Journal of the Ceramic Society of Japan 129 [1] 22-31 2021 ...

FULL PAPER

Effect of chemical composition on mass transferin Y2Ti2O7 under oxygen potential gradient at high temperatures

Makoto TANAKA1,³, Tsuneaki MATSUDAIRA1, Emi KAWAI1, Naoki KAWASHIMA1,Ushio MATSUMOTO1,2, Takafumi OGAWA1, Miyuki TAKEUCHI3 and Satoshi KITAOKA1,³³

1Japan Fine Ceramics Center, 2–4–1 Mutsuno, Atsuta-ku, Nagoya 456–8587, Japan2Department of Materials Science and Engineering, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606–8501, Japan3The University of Tokyo, 2–11–6 Yayoi, Bunkyo-ku, Tokyo 113–8656, Japan

The oxygen shielding properties and structural stability of polycrystalline Y2Ti2O7 (YT) solid solution wafers,which were cut from a sintered body and served as models for environmental barrier coatings, were evaluatedby the oxygen permeation technique at high temperatures. Here, we examined the effect of compositions by usingtwo samples with slightly different Y/Ti molar ratios. The oxygen permeability constants for YT increaseddramatically with a slight increment in the Y/Ti molar ratio, and the activation energy for oxygen permeationmarkedly decreased. Oxygen permeation in the YT was controlled by the diffusion of oxide ions in the crystal.Almost no decomposition of the YT phase occurred due to migration of the constituent cations at hightemperatures, indicating high structural stability under an oxygen potential gradient. The crystal structure wasidentified as the YT-based pyrochlore structure from Rietveld refinements of synchrotron radiation X-raypowder diffraction data, based on information on the composition dependence of the defect concentrations in thecrystals estimated by first principles calculations. The diffusion path for oxide ions in the crystal at hightemperature was also investigated based on a spatial distribution map described by the bond valence summethod. Finally, the mechanisms for the uptake of oxygen molecules on the YT surface exposed to a high oxygenpartial pressure and the subsequent diffusion of oxide ions in the YT crystals were clarified.©2021 The Ceramic Society of Japan. All rights reserved.

Key-words : Y2Ti2O7, Solid solutions, Oxygen permeation, Diffusion, High temperature, Defects, X-ray powderdiffraction, First-principles calculations

[Received July 28, 2020; Accepted October 20, 2020]

1. Introduction

Environmental barrier coatings (EBCs) for silicon car-bide fiber-reinforced silicon carbide ceramic matrix com-posite (SiC/SiC) components are essential in advancedairplane engines because of their capability for inhibitingoxidation and subsequent volatilization of the protectiveoxide scale under a high-temperature combustion gasenvironment.1)­3) In particular, advanced EBCs that exhibitthermal reflectivity are expected to lower the temperatureat the interface between the EBC and SiC/SiC substrate.Consequently, oxidative degradation of the SiC/SiC sub-strate would be drastically suppressed and the amount ofcooling air required for the SiC/SiC substrate would alsobe significantly reduced. A periodic layered structure

consisting of two different oxide materials having a largedifference in refractive indices is capable of reflectingthermal radiation energy, as a consequence of interferenceof electromagnetic waves.4),5) We have previously pro-posed a periodic layered EBC composed of heat-resistantoxides such as Y2Ti2O7 (YT, high index) and Al2O3 (lowindex), for reflection of thermal radiation energy as well asproviding a barrier to the oxidation and volatilization.6),7)

Each oxide layer in the EBC is exposed to a large oxy-gen potential gradient (d®O) at elevated temperatures dur-ing use, resulting in development of the driving forces forthe inward diffusion of oxide ions and outward diffusion -of cations in accordance with the Gibbs­Duhem relation-ship. In general, when only oxide ions are transfered in anoxide film exposed to d®O, the film structure is main-tained. However, the transfer of cations in the film inducesdecomposition of the film. This means that the thermalradiation energy reflection function is destroyed by thecollapse of the periodic layered EBC. Therefore, it is nec-essary to clarify the mass transfer in each of the constituentlayers to understand and control the structural stability aswell as the oxygen shielding function.

³ Corresponding author: M. Tanaka; E-mail: [email protected]

³³ Corresponding author: S. Kitaoka; E-mail: [email protected]

³³³ Preface for this article: DOI http://doi.org/10.2109/jcersj2.129.P1-1

Journal of the Ceramic Society of Japan 129 [1] 22-31 2021

DOI http://doi.org/10.2109/jcersj2.20165 JCS-Japan

©2021 The Ceramic Society of Japan22This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by-nd/4.0/),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In prior works, we have elucidated the mass transferprocesses within the candidate constituent oxides of EBCsby determining the oxygen permeability constants forwafers cut from sintered bodies serving as modelEBCs.8)­17) This technique provides accurate evaluationof the intrinsic mass transfer for environmental shieldingmaterials under steady-state conditions where the d®O

applied to the wafers and the diffusion length are keptconstant. In this technique, the upper and lower surfacesof the wafer are exposed to gases with different oxygenpartial pressures (PO2

). While the dissociative adsorption ofoxygen molecules will proceed at the higher PO2

surface[the PO2

(hi) surface], the reverse reaction progresses on theopposite surface with a lower PO2

[the PO2(lo) surface].

Therefore, the mass transfer mechanisms through the oxidefilms comprising the EBC can be simplified and analyzed.

For the case of high-purity polycrystalline Al2O3 used inperiodic layered EBCs,8)­13) the oxygen permeation pro-ceeded via grain boundary (GB) diffusion of oxide ionsfrom the PO2

(hi) surface side to the PO2(lo) surface side,

along with simultaneous GB diffusion of Al ions in theopposite direction. The chemical potentials, GB diffusioncoefficients, and fluxes of the ions in Al2O3 wafers with anapplied d®O were calculated from the oxygen permeabilityconstants. The fluxes of the ions at the outflow side of thewafer were significantly larger than those at the inflowside. Moreover, the electronic transference number nearthe PO2

(hi) surface was found to approach unity on appli-cation of a d®O. For polycrystalline YT, which is anotheroxide used in periodic layered EBCs, however, the oxygenshielding properties and the mass transfer mechanism athigh temperatures are still unknown.

YT is pyrochlore-type oxide (space group Fd�3m) withthe general formula A2B2O7, and is described as a defectivefluorite solid solution,18),19) in which cations form a face-centered cubic lattice and 1/8 of the anions are removedto ensure charge neutrality. Various properties of YT havebeen investigated with a view to considering possibleapplications in the fields of photocatalysis,20),21) dielec-trics,22),23) and fuel cells.24),25) In addition, since YT hashigh chemical stability in severe environments, it hasattracted attention as a material for safe disposal ofactinide-containing nuclear waste,26),27) the reinforcingphase in oxide particle dispersion strengthened steel,28),29)

and corrosion-resistant molten-metal containers.30),31)

In general, the electrical characteristics of pyrochloretype oxides are expressed by the diffusion of charged parti-cles in the oxides. Therefore, these characteristics stronglydepend on the chemical composition of the oxides and onthe surrounding environment to which they are exposed.It goes without saying that the oxygen shielding of EBCmaterials is also controlled by the movement of chargedparticles. Hence, we will focus on previous research on theeffects of chemical composition and PO2

on the electricalcharacteristics of YT. The total electrical conductivity ofYT in the low PO2

region is dominated by the electricalconductivity, which is proportional to the ¹1/4 power ofPO2

, while the ionic conductivity is independent of PO2

and tends to be predominant in the high PO2region. More-

over, the change in the type of electrical conduction occursat higher PO2

as the temperature increases.32),33) At lowertemperature, the conduction mechanism for electrons hasbeen experimentally shown to be hopping conductioninvoving small polarons.34),35) There is no information onthe electrical properties or the conduction mechanism forYT at temperatures above 1273K under application ofd®O.In this study, therefore, the oxygen shielding properties

and structural stability of polycrystalline YT solid solutionwafers, serving as model EBC films, were precisely eval-uated by the oxygen permeation technique at high temper-atures. In order to clarify the oxygen shielding propertiesof the YT solid solutions, the characteristics were alsocompared with that of 10mol% yttria stabilized zirconia(10YSZ), which is a typical oxide ion conductor. Thediffusion coefficients for the oxide ions and the electronictransference numbers were also determined for the YTwafers. Additionally, first-principles calculations based ondensity functional theory (DFT) were employed to assessthe concentrations of point defects over a compositionrange of YT. The local structure of YT crystals was ana-lyzed by synchrotron X-ray diffraction (XRD). Finally, theeffect of the chemical composition on the mass transfer inthe YT solid solutions under application of a d®O at hightemperatures was investigated based on the combinedresults.

2. Experimental procedure

2.1 Sample preparationRaw YT powders were synthesized by ultrasonic spray

pyrolysis, which allows for superior control of the prod-uct composition, using a precursor solution composed ofY(NO3)3 and TiCl4 aqueous solution. The Y/Ti molarratios for the aqueous solutions were controlled to fabri-cate single-phase YT solid solutions having two compo-sitions, one of which was almost stoichiometric and theother of which was Y-rich. The synthesized raw powderswere calcined at 1073K for 1 h in air. After that, the cal-cined powders were molded under a uniaxial pressure of20MPa and subjected to cold isostatic pressing at 245MPa. Subsequently, the compact bodies were sintered inair at 1973K for 5 h. In addition, a polycrystalline 10YSZsample was also prepared for comparison of the oxygenshielding properties. 10YSZ powder (TZ-10YS, Tosohceramics Co., Ltd.) was molded in the same way as the YTsamples. The compact body was sintered by two-step sin-tering. The temperature profile for the first step was heat-ing at 5K/min to 1523K, then cooling at 50K/min to1323K, followed by holding for 50 h. The profile for thesecond step was heating at 5K/min to 1773K, followedby holding for 5 h, and finally cooling at 5K/min to roomtemperature. The wafer samples were ground and polishedto a mirror-like finish to obtain polycrystalline wafer spec-imens with final dimensions of ∅11.5 to ∅23.5mm © 0.25mm. Figure 1 presents an XRD pattern for the YT-1sample obtained using Cu-K¡ radiation. The pattern

Journal of the Ceramic Society of Japan 129 [1] 22-31 2021 JCS-Japan

23

demonstrates the presence of single-phase YT, and YT-2also exhibited only the YT phase (data not shown). The Y/Ti molar ratios for the YT samples were confirmed byinductively coupled plasma optical emission spectroscopy(ICP-OES), and the results are shown in Table 1. Thenear-stoichiometric and Y-rich samples are described asYT-1 and YT-2, respectively. The Y/Ti molar ratios forYT-1 and YT-2 measured by ICP-OES were 1.006 and1.013, respectively. The relative densities of all samplesused for the oxygen permeation tests were found to bemore than 98% of the theoretical densities.

In this study, quenched YT powders were also fabricat-ed for analysis of the crystal structure of the wafer samplesduring the oxygen permeation tests at high temperatures.The YT raw powders synthesized by the same method asthe YT sintered bodies were annealed in a Pt crucible at1773K for 5 to 20 h. Subsequently, the crucible includingthe powder was taken out of the furnace at 1773K, andquenched in water at room temperature. The compositionsof the quenched YT powder samples, which were mea-sured by ICP-OES, were confirmed to be close to those ofthe corresponding wafer samples. Therefore, the symbolsfor these powder samples were the same as those used forthe wafer samples, indicated in Table 1.

2.2 Oxygen permeation testsThe oxygen permeabilities of the YT wafers were eval-

uated by a measurement procedure previously used for aseries of EBC candidate materials.8),9),12)­16) Each YTwafer was set between two alumina tubes in a furnace.Platinum gaskets were used to create a seal between thewafer and the tubes by loading weights on top of the uppertube. High-purity Ar with oxygen gas at approx. 1 Pa as animpurity was supplied to both sides of the sample at a flowrate of 1.67 © 10¹6m3/s. While monitoring PO2

in theupper and lower chambers with an oxygen sensor, a gas-tight seal was achieved by heating at 1893K. After that,when the monitored value became constant at the measure-

ment temperature, the values of PO2in the upper and lower

chambers were measured and used as the backgroundvalue. The total pressure in each chamber was 105 Pa.Then, the wafer was exposed to d®O in the thicknessdirection by supplying either pure O2 or Ar with 1 to 30-vol% O2 to the upper chamber. When the oxygen perme-ation reached a steady state after a predetermined period oftime, PO2

in the lower chamber was measured. The oxygenpermeability constant PL [mol/(m·s)] was calculated fromthe difference from the background value based on Eq. (1).

PL ¼ Cp �Q � LVst � S

; ð1Þ

where P is oxygen permeability, L is the wafer thickness,Cp is the concentration of permeated oxygen molecules, Qis the gas flow rate, Vst is the standard molar volume ofideal gas, and S is the wafer permeation area.

2.3 Diffusibility of oxide ionsOxygen permeation experiments with oxygen tracer gas

18O2 were also performed to clarify the diffusion paths ofoxide ions in the YTwafer. During the permeation test, theYT wafer was exposed to a P16O2

(hi)/P16O2(lo) of 104 Pa/

1 Pa at 1773K for 3 h. Subsequently, the 16O2 in thePO2

(hi) chamber was changed to 18O2 and maintained for240 s. Cross-sections of the exposed wafers were cut and18O mapping of the cross-sections near the PO2

(hi) sur-faces were performed by secondary ion mass spectrometry(SIMS, Nano SIMS 50L, CAMECA, France) with a Cs+

beam diameter of 80 nm. Figure 2 shows an 18O map ofthe cross-section for a YT-1 wafer after the treatment. The18O was distributed almost uniformly both inside thegrains and at the GBs, so oxide ions in the YTwafer exhib-ited lattice diffusion. The lattice diffusion coefficient, DO,for oxide ions in the YT wafer was determined from the18O concentration depth profiles. Specifically, in order toobtain clear profiles of the 18O concentration gradient atthe same temperature, a measurement temperature of1473K was selected. The retention times for YT-1 and YT-2 were set to 3240 and 600 s, respectively. After that,18O depth profiling was performed by SIMS (IMS-7f,

Fig. 1. XRD pattern of surface of YT-1 wafer.

Table 1. Chemical composition of samples

TypeY/Ti molar ratio

YT-1 YT-2

Oxygen permeation test Bulk 1.006 1.013Structural characterization Powder 1.003 1.016

Fig. 2. SIMS-18O map of cross-section near PO2(hi) surface of

YT-1 wafer exposed to P18O2(hi)/P16O2

(lo) ratio of 104 Pa/1 Pa at1773K for 240 s.

Tanaka et al.: Effect of chemical composition on mass transfer in Y2Ti2O7 under oxygen potential gradient at high temperaturesJCS-Japan

24

CAMECA, France). The DO value for the YT wafers wascalculated by a conventional method using Eq. (2).15),17)

Cz � Cs

Cbg � Cs

¼ erfz

2ffiffiffiffiffiffiffiffiDOt

p� �

; ð2Þ

where z is the penetration depth, t is the measurement time,Cz is the 18O fraction at a depth z, Cs is the 18O fraction atthe surface, and Cbg is the 18O fraction based on its naturalabundance (0.00204).

2.4 First-principles calculationsThe concentration of point defects with charge q in a

crystalline material, Dq, can be calculated from the defectformation energy via36)

CðDqÞ ¼ NsðDÞ exp � EdðDqÞkT

� �: ð3Þ

Here, C(Dq), Ed(Dq), and Ns(D) indicate the concen-tration, the defect formation energy, and the number ofsites in the lattice, respectively, associated with Dq defects.The defect formation energy is given by36)

EdðDqÞ ¼ EDFTðDqÞ � EDFTð;Þþ

Xiat�Niat ðDÞ®iat þ q®e: ð4Þ

Here, EDFT(Dq) and EDFTð;Þ are the DFT energies forthe simulation cells with Dq and without any defects,respectively. �Niat (D) is the change in the number ofatoms of iat species on creating the defect in the host, and®iat is the chemical potential of iat. ®e is the chemicalpotential of electrons, which is determined via the chargeneutrality condition among the charged defects and elec-tronic carriers, i.e., free electrons and holes, for givenvalues of the atomic chemical potential (®iat ).

In this work, the oxygen chemical potential was cal-culated from that for oxygen gas molecules based on theassumption that oxygen atoms in YT equilibrate with anideal oxygen gas which has two thermodynamic quanti-ties: oxygen partial pressure and temperature. Here, theenergy of an oxygen molecule at zero temperature wascalculated by DFT, and the NIST-JANAF thermomechan-ical table37) was referenced to obtain the free energy at afinite temperature. The chemical potentials for Y and Tiatoms were calculated to satisfy the condition that thenumber of atoms in the YT cell equals the input values.The inputs were determined from a target Y/Ti ratio underthe condition that the sum of the numbers of Y and Tiatoms equals the value for the stoichiometric composition.We examined Y/Ti ratios from 0.995 to 1.015.

DFT calculations were performed using the projectoraugmented wave (PAW) method, as implemented in theVASP code.38) For the exchange­correlation functional,we used the HSE06 hybrid functional.39) The cut-off ener-gy for planewave bases was set to 400 eV for the relaxa-tion of internal parameters only and 550 eV when thelattice constants were also optimized. The defect forma-tion energy expressed by Eq. (3) in charged systems caninvolve artificial contributions due to interactions between

periodically aligned supercells and unintended electrostaticpotential shifts, so the correction of the generalized-FNVscheme40),41) was adopted by using a dielectric constant of50, which is near the experimental value of 5442) and ourcalculated value of 50.3 within the GGA-functional frame-work. The cubic unit cell of the pyrochlore structure wasused in the calculations of defect formation energies andthe Brillouin zone was sampled by using a 2 © 2 © 2k-grid mesh.

2.5 Analysis of crystal structureThe crystal structures of the YT solid solutions were

accurately analyzed by powder XRD patterns obtainedusing a synchrotron X-ray diffractometer (PILATUS100K, DECTRIS Ltd.) with an energy of 16.9 keV, a stepsize of 0.01°, and an exposure time of 300 s. Diffractiondata for CeO2 were used to correct the wavelength of thesynchrotron X-rays. The quenched powders were loadedinto a Lindemann glass capillary with a diameter of 0.3mm. The transmittance of the powder in the capillary wasmeasured to correct for the effect of absorption, and thenthe corrections were reflected in the structural analysis.Structural parameters were refined by the Rietveld methodusing RIETAN-FP.43) The crystal structure model em-ployed for the Rietveld analysis was determined based onthe chemical composition of the defect concentration in theYT crystal estimated by the first-principles calculationsdescribed in section 2.4. The migration route of oxide ionsin the crystal was analyzed by bond valence sum (BVS)calculations using the computer program PyAbstantia.44)

The resulting BVS map was drawn using VESTA.45)

3. Results and discussion

3.1 Oxygen permeabilityThe oxygen permeability constant, PL, for YT-1, YT-2,

and 10YSZ was measured under a constant d®O with aPO2

(hi)/PO2(lo) ratio of 105 Pa/1 Pa at temperatures rang-

ing from 1273 to 1773K. Figure 3 shows the relationshipbetween the PL and the reciprocal of absolute temperature.The PL for YT-1 was almost same as that for 10YSZ at1773K, but became smaller than that for 10YSZ at lowertemperatures. The log(PL) values for all samples wereproportional to T¹1. The PL for YT-2 was significantlylarger than those for YT-1 and YSZ, and the slope of thestraight line for YT-2 was smaller than that for YT-1.Hence, the PL value for YT was found to greatly increasewith only a slight increment in the Y/Ti molar ratio.Figure 4 shows the PL values for the samples as a

functions of PO2(hi) at 1773K, at a constant PO2

(lo) of1 Pa. The larger the PO2

(hi) value on the horizontal axis,the larger the d®O becomes. The PL values for all samplesgrew proportionally with the PO2

(hi) value on a loga-rithmic scale. The power constants, n, of YT-1 and YT-2corresponding to the slopes of these straight lines were 1/6and 1/4, respectively. The n value for YT-2 was the sameas that for 10YSZ. The n value depends on the valence ofdefects, namely diffusing charged species, generated orannihilated on the PO2

(hi) surface. Therefore, the mass

Journal of the Ceramic Society of Japan 129 [1] 22-31 2021 JCS-Japan

25

transfer of YT appeared to be drastically changed by only aslight shift in the chemical composition to the Y-rich side.

As an example, Fig. 5 shows SEM micrographs ofPO2

(hi) and PO2(lo) surfaces and cross-sections of the

YT-1 wafer exposed to PO2(hi)/PO2

(lo) ratio of 105 Pa/1 Pa at 1773K for 10 h. Thermal etching-type equilibriumgrooves are observed along the GBs on both surfaces. Inaddition, energy dispersive X-ray spectroscopy analysisof the cross-sections near both surfaces confirmed that nocomposition change occurred. Therefore, the decompo-sition of the YT phase due to migration of the constit-uent cations was negligible at high temperatures. In otherwords, the YT solid solutions appeared to maintain struc-tural stability at high temperatures during the applicationof d®O.

Then, the activation energy for oxygen permeationthrough the YT wafers was determined based on the PLvalues. The PL values can be expressed by Eq. (5) withPO2

(hi) and PO2(lo).12),15),16)

PL ¼ AO½PO2ðhiÞn � PO2

ðloÞn� ð5Þ

where AO is an experimental constant and n is a powerconstant determined from the PO2

dependence of the PLvalue shown in Fig. 4. AO is given by the Arrhenius formof Eq. (6).

AO ¼ A�O exp

�QðkJ=molÞRT

� �ð6Þ

where R is the gas constant, T is the absolute temperature,Q is the activation energy, and A�

O is the frequency factor.Figure 6 presents an Arrhenius plot of AO for each

wafer exposed to a PO2(hi)/PO2

(lo) ratio of 105 Pa/1 Pa.The A�

O values for YT-1, YT-2 and 10YSZ were 3.472mol·s¹1 Pa­1/6, 2.481 © 10¹3 and 1.493 © 10¹3

mol·s¹1 Pa­1/4, respectively. Additionally, the oxygen per-meation activation energies for YT-1, YT-2 and 10YSZwere 269, 151 and 172 kJ/mol, respectively. The activa-tion energies for the YT wafers determined in this studywere relatively larger than those (103,32) 79 kJ/mol33))determined from the electrical conductivity of YT fabri-cated by the solid-phase method at high temperature. Incontrast, the activation energy for 10YSZ was close to thepreviously reported value (199 kJ/mol46)).

3.2 Diffusibility of oxide ionsThe diffusion coefficient and transport number for oxide

ions in YT-1 and YT-2 were determined from the oxygen

Fig. 3. Oxygen permeability constants as a function of T¹1 forYT-1, YT-2 and 10YSZ wafers exposed to PO2

(hi)/PO2(lo) ratio

of 105 Pa/1Pa.

Fig. 4. Oxygen permeability constants, PL, for YT-1, YT-2 and10YSZ wafers as function of PO2

(hi) values at 1773K, holdingPO2

(lo) constant at 1 Pa.

Fig. 5. SEM micrographs of PO2(hi) and PO2

(lo) surfaces andcross-sections of YT-1 wafer exposed to PO2

(hi)/PO2(lo) ratio of

105 Pa/1Pa at 1773K for 10 h.

Tanaka et al.: Effect of chemical composition on mass transfer in Y2Ti2O7 under oxygen potential gradient at high temperaturesJCS-Japan

26

permeation data using a conventional technique.13),15) Theoxygen permeation constant, Px, at an arbitrary position, x,in the wafer depth direction is expressed by Eq. (7).

Px ¼ AO½PO2ðxÞn � PO2

ðloÞn� ð7Þwhere PO2

(x) is defined as PO2in equilibrium with the

chemical potential of oxygen at position x. Hence Eq. (8)is derived by combining Eqs. (5) and (7).

x

L¼ PO2

ðxÞn � PO2ðloÞn

PO2ðhiÞn � PO2

ðloÞn ð8Þ

Therefore, the PO2(x) value at an arbitrary position in

the film thickness direction can be obtained for a film sub-jected to a d®O consisting of PO2

(hi) and PO2(lo). Further-

more, the diffusion coefficient for oxide ions, DO, can beexpressed by Eq. (9).

DO ¼ nAO

CO � te0PO2

ðxÞn ð9Þ

Here, CO is the molar concentration of oxide ions perunit volume, and te0 is the electronic transference number.That is, the DO value at an arbitrary position in the filmgiven by Eq. (9) depends on PO2

(x) and te0 . In this study,te0 for each wafer was assumed to be constant in the filmthickness direction.

Figure 7 presents plots of erf ¹1[(Cz ¹ Cs)/(Cbg ¹ Cs)]as a function of the penetration depth for the YT-1 and YT-2 wafers exposed to a P18O2

(hi)/P16O2(lo) ratio of 104 Pa/

1 Pa at 1473K. The DO values for oxide ions were deter-mined from the slopes of the straight lines approximatedby Eq. (2). The DO values for oxide ions in YT-1 and YT-2measured at 1473K were 1.26 © 10¹14 and 8.93 © 10¹13

m2·s¹1, respectively. This indicated that DO increased sig-nificantly when the chemical composition of YT becameslightly Y-rich. Figure 8 shows the equilibrium partialpressure of oxygen, PO2

(x), as a function of the normalizedthickness, x/L, for YT-1 and YT-2 wafers exposed to aPO2

(hi)/PO2(lo) ratio of 104 Pa/1 Pa at 1473K. The differ-

ence in the shape of the curves reflects the difference in then values. In order to calculate DO at an arbitrary position

in the wafer by substituting the PO2(x) value in Fig. 8 into

Eq. (9), the corresponding te0 value is required. If te0 isassumed to be constant in the wafer thickness direction, itcan be determined by a curve through the experimentalvalue shown in Fig. 7, calculated using Eq. (9) with thePO2

(x) values. Figure 9 presents DO for oxide ions as afunction of the normalized thickness, x/L, for YT-1 andYT-2 wafers exposed to a PO2

(hi)/PO2(lo) ratio of 104 Pa/

1 Pa at 1473K. The electronic transference numbers forYT-1 and YT-2 determined from Fig. 9 were 0.70 and0.33, respectively. The contribution of ionic conductivitywas found to be markedly increased by a slight increase inY content.

3.3 Concentrations of point defectsIn order to investigate the stability of point defects in

YT using DFT, we examined the following intrinsic pointdefects: V ��

Oð48fÞ, V��Oð8bÞ, O

00ð8aÞ, V

0000Ti , V

00Y, Ti

�Y, Y

0Ti, and Ti0Ti.

The formal charges of ions were assumed to be maintained

Fig. 6. Arrhenius plots of AO for YT-1, YT-2 and 10YSZwafers exposed to PO2

(hi)/PO2(lo) ratio of 105 Pa/1Pa.

Fig. 7. Plots of erf ¹1[(Cz ¹ Cs)/(Cbg ¹ Cs)] as function of pen-etration depth for YT-1 and YT-2 wafers exposed to P18O2

(hi)/P16O2

(lo) of 104 Pa/1 Pa at 1473K.

Fig. 8. Equilibrium partial pressure of oxygen as function ofnormalized thickness, x/L, for YT-1 and YT-2 wafers exposed toPO2

(hi)/PO2(lo) of 104 Pa/1Pa at 1473K.

Journal of the Ceramic Society of Japan 129 [1] 22-31 2021 JCS-Japan

27

except in the case of Ti0Ti, which is a small polaron formedby an electron localized on a Ti atom. The obtained con-centrations of point defects in YT at 1600K under PO2

of104 Pa are shown in Fig. 10. The concentrations of V ��

Oð8bÞ,V 0000Ti , V

000Y , free electrons and holes are not displayed in the

figure because they are smaller than the lower limit. Wesummarize the insights gained on the defect chemistry ofYT in the following three points:

i) The concentration of the small polaron Ti0Ti is prom-inently higher than that of free electrons. The formation ofsmall polaron with trapped electrons in YT has beendiscussed based on the results of electric conductivity andthermoelectric power measurements.33)­35) In these pre-vious studies, the polarons were considered to form onlyon oxygen vacancies. In contrast, our calculation resultsshow the possibility of the formation of a self-trapped

polaron (Ti0Ti) as a source of the small polarons in YT. Inour calculations, oxygen vacancies with doubly trappedelectrons (V�

Oð48fÞ) are also stabilized, and were confirmedto reach a concentration comparable to that of Ti0Ti depend-ing on the equilibrium conduction. However, these areoutside the scope of this paper and omitted here in theinterest of brevity.ii) Y0

Ti and Ti�Y are balanced at compositions near stoi-chiometry (Y/Ti³1.0), which suggests cation mixing asobserved in Yb2+xTi2¹xO7¹x/2 solid solutions,47) but thebalance is easily upset by a change in Y/Ti ratio. The con-centration of Y0

Ti becomes large compared to that of Ti�Y asY/Ti increases on the Y-rich side and is balanced withV ��Oð48fÞ.iii) V ��

Oð48fÞ is predominant over a wide examined rangecompared to V ��

Oð8bÞ. Consequently, oxygen vacancies areconsidered to be mostly formed at 48f sites during theoxygen permeation tests. We also found that the concen-tration of V ��

Oð48fÞ is appreciably larger than that of O00ð8aÞ for

Y-rich conditions (Y/Ti > 1.0).Additionally, we examined the temperature dependence

of concentrations of point defects for the O2- and Y2O3-rich condition and confirmed that similar tendencies to theabove three points were commonly found in the temper-ature range in which the oxygen permeation tests wereperformed.

3.4 Analysis of crystal structureThe crystal structure of the quenched YT powders with

different Y/Ti ratios, which was believed to be maintainedduring the oxygen permeation tests at 1773K, was clar-ified by synchrotron XRD measurements and subsequentRietveld analysis. The crystal structure model for theRietveld analysis was determined based on the defectconcentrations estimated by first-principles calculations.As described in section 3.3, the concentration of Y0

Ti

increases with increasing Y/Ti ratio, while that of Ti�Ydecreases. For the case of the stoichiometric composi-tion of Y/Ti = 1, the concentration of these defects is thealmost same. Therefore, a condition was set for the occu-pancy factors for the cation sites under which mixing ofcations positioned in 16d and 16c sites can occur. Becausethe concentration of V ��

Oð48fÞ was calculated to be signifi-cantly higher than that of V ��

Oð8bÞ, the oxygen vacancieswere assumed to exist only as V ��

Oð48fÞ. In addition, whenthe Y/Ti ratio was greater than 1, the concentration ofO00

ð8aÞ was extremely low compared with the other defectsas shown in Fig. 10. Therefore, it was assumed that O00

ð8aÞwas never formed in the quenched powders. Furthermore,the occupancy factors for each site were constrained tomaintain both the Y/Ti ratios confirmed by ICP-OES andelectrical neutrality.Figure 11 presents a Rietveld refinement pattern ob-

tained from the YT-1 powder. The experimental pattern iscoincident with the calculated one. Table 2 summarizesthe structural parameters and reliability indices obtainedby Rietveld refinement with the pyrochlore structure(space group Fd�3m). The accuracy of the fitting is

Fig. 9. Diffusion coefficients for oxygen as a function ofnormalized thickness, x/L, for YT-1 and YT-2 wafers exposed toPO2

(hi)/PO2(lo) of 104 Pa/1Pa at 1473K, with electronic trans-

ference numbers of 0.70 and 0.33, respectively.

Fig. 10. Concentration of point defects in Y2Ti2O7 as functionof Y/Ti ratio, obtained from DFT calculations at 1600K underPO2

of 104 Pa.

Tanaka et al.: Effect of chemical composition on mass transfer in Y2Ti2O7 under oxygen potential gradient at high temperaturesJCS-Japan

28

sufficient to derive the crystal structure factor from theobtained reliability indices. The lattice constant, the degreeof cation mixing, the coordinates of the 48f site, and theisotropic atomic displacement parameter for each site forthe quenched powders with different Y/Ti ratios arealmost the same.

Figure 12 shows a BVS map for oxide ions in YT-1viewed along the [100] direction with a quarter of the unitcell. The yellow region is related to the migration route ofthe oxide ions, which move away from the 8b sites. It isclear that the 48f sites and the vicinity of the 8a sites arethe main route for the oxide ions. These tendencies werethe same as those for YT-2.

3.5 Mass transfer mechanismThe mass transfer mechanism through the YT will be

discussed based on the obtained oxygen permeation data

and the crystal structure analysis including the defects. Thepower constants, n, determined from the d®O dependenceof the PL values shown in Fig. 4, were related to theuptake reaction of oxygen molecules on the PO2

(hi) sur-face. Since n for YT-1 is 1/6, it is presumed that the oxy-gen molecules were adsorbed and dissociated, followed bybeing incorporated in the O00

ð8aÞ sites on the PO2(hi) surface,

according to the reaction in Eq. (10).

1=2O2 ! O00ð8aÞ þ 2h� ð10Þ

The equilibrium constant for Eq. (10) is expressed byEq. (11).

KEq:8 ¼O00

ð8aÞ� �

p2

P1=2O2

ð11Þ

Eq. (12) is derived by substituting p ¼ 2 O00ð8aÞ

� �into

Eq. (11).

O00ð8aÞ

� � ¼ KEq:9

3

� �1=3

P1=6O2

/ P1=6O2

ð12Þ

Hence, [O00ð8aÞ] on the PO2

(hi) surface is proportional toPO2

to the 1/6-th power. However, when the Y/Ti molar

Fig. 11. Rietveld refinement pattern for YT-1. Red crosses and blue lines denote observed and calculatedintensities, respectively. Green marks are positions of Bragg reflections. The line at the bottom plots thedifferences between observed and calculated intensities.

Table 2. Crystallographic parameters and reliability indices forsamples

Y/Ti molar ratio 1.003 1.016

Crystallographic parametersa (¡) 10.09750(2) 10.09750(2)µtheo (g/cm3) 4.975999 4.981536x (O48f ) 0.32812(9) 0.32830(8)g (Y; 16d) 0.9842(10) 0.9825(9)g (Y; 16c) 0.0173(10) 0.0254(9)g (Ti; 16d) 0.0158(10) 0.0175(9)g (Ti; 16c) 0.9827(10) 0.9746(9)g (O; 48f ) 0.9998(10) 0.9987(9)g (O; 8a) 0 0g (O; 8b) 1 1U (16d) (¡2) 0.00692(7) 0.00694(6)U (16c) (¡2) 0.00559(9) 0.00574(8)U (48f ) (¡2) 0.00733(25) 0.00693(22)U (8b) (¡2) 0.00313(54) 0.00243(48)

Reliability indicesRwp 5.078 4.177RB 1.374 1.561RF 0.918 1.034S 0.6037 0.4596

Fig. 12. BVS map for oxide ion in YT-1 viewed along the[100] direction with quarter unit cell. The isosurface level is 0.4.

Journal of the Ceramic Society of Japan 129 [1] 22-31 2021 JCS-Japan

29

ratio is 1 or more, [O00ð8aÞ] in the crystal is extremely small

compared with [V ��Oð48fÞ]. In other words, the defect species

predicted from the oxygen permeation data, in which theymainly contributes to the uptake of oxygen molecules onthe PO2

(hi) surface, is different from that estimated fromthe first-principles calculations in Fig. 10. The reason forthis discrepancy is probably related to the fact that theoxygen permeation data were acquired in the steady state,whereas the defect concentrations obtained by the first-principles calculations were estimated by assuming a ther-modynamic equilibrium state. That is, because [V ��

Oð48fÞ] isrelatively low for compositions close to the stoichiometriccomposition, inward migration of oxide ions throughV ��Oð48fÞ and the vicinity of O00

ð8aÞ inside YT is considered tobe slow. Consequently, V ��

Oð48fÞ sites on the PO2(hi) sur-

face and in its vicinity were saturated immediately by theuptake of oxygen molecules around them during oxygenpermeation, so that O00

ð8aÞ might act as the main uptakesites.

On the other hand, since n for YT-2 is 1/4, the incor-poration mechanism for oxygen molecules into the PO2

(hi)surface is different from that for YT-1. To order to satisfythe electrical neutrality condition, a large amount of V ��

Oð48fÞis introduced into the crystal according to Eq. (13) asshown in Fig. 10.

Y2O3 ! 2Y0Ti þ 3O�

O þ V ��Oð48fÞ ð13Þ

Additionally, since the contribution of ionic conductionin YT-2 was concluded to be clearly larger than that in YT-1 by considering the te0 values determined by the oxygenpermeation tests, migration of the oxide ions throughV ��Oð48fÞ sites and the vicinity of O00

ð8aÞ was thought to beaccelerated by the material being highly Y-rich. As aresult, the reactions in Eqs. (10) and (14) can progresssimultaneously without annihilation of V ��

Oð48fÞ sites on thePO2

(hi) surface during oxygen permeation. The equilib-rium constant for Eq. (14) is expressed by Eq. (15).

1=2O2 þ V ��O ! O�

O þ 2h� ð14Þ

KEq:12 ¼p2

P1=2O2

V ��Oð48fÞ

� � ð15Þ

At this point, the relationship in Eq. (16) is defined bysatisfying charge neutrality

2 V ��Oð48fÞ

� �� Y0Ti

� �þ p� 2 O00ð8aÞ

� � ¼ 0 ð16Þ

[V ��Oð48fÞ] and [Y0

Ti] are much larger than p and [O00ð8aÞ] so

the relational expressions of 2½V ��O� � ½Y0

Ti� ’ 0 and p =2[O00

ð8aÞ] are established. Moreover, [V ��Oð48fÞ] can be consid-

ered to be independent of the PO2(hi) value. Eventually,

Eq. (17) is derived from Eq. (15). Therefore, [O00ð8aÞ] on the

PO2(hi) surface is proportional to PO2

to the 1/4-th power.

O00ð8aÞ

� � ¼ 1

2KEq:12 V ��

Oð48fÞ� � 1=2P1=4O2

/ P1=4O2

ð17Þ

Finally, the oxygen permeation activation energies forYT-1 and YT-2 will be discussed. As described in section3.4, the U values and the migration route of the oxide ions

in the YT-1 crystal were almost the same as those for YT-2. From these results, the migration route and the corre-sponding height of the diffusion barrier are believed to bealmost the same independent of the chemical composition.Nevertheless, the activation energy for oxygen permeationstrongly depends on the composition. This is probablyrelated to the fact that [V ��

Oð48fÞ] for YT-1 increases expo-nentially with rising temperature, while that for YT-2 isalmost constant. Actually, the activation energy differencebetween YT-1 and YT-2, 118 kJ/mol, is close to the defectformation energy for V ��

Oð48fÞ at 1773K for the chemicalcomposition of YT-1, 114 kJ/mol, which was estimated byfirst-principles calculations. Therefore, it is reasonable toconclude that the exponential increase in [V ��

Oð48fÞ] for YT-1is due to the rise in temperature.

4. Conclusion

The oxygen shielding properties and structural stabilityof YT solid solutions having slightly different chemicalcompositions, YT-1 and YT-2, were quantitatively eval-uated by the oxygen permeation technique in the temper-ature range from 1273 to 1773K. The results showed thatthe oxygen permeability constants increased significantlywith only a slight increase in the Y/Ti molar ratio, and thecorresponding activation energy was clearly lowered.Oxygen permeation in both YT samples was controlledby the diffusion of oxide ions in the crystal lattice. Thedecomposition of the YT phase due to migration of theconstituting cations at high temperatures was negligible.Therefore, the YT solid solutions were considered tomaintain structural stability at high temperatures duringthe application of d®O.For YT-1 having a near-stoichiometric composition,

oxygen molecules around the PO2(hi) surface were incor-

porated into O00ð8aÞ sites on the surface exposed to d®O. For

YT-2 having an Y-rich composition, they were taken intoV ��Oð48fÞ sites on the surface, for which [V ��

Oð48fÞ] was inde-pendent of the PO2

(hi) values, in addition to the O00ð8aÞ sites.

Moreover, the migration route for oxide ions in the crystalat high temperature was investigated based on the spatialdistribution map described by the BVS method. The crys-tal structure was identified as the YT-based pyrochlorestructure from Rietveld refinement of synchrotron radia-tion X-ray powder diffraction data, based on informationon the composition dependence of the defect concentra-tions in the crystals estimated by the first principle calcu-lations. The migration route for the oxide ions in the crys-tals and the corresponding height of the diffusion barrierare thought to be almost the same regardless of the dif-ference in chemical composition. Nevertheless, the acti-vation energy for oxygen permeation strongly dependedon the composition. This is probably related to the factthat [V ��

Oð48fÞ] for YT-1 increased exponentially with risingtemperature, while that for YT-2 was almost constant.

Acknowledgement This work was supported in part byJSPS KAKENHI Grant Number JP19H05792, and theNanotechnology-Platform-Project by the Ministry of Educa-

Tanaka et al.: Effect of chemical composition on mass transfer in Y2Ti2O7 under oxygen potential gradient at high temperaturesJCS-Japan

30

tion, Culture, Sports, Science and Technology, Japan GrantNumber JPMXP09A19UT0035, Advanced Low CarbonTechnology Research and Development Program from theJapan Science and Technology Agency.

References1) K. N. Lee, D. S. Fox, J. I. Eldridge, D. Zhu, R. C.

Robinson, N. P. Bansal and R. A. Miller, J. Am. Ceram.Soc., 86, 1299­1306 (2003).

2) H. E. Eaton and G. D. Linsey, J. Eur. Ceram. Soc., 22,2741­2747 (2002).

3) K. N. Lee, Surf. Coat. Tech., 133–134, 1­7 (2000).4) T. Naganuma and Y. Kagawa, Acta. Mater., 52, 5645­

5653 (2004).5) M. J. Kelly, D. E. Wolfe and J. Singh, Int. J. Appl.

Ceram. Tec., 3, 81­93 (2006).6) M. Tanaka, T. Matsudaira, M. Wada, S. Kitaoka, M.

Yoshida, O. Sakurada and Y. Kagawa, J. Soc. Mater.Sci. Jpn., 64, 431­437 (2015).

7) M. Tanaka, S. Kitaoka, M. Yoshida, O. Sakurada, M.Hasegawa, K. Nishioka and Y. Kagawa, J. Eur. Ceram.Soc., 37, 4155­4161 (2017).

8) M. Wada, T. Matsudaira and S. Kitaoka, J. Ceram. Soc.Jpn., 119, 832­839 (2011).

9) T. Matsudaira, M. Wada, T. Saitoh and S. Kitaoka, Acta.Mater., 59, 5440­5450 (2011).

10) T. Ogawa, A. Kuwabara, C. A. J. Fisher, H. Moriwake,K. Matsunaga, K. Tsuruta and S. Kitaoka, Acta. Mater.,69, 365­371 (2014).

11) T. Ogawa, S. Kitaoka, A. Kuwabara, C. A. J. Fisher andH. Moriwake, Scripta Mater., 100, 66­69 (2015).

12) S. Kitaoka, J. Ceram. Soc. Jpn., 124, 1100­1109 (2016).13) T. Matsudaira, S. Kitaoka, N. Shibata, Y. Ikuhara, M.

Takeuchi and T. Ogawa, Acta. Mater., 151, 21­30(2018).

14) S. Kitaoka, T. Matsudaira, D. Yokoe, T. Kato and M.Takata, J. Am. Ceram. Soc., 100, 3217­3226 (2017).

15) M. Wada, T. Matsudaira, N. Kawashima, S. Kitaoka andM. Takata, Acta. Mater., 135, 372­381 (2017).

16) S. Kitaoka, T. Matsudaira, M. Wada, T. Saito, M.Tanaka and Y. Kagawa, J. Am. Ceram. Soc., 97, 2314­2322 (2014).

17) T. Nakagawa, I. Sakaguchi, N. Shibata, K. Matsunaga,T. Mizoguchi, T. Yamamoto, H. Haneda and Y. Ikuhara,Acta. Mater., 55, 6627­6633 (2007).

18) N. Mizutani, Y. Tajima and M. Kato, J. Am. Ceram.Soc., 59, 168 (1976).

19) T. A. Schaedler, O. B. Fabrichnaya and C. G. Levi,J. Eur. Ceram. Soc., 28, 2509­2520 (2008).

20) M. Higashi, R. Abe, K. Sayama, H. Sugihara and Y.Abe, Chem. Lett., 34, 1122­1123 (2005).

21) R. Abe, M. Higashi, K. Sayama, Y. Abe and H.Sugihara, J. Phys. Chem. B, 110, 2219­2226 (2006).

22) J. Y. Ding, Y. Xiao, Z. F. Wang, L. X. Wang and Q. T.Zhang, J. Inorg. Mater., 26, 327­331 (2011).

23) J. Y. Ding, Y. Xiao, Y. Lu, T. T. Tao and Q. T. Zhang,Rare Metals, 30, 624­627 (2011).

24) J. K. Gill, O. P. Pandey and K. Singh, Int. J. HydrogenEnerg., 37, 3857­3864 (2012).

25) S. Kramer, M. Spears and H. L. Tuller, Solid StateIonics, 72, 59­66 (1994).

26) L. Kong, Y. Zhang and I. Karatchevtseva, J. Nucl.Mater., 494, 29­36 (2017).

27) K. Zhang, G. Wen, H. Zhang and Y. Teng, J. Nucl.Mater., 465, 1­5 (2015).

28) S. Yamashita, N. Akasaka and S. Ohnuki, J. Nucl.Mater., 329–333, 377­381 (2004).

29) V. Badjeck, M. G. Walls, L. Chaffron, J. Malaplate andK. March, J. Nucl. Mater., 456, 292­301 (2015).

30) S. T. Nguyen, T. Nakayama, H. Suematsu, T. Suzuki, M.Nanko, H. B. Cho, M. T. T. Huynh, W. Jiang and K.Niihara, J. Eur. Ceram. Soc., 35, 2651­2662 (2015).

31) M. Nagasaka, M. Yoshida, O. Sakurada, M. Tanaka, S.Kitaoka and O. Yamakawa, Zairyo-to-Kankyo, 64, 240­243 (2015).

32) K. Uematsu, K. Shinozaki, O. Sakurai, N. Mizutani andM. Kato, J. Am. Ceram. Soc., 62, 219­221 (1979).

33) S. Yamaguchi, K. Kobayashi, K. Abe, S. Yamazaki andY. Iguchi, Solid State Ionics, 113–115, 393­402 (1998).

34) D. Goldschmidt and H. L. Tuller, Phys. Rev. B, 34,5558­5561 (1986).

35) D. Goldschmidt, Cryst. Latt. Def. Amorp., 15, 203­209(1987).

36) C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer,G. Kresse, A. Janotti and C. G. Van de Walle, Rev. Mod.Phys., 86, 253­305 (2014).

37) M. W. Chase, Jr., “NIST-JANAF ThermochemicalTables”, American Institute of Physics, Woodbury, NY(1998).

38) G. Kresse and J. Furthmüller, Phys. Rev. B, 54, 11169­11186 (1996).

39) J. Heyd, G. E. Scuseria and M. Ernzerhof, J. Chem.Phys., 118, 8207­8215 (2003).

40) C. Freysoldt, J. Neugebauer and C. G. Van de Walle,Phys. Rev. Lett., 102, 016402 (2009).

41) Y. Kumagai and F. Oba, Phys. Rev. B, 89, 195205(2014).

42) T. T. Tao, L. X. Wang and Q. T. Zhang, J. Alloy.Compd., 486, 606­609 (2009).

43) F. Izumi and K. Momma, Solid State Phenom., 130, 15­20 (2007).

44) S. Nishimura, PyAbstantia (2017) http://shinichinishimura.github.io/pyabst/.

45) K. Momma and F. Izumi, J. Appl. Crystallogr., 44,1272­1276 (2011).

46) E. L. Courtright and J. T. Prater, US DOE Rep., PNL-SA-20302 (1992).

47) K. Asai, M. Tanaka, T. Ogawa, U. Matsumoto, N.Kawashima, S. Kitaoka, F. Izumi, M. Yoshida and O.Sakurada, J. Solid State Chem., 287, 121328 (2020).

Journal of the Ceramic Society of Japan 129 [1] 22-31 2021 JCS-Japan

31