
concentrations of vacancies on the A- and B-sublattices decrease stronger by decreasing the
oxygen partial pressure. The increase of oxygen vacancies by decreasing the oxygen partial
pressure on the other hand is weaker when chromium is present. At T = 1273 K and 2Op =
1 Pa, which is the expected 2Op at the LSM/YSZ interface at 250 mA cm-2 current load, the
site fractions of cation vacancies on the A- and B-sublattices for LSM(Cr) are y(Va)A =
1.98x10-6, y(Va)B=4.3x10-6, whereas in LSM y(Va)A = 3.086x10-6 and y(Va)B = 7.096x10-6 are
calculated. The concentration of oxygen vacancies at 1 Pa and T = 1273 K in LSM(Cr) is
slightly higher than in LSM, y(Va)C = 3.01x10-5 in LSM(Cr),compared to y(Va)C = 2.57x10-5
in LSM. A pronounced drop of cation and oxygen vacancies is calculated at 1273 K and 2Op =
10-1 Pa, the expected oxygen partial pressure at the TPB under a high current load of 300 mA
cm-2: the concentration of oxygen vacancies in LSM(Cr) is y(Va)C = 3.39x10-5, compared to
y(Va)C = 9.48x10-5 in LSM. This means that if the oxygen partial pressure at the LSM/YSZ
interface strongly decreases the vacancy concentrations will drop significantly.
The concentrations of Cr3+ and Cr4+ in LSM(Cr) increase when the temperature increases and
the oxygen partial pressure decreases.
The calculated compositions of tetragonally distorted spinel (Fig. 5.3.6 a, next page) and
cubic spinel (Fig. 5.3.6 b) formed during chromium “poisoning” show a strong dependence
upon the oxygen partial pressure: only under low oxygen partial pressures a significant
amount of chromium is found in the spinel phase, whereas at higher oxygen partial pressures
the spinel phase has a composition close to Mn3O4. At T = 1073 K the spinel phase contains
less chromium than at T = 1273 K.
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Thermodynamic calculations of impacts of Cr on LSM cathodes
157
Fig. 5.3.6 Calculated site fractions of ions in cubic spinel (6 a) and tetragonally distorted
spinel (6 b) formed during chromium “poisoning” at T = 1273 K and 1073 K
5.3.2 Thermodynamic calculations of (La0.8Sr0.2)0.9MnO3-δ contaminated by chromium
From Fig. 5.3.7 it is obvious that in this widely used LSM composition Cr-“poisoning” leads
to the formation of additional phases already at high oxygen partial pressures: A small amount
of about 5 mol% of the pure spinel endmember, tetragonally distorted Mn3O4 (t-sp) is
expected to form. At T = 1073 K Mn2O3 is stable in a Cr-contaminated LSM cathode with
excess Mn in air.
Fig. 5.3.7 phase fractions in Cr-“poisoned” (La0.8Sr0.2)0.9MnO3-δ as a function of
oxygen partial pressure at T = 1273 K and 1073 K and μ(CrO3) = −300000 J mol-1
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Thermodynamic calculations of impacts of Cr on LSM cathodes
158
In Fig. 5.3.8 the compositional changes of cubic spinel are plotted as a function of oxygen
partial pressure at T = 1273 K. In general, the compositions of the spinel phases formed
during chromium “poisoning” become richer in Cr under more reducing conditions, as in the
case of cation-stoichiometric LSM.
Fig. 5.3.8 Calculated site fractions of ions in cubic spinel formed
during chromium “poisoning” at T = 1273 K
It is interesting whether the consequences of chromium for the concentrations of defects in
LSM(Cr) with excess Mn are more or less pronounced than in cation-stoichiometric
LSM(Cr): Phase equilibria and defect concentrations in a (La0.8Sr0.2)0.9MnO3-δ cathode are
shown in Fig. 5.3.9 (next page).
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Thermodynamic calculations of impacts of Cr on LSM cathodes
159
Fig. 5.3.9 Phase equilibria in Cr-“poisoned” (La0.8Sr0.2)0.9(Mn,Cr)O3-δ and defect
concentrations in (La0.8Sr0.2)0.9(Mn,Cr)O3-δ as a function of oxygen partial pressure at T =
1273 and μ(CrO3) = −300000 J mol-1. The vertical line indicates the boundary between
different phase equilibria
Fig. 5.3.10 (next page) is a comparison of defect concentrations of (La0.8Sr0.2)0.9MnO3-δ with
Cr (broken lines in Fig. 5.3.10) and without Cr (solid lines in Fig. 5.3.10) at 1273 K. The
vacancy concentrations on the A-sites and B-sites of the Cr-contaminated perovskite phase
are basically in the middle between these vacancy concentrations in LSM. In LSM(Cr) the
concentrations of these cation vacancies drop strongly at low 2Op . Mn2+ is higher in LSM(Cr)
than in LSM at higher 2Op , and the concentration of oxygen vacancies is lower in LSM(Cr)
than in LSM at relatively high and low 2Op .
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Thermodynamic calculations of impacts of Cr on LSM cathodes
160
Fig. 5.3.10 Defect concentrations in (La0.8Sr0.2)0.9(Mn,Cr)O3-δ (dashed lines) and
(La0.8Sr0.2)0.9MnO3-δ (solid lines) as a function of oxygen partial pressure at T = 1273.
Calculated concentrations of all species in LSM(Cr) and tetragonally distorted spinel in
equilibrium are listed in Table 5.3.1.
Table 5.3.1 Compositions of LSM(Cr) and spinel in equilibrium at different T at pO2=1
Pa with and without Cr.
5.3.3 Thermodynamic testing of LSM with Mn-deficiency
Only in a cathode with Mn-deficiency it is possible to push the formation of additional phases
towards a lower oxygen partial pressure: for the case of La0.871Sr0.148Mn0.947O3-δ spinel
formation becomes important only at2Op < 0.1 Pa, as it is illustrated in Fig. 5.3.11, next page.
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Thermodynamic calculations of impacts of Cr on LSM cathodes
161
Fig. 5.3.11 Phase fractions in a Cr-“poisoned” Mn-deficient LSM as a function of
oxygen partial pressure at T = 1273 and 1073 K and μ(CrO3) = −300000 J mol-1.
The influence of chromium on defect concentrations in La0.871Sr0.148(Mn,Cr)0.947O3-δ is
illustrated in Fig. 5.3.12, next page: The concentration of oxygen vacancies in
La0.871Sr0.148(Mn,Cr)0.947O3-δ is half of an order of magnitude higher than in
(La0.8Sr0.2)0.9MnO3-δ at high oxygen partial pressures. However, after reaching a plateau at
2Op = 103 Pa, y(Va)C even decrease slightly towards lower 2Op , and the concentration of
oxygen vacancies is almost an order of magnitude lower then in (La0.8Sr0.2)0.9MnO3-δ at 2Op =
10-1 Pa.
Page 162
Thermodynamic calculations of impacts of Cr on LSM cathodes
162
Fig. 5.3.12 Phase equilibria in Cr-“poisoned” Mn-deficient LSM and defect concentrations in
La0.871Sr0.148(Mn,Cr)0.947O3-δ as a function of oxygen partial pressure at T = 1273 K and
μ(CrO3) = −300000 J mol-1 (solid lines). Dashed lines indicate the defect concentrations in
(La0.8Sr0.2)0.9MnO3 without chromium. Vertical lines indicate boundaries between different
phase equilibria
5.3.4 Formation of Cr2O3
This phase was not found in the thermodynamic calculations, and thus its formation is
kinetically controlled. One can get an idea about the degree of metastability of a phase by
calculating its thermodynamic driving force. This is the amount of energy that is needed to
bring the phase to its stable state. The more negative the driving force, the more energy is
needed to stabilize the phase, and the driving force for the formation of the phase is low. If the
driving force is 0, the phase is thermodynamically stable. In Fig. 5.3.13 (next page) the
driving force of Cr2O3 is plotted as a function of temperature at two different 2Op in a LSM
cathode with excess Mn under Cr-“poisoning”.
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Thermodynamic calculations of impacts of Cr on LSM cathodes
163
Fig. 5.3.13 Driving force of Cr2O3 as a function of temperature
at different 2Op at μ(CrO3) = −300000 J mol-1.
The driving force for the formation of Cr2O3 is less negative at higher oxygen partial
pressures.
5.4 Discussion
In the following the results of the thermodynamic calculations are compared to experimental
findings on chromium poisoning from the literature. Interpretations are given, which of the
chromium poisoning mechanisms occur under thermodynamic control.
By carrying out equilibrium calculations of state-of-the-art LSM cathodes with the
compositions La0.9Sr0.1MnO3-δ and (La0.8Sr0.2)0.9MnO3-δ at constant chromium in the gas phase
it was tested if spinel formation would be favored thermodynamically under low oxygen
partial pressure, i.e. close to the electrode-electrolyte interface under polarization conditions.
The calculations showed that this is indeed the case. As the A-sublattice of the spinel is
completely filled by Mn2+ under the cell operation conditions, and the only source for this
species is LSM, it is obvious that spinel formation will be associated with increasing Mn2+ in
LSM. Thus, as Mn2+ in LSM increases as a function of decreasing 2Op , also the amount of
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Thermodynamic calculations of impacts of Cr on LSM cathodes
164
spinel formed is higher at low oxygen partial pressure. Cr-gas reveals increasing affinity to
LSM towards the electrode-electrolyte interface: both Cr solid solution in LSM and spinel
formation increase under decreasing the oxygen partial pressure.
From the calculation it is interpreted that the spinel phase that forms under Cr-“poisoning” of
the cathode will contain a high amount of Mn, if the oxygen partial pressure at the
cathode/electrolyte interface is about 1 Pa. Only at lower 2Op significant Cr is incorporated in
the spinel phase, with the stoichiometric MnCr2O4 phase forming at about 2Op = 10-1 Pa.
Though spinel formation is thermodynamically driven in Cr-contaminated SOFC, it seems
that spinel formation per se is not one of the keys of severe cell degradation due to chromium,
but the affinity of Cr-gas to the LSM surface, as even very small Cr contamination in the ppm
range apparently leads to a dramatic decrease of the oxygen diffusion in LSM[22].
From impedance spectroscopy analyses it was consistently concluded that the oxygen
diffusion is severely influenced by chromium. The thermodynamic calculations showed that
Cr interacting with LSM leads to a change of the defect chemistry of the perovskite phase,
and particularly to a decreasing amount of oxygen vacancies at high temperatures and low
oxygen partial pressures. As the formation of oxygen vacancies in LSM is inhibited, oxygen
diffusion to the triple phase boundary is retarded. The results of the thermodynamic defect
chemistry calculations of LSM(Cr) thus indicate that the deterioration of the oxygen diffusion
is higher under at decreased oxygen partial pressures reflecting high current loads.
Cr2O3 is found in degraded SOFC, particularly under high current load. However this phase
was not found in the thermodynamic calculations, and its driving force remains negative
under SOFC operating conditions. This means that its formation is kinetically controlled.
Even though Cr2O3 is not a thermodynamically stable phase in Cr-contaminated SOFC, a
strong tendency exists for CrO3(g) to be reduced to Cr2O3(s) at the TPB, as the reduction
reaction has a large negative ΔG. It was also mentioned earlier that a high tendency for the
precipitation of Cr2O3(s) from CrO3(g) exists[23]. In addition to the adsorption process it is
expected that a great many of Cr-gas molecules are driven further to the energy valley for
their reduction, namely the TPB. Thus it is non-contradictory that coupling of Cr-gas to LSM
and subsequent spinel formation at the LSM surface, and the reduction of CrO3 (g) at the TPB
leading to the metastable reduction product Cr2O3(s) occur simultaneously. An alternative way
to form Cr2O3 was discussed by Konysheva et al.[24]: The kinetic decomposition of the spinel
phase may occur in an oxgen partial pressure gradient due to different mobilities of Mn2+ and
Cr3+.
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Thermodynamic calculations of impacts of Cr on LSM cathodes
165
In addition to the inhibiting of oxygen diffusion to the TPB and blocking of active triple phase
boundary sites by the thermodynamically controlled formation of spinel and the kinetically
driven formation of Cr2O3(s) and thus retarded diffusion of oxygen ions into the electrolyte,
further unwanted consequences of chromium poisoning can be ascribed to the low electrical
conductivity of Cr2O3[25]. Also Cr-Mn-spinel and Cr-doped LSM are significantly less
conductive than pure LSM[26-29]. The electrical conductivity of Cr-Mn spinel decreases as its
Cr-content increases. From the thermodynamic calculations it can be predicted that increasing
the current load will lead to the formation of a spinel phase with a low electrical conductivity.
The ohmic resistance of spinel will also increase due to more Cr dissolved in spinel as the
amount of deposits of chromium in the cathode increases as a function of time. Furthermore it
is expected that the electrical conductivity of LSM is influenced by chromium particularly
under high current loads, as chromium leads to decreased concentrations of cation and oxygen
vacancies in LSM(Cr) relative to LSM under such operating conditions of SOFC.
5.5 Conclusions
Thermodynamic calculations of LSM contaminated by chromium showed that the formation
of spinel is thermodynamically driven, whereas Cr2O3 is a metastable phase that forms under
kinetic control in degraded SOFC. The formation of spinel is favored under low oxygen
partial pressures, thus in an SOFC under current load this phase is found predominantly at the
LSM/YSZ interface.
The interaction between chromium and LSM leads to changes of the defect chemistry of the
LSM perovskite phase. Particularly diminished concentration of oxygen vacancies relative to
LSM without chromium may be a reason for the inhibited oxygen diffusion in degraded
SOFC at high temperatures and high current loads . This is also true for Mn-deficient LSM
compositions, though the formation of spinel can be restricted to lower oxygen partial
pressures. Its defect chemistry is particularly problematic at low oxygen partial pressures, the
concentration of oxygen vacancies being strongly diminished relative to LSM with excess
Mn. Anyway the use of a Mn-deficient LSM cathode for SOFC is not recommended due to
the formation of electrically isolating zirconate.
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Thermodynamic calculations of impacts of Cr on LSM cathodes
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By lowering the operation temperature of SOFC additional phases are expected to form at
lower oxygen partial pressures. Thus it is expected that in this case the consequences of Cr-
poisoning will persist particularly at high current loads.
From the thermodynamic point of view it can be summarized that there are neither optimized
SOFC operating conditions nor optimized LSM compositions that eliminate the chromium
problem in SOFC with LSM cathode and Cr-alloy interconnect. Even though the deterioration
of the cell performance due to chromium is expected to be less pronounced when the
operation temperature and current load is decreased, chromium “poisoning” of SOFC with an
LSM cathode and Cr-alloy interconnect can only be prevented by applying effective coatings
that act as diffusion barrier in combination with additional functional layers. Furthermore,
interaction between Mn from LSM with Cr may be cumbered by proper doping of the
perovskite with further B-site cations.
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169
Appendix
La-Cr databasea)
@@ Database La-Cr, Povoden-Karadeniz 2008 @@ GO G ENTER-ELEMENT LA CR VA @@ELEMENT NAME REF. STATE ATOMIC MASS H0 S0 AMEND-ELEMENT LA DOUBLE_HCP(ABAC) 1.3891E+02 6.6651E+03 5.6902E+01,, AMEND-ELEMENT CR BCC_A2 5.1996E+01 4.0500E+03 2.35429E+01,, AMEND-ELEMENT VA VACUUM 0 0 0,, @@ ---------------------------------------------------------- @@ Functions @@ ---------------------------------------------------------- @@ Standard data for elements, Dinsdale 1991 @@ La, double hcp ENTER-SYMBO FUNCTION GHSERLA 298.15 -7968.403+120.284604*T-26.34*T*LN(T)-.001295165*T**2; 550 Y -3381.413+59.06113*T-17.1659411*T*LN(T)-.008371705*T**2 +6.8932E-07*T**3-399448*T**(-1); 2000 Y -15608.882+181.390071*T-34.3088*T*LN(T); 4000 N @@ Cr, bcc ENTER-SYMBO FUNCTION GHSERCR 298.15 -8856.94+157.48*T-26.908*t*LN(T)+0.00189435*T**2 -1.47721E-06*T**3+139250*T**(-1); 2180 Y -34869.344+344.18*T-50.0*T*LN(T)-2.88526E+32*T**(-9); 6000 N @@------------------------------------------------------------------- @@ Solid metals, Dinsdale 1991 @@ La, bcc ENTER-SYMBO FUNCTION GLABCC 298.15 -3952.161+88.072353*T-21.7919*T*LN(T)-0.004045175*T**2 -5.25865E-07*T**3; 800 Y +321682.673-3565.08252*T+513.440708*T*LN(T)-0.387295093*T**2 +4.9547989E-05*T**3-36581228*T**(-1); 1134 Y -16377.894+218.492988*T-39.5388*T*LN(T); 1193 Y -136609.91+1123.34397*T-163.413074*T*LN(T)+0.053968535*T**2 -4.056395E-06*T**3+21167204*T**(-1); 2000 Y -8205.988+174.836315*T-34.3088*T*LN(T); 4000 N @@ La, fcc ENTER-SYMBO FUNCTION GLAFCC 298.15
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170
-6109.797+89.878761*T-21.7919*T*LN(T)-0.004045175*T**2 -5.25865E-07*T**3; 1134 Y -124598.976+955.878375*T-139.346741*T*LN(T)+0.042032405*T**2 -3.066199E-06*T**3+20994153*T**(-1); 2000 Y -12599.386+178.54399*T-34.3088*T*LN(T); 4000 N @@ ---------------------------------------------------------------------- @@ Liquid metal functions, Dinsdale 1991 @@ La ENTER-SYMBO FUNCTION GLALIQ 298.15 +5332.653+18.23012*T-11.0188191*T*LN(T)-0.020171603*T**2 +2.93775E-06*T**3-133541*T**(-1); 1134 Y -3942.004+171.018431*T-34.3088*T*LN(T); 4000 N @@ Cr ENTER-SYMBO FUNCTION GCR_L 298.15 +15483.015+146.059775*T-26.908*T*LN(T)+.00189435*T**2 -1.47721E-06*T**3+139250*T**(-1)+2.37615E-21*T**7; 2180 Y -16459.984+335.616317*T-50*T*LN(T); 6000 N @@------------------------------------------------------------ @@ Gas functions @@ La gas, from SGTE @@ La(g) ENTER-SYMBO FUNCTION F12026T 298.15 +422273.955-30.3347881*T-22.06299*T*LN(T)-0.005444405*T**2 +4.71447833E-07*T**3+102710.1*T**(-1); 600 Y +426628.905-85.4786162*T-13.83676*T*LN(T)-0.011938995*T**2 +1.33826017E-06*T**3-312130.2*T**(-1); 1300 Y +404460.17+114.016725*T-42.00406*T*LN(T)+0.0037094435*T**2 -2.70261E-07*T**3+2891891*T**(-1); 3200 Y +497751.747-246.085237*T+2.791973*T*LN(T)-0.006002155*T**2 +1.30043383E-07*T**3-34158815*T**(-1); 8200 Y -92343.0441+773.338363*T-111.0188*T*LN(T)+0.0037862445*T**2 -2.82257667E-08*T**3+5.418475E+08*T**(-1); 10000 N @@ Cr gas, from SGTE ENTER-SYMBO FUNCTION F7491T 298.15 +390765.331-31.5192158*T-21.36083*T*LN(T)+7.253215E-04*T**2 -1.588679E-07*T**3+10285.15*T**(-1); 1100 Y +393886.928-44.1074654*T-19.96003*T*LN(T)+.001513089*T**2 -4.23648333E-07*T**3-722515*T**(-1); 6000 N @@ Cr2 gas, from SGTE ENTER-SYMBOL FUNCTION F7763T 298.15 +598511.403+41.5353212*T-40.56798*T*LN(T)+.004961847*T**2 -1.61216717E-06*T**3+154422.85*T**(-1); 800 Y +613345.232-104.207991*T-19.7643*T*LN(T)-.007085085*T**2 -4.69883E-07*T**3-1738066.5*T**(-1); 1400 Y +642608.843-369.28626*T+17.64743*T*LN(T)-.02767321*T**2
Page 171
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171
+1.605906E-06*T**3-5831655*T**(-1); 2300 Y +553119.895+159.188555*T-52.07969*T*LN(T)-.004229401*T**2 +1.5939925E-07*T**3+14793625*T**(-1); 3900 Y +347492.34+623.137623*T-105.0428*T*LN(T)+3.9699545E-04*T**2 +1.51783483E-07*T**3+1.4843765E+08*T**(-1); 5800 Y -484185.055+2598.25559*T-334.7145*T*LN(T)+.028597625*T**2 -4.97520167E-07*T**3+7.135805E+08*T**(-1); 6000 N @@ -------------------------------------------------------------------- @@ Phases @@ ------------------------------------------------------------------- @@ Metals @@ La, dhcp ENTER-PHASE LADHCP,, 2 1 0.5 LA ; VA;,,, ENTER-PAR G(LADHCP,LA:VA;0) 298.15 +GHSERLA;,,, @@ La, fcc ENTER-PHASE LAFCC,, 2 1 1 LA; VA;,,, ENTER-PAR G(LAFCC,LA:VA;0) 298.15 +GLAFCC;,,, @@ ----------------------------------------------------------------- @@ Alloys @@ BCC_A2 ALLOY ENTER-PHASE BCC,, 2 1 3 LA CR; VA;,,, AMEND-PHASE-DESC BCC MAGN -1 0.4 ENTER-PAR TC(BCC,CR:VA;0) 298.15 -311.5;,,, ENTER-PAR BMAGN(BCC,CR:VA;0) 298.15 -0.008;,,, ENTER-PAR G(BCC,LA:VA;0) 298.15 +GLABCC;,,, ENTER-PAR G(BCC,CR:VA;0) 298.15 +GHSERCR;,,, ENTER-PAR L(BCC,LA,CR:VA;0) 298.15 83500;,,, @@ -------------------------------------------------------------------------- @@ Liquid, ideal extension from lower-order systems ENTER-PHASE LIQ,, 2 1 1 LA CR; VA;,,, AMEND-PHASE LIQ COMP 2,,,,,,,, ENTER-PAR G(LIQ,LA:VA;0) 298.15 +GLALIQ;,,, ENTER-PAR G(LIQ,CR:VA;0) 298.15 +GCR_L;,,, @@ Interaction parameters from binaries ENTER-PAR L(LIQ,LA,CR:VA;0) 298.15 60713-5.49*t;,,, ENTER-PAR L(LIQ,LA,CR:VA;1) 298.15 64573-23*t;,,, @@------------------------------------------------------------ @@ Gas ENTER-PHASE GAS G 1 LA CR CR2;,,, ENTER-PAR G(GAS,LA;0) 298.15 +F12026T+RTLNP;,,, ENTER-PAR G(GAS,CR;0) 298.15 +F7491T+RTLNP;,,,, ENTER-PAR G(GAS,CR2;0) 298.15 +F7763T+RTLNP;,,, @@ GO PAR SET-OUT-LEVEL,,,,, N,, set-interactive
a)databases scripts can be used in Thermocalc with the extension .tcm
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172
La-Sr-Mn-Cr-O-(H) oxide database
@@ LA-SR-Mn-CR-O-(H) oxide, Povoden-Karadeniz @@ @@ Database La-Sr-Mn-Cr-O-(H), first version: Feb2006 by Povoden. @@ Actual version: Dec2008 by Povoden-Karadeniz @@ @@ COMMENTS @@ @@ Sr-Cr-O liquid: simple description; associate at composition SrCrO4 can @@ help for better fit to experiments – future work @@ @@ No data exist for Sr-Mn-Cr-O. Solubility of Cr in SrMnO3 not known @@ --> Subsystem Sr-Mn-Cr-O is a purely ideal extention @@ @@ no oxygen solubility in La-oxide description (taken from Zinkevich et @@ al.) considered @@ @@ Quinary Ruddlesden popper phase is very tentative, as only few phase @@ diagram data exist! @@ -------------------------------------------------------------------- GO G ENTER-ELEMENT LA SR MN CR O VA H @@ELEMENT NAME REF. STATE ATOMIC MASS H0 S0 AMEND-ELEMENT LA DOUBLE_HCP(ABAC) 1.3891E+02 6.6651E+03 5.6902E+01,, AMEND-ELEMENT SR SR_FCC_A1 8.7620E+01 6.5680E+03 5.5694E+01,, AMEND-ELEMENT MN CBCC_A12 5.4938E+01 4.9960E+03 3.2008E+01,, AMEND-ELEMENT CR BCC_A2 5.1996E+01 4.0500E+03 2.35429E+01,, AMEND-ELEMENT O 1/2_MOLE_O2(G) 1.5999E+01 4.3410E+03 1.0252E+02,, AMEND-ELEMENT H 1/2_MOLE_H2(G) 0.1008E+01 0 0.65340E+02,, AMEND-ELEMENT VA VACUUM 0 0 0,, @@ @@ -------------------------------------------------------------------- @@ Species @@ -------------------------------------------------------------------- ENTER-SPECIES LA+2 LA/+2 ENTER-SPECIES LA+3 LA/+3 ENTER-SPECIES SR+2 SR/+2 ENTER-SPECIES MN+2 MN/+2 ENTER-SPECIES MN+3 MN/+3 ENTER-SPECIES MN+4 MN/+4 ENTER-SPECIES O2 O2 ENTER-SPECIES O3 O3 ENTER-SPECIES O-2 O/-2 ENTER-SPECIES SRO SRO ENTER-SPECIES SRO2 SRO2 ENTER-SPECIES CR+2 CR/+2 ENTER-SPECIES CR+3 CR/+3 ENTER-SPECIES CR+4 CR/+4 ENTER-SPECIES CR+6 CR/+6 ENTER-SPECIES CR1O1 CR1O1 ENTER-SPECIES CR1O2 CR1O2 ENTER-SPECIES CR1O3 CR1O3
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ENTER-SPECIES CR2O3 CR2O3 ENTER-SPECIES CR3O4 CR3O4 ENTER-SPECIES CRH1 CRH1 ENTER-SPECIES CRH1O1 CRH1O1 ENTER-SPECIES CRH1O2 CRH1O2 ENTER-SPECIES CRH1O3 CRH1O3 ENTER-SPECIES CRH2O2 CRH2O2 ENTER-SPECIES CRH2O3 CRH2O3 ENTER-SPECIES CRH2O4 CRH2O4 ENTER-SPECIES CRH3O3 CRH3O3 ENTER-SPECIES CRH3O4 CRH3O4 ENTER-SPECIES CRH4O4 CRH4O4 ENTER-SPECIES CRH4O5 CRH4O5 ENTER-SPECIES CRH5O5 CRH5O5 ENTER-SPECIES CRH6O6 CRH6O6 ENTER-SPECIES H2 H2 ENTER-SPECIES H2O1 H2O1 ENTER-SPECIES H1O1 H1O1 ENTER-SPECIES H1O2 H1O2 ENTER-SPECIES H2O2 H2O2 @@ @@ ---------------------------------------------------------- @@ Functions @@ ---------------------------------------------------------- @@ SER Lattice stabilities, Dinsdale 1991 @@ La, double hcp ENTER-SYMBO FUNCTION GHSERLA 298.15 -7968.403+120.284604*T-26.34*T*LN(T)-.001295165*T**2; 550 Y -3381.413+59.06113*T-17.1659411*T*LN(T)-.008371705*T**2 +6.8932E-07*T**3-399448*T**(-1); 2000 Y -15608.882+181.390071*T-34.3088*T*LN(T); 4000 N @@ Sr, fcc ENTER-SYMBO FUNCTION GHSERSR 298.15 -7532.367+107.183879*T-23.905*T*LN(T)-4.61225E-3*T**2 -1.67477E-07*T**3-2055*T**(-1); 820 Y -13380.102+153.196104*T-30.0905432*T*LN(T)-3.251266E-3*T**2 +1.84189E-07*T**3+850134*T**(-1); 3000 N @@ Mn, cbcca12 ENTER-SYMBO FUNCTION GHSERMN 298.15 -8115.27966+130.059572*T-23.4582*T*LN(T)-0.00734768*T**2 +69827.1*T**(-1); 1519 Y -28733.41+312.2648*T-48*T*LN(T)+1.656847E30*T**(-9); 2000 N @@ Cr, bcc ENTER-SYMBO FUNCTION GHSERCR 298.15 -8856.94+157.48*T-26.908*t*LN(T)+0.00189435*T**2 -1.47721E-06*T**3+139250*T**(-1); 2180 Y -34869.344+344.18*T-50.0*T*LN(T)-2.88526E+32*T**(-9); 6000 N @@ O1, (1/2 O2) ENTER-SYMBO FUNCTION GHSEROO 298.15 -3480.872255-25.5028601*T-11.1355068*T*LN(T)-0.005098873*T**2 +6.6184604E-07*T**3-38364.8742*T**(-1); 1000 Y
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-6568.76015+12.66000166*T-16.8138015*T*LN(T)-5.9579637E-04*T**2 +6.78055555E-09*T**3+262904.778*T**(-1); 3300 Y -13986.728+31.259625*T-18.9536*T*LN(T)-4.25243E-04*T**2 +1.0721E-08*T**3+4383200*T**(-1); 6000 N @@------------------------------------------------------------ @@ Binary oxides, optimized @@ La-oxides, Zinkevich 2006 ENTER-SYMBO FUNCTION GLA2O3D 298.15 -1833257+692.9664*T-120.629*T*LN(T)-0.006854*T**2 +808000*T**(-1)-1E7*T**(-2);,,, ENTER-SYMBO FUNCTION GLA2O3H 298.15 32350-13.986*T+GLA2O3D;,,, ENTER-SYMBO FUNCTION GLA2O3X 298.15 43192-18.555*T+GLA2O3D;,,, @@ Sr-oxides, Risold 1996 @@ SrO ENTER-SYMBO FUNCTION GSROSOL 298.15 -607870+268.9*T-47.56*T*LN(T)-0.00307*T**2 +190000*T**(-1);,,, @@ SrO2 ENTER-SYMBO FUNCTION GSRO2SOL 298.15 +GSROSOL+GHSEROO-43740+70*T;,,, @@ Mn-oxides, Grundy 2003 @@ MANGANOSITE, MNO ENTER-SYMBO FUNCTION GMN1O1 298.15 -4.02477557E+05+2.59355626E+02*T-4.68352649E+01*T*LN(T) -3.85001409E-03*T**2+2.12922234E+05*T**(-1);,,, @@ PYROLYSITE, MN1O2 ENTER-SYMBO FUNCTION GMN1O2 298.15 -5.45091278E+05+3.95379396E+02*T-6.52766201E+01*T*LN(T) -7.80284521E-03*T**2+6.64955386E+05*T**(-1);,,, @@ @@ MN2O3-FUNCTION, MODIFIED, Grundy 2006 ENTER-SYMBO FUNCTION GMN2O3 298.15 -9.96393E+05+5.6846E+02*T-9.911E+01*T*LN(T)-2.056E-02*T**2 +6.0822E+05*T**(-1);,,, @@ ALPHA-HAUSMANNITE, ALPHA-MN3O4 (DISTORTED) ENTER-SYMBO FUNCTION GTMN3O4 298.15 -1.43703676E+06+8.89567858E+02*T-1.54747566E+02*T*LN(T) -1.74079033E-02*T**2+9.86138663E+05*T**(-1);,,, @@ BETA-HAUSMANNITE, BETA-MN3O4 (CUBIC) ENTER-SYMBO FUNCTION GCMN3O4 298.15 -1.41618912E+06+8.75120338E+02*T-1.54747566E+02*T*LN(T) -1.74079033E-02*T**2+9.86138663E+05*T**(-1);,,, @@ Cr-O oxides, Povoden 2005 @@ METASTABLE CRO ENTER-SYMBO FUNCTION GCR1O1 298.15 +0.5*GCR2O3-0.5*GHSEROO+255269-53.82*T;,,, @@ ESKOLAITE, Cr2O3 ENTER-SYMBO FUNCTION GCR2O3 298.15 -1.164542E+06+7.2856E+02*T-119.8*T*LN(T)-4.97E-03*T**2 +1.05E+06*T**(-1);,,, @@ reduced neutral endmember of CR2O3 ENTER-SYMBO FUNCTION GCRO0 298.15 +108305+GCR2O3+0.66666666667*GHSERCR;,,, @@ CR-SPINEL CR3O4 ENTER-SYMBO FUNCTION GCR3O4 298.15 +1.5*GCR2O3-0.5*GHSEROO+280045-93.76*T;,,, @@ --------------------------------------------------------------
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@@ Ternary oxides, optimized (except perovskite functions) @@ @@ Functions of the La-Sr-O system, Grundy 2004 ENTER-SYMBO FUNCTION SR_ALPHA 298.15 +2*GSROSOL+2.5E+04;,,, ENTER-SYMBO FUNCTION SRH_ALPH 298.15 +2*GSROSOL+2.5E+04;,,, ENTER-SYMBO FUNCTION SRX_ALPH 298.15 +2*GSROSOL+2.5E+04;,,, ENTER-SYMBO FUNCTION LA_BETA 298.15 +GLA2O3D+2.158E+04;,,, ENTER-SYMBO FUNCTION RE_ALPHA 298.15 0;,,, ENTER-SYMBO FUNCTION RE_BETA 298.15 0;,,, @@ @@ Functions of the La-Mn-O system, Grundy et al. 2005 ENTER-SYMBO FUNCTION GL2MNO4 298.15 +GLA2O3D+GMN1O1+6.26029731E+04-3.71704891E+01*T;,,, @@ @@ Functions of the La-Cr-O system, Povoden 2008 @@ LA2CRO6 ENTER-SYMBO FUNCTION GLA2CRO6 298.15 GLA2O3D+0.5*GCR2O3+1.5*GHSEROO-73045-4.14*T;,,, @@ intermediate La-chromates @@ LA16 @@ ENTER-SYMBO FUNCTION GLA16 298.15 @@ 8*GLA2O3D+3.5*GCR2O3+9.5*GHSEROO-540404-9.55*T;,,, @@ LA7 @@ ENTER-SYMBO FUNCTION GLA7 298.15 @@ 3.5*GLA2O3D+GCR2O3+2.5*GHSEROO-154101-2.799*T;,,, @@ LA2CR3O12 ENTER-SYMBO FUNCTION GLA2CR3 298.15 GLA2O3D+1.5*GCR2O3+4.5*GHSEROO-371557+205*T;,,, @@ @@ Functions of the Sr-Mn-O system, Grundy 2004 @@ HEX Phase ENTER-SYMBO FUNCTION GSM4_HEX 298.15 +GSROSOL+GMN1O2-1.11300000E+05;,,, ENTER-SYMBO FUNCTION GSM3_HEX 298.15 +GSROSOL+0.5*GMN2O3-7.73000000E+03 -1.70000000E+01*T;,,, @@ SrMn3Oz as SrMnO3_Mn2O3 ENTER-SYMBO FUNCTION GSM4OZ 298.15 +GMN2O3+GSM4_HEX-8.79100000E+03;,,, ENTER-SYMBO FUNCTION GSM3OZ 298.15 +GMN2O3+GSM3_HEX-2.19200000E+04;,,, @@ RP1 ENTER-SYMBO FUNCTION GS4O_RP1 298.15 +2*GSROSOL+GMN1O2-1.32830000E+05;,,, ENTER-SYMBO FUNCTION GL3O_RP1 298.15 +GSROSOL+0.5*GLA2O3D+0.5*GMN2O3-68300;,,, @@ RP2 ENTER-SYMBO FUNCTION GS4O_RP2 298.15 +3*GSROSOL+2*GMN1O2-8.99100000E+04-90*T;,,, ENTER-SYMBO FUNCTION GL3O_RP2 298.15 +GSROSOL+GLA2O3D+GMN2O3-137400;,,, @@ RP3 ENTER-SYMBO FUNCTION GSM4_RP3 298.15 +4*GSROSOL+3*GMN1O2-3.78500000E+05;,,, @@ Sr7Mn4O1
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ENTER-SYMBO FUNCTION GS7M4 298.15 +7*GSROSOL+4*GMN1O2-6.12450000E+05+50*T;,,, @@ @@ Functions of the Sr-Cr-O system, Povoden 2008 @@ SRCR2O4 ENTER-SYMBO FUNCTION GSC2O4 298.15 +GSROSOL+GCR2O3+98000-95.5*T;,,, @@ SR2CRO4 ENTER-SYMBO FUNCTION GS2CO4 298.15 2*GSROSOL+0.5*GCR2O3+0.5*GHSEROO-145000+50*T;,,, @@ SR3CR2O8 ENTER-SYMBO FUNCTION GS3C2O8 298.15 +2.66666667*GSROSOL+GCR2O3+2.333333333333*GHSEROO -508507+219*T;,,, @@ SRCRO4 ENTER-SYMBO FUNCTION GSCO4 298.15 +GSROSOL+0.5*GCR2O3+1.5*GHSEROO-273771 +131.6*T;,,, @@ SRCR2O7 ENTER-SYMBO FUNCTION GSC2O7 298.15 +GSROSOL+GCR2O3+3*GHSEROO-325047+196*T;,,, @@ @@ Functions of the Mn-Cr-O system, Povoden 2005 @@ CUBIC SPINEL ENTER-SYMBO FUNCTION GSPINEL 298.15 0.666666667*GCR3O4+.33333333334*GCMN3O4-210795.3+61.69*T;,,, @@ TETRAGONALLY DISTORTED SPINEL ENTER-SYMBO FUNCTION GTSPINEL 298.15 0.666666667*GCR3O4+.33333333334*GTMN3O4-200942+75.1*T;,,, @@ @@ Functions of the La-Sr-Cr-O oxide system, Povoden 2008 @@ Ruddlesden Popper phase ENTER-SYMBO FUNCTION GREFRP 298.15 +2*GSROSOL+0.5*GCR2O3+0.5*GHSEROO;,,, ENTER-SYMBO FUNCTION GLCR3O_RP1 298.15 +GLACRO3+GSROSOL+7000-25*t;,,, @@ ---------------------------------------------------------------- @@ Perovskite functions @@ Grundy 2005 @@ Charge compensated by Mn+4 (correct) ENTER-SYMBO FUNCTION GL3O 298.15 +0.5*GLA2O3D+0.5*GMN2O3-63367+51.77*T-7.19*T*LN(T) +232934*T**(-1);,,, @@ ENTER-SYMBO FUNCTION GL3OL 298.15 +0.5*GLA2O3D+0.5*GMN2O3-63367+51.77*T-7.19*T*LN(T) +232934*T**(-1)-3429+4.72*t;,,, @@ ENTER-SYMBO FUNCTION GL3OR 298.15 +0.5*GLA2O3D+0.5*GMN2O3-63367+51.77*T-7.19*T*LN(T) +232934*T**(-1)+400-0.4*t;,,, ENTER-SYMBO FUNCTION GL2O 298.15 +0.5*GLA2O3D+GMN1O1+27672;,,, ENTER-SYMBO FUNCTION GL4O 298.15 +0.5*GLA2O3D+0.75*GMN1O2-91857+20.31*T;,,, ENTER-SYMBO FUNCTION GV4O 298.15 +0.333333*GLA2O3D+GMN1O2-53760;,,, ENTER-SYMBO FUNCTION GVVV 298.15 +6*GL2O+4*GL4O+3*GV4O-12*GL3O-254212;,,, ENTER-SYMBO FUNCTION GMS3O 298.15 +GSROSOL+0.5*GMN2O3-7.73000000E+03-1.44550000E+04
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-1.70000000E+01*T;,,, ENTER-SYMBO FUNCTION GMS4O 298.15 +GSROSOL+GMN1O2-1.11300000E+05+2.26500000E+04 -7.69000000E+00*T;,,, ENTER-SYMBO FUNCTION ANTI 298.15 +547422;,,, @@ Reciprocals: all 0!!!!! @@ @@ Povoden 2008 @@ LaCrO3-PEROVSKITE ENTER-SYMBO FUNCTION GLACRO3 298.15 0.5*GLA2O3D+0.5*GCR2O3-73591+2.38*T-0.68*T* LN(T);,,, ENTER-SYMBO FUNCTION GALACRO3 298.15 +GLACRO3-340+0.63*t;,,, @@ (LaSr)CrO3+/-delta-Perovskite @@ Reference SrCrVa3 ENTER-SYMBO FUNCTION GS4V 298.15 GSROSOL+0.5*GCR2O3-2.5*GHSEROO;,,, @@ Function for neutral endmember SrCrO3 ENTER-SYMBO FUNCTION GS4O 298.15 GSROSOL+0.5*GCR2O3+0.5*GHSEROO+10222-55.52*t;,,, @@ Function for neutral endmember SR(CR+3,VA)O3 ENTER-SYMBO FUNCTION GN 298.15 +GSROSOL+0.5*GCR2O3+11.2386*T+135166-88.42*t;,,, @@ Functions for defect chemistry ENTER-SYMBO FUNCTION GVCR4O 298.15 0.5*GCR2O3+0.5*GHSEROO-291802-250*t;,,, ENTER-SYMBO FUNCTION GLACR4O 298.15 0.33333*GLA2O3D+.5*GCR2O3+0.5*GHSEROO-200000;,,, @@ ---------------------------------------------------------------------- @@ LIQUID FUNCTIONS @@ ---------------------------------------------------------------------- @@ Liquid metal functions, Dinsdale 1991 @@ La ENTER-SYMBO FUNCTION GLALIQ 298.15 +5332.653+18.23012*T-11.0188191*T*LN(T)-0.020171603*T**2 +2.93775E-06*T**3-133541*T**(-1); 1134 Y -3942.004+171.018431*T-34.3088*T*LN(T); 4000 N @@ Sr ENTER-SYMBO FUNCTION GSRLIQ 298.15 +2194.997-10.118994*T-5.0668978*T*LN(T)-3.1840595E-2*T**2 +4.981237E-06*T**3-265559*T**(-1); 1050 Y -10855.29+213.406219*T-39.463*T*LN(T); 3000 N @@ Mn ENTER-SYMBO FUNCTION GMN_L 298.15 +GHSERMN+17859.91-12.6208*T-4.41929E-21*T**7; 1519 Y +GHSERMN+18739.51-13.2288*T-1.656847E30*T**(-9); 3000 N @@ Cr ENTER-SYMBO FUNCTION GCR_L 298.15 +15483.015+146.059775*T-26.908*T*LN(T)+.00189435*T**2 -1.47721E-06*T**3+139250*T**(-1)+2.37615E-21*T**7; 2180 Y -16459.984+335.616317*T-50*T*LN(T); 6000 N @@ ---------------------------------------------------------------------
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@@ Liquid oxide functions, optimized @@ liquid La2O3, Zinkevich 2006 ENTER-SYMBO FUNCTION GLA2O3LIQ 298.15 -1833257+692.9664*T-120.629*T*LN(T)-0.006854*T**2 +808000*T**(-1)-1E7*T**(-2)+141329-56.6220*T;,,, @@ liquid SrO, Risold ENTER-SYMBO FUNCTION GSROLIQ 298.15 -566346+449*T-73.1*T*LN(T);,,, @@ liquid Mn oxides, Grundy ENTER-SYMBO FUNCTION GMN1O1_L 298.15 GMN1O1+4.39465890E+04-2.06284295E+01*T;,,, ENTER-SYMBO FUNCTION GMN2O3_L 298.15 +2*GMN1O1+GHSEROO-6.49525609E+04+4.31437957E+01*T;,,, @@ liquid Cr oxides, Povoden ENTER-SYMBO FUNCTION GCR1O1_L 298.15 0.5*GCR2O3-0.5*GHSEROO+339673-121.4*T;,,, ENTER-SYMBO FUNCTION GCR2O3_L 298.15 GCR2O3+439078-169*T;,,, @@------------------------------------------------------------------- @@ LIQUID WATER, from T.C.R.A.S. Class: 4 ENTER-SYMBO FUNCTION GH2O_L 298.15 -332319.671+1078.59563*T-186.8669*T*LN(T) +.2320948*T**2-9.14296167E-05*T**3+978019*T**(-1); 500 Y -62418.8788-3288.18729*T+495.1304*T*LN(T) -.504926*T**2+4.917665E-05*T**3-18523425*T**(-1); 540 Y -8528143.9+142414.45*T-22596.19*T*LN(T) +27.48508*T**2-.00631160667*T**3+5.63356E+08*T**(-1); 600 Y -331037.282+741.178604*T-117.41*T*LN(T); 601 N @@ ------------------------------------------------------------------------ @@ GAS FUNCTIONS @@ --------------------CHROMIUM GAS---------------------------------------- @@ CR Gas: SGTE v 3.0 (1998), source: Thermocenter of russian academy @@ of science (T.C.R.A.S), Class: 4 @@ SGTE=scientific group thermodata Europe @@ ENTER-SYMBO FUNCTION F7491T 298.15 +390765.331-31.5192158*T-21.36083*T* LN(T) +7.253215E-04*T**2-1.588679E-07*T**3+10285.15*T**(-1); 1100 Y +393886.928-44.1074654*T-19.96003*T*LN(T)+.001513089*T**2 -4.23648333E-07*T**3-722515*T**(-1); 6000 N @@ CR1O1 Gas (SGTE 1998; from T.C.R.A.S Class: 5) ENTER-SYMBO FUNCTION F7705T 298.15 +176483.869-31.9513659*T-30.2897*T*LN(T)-.00607059*T**2 +9.229905E-07*T**3+35263.135*T**(-1); 900 Y +170853.62+32.1684007*T-39.74749*T*LN(T)+.00119977*T**2 -1.52515733E-07*T**3+682877*T**(-1); 4000 Y +307209.502-414.237405*T+14.48744*T*LN(T)-.008463125*T**2 +1.722975E-07*T**3-64209900*T**(-1); 8400 Y -403765.708+805.224944*T-121.5329*T*LN(T)+.003139382*T**2 -1.36845867E-08*T**3+6.35563E+08*T**(-1); 10000 N @@ CR1O1 Gas, REASSESSED BY MING CHEN (2006) BASED ON EBBINGHAUS (1993) ENTER-SYMBO FUNCTION GCR1O1_G 298.15 +173449.4-33.083*T-30.097*T*LN(T)-0.0063*T**2 +31300*T**(-1)+9.5567E-7*T**3; 1000 Y +167489.3+37.31*T-40.555*T*LN(T)+0.00148*T**2 +873600*T**(-1)+1.69E-7*T**3;
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3000 N @@ CR1O2 Gas, reassessment Chen 2006, based on Ebbinghaus 1993 ENTER-SYMBO FUNCTION GCR1O2_G 298.15 -109942.78+10.59*T-39.526*T*LN(T)-0.0155*T**2 +245800*T**(-1)+2.43E-6*T**3; 1000 Y -118120+123.81*T-56.696*T*LN(T)-0.00012*T**2 +932050*T**(-1)-8.01667E-8*T**3; 3000 N @@ CR1O3 Gas, reassessed by Ming Chen 2006, based on Ebbinghaus 1993 ENTER-SYMBO FUNCTION GCR1O3_G 298.15 -341231.99+130.61*T-57.2*T*LN(T)-.0216*T**2 +428900*T**(-1)+3.401E-6*T**3; 1000 Y -354716.09+299.89*T-82.569*T*LN(T)-0.00016*T**2 +1814700*T**(-1)+7.33E-9*T**3; 3000 N @@-------------------OXYGEN GAS------------------------------------- @@ O Gas (JANAF 1982, assessment dated 3/77 from SGTE) ENTER-SYMBO FUNCTION F13349T 298.15 +243206.494-20.8612582*T-21.01555*T*LN(T)+1.2687055E-04*T**2 -1.23131283E-08*T**3-42897.09*T**(-1); 2950 Y +252301.423-52.0847281*T-17.21188*T*LN(T)-5.413565E-04*T**2 +7.64520667E-09*T**3-3973170.5*T**(-1); 6000 N @@ O3 Gas (SGTE 1998; from T.C.R.A.S Class: 4) ENTER-SYMBO FUNCTION F14021T 298.15 +130696.944-37.9096643*T-27.58118*T*LN(T)-.02763076*T**2 +4.60539333E-06*T**3+99530.45*T**(-1); 700 Y +114760.623+176.626737*T-60.10286*T*LN(T)+.00206456*T**2 -5.17486667E-07*T**3+1572175*T**(-1); 1300 Y +49468.3956+710.09482*T-134.3696*T*LN(T)+.039707355*T**2 -4.10457667E-06*T**3+12362250*T**(-1); 2100 Y +866367.075-3566.80563*T+421.2001*T*LN(T)-.1284109*T**2 +5.44768833E-06*T**3-2.1304835E+08*T**(-1); 2800 Y +409416.383-1950.70834*T+223.4437*T*LN(T)-.0922361*T**2 +4.306855E-06*T**3-21589870*T**(-1); 3500 Y -1866338.6+6101.13383*T-764.8435*T*LN(T)+.09852775*T**2 -2.59784667E-06*T**3+9.610855E+08*T**(-1); 4900 Y +97590.043+890.798361*T-149.9608*T*LN(T)+.01283575*T**2 -3.555105E-07*T**3-2.1699975E+08*T**(-1); 6000 N @@ -------------O-H GAS----------------------------------- @@ H2 Gas (JANAF THERMOCHEMICAL TABLES SGTE) ENTER-SYMBO FUNCTION H2GAS 298.15 -9522.97393+78.5273873*T-31.35707*T*LN(T)+0.0027589925*T**2 -7.46390667E-07*T**3+56582.3*T**(-1); 1000 Y +180.108664-15.6128262*T-17.84857*T*LN(T)-0.00584168*T**2 +3.14618667E-07*T**3-1280036*T**(-1); 2100 Y -18840.1663+92.3120249*T-32.05082*T*LN(T)-0.0010728235*T**2 +1.14281783E-08*T**3+3561002.5*T**(-1); 6000 N @@ H Gas (JANAF 1982, assessment dated 3/77 from SGTE) ENTER-SYMBO FUNCTION HGAS 298.15 +211801.621+24.4989821*T-20.78611*T*LN(T); 6000 N @@ H2O1 Gas (SGTE 1998; from T.C.R.A.S Class: 4) ENTER-SYMBO FUNCTION F10963T 298.15 -250423.434+4.45470312*T-28.40916*T*LN(T) -.00623741*T**2-6.01526167E-08*T**3-64163.45*T**(-1); 1100 Y -256145.879+30.1894682*T-31.43044*T*LN(T) -.007055445*T**2+3.05535833E-07*T**3+1246309.5*T**(-1); 2800 Y
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-268423.418+116.690197*T-42.96842*T*LN(T) -.003069987*T**2+6.97594167E-08*T**3+2458230.5*T**(-1); 8400 Y -489068.882+553.259882*T-92.4077*T*LN(T) +.0016703495*T**2-1.32333233E-08*T**3+1.765625E+08*T**(-1); 18000 Y -165728.771+239.645643*T-59.77872*T*LN(T) +2.213599E-04*T**2-1.2921095E-09*T**3-4.1931655E+08*T**(-1); 20000 N @@ H1O1 Gas (SGTE 1998; from T.C.R.A.S Class: 1) ENTER-SYMBO FUNCTION F10666T 298.15 +30698.6898+15.9096451*T-29.97699*T*LN(T) +.001713168*T**2-6.799205E-07*T**3-25503.82*T**(-1); 3000 Y +31735.5127-12.686636*T-25.42186*T*LN(T) -.003149545*T**2+1.34404917E-07*T**3+116618.65*T**(-1); 8600 Y +41016.0783-20.7343256*T-24.94216*T*LN(T) -.0023107985*T**2+5.91863E-08*T**3-6415210*T**(-1); 18000 Y -154907.953+370.326117*T-69.24542*T*LN(T) +.0019361405*T**2-1.47539017E-08*T**3+1.4391015E+08*T**(-1); +326722.277-65.0792741*T-24.2768*T*LN(T) +6.42189E-05*T**2-1.30298483E-10*T**3-8.292415E+08*T**(-1); 20000 N @@ H1O2 Gas (SGTE 1998; from T.C.R.A.S Class: 4) ENTER-SYMBO FUNCTION F10729T 298.15 +1075.64106-55.242048*T-24.45435*T*LN(T) -.018507875*T**2+2.36297E-06*T**3-29469.05*T**(-1); 800 Y -7932.99164+54.2016233*T-40.775*T*LN(T) -.00501027*T**2+2.122915E-07*T**3+925845*T**(-1); 3600 Y -67875.8961+275.406716*T-68.1173*T*LN(T) +6.12331E-04*T**2-6.573855E-09*T**3+26048030*T**(-1); 6000 N @@ H2O2 Gas (JANAF SECOND EDIT SGTE) ENTER-SYMBO FUNCTION F10983T 298.15 -147258.971-37.1497212*T-26.10636*T*LN(T) -.036948065*T**2+6.659505E-06*T**3+65357.65*T**(-1); 700 Y -156470.505+120.191295*T-50.94271*T*LN(T) -.007931945*T**2+4.29733833E-07*T**3+684985.5*T**(-1); 1500 N @@-------------------CR-O-H GAS---------------------------------------- @@ CR(OH)1 Gas REASSESSED BY MING CHEN (2006) BASED ON EBBINGHAUS (1993) ENTER-SYMBO FUNCTION GCRH1O1_G 298.15 +68260+52.87*T-46.257*T*LN(T) -0.002*T**2+185600*T**(-1)-1.51E-7*T**3; 1000 Y 56684+136.53*T-57.551*T*LN(T) +0.0018*T**2+2218000*T**(-1)-2.75E-7*T**3; 3000 N @@ CRO(OH)1 Gas REASSESSED BY MING CHEN (2006) BASED ON EBBINGHAUS (1993) ENTER-SYMBO FUNCTION GCRH1O2_G 298.15 -274384.32+190.52*T-74.175*T*LN(T) +0.0031*T**2+266750*T**(-1)-9.135E-7*T**3; 1000 Y -276268.52+180.7*T-72.053*T*LN(T) -0.0015*T**2+938850*T**(-1)+5.15E-8*T**3; 3000 N @@ CRO2(OH) Gas, combined assessment Chen 2006 @@ based on Ebbinghaus 1995 @@ and from Povoden based on Kim and Belton 1974 @@ (data suggested by Opila 2007) ENTER-SYMBO FUNCTION GCRH1O3_G 298.15 -497678+273.77*T-83.724*T*LN(T) -0.0146*T**2+715900*T**(-1)+2.39E-6*T**3; 1000 Y -492562+351.47*T-96.9*T*LN(T) -.0018*T**2+1338300*T**(-1)+9.334E-8*T**3; 3000 N @@ CR(OH)2 Gas, assessment Chen 2006, based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH2O2_G 298.15 -351288.4+195.86*T-75.927*T*LN(T) -0.0007*T**2+243850*T**(-1)-9.2E-7*T**3; 1000 Y
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-359644+228.97*T-79.455*T*LN(T) -0.004*T**2+2094950*T**(-1)+1.91E-7*T**3; 3000 N @@ CRO(OH)2 Gas, assessment Chen 2006 based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH2O3_G 298.15 -578683+391.2*T-109.525*T*LN(T) -0.00056*T**2+663150*T**(-1)-5.67833E-07*T**3; 1000 Y -582354+394.6*T-109.25*T*LN(T) -0.004*T**2+1.8967E-07*T**3+1688150*T**(-1); 3000 N @@ CRO2(OH)2 Gas, combined assessment Chen 2006 @@ based on Ebbinghaus 1995 @@ and from Povoden-Karadeniz based on Opila 2007 ENTER-SYMBO FUNCTION GCRH2O4_G 298.15 -787712+400*T-107.819*T*LN(T) -0.019*T**2+513600*T**(-1)+1.9958E-06*T**3; 1000 Y -806262+567*T-131.457*T*LN(T) -0.0049*T**2+3311450*T**(-1)+2.545E-7*T**3; 3000 N @@ CR(OH)3 Gas, assessment Chen 2006, based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH3O3_G 298.15 -650064.7+464.37*T-125.5*T*LN(T) +0.006*T**2+498450*T**(-1)-2.378E-6*T**3; 1000 Y -656538+448.3*T-121.16*T*LN(T) -0.006*T**2+2525450*T**(-1)+2.93E-7*T**3; 3000 N @@ CRO(OH)3 Gas, assessment Chen 2006, based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH3O4_G 298.15 -851590.83+534.3*T-137.098*T*LN(T) -0.0099*T**2+770750*T**(-1)+5.8867E-7*T**3; 1000 Y -861477.76+600.74*T-146.002*T*LN(T) -0.0065*T**2+2669300*T**(-1)+3.35E-7*T**3; 3000 N @@ CR(OH)4 Gas, assessment Chen 2006, based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH4O4_G 298.15 -902751.6+712.5*T-163*T*LN(T) +0.004*T**2+785800*T**(-1)-2.355E-6*T**3; 1000 Y -909897.86+694.973194012145*T-158.41*T*LN(T) -0.0086*T**2+3058600*T**(-1)+4.3E-7*T**3; 3000 N @@ CR(OH)5 Gas, assessment Chen 2006, based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH5O5_G 298.15 -978211.05+820.9*T-190.524*T*LN(T) -0.0054*T**2+1023500*T**(-1)-1.11767E-6*T**3; 1000 Y -991549.1+867.6*T-195.2*T*LN(T) -0.01*T**2+4151100*T**(-1)+5.7467E-7*T**3; 3000 N @@ CR(OH)6 Gas, assessment Chen 2006, based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH6O6_G 298.15 -1029121.12+967.89*T-216.86*T*LN(T) -0.008*T**2+840600*T**(-1)-1.77E-6*T**3; 1000 Y -1053466+1080.45*T-229.874*T*LN(T) -0.014*T**2+6008850*T**(-1)+7.34E-7*T**3; 3000 N @@ CRO(OH)4 Gas, assessment Chen 2006, based on Ebbinghaus 1993 ENTER-SYMBO FUNCTION G_CRH4O5 298.15 -976204+672.6*T-162.049*T*LN(T) -0.014*T**2+1.35E-07*T**3+665100*T**(-1); 1000 Y -997791.8+813.97*T-180.65*T*LN(T) -0.0096*T**2+4.945E-07*T**3+4671850*T**(-1); 3000 N @@ CRH1 Gas (SGTE 1998; from T.C.R.A.S Class: 4) ENTER-SYMBO FUNCTION F7586T 298.15 +432449.026-56.386334*T-22.37019*T*LN(T) -.00994042*T**2+1.18913267E-06*T**3-77266.05*T**(-1); 1000 Y +421602.4+51.9865812*T-37.99681*T*LN(T) +3.349852E-04*T**2-1.13133917E-07*T**3+1368173*T**(-1); 3500 Y +587860.713-424.36214*T+18.6022*T*LN(T) -.007723995*T**2+7.99444833E-08*T**3-86705500*T**(-1); 5500 Y +1270342.46-2142.60191*T+219.9391*T*LN(T)
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-.034109635*T**2+7.277845E-07*T**3-5.20451E+08*T**(-1); 6000 N @@ @@ @@ -------------------------------------------------------------------- @@ Phases @@ ------------------------------------------------------------------- @@ Binary oxides @@ @@ Sr oxides, Risold @@ ENTER-PHASE SRO2,, 1 SRO2;,,, ENTER-PAR G(SRO2,SRO2;0) 298.15 +GSRO2SOL;,,, @@ @@ Mn oxides, Grundy @@ @@ STOICHIOMETRIC PYROLYSITE, MN1O2 ENTER-PHASE MN1O2,, 2 1 2 MN; O;,,, ENTER-PAR G(MN1O2,MN:O;0) 298.15 +GMN1O2;,,, @@ ---------------------------------------------------------------------- @@ Ternary oxides @@ @@ LA-SR-O, Grundy, Chen @@ ENTER-PHASE LA2O3SS,, 2 2 3 LA+2 LA+3 SR+2; O-2 VA;,,, ENTER-PAR G(LA2O3SS,LA+2:O-2;0) 298.15 +GLAO;,,, ENTER-PAR G(LA2O3SS,LA+2:VA;0),, +GLAO-GHSEROO;,,, ENTER-PAR G(LA2O3SS,LA+3:O-2;0) 298.15 +GLA2O3D;,,, ENTER-PAR G(LA2O3SS,LA+3:VA;0),, +GLA2O3D-3*GHSEROO;,,, ENTER-PAR G(LA2O3SS,SR+2:O-2;0),, +SR_ALPHA+GHSEROO +15.87691*T;,,, ENTER-PAR G(LA2O3SS,SR+2:VA;0),, +SR_ALPHA-2*GHSEROO +15.87691*T;,,, ENTER-PAR L(LA2O3SS,LA+3,SR+2:O-2;0) 298.15 +2.149E+05-7.81E+01*T;,,, ENTER-PAR L(LA2O3SS,LA+3,SR+2:VA;0) 298.15 +2.149E+05-7.81E+01*T;,,, @@ ENTER-PHASE LA2O3_HEXSS,, 2 2 3 LA+3 SR+2; O-2 VA;,,, ENTER-PAR G(LA2O3_HEXSS,LA+3:O-2;0),, +GLA2O3H;,,, ENTER-PAR G(LA2O3_HEXSS,LA+3:VA;0),, +GLA2O3H-3*GHSEROO;,,, ENTER-PAR G(LA2O3_HEXSS,SR+2:O-2;0),, +SRH_ALPH+GHSEROO+15.87691*T;,,, ENTER-PAR G(LA2O3_HEXSS,SR+2:VA;0),, +SRH_ALPH-2*GHSEROO
+15.87691*T;,,, ENTER-PAR L(LA2O3_HEXSS,LA+3,SR+2:O-2;0) 298.15 +193600-78.1*T;,,, ENTER-PAR L(LA2O3_HEXSS,LA+3,SR+2:VA;0) 298.15 +193600-78.1*T;,,, @@ ENTER-PHASE LA2O3_CUBSS,, 2 2 3 LA+3 SR+2; O-2 VA;,,, ENTER-PAR G(LA2O3_CUBSS,LA+3:O-2;0),, +GLA2O3X;,,, ENTER-PAR G(LA2O3_CUBSS,LA+3:VA;0),, +GLA2O3X-3*GHSEROO;,,, ENTER-PAR G(LA2O3_CUBSS,SR+2:O-2;0),, +SRX_ALPH+GHSEROO+15.87691*T;,,, ENTER-PAR G(LA2O3_CUBSS,SR+2:VA;0),, +SRX_ALPH-2*GHSEROO+15.87691*T;,,, ENTER-PAR L(LA2O3_CUBSS,LA+3,SR+2:O-2;0) 298.15 +168700-78.1*T;,,, ENTER-PAR L(LA2O3_CUBSS,LA+3,SR+2:O-2;1) 298.15 -20000;,,, ENTER-PAR L(LA2O3_CUBSS,LA+3,SR+2:VA;0) 298.15 +168700-78.1*T;,,, ENTER-PAR L(LA2O3_CUBSS,LA+3,SR+2:VA;1) 298.15 -20000;,,, @@ La4SrO7 as BETA phase ENTER-PHASE BETA,, 2 2 3 LA+3 SR+2; O-2 VA;,,, ENTER-PAR G(BETA,LA+3:O-2;0),, +LA_BETA;,,, ENTER-PAR G(BETA,LA+3:VA;0),, +LA_BETA-3*GHSEROO;,,, ENTER-PAR G(BETA,SR+2:O-2;0),, +SR_ALPHA+416100+GHSEROO -0.33333333*RE_BETA
+15.87691*T;,,,
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ENTER-PAR G(BETA,SR+2:VA;0),, +SR_ALPHA+416100-2*GHSEROO +0.66666667*RE_BETA+15.87691*T;,,, ENTER-PAR L(BETA,LA+3,SR+2:O-2;0) 298.15 -121000-237.8*T;,,, ENTER-PAR L(BETA,LA+3,SR+2:VA;0) 298.15 -121000-237.8*T;,,, @@ La4Sr3O9, Stoichiometric ENTER-PHASE LA4SR3O9,, 3 4 3 9 LA+3; SR+2; O-2;,,, ENTER-PAR G(LA4SR3O9,LA+3:SR+2:O-2;0),, +2*GLA2O3D+3*GSROSOL+229800 -136.75*T;,,, @@ SrO Solid Solution ENTER-PHASE SRO,, 2 1 1 LA+3 SR+2 VA; O-2;,,, ENTER-PAR G(SRO,LA+3:O-2;0),, +0.5*GLA2O3D+113700;,,, ENTER-PAR G(SRO,SR+2:O-2;0),, +GSROSOL;,,, ENTER-PAR G(SRO,VA:O-2;0),, 0;,,, @@ @@ LA-MN-O, Grundy @@ ENTER-PHASE L2MNO4,, 3 2 1 4 LA+3; MN+2; O-2;,,, ENTER-PAR G(L2MNO4,LA+3:MN+2:O-2;0) 298.15 +GL2MNO4;,,, @@ ENTER-PHASE LMN2O5,, 4 1 1 1 5 LA+3; MN+3; MN+4; O-2;,,, ENTER-PAR G(LMN2O5,LA+3:MN+3:MN+4:O-2;0) 298.15 +GLMN2O5;,,, @@ @@ LA-CR-O, Povoden @@ @@ STOICHIOMETRIC LA2CRO6 ENTER-PHASE LA2CRO6,, 3 2 1 6 LA+3; CR+6; O-2;,,, ENTER-PAR G(LA2CRO6,LA+3:CR+6:O-2;0) 298.15 +GLA2CRO6;,,, @@ intermediate La-chromates @@ STOICHIOMETRIC LA16 @@ ENTER-PHASE LA16,, 3 16 7 44 LA; CR; O;,,, @@ ENTER-PAR G(LA16,LA:CR:O;0) 298.15 +GLA16;,,, @@ STOICHIOMETRIC LA7 @@ ENTER-PHASE LA7,, 3 7 2 16 LA; CR; O;,,, @@ ENTER-PAR G(LA7,LA:CR:O;0) 298.15 +GLA7;,,, @@ @@ STOICHIOMETRIC LA2CR3O12 ENTER-PHASE LA2CR3,, 3 2 3 12 LA+3; CR+6; O-2;,,, ENTER-PAR G(LA2CR3,LA+3:CR+6:O-2;0) 298.15 +GLA2CR3;,,, @@ @@ SR-MN-O, Grundy @@ ENTER-PHASE SR7MN4O15,, 3 7 4 15 SR+2; MN+4; O-2;,,, ENTER-PAR G(SR7MN4O15,SR+2:MN+4:O-2;0),, +GS7M4;,,, @@ ENTER-PHASE SRMN3O6,, 5 1 2 3 1 3 SR+2; MN+3; O-2; MN+3 MN+4; O-2 VA;,,, ENTER-PAR G(SRMN3O6,SR+2:MN+3:O-2:MN+3:O-2;0),, +GSM3OZ+0.5*GHSEROO +11.23859*T;,,, ENTER-PAR G(SRMN3O6,SR+2:MN+3:O-2:MN+3:VA;0),, +GSM3OZ-2.5*GHSEROO +11.23859*T;,,, ENTER-PAR G(SRMN3O6,SR+2:MN+3:O-2:MN+4:O-2;0),, +GSM4OZ;,,, ENTER-PAR G(SRMN3O6,SR+2:MN+3:O-2:MN+4:VA;0),, +GSM4OZ-3*GHSEROO;,,, @@ ENTER-PHASE SR4MN3O10,, 3 4 3 10 SR+2; MN+4; O-2;,,, ENTER-PAR G(SR4MN3O10,SR+2:MN+4:O-2;0),, +GSM4_RP3;,,, @@ ENTER-PHASE SRMNO3_HEX,, 3 1 1 3 SR+2; MN+3 MN+4; O-2 VA;,,, ENTER-PAR G(SRMNO3_HEX,SR+2:MN+3:O-2;0),, +GSM3_HEX+0.5*GHSEROO
+11.23859*T;,,, ENTER-PAR G(SRMNO3_HEX,SR+2:MN+3:VA;0),, +GSM3_HEX-2.5*GHSEROO
+11.23859*T;,,,
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ENTER-PAR G(SRMNO3_HEX,SR+2:MN+4:O-2;0),, +GSM4_HEX;,,, ENTER-PAR G(SRMNO3_HEX,SR+2:MN+4:VA;0),, +GSM4_HEX-3*GHSEROO;,,, @@ @@ RP2, Grundy modified it in LSM modeling ENTER-PHASE RP2,, 4 1 2 2 7 SR+2; SR+2; MN+3 MN+4; O-2;,,, ENTER-PAR G(RP2,SR+2:SR+2:MN+3:O-2;0) 298.15 +3*GSROSOL+GMN2O3+GHSEROO;,,, ENTER-PAR G(RP2,SR+2:SR+2:MN+4:O-2;0) 298.15 +GS4O_RP2;,,, @@ @@ SR-CR-O, Povoden @@ @@ SRCR2O4 ENTER-PHASE SC2O4,, 3 1 2 4 SR+2; CR+3; O-2;,,, ENTER-PAR G(SC2O4,SR+2:CR+3:O-2;0) 298.15 +GSC2O4;,,, @@ SR2CRO4 ENTER-PHASE S2CO4,, 3 2 1 4 SR+2; CR+4; O-2;,,, ENTER-PAR G(S2CO4,SR+2:CR+4:O-2;0) 298.15 +GS2CO4;,,, @@ @@ SR2.67CR2O8 ENTER-PHASE S3C2N,, 3 2.666667 2 8 SR; CR; O;,,, ENTER-PAR G(S3C2N,SR:CR:O;0) 298.15 +GS3C2O8;,,, @@ SRCRO4, Povoden-Karadeniz ENTER-PHASE SCO4,, 3 1 1 4 SR+2; CR+6; O-2;,,, ENTER-PAR G(SCO4,SR+2:CR+6:O-2;0) 298.15 +GSCO4;,,, @@ SRCR2O7, doubtful phase @@ ENTER-PHASE SC2O7,, 3 1 2 7 SR+2; CR+6; O-2;,,, @@ ENTER-PAR G(SC2O7,SR+2:CR+6:O-2;0) 298.15 +GSC2O7;,,, @@ @@ CR-MN-O, Povoden @@ @@ NONSTOICHIOMETRIC MANGANOSITE (MNO) SOLID SOLUTION, Grundy, Povoden-K. ENTER-PHASE MNO_HALIT,, 2 1 1 MN+2 MN+3 CR+3 VA; O-2;,,, ENTER-PAR G(MNO_HALIT,MN+2:O-2;0) 298.15 +GMN1O1;,,, ENTER-PAR G(MNO_HALIT,MN+3:O-2;0) 298.15 +GMN1O1-21883.5213 -22.1853365*T;,,, ENTER-PAR G(MNO_HALIT,CR+3:O-2;0) 298.15 +0.5*GCR2O3-7.93845*T +71549.3;,,, ENTER-PAR G(MNO_HALIT,VA:O-2;0) 298.15 0;,,, ENTER-PAR L(MNO_HALIT,MN+2,MN+3:O-2;0) 298.15 -4.21048766E+04;,,, ENTER-PAR L(MNO_HALIT,MN+2,MN+3:O-2;1) 298.15 +4.65131533E+04;,,, @@ @@ Mn2O3 (Compatible with C-Y2O3, Grundy, Chen, Povoden-Karadeniz) ENTER-PHASE MN2O3,, 3 2 3 1 MN+3 CR+3; O-2 VA; O-2 VA;,,, AMEND-PHASE MN2O3 MAGN,, .28 ENTER-PAR TC(MN2O3,MN+3:O-2:VA;0) 298.15 +309;,,, ENTER-PAR TC(MN2O3,CR+3:O-2:VA;0) 298.15 +308.6;,,, ENTER-PAR BMAGN(MN2O3,MN+3:O-2:VA;0) 298.15 +0.59;,,, ENTER-PAR BMAGN(MN2O3,CR+3:O-2:VA;0) 298.15 +3;,,, ENTER-PAR G(MN2O3,MN+3:O-2:VA;0) 298.15 +GMN2O3;,,, ENTER-PAR G(MN2O3,MN+3:O-2:O-2;0) 298.15 +GMN2O3+GHSEROO +100000+15.87691*T;,,, ENTER-PAR G(MN2O3,MN+3:VA:O-2;0) 298.15 +GMN2O3-2*GHSEROO +100000+15.87691*T;,,, ENTER-PAR G(MN2O3,MN+3:VA:VA;0) 298.15 +GMN2O3-3*GHSEROO;,,, ENTER-PAR G(MN2O3,CR+3:O-2:VA;0) 298.15 +GCR2O3+3459;,,, ENTER-PAR G(MN2O3,CR+3:O-2:O-2;0) 298.15 +GCR2O3+GHSEROO +100000+15.87691*T;,,, ENTER-PAR G(MN2O3,CR+3:VA:O-2;0) 298.15 +GCR2O3-2*GHSEROO +100000+15.87691*T;,,, ENTER-PAR G(MN2O3,CR+3:VA:VA;0) 298.15 +GCR2O3-3*GHSEROO;,,, @@ @@ ESKOLAITE, NONSTOICHIOMETRIC CR2O3 SOLID SOLUTION, Povoden-Karadeniz
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ENTER-PHASE CR2O3,, 3 2 1 3 MN+3 CR+2 CR+3; CR+3 VA; O-2;,,, AMEND-PHASE CR2O3 MAGN,, .28 ENTER-PAR TC(CR2O3,MN+3:CR+3:O-2;0) 298.15 +309;,,, ENTER-PAR TC(CR2O3,MN+3:VA:O-2;0) 298.15 +309;,,, ENTER-PAR TC(CR2O3,CR+2:CR+3:O-2;0) 298.15 +308.6;,,, ENTER-PAR TC(CR2O3,CR+2:VA:O-2;0) 298.15 +308.6;,,, ENTER-PAR TC(CR2O3,CR+3:CR+3:O-2;0) 298.15 +308.6;,,, ENTER-PAR TC(CR2O3,CR+3:VA:O-2;0) 298.15 +308.6;,,, ENTER-PAR BMAGN(CR2O3,MN+3:CR+3:O-2;0) 298.15 +0.59;,,, ENTER-PAR BMAGN(CR2O3,MN+3:VA:O-2;0) 298.15 +0.59;,,, ENTER-PAR BMAGN(CR2O3,CR+2:CR+3:O-2;0) 298.15 +3;,,, ENTER-PAR BMAGN(CR2O3,CR+2:VA:O-2;0) 298.15 +3;,,, ENTER-PAR BMAGN(CR2O3,CR+3:CR+3:O-2;0) 298.15 +3;,,, ENTER-PAR BMAGN(CR2O3,CR+3:VA:O-2;0) 298.15 +3;,,, ENTER-PAR G(CR2O3,MN+3:CR+3:O-2;0) 298.15 +GMN2O3+GSERCR+39503;,,, ENTER-PAR G(CR2O3,MN+3:VA:O-2;0) 298.15 +GMN2O3+39503;,,, ENTER-PAR G(CR2O3,CR+2:CR+3:O-2;0) 298.15 +GCRO0 +.33333333334*GHSERCR -5.2923*T;,,, ENTER-PAR G(CR2O3,CR+2:VA:O-2;0) 298.15 +GCRO0 -0.666666666667*GHSERCR -5.2923*T;,,, ENTER-PAR G(CR2O3,CR+3:CR+3:O-2;0) 298.15 +GCR2O3+GHSERCR;,,, ENTER-PAR G(CR2O3,CR+3:VA:O-2;0) 298.15 +GCR2O3;,,, @@ @@ CUBIC SPINEL, Grundy, Povoden-Karadeniz ENTER-PHASE CMNCR2O4,, 3 1 2 4 MN+2 CR+2; MN+3 CR+3; O-2;,,, ENTER-PAR G(CMNCR2O4,MN+2:CR+3:O-2;0) 298.15 +GSPINEL;,,, ENTER-PAR G(CMNCR2O4,CR+2:CR+3:O-2;0) 298.15 +GCR3O4;,,, ENTER-PAR G(CMNCR2O4,MN+2:MN+3:O-2;0) 298.15 +GCMN3O4;,,, ENTER-PAR G(CMNCR2O4,CR+2:MN+3:O-2;0) 298.15 +GCR3O4+GCMN3O4-GSPINEL;,,, @@ DISTORTED_SPINEL, Grundy, Povoden-Karadeniz ENTER-PHASE TMNCR2O4,, 3 1 2 4 MN+2; MN+3 CR+3; O-2;,,, ENTER-PAR G(TMNCR2O4,MN+2:MN+3:O-2;0) 298.15 +GTMN3O4;,,, ENTER-PAR G(TMNCR2O4,MN+2:CR+3:O-2;0) 298.15 +GTSPINEL;,,, @@ ------------------------------------------------------------------------ @@ Quaternary oxides @@ @@ La-Sr-Mn-O, Grundy @@ ENTER-PHASE LS3MN2O7,, 4 1 2 2 7 SR+2; LA+3 SR+2; MN+3 MN+4; O-2;,,, ENTER-PAR G(LS3MN2O7,SR+2:LA+3:MN+3:O-2;0) 298.15 +GL3O_RP2;,,, ENTER-PAR G(LS3MN2O7,SR+2:LA+3:MN+4:O-2;0) 298.15 +GL3O_RP2+GS4O_RP2
-3*GSROSOL -GMN2O3-GHSEROO-R_RP2;,,, ENTER-PAR G(LS3MN2O7,SR+2:SR+2:MN+3:O-2;0) 298.15 +3*GSROSOL+GMN2O3
+GHSEROO;,,, ENTER-PAR G(LS3MN2O7,SR+2:SR+2:MN+4:O-2;0) 298.15 +GS4O_RP2;,,, @@ ------------------------------------------------------------------------ @@ Quinary phases, ideal extensions from lower-order systems @@ @@ high temperature rhombohedral perovskite, Grundy, Povoden-Karadeniz ENTER-PHASE RPEROV,, 3 1 1 3 LA+3 SR+2 VA; MN+2 MN+3 MN+4 CR+3 CR+4 VA; O-2 VA;,,, @@ ENTER-PAR G(RPEROV,SR+2:MN+2:O-2;0),, +GMS3O+GL2O-GL3OR+GHSEROO
+22.47717*T;,,, ENTER-PAR G(RPEROV,SR+2:MN+3:O-2;0),, +GMS3O+0.5*GHSEROO+11.23859*T;,,, ENTER-PAR G(RPEROV,SR+2:MN+4:O-2;0),, +GMS4O;,,, ENTER-PAR G(RPEROV,SR+2:MN+2:VA;0),, +GMS3O+GL2O-GL3OR-2*GHSEROO+22.47717*T;,,,
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ENTER-PAR G(RPEROV,SR+2:MN+3:VA;0),, +GMS3O-2.5*GHSEROO+11.23859*T;,,, ENTER-PAR G(RPEROV,SR+2:MN+4:VA;0),, +GMS4O-3*GHSEROO;,,, ENTER-PAR G(RPEROV,SR+2:CR+3:O-2;0),, +GN+0.1666667*GS4O
-0.16666667*GS4V;,,, ENTER-PAR G(RPEROV,SR+2:CR+3:VA;0),, +GN-0.8333333*GS4O
+0.8333333*GS4V;,,, ENTER-PAR G(RPEROV,SR+2:VA:O-2;0),, +GMS3O-GL3OR+2*GL4O
-1.5*GV4O+0.5*GVVV +2*GHSEROO+12.62121*T;,,, ENTER-PAR G(RPEROV,SR+2:VA:VA;0),, +GMS3O+2*GL4O-1.5*GV4O
+0.5*GVVV-GL3OR -GHSEROO+12.62121*T;,,, ENTER-PAR G(RPEROV,LA+3:MN+2:O-2;0),, +GL2O+0.5*GHSEROO+11.2386*T;,,, ENTER-PAR G(RPEROV,LA+3:MN+2:VA;0),, +GL2O-2.5*GHSEROO+11.2386*T;,,, ENTER-PAR G(RPEROV,LA+3:MN+3:O-2;0),, +GL3OR;,,, ENTER-PAR G(RPEROV,LA+3:MN+3:VA;0),, +GL3OR-3*GHSEROO;,,, ENTER-PAR G(RPEROV,LA+3:MN+4:O-2;0),, +0.66667*GL4O+0.5*GV4O
-0.166667*GVVV -0.5*GHSEROO+5.76318*T;,,, ENTER-PAR G(RPEROV,LA+3:MN+4:VA;0),, +0.66667*GL4O+0.5*GV4O
-0.166667*GVVV -3.5*GHSEROO+5.76318*T;,,, ENTER-PAR G(RPEROV,LA+3:VA:O-2;0),, +2*GL4O-1.5*GV4O+0.5*GVVV
+1.5*GHSEROO +1.41263*T;,,, ENTER-PAR G(RPEROV,LA+3:VA:VA;0),, +2*GL4O+0.5*GVVV-1.5*GV4O
-1.5*GHSEROO+1.41263*T;,,, ENTER-PAR G(RPEROV,VA:MN+3:O-2;0),, +GL3OR+1.5*GV4O+0.5*GVVV-2*GL4O +1.5*GHSEROO-1.41263*T;,,, ENTER-PAR G(RPEROV,VA:MN+4:O-2;0),, +2*GV4O+0.33333*GVVV-1.33333*GL4O +GHSEROO+4.35056*T;,,, ENTER-PAR G(RPEROV,VA:MN+2:VA;0),, +GL2O+1.5*GV4O+0.5*GVVV-2*GL4O -GHSEROO+9.82596*T;,,, ENTER-PAR G(RPEROV,VA:MN+3:VA;0),, +GL3OR+1.5*GV4O+0.5*GVVV-2*GL4O -1.5*GHSEROO-1.41263*T;,,, ENTER-PAR G(RPEROV,VA:MN+4:VA;0),, +2*GV4O+0.3333*GVVV-1.333*GL4O -2*GHSEROO+4.35057*T;,,, ENTER-PAR G(RPEROV,VA:VA:O-2;0),, +GVVV+3*GHSEROO;,,, ENTER-PAR G(RPEROV,VA:VA:VA;0),, +GVVV;,,, ENTER-PAR G(RPEROV,LA+3:CR+3:O-2;0),, +GLACRO3;,,, ENTER-PAR G(RPEROV,LA+3:CR+3:VA;0),, +GLACRO3-3*GHSEROO;,,, ENTER-PAR G(RPEROV,VA:CR+3:O-2;0),, +GLACRO3+1.5*GVCR4O+0.5*GVVV
-2*GLACR4O+1.5*GHSEROO -1.41263*T;,,,
ENTER-PAR G(RPEROV,VA:CR+3:VA;0),, +GLACRO3+1.5*GVCR4O+0.5*GVVV -2*GLACR4O-1.5*GHSEROO -1.41263*T;,,,
ENTER-PAR G(RPEROV,LA+3:CR+4:VA;0),, GS4O-GN-0.1666667*GS4O +0.16666667*GS4V+GLACRO3
-3*GHSEROO;,,, ENTER-PAR G(RPEROV,LA+3:CR+4:O-2;0),, GS4O+GLACRO3-GN-0.1666667*GS4O +0.16666667*GS4V;,,, ENTER-PAR G(RPEROV,SR+2:CR+4:O-2;0),, +GS4O;,,, ENTER-PAR G(RPEROV,SR+2:CR+4:VA;0),, +GS4V;,,, ENTER-PAR G(RPEROV,VA:CR+4:O-2;0),, +2*GVCR4O+0.33333*GVVV
-1.33333*GLACR4O +GHSEROO+4.35056*T;,,, ENTER-PAR G(RPEROV,VA:CR+4:VA;0),, +2*GVCR4O+0.3333*GVVV
-1.333*GLACR4O -2*GHSEROO+4.35057*T;,,, @@ Optimized interactions
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ENTER-PAR L(RPEROV,LA+3,SR+2:MN+2:VA;1),, -136600;,,, ENTER-PAR L(RPEROV,LA+3,SR+2:MN+2:O-2;1),, -136600;,,, ENTER-PAR L(RPEROV,LA+3,SR+2:MN+4:VA;1),, -117000;,,, ENTER-PAR L(RPEROV,LA+3,SR+2:MN+4:O-2;1),, -117000;,,, ENTER-PAR L(RPEROV,LA+3:CR+3,MN+3:O-2;0),, 9248.6;,,, ENTER-PAR L(RPEROV,LA+3,SR+2:MN+3:O-2;0) 298.15 -1.5*t;,,, ENTER-PAR L(RPEROV,LA+3:CR+4,VA:O-2;0),, 250000;,,, ENTER-PAR L(RPEROV,LA+3:CR+3,VA:O-2;0),, 250000;,,, ENTER-PAR L(RPEROV,LA+3:MN+4,MN+3:O-2;1) 298.15 185;,,, ENTER-PAR L(RPEROV,LA+3:MN+4,VA:O-2;0),, -2;,,, ENTER-PAR L(RPEROV,LA+3,VA:MN+4:O-2;0),, 20;,,, ENTER-PAR L(RPEROV,LA+3:CR+3,MN+3:O-2;0) 298.15 3766;,,, ENTER-PAR L(RPEROV,LA+3:CR+3,MN+3:O-2;1) 298.15 -1297;,,, @@ next two interaction parameters can be used to fit @@ Cr4+ amount in perovskite ENTER-PAR L(RPEROV,SR+2:CR+4,MN+3:O-2;0) 298.15 0;,,, ENTER-PAR L(RPEROV,SR+2:CR+4,MN+4:O-2;0) 298.15 0;,,, @@ @@ Ruddlesden-Popper phase, preliminary, scarce experimental data @@ ENTER-PHASE RP,, 5 1 1 1 3 1 SR+2; LA+3 SR+2; MN+3 MN+4 CR+3 CR+4; O-2; @@ O-2;,,, @@ ENTER-PAR G(RP,SR+2:SR+2:CR+4:O-2:O-2;0) 298.15 GS2CO4;,,, @@ ENTER-PAR G(RP,SR+2:LA+3:CR+3:O-2:O-2;0) 298.15 +GLCR3O_RP1;,,, @@ ENTER-PAR G(RP,SR+2:LA+3:CR+4:O-2:O-2;0) 298.15 GS2CO4+GLCR3O_RP1 @@ -GREFRP;,,, @@ ENTER-PAR G(RP,SR+2:SR+2:CR+3:O-2:O-2;0) 298.15 GREFRP;,,, @@ ENTER-PAR L(RP,SR+2:SR+2,LA+3:CR+3:O-2:O-2;0) 298.15 100000;,,, @@ ENTER-PAR L(RP,SR+2:SR+2,LA+3:CR+4:O-2:O-2;0) 298.15 100000;,,, @@ ENTER-PAR G(RP,SR+2:SR+2:MN+3:O-2:O-2;0) 298.15 +2*GSROSOL+0.5*GMN2O3 @@ +0.5*GHSEROO;,,, @@ ENTER-PAR G(RP,SR+2:SR+2:MN+4:O-2:O-2;0) 298.15 +GS4O_RP1;,,, @@ ENTER-PAR G(RP,SR+2:LA+3:MN+3:O-2:O-2;0) 298.15 +GL3O_RP1;,,, @@ ENTER-PAR G(RP,SR+2:LA+3:MN+4:O-2:O-2;0) 298.15 +GL3O_RP1+GS4O_RP1 @@ -2*GSROSOL-0.5*GMN2O3 @@ -0.5*GHSEROO;,,, @@ ------------------------------------------------------------------------ @@ Liquid, ideal extension from lower-order systems, Povoden-Karadeniz ENTER-PHASE IONIC_LIQUID Y LA+3 SR+2 MN+2 MN+3 CR+2 CR+3; O-2 VA;,,, AMEND-PHASE IONIC_LIQUID COMP 2,,,,,,,, ENTER-PAR G(ION,LA+3:O-2;0) 298.15 +GLA2O3LIQ;,,, ENTER-PAR G(ION,LA+3:VA;0) 298.15 +GLALIQ;,,, ENTER-PAR G(ION,SR+2:O-2;0) 298.15 +2*GSROLIQ;,,, ENTER-PAR G(ION,SR+2:VA;0) 298.15 +GSRLIQ;,,, ENTER-PAR G(ION,MN+2:O-2;0) 298.15 +2*GMN1O1_L;,,, ENTER-PAR G(ION,MN+2:VA;0) 298.15 +GMN_L;,,, ENTER-PAR G(ION,MN+3:O-2;0) 298.15 +GMN2O3_L;,,, ENTER-PAR G(ION,MN+3:VA;0) 298.15 +2*GMN_L+GMN2O3_L-3*GMN1O1_L;,,, ENTER-PAR G(ION,CR+2:O-2;0) 298.15 2*GCR1O1_L;,,, ENTER-PAR G(ION,CR+2:VA;0) 298.15 +GCR_L;,,, ENTER-PAR G(ION,CR+3:O-2;0) 298.15 +GCR2O3_L;,,, ENTER-PAR G(ION,CR+3:VA;0) 298.15 +2*GCR_L+GCR2O3_L-3*GCR1O1_L;,,, @@ Interaction parameters from binaries ENTER-PAR L(ION,MN+2:O-2,VA;0) 298.15 1.29519000E+05;,,, ENTER-PAR L(ION,MN+2:O-2,VA;1) 298.15 -4.54590000E+04;,,, ENTER-PAR L(ION,MN+2,MN+3:O-2;0) 298.15 -3.38590000E+04;,,, ENTER-PAR L(ION,CR+2:O-2,VA;0) 298.15 +121000;,,, ENTER-PAR L(ION,CR+3:O-2,VA;0) 298.15 +121000;,,, @@ Interaction parameters from ternaries ENTER-PAR L(ION,LA+3,MN+2:O-2;0) 298.15 -119062;,,, ENTER-PAR L(ION,LA+3,MN+2:VA;0) 298.15 +11368;,,, ENTER-PAR L(ION,LA+3,MN+2:VA;1) 298.15 -11316.4;,,,
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ENTER-PAR L(ION,LA+3,MN+2:VA;4) 298.15 -9111;,,, ENTER-PAR L(ION,LA+3,MN+3:O-2;0) 298.15 -119062;,,, ENTER-PAR L(ION,SR+2,MN+2:O-2;0) 298.15 -176300;,,, ENTER-PAR L(ION,SR+2,MN+2:VA;0) 298.15 +46000;,,, ENTER-PAR L(ION,SR+2,MN+3:O-2;0) 298.15 -176300;,,, ENTER-PAR L(ION,MN+2,CR+2:VA;0) 298.15 -15009+13.6587*T;,,, ENTER-PAR L(ION,MN+2,CR+2:VA;1) 298.15 +504+0.9479*T;,,, ENTER-PAR L(ION,MN+3,CR+3:O-2;0) 298.15 -188487.7;,,, ENTER-PAR L(IONIC,LA+3,CR+2:O-2;0) 298.15 -101850;,,, ENTER-PAR L(IONIC,LA+3,CR+3:O-2;0) 298.15 -101850;,,, ENTER-PAR L(IONIC,LA+3,CR+2:O-2;1) 298.15 -39016;,,, ENTER-PAR L(IONIC,LA+3,CR+3:O-2;1) 298.15 -39016;,,, ENTER-PAR L(IONIC,LA+3,CR+2:VA;0) 298.15 +60713-5.49*T;,,, ENTER-PAR L(IONIC,LA+3,CR+2:VA;1) 298.15 +64573-23*T;,,, ENTER-PAR L(ION,SR+2,CR+2:VA;0) 298.15 200000;,,, ENTER-PAR L(ION,SR+2,CR+3:O-2;0) 298.15 -619869;,,, ENTER-PAR L(ION,SR+2,CR+3:O-2;1) 298.15 -179575;,,, ENTER-PAR L(ION,SR+2,CR+2:O-2;0) 298.15 -619869;,,, ENTER-PAR L(ION,SR+2,CR+2:O-2;1) 298.15 -179575;,,, @@------------------------------------------------------------ @@ Cr-GAS, SGTE and reassessments by Chen, Povoden-Karadeniz ENTER-PHASE GAS G 1 CR CR1O1 CR1O2 CR1O3 O O2 O3 H2 H H2O1 H1O1 H1O2 H2O2 CRH1 CRH1O1 CRH1O2 CRH1O3 CRH2O2 CRH2O3 CRH2O4 CRH3O3 CRH3O4 CRH4O4 CRH4O5 CRH5O5 CRH6O6;,,, ENTER-PAR G(GAS,CR1O1;0) 298.15 +GCR1O1_G+RTLNP;,,, ENTER-PAR G(GAS,CR1O2;0) 298.15 +GCR1O2_G+RTLNP;,,, ENTER-PAR G(GAS,CR1O3;0) 298.15 +GCR1O3_G+RTLNP;,,, ENTER-PAR G(GAS,O;0) 298.15 +F13349T+RTLNP; 6000 N ENTER-PAR G(GAS,O2;0) 298.15 +F13704T+RTLNP; 20000 N ENTER-PAR G(GAS,O3;0) 298.15 +F14021T+RTLNP; 6000 N ENTER-PAR G(GAS,H2;0) 298.15 +H2GAS+RTLNP; 6000 N ENTER-PAR G(GAS,H;0) 298.15 +HGAS+RTLNP; 6000 N ENTER-PAR G(GAS,H2O1;0) 298.15 +F10963T+RTLNP; 20000 N ENTER-PAR G(GAS,H1O1;0) 298.15 +F10666T+RTLNP; 20000 N ENTER-PAR G(GAS,H1O2;0) 298.15 +F10729T+RTLNP; 6000 N ENTER-PAR G(GAS,H2O2;0) 298.15 +F10983T+RTLNP; 1500 N ENTER-PAR G(GAS,CRH1;0) 298.15 +F7586T+RTLNP; 6000 N ENTER-PAR G(GAS,CRH1O1;0) 298.15 +GCRH1O1_G+RTLNP;,,, ENTER-PAR G(GAS,CRH1O2;0) 298.15 +GCRH1O2_G+RTLNP;,,, ENTER-PAR G(GAS,CRH1O3;0) 298.15 +GCRH1O3_G+RTLNP;,,, ENTER-PAR G(GAS,CRH2O2;0) 298.15 +GCRH2O2_G+RTLNP;,,, ENTER-PAR G(GAS,CRH2O3;0) 298.15 +GCRH2O3_G+RTLNP;,,, ENTER-PAR G(GAS,CRH2O4;0) 298.15 +GCRH2O4_G+RTLNP;,,, ENTER-PAR G(GAS,CRH3O3;0) 298.15 +GCRH3O3_G+RTLNP;,,, ENTER-PAR G(GAS,CRH3O4;0) 298.15 +GCRH3O4_G+RTLNP;,,, ENTER-PAR G(GAS,CRH4O4;0) 298.15 +GCRH4O4_G+RTLNP;,,, ENTER-PAR G(GAS,CRH5O5;0) 298.15 +GCRH5O5_G+RTLNP;,,, ENTER-PAR G(GAS,CRH6O6;0) 298.15 +GCRH6O6_G+RTLNP;,,, ENTER-PAR G(GAS,CRH4O5;0) 298.15 +GCRH4O5_G+RTLNP;,,, @@ @@ CRO3 reference gas ENTER-PHASE CRGAS,, 1 CR1O3;,,, ENTER-PAR G(CRGAS,CR1O3;0) 298.15 +GCR1O3_G+RTLNP;,,, @@ @@ H2O reference gas ENTER-PHASE STEAM,, 1 H2O1;,,, ENTER-PAR G(STEAM,H2O1;0) 298.15 +F10963T+RTLNP; 20000 N @@ @@ O2 reference gas ENTER-PHASE O2GAS,, 1 O2;,,,
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ENTER-PAR G(O2GAS,O2;0) 298.15 +2*GHSEROO+RTLNP;,,, @@ GO PAR @@ SET-OUT-LEVEL,,,,, N,, set-interactive
Page 190
Curriculum vitae
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Curriculum Vitae
Personal data
Povoden-Karadeniz, Erwin
Date and place of birth: March 18, 1973, Graz, Austria
Education
01/2005 – 12/2008
Ph. D. thesis: „ Thermodynamic Database of the La-Sr-Mn-Cr-O Oxide System and
Applications to Solid Oxide Fuel Cells“, Nonmetallic Inorganic Materials, Prof. Dr. Ludwig
J. Gauckler, Department of Materials, ETH Zurich, Switzerland.
1992-1999
Geoscience Studies, Karl-Franzens University Graz
Master thesis: „Kontaktmetamorphose und Fluid-Gestein-Interaktion in der östlichen
Monzoni Kontaktaureole“, Prof. Dr. Georg Hoinkes and Prof. Dr. Rainer Abart
1983-1991
Realistisches Gymnasium, Pestalozzistrasse 5, Graz
1979-1983
Elementary School, Berliner Ring, Graz
Publications
R. Abart, N. Badertscher, M. Burkhard, and E. Povoden, Oxygen, carbon and strontium
isotope systematics in two profiles across the Glarus thrust: implications for fluid flow, Contr.
Miner. Petrol., 2002, 143, pp. 192-208.
Page 191
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191
E. Povoden, M. Horacek, and R. Abart, Contact metamorphism of siliceous dolomite and
impure limestones from the Werfen formation in the eastern Monzoni contact aureole, Miner.
Petrol., 2002, 76, pp. 99-120.
A.N. Grundy, E. Povoden, T. Ivas, and L.J. Gauckler, Calculation of defect chemistry using
the CALPHAD approach, Calphad, 2006, 30, pp. 33-41.
E. Povoden, A.N. Grundy, and L.J. Gauckler, Thermodynamic assessment of the Mn-Cr-O
system for solid oxide fuel cell (SOFC) materials, Int. J. Mater. Res., 2006, 97, pp. 569-78.
E. Povoden, A.N. Grundy, and L.J. Gauckler, Thermodynamic reassessment of the Cr-O
system in the framework of solid oxide fuel cell (SOFC) research, J. Phase Equilib. Diff.,
2006, 27, pp. 353-62.
E. Povoden, A.N. Grundy, M. Chen, and L.J. Gauckler, Thermodynamic assessment of the
La-Cr-O system, J. Phase Equilib.Diff., 2009, 1, pp. 12-27.
E. Povoden-Karadeniz, A.N. Grundy, M. Chen, T. Ivas, and L.J. Gauckler, Thermodynamic
assessment of the La-Fe-O system, J. Phase Equilib. Diff. (accepted)
E. Povoden, M. Chen, A.N. Grundy, and L.J. Gauckler, Thermodynamic La-Sr-Mn-Cr-O
oxide database for solid oxide fuel cell applications, to be submitted.
E. Povoden, T. Ivas, M. Chen, and L.J. Gauckler, Thermodynamic calculations of impacts of
chromium on Sr-doped Lanthanum manganite (LSM) cathodes for solid oxide fuel cells
(SOFC), to be submitted.
E. Povoden, T. Ivas, and L.J. Gauckler, Degradation of planar solid oxide fuel cells with
(La1-xSrx)1-yMnO3 cathodes and Cr-alloy interconnects, to be submitted.
Presentations
Assessment of the Cr-O system in the frame of SOFC research
E. Povoden, A.N. Grundy, and L.J. Gauckler
Page 192
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192
Poster Presentation
CALPHAD XXXIV, Maastricht, Netherlands, May 06th -11th, 2005
Thermodynamic assessment of the Cr-Mn-O system for solid oxide fuel cell (SOFC)
materials
E. Povoden
Oral Presentation
1st EMPA symposium for Ph.D. students, EMPA Dübendorf, Switzerland, October 20th, 2005
Thermodynamic Assessment of the Cr-Mn-O System for Solid Oxide Fuel Cell (SOFC)
Materials
E. Povoden, A.N. Grundy, and L.J. Gauckler
Oral Presentation
3rd Fuel Cell Research Symposium, EMPA Dübendorf, Switzerland, March 16th, 2006
Thermodynamic assessment of the La-Mn-Cr-O system for applications on solid oxide fuel
cell (SOFC) materials using the CALPHAD approach
E. Povoden, A.N. Grundy, and L.J. Gauckler
Oral Presentation
Thermo 2006, Boulder, Colorado, USA, August 4th, 2006
Thermodynamic assessment of the La-Mn-Cr-O system for applications on solid oxide fel cell
(SOFC) materials
E. Povoden, A.N. Grundy, and L.J. Gauckler
Oral Presentation
HTMC XII, Vienna, Austria, September 18th – 22nd, 2006
The BiO3/2-SbO3/2-ZnO Phase Diagram at 1115°C in air
E. Povoden, Z. Peng, and L.J. Gauckler
Poster Presentation
CALPHAD XXXVI, Pennsylvania State University, Pennsylvania, USA, May 6th – 11th,
2007
Thermodynamic assessment of the La-Cr-O and LaO3/2-MnOx-CrO3/2 Systems
Page 193
Curriculum vitae
193
E. Povoden, A.N. Grundy, and L.J. Gauckler
Oral Presentation
CALPHAD XXXVI, Pennsylvania State University, Pennsylvania, USA, May 6th – 11th,
2007
Thermodynamic modeling for solid oxide fuel cell research - The La-Sr-Mn-Cr-O system
E. Povoden
Oral Presentation
2nd MRC Graduate Symposium , ETH Zurich, June 27th, 2007
The thermodynamic LaO1.5-SrO-MnO1.5-CrO1.5 and LaO1.5-SrO-FeO1.5-CrO1.5 databases for
SOFC applications using the CALPHAD approach
E. Povoden
Oral Presentation
Guest Talk, Lehrstuhl für physikalische Chemie, Monatnuniversität Leoben, March 28th, 2008
Thermodynamic LaO1.5-SrO-MnO1.5-CrO1.5 and LaO1.5-SrO-FeO1.5-CrO1.5 databases for solid
oxide fuel cells (SOFC) applications
E. Povoden, M. Chen, A.N. Grundy, and L.J. Gauckler
Oral Presentation
CALPHAD XXXVII, Saariselkä, Finland, June 16th – 21st, 2008
Page 194
Erratum, p. 109, lines 7-14 and Table 4.3.3, p. 112
According to the latest discussion by B. Hallstedt et al., Calphad, 2007, 31(1), p 28-
37 the correct model is (La,Cr)(O,Va)3 and not (La,Cr)(O,Va)1.5: “…in case there is
information of the ordering of element X between different vacant positions in bcc
described by (Me)1(Va)1(Va)1(Va)1 this is taken into account, otherwise the
disordered model for interstitials in bcc, (Me)1(Va,X)3 is to be used…” Thus the
model was also corrected in the thermodynamic assessment of the La-Fe-O system,
Povoden-Karadeniz et al., J. Phase Equilib. Diff., accepted.
The following argumentation for modeling of the oxygen solubility in bcc using
(physically wrong!) Me(O,Va)1.5 was given in a preliminary manuscript of the La-Fe-
O system and is repeated here for the sake of clarification:
“…as there are three octahedral interstitial sites per metal atom in the bcc unit cell
located on the cube faces and cube edges Me(Va,O)3 is undoubtedly a reasonable
model description for the oxygen solubility in bcc. In previous papers the authors have
proposed the model Me(Va,O)1.5 based on the argument, that it is energetically very
unfavorable to simultaneously occupy both the octahedral interstitial sites on the cube
faces and cube edges as these lie very close to each other. A further reason why we
use this description is that for SOFC applications we are primarily interested in the
oxide portion of the phase diagram and we have found that the endmember Me(O)3
used to describe oxygen solubility in the metallic phase can inadvertently appear in
the oxide portion of the phase diagram. For these reasons, and in order to keep this
assessment compatible with our previous assessments we reassess the oxygen
solubility in bcc Fe using the model (Fe)(O,Va)1.5….”