Ionic conductivity in nano-scale CeO2/YSZ heterolayers

1

Ionic Conductivity in Nano-Scale CeO2/YSZ Heterolayers

Thi X. T. Sayle, a

Stephen C. Parkerb and Dean C. Sayle*

a

a Dept. Environmental and Ordnance Systems, Cranfield University, Defence Academy of the United

Kingdom, Shrivenham, Swindon, UK.

b Dept. Chemistry, University of Bath, Claverton Down, Bath, Avon, UK.

* corresponding author [email protected]

ABSTRACT CeO2 based materials are promising candidates as solid oxide electrolytes within fuel cell systems. In this

capacity, the oxygen anion conductivity is pivotal. Sata et al., [Nature 408, 946-949, 2000] demonstrated

the ability to ‘fine tune’ conductivities in BaF2 and CaF2 by generating BaF2/CaF2 heterolayers with

different nanoscale film thicknesses. The resulting fluoride ion conductivities were found to be orders of

magnitude higher compared with the component BaF2 and CaF2 materials. Similarly, it may be possible

to fabricate CeO2 thin films with tuneable conductivities. In this study, we explore this possibility using

atomistic simulation. In particular, simulated amorphisation and recrystallisation was used to generate an

atomistic model for a CeO2/YSZ (yttrium stabilised zirconia) heterolayered system and, using this model,

the ionic diffusivity, conductivity and associated activation energy barriers were calculated. However, in

contrast to the BaF2/CaF2 system, the heterolayered CeO2/YSZ system did not exhibit exemplary

transport properties compared with the parent materials. This study describes a framework simulation

procedure, which can be used in partnership with experiment, to explore a variety microstructural features

that may facilitate an increase in the ionic conductivity of heterolayered systems.

INTRODUCTION Ceria, CeO2 has attracted much interest recently, owing to its exploitation in a diverse range of

applications spanning, for example, exhaust catalysis to solid oxide fuel cells [1

2

3]. There are several

attributes associated with ceria that make this material useful in the various applications: In catalysis,

ceria can expose, at its surface, labile surface oxygen ions [4 5

6 7 8], which is important with respect to

automobile exhaust catalysis because the surface oxygens can be easily extracted to oxidize CO to CO2 [4

9]. Moreover, the material has the ability to release a high percentage of oxygen, which is necessary to

2

promote tenable oxidations (for a related reference see [10

]). Notwithstanding the high level of oxygen

loss, the reduced material xxx

OCeCe

2

3

2

4

21remains stable and retains its fluorite structure to high (over

1000oC) temperatures (for example see: [

11]), which also facilitates facile transport of oxygen ions

through the lattice. These essential attributes enable ceria to store and transport oxygen to the surfaces to

facilitate oxidation. Once the oxygen has been extracted, the resulting surface vacancy must move

relatively easily to the ‘bulk’ [12

] thereby replenishing the surface oxygens. The oxygen debt then has to

be repaid for the system to act as a catalyst. This can be achieved by extracting oxygen from another

exhaust gas – NO2 – and reducing this material to N2 [13

]. CeO2 acts therefore as a dual oxidiser/reductor.

Here, oxygen anion conduction is central in maintaining the process.

The ability to increase or to control the oxygen anion conductivity within CeO2 would have important

implications for applications such as fuel cells and catalysis. Indeed, considerable efforts are being made

in this area, which reflects the importance of this material. These include, for example, doping with a

variety of materials [14

], supporting the material on a substrate [15

16

], traversing down to the nanoscale

(nanoparticles, nanorods) [17

18

9]. A milestone in solid-state chemistry/physics was the ability to generate

‘tuneable’ properties via structural manipulation. In particular Sata and co-workers, showed that the

fluoride ion conductivity of BaF2/CaF2 heterolayers could be controlled by modifying the thickness of the

BaF2 and CaF2 heterolayers. Clearly, the ability to control (as compared with simply increase) the oxide

ion conductivity and hence the transport of oxygen ions within CeO2 via a structural manipulation is an

intriguing possibility.

Here, we explore, using atomistic computer simulation, whether a system comprising thin films of CeO2,

sandwiched between thin films of YSZ, influences the oxide ion conductivity compared with the

component bulk materials. Our aim is to change the oxygen ion conductivity in ceria by generating

CeO2/YSZ heterolayers in an analogous fashion to that demonstrated by Sata and co-workers [19

] on

BaF2/CaF2 heterolayers. In the first part of the study we describe how realistic models for CeO2/YSZ

heterostructures can be generated, and in the second, the self diffusion, ionic conductivity and associated

activation energies are calculated and compared with the component CeO2 and YSZ materials.

One of the central requirements for modelling ionic conductivity in a complex heterolayered system, is to

ensure that all the significant microstructural features that are likely to influence ionic transport are

considered [20

]. These include, for example, interfacial configurations, misfit dislocations, low interfacial

3

densities, point defects including vacancies, interstitials and substitutionals, intermixing across the

interfacial layers, lattice strain, grain boundaries. All of which can have a profound influence on the

conductivity [21

]. One advantage of atomistic simulation over experiment is that one can explore the

influence of structural features individually and in isolation to see what effect each has on the

conductivity. For example, it is possible to generate a variety of interfacial configurations using a Near

Coincidence site lattice theory [22

23

]. Procedures are also available for generating atomistic

configurations for dislocations [24

] and grain-boundaries [25

26

] in otherwise perfect materials. Monte-

Carlo techniques can be used to introduce point defects at particular concentrations into a material [27

].

Once the models have been generated, pertinent properties can then be calculated using these models and

compared with the properties of the (perfect) parent material, which does not include the particular

microstructural feature. In this way the influence of a specific microstructural feature on a particular

property can be elucidated. This information is important to the experimentalist who might be persuaded

to direct the synthesis of the material to introduce or inhibit particular microstructural features to best suit

desired characteristics or properties.

A limitation of this approach is that the various microstructural features are likely to act in synergy in

influencing the properties. Synergistic effects cannot be elucidated by deconvoluting individual

microstructural features. Accordingly, models that include all the important and experimentally observed

structural features must be generated in addition to models that include individual and isolated

microstructural features.

A viable approach for introducing a variety of microstructural features into a single simulation cell is to

use an evolutionary simulation procedure – ‘Amorphisation and Recrystallisation’ (A&R), which has

been shown to be a useful tool in evolving complex microstructural features within oxide materials [28

29

].

And it is models generated using A&R that are used in this present study to explore ionic transport in

CeO2/YSZ heterolayers.

Theoretical Methods In this section, we describe briefly, the potential models used to represent the interactions between

the ions comprising the CeO2/YSZ system, the code used to perform the dynamical simulations and

the amorphisation and recrystallisation strategy, used to evolve the atomistic structure of the system.

4

The final section describes the procedure for generating an atomistic model for the CeO 2/YSZ system

and calculating various transport properties.

Potential Models and simulation code

The calculations presented in this study are based upon the Born model of the ionic solid in which the

ions interact via attractive long-range Coulombic terms balanced by short range repulsive

interactions. The rigid ion model potential parameters, used in this present study, are presented in

table 1. These potentials have been used successfully to explore oxygen vacancy formation energies

[30

4] and Ce

4+/Ce

3+ reduction within CeO2-ZrO2 solid solutions [

31] and CeO2 thin films supported on

YSZ [32

]. Accordingly, we suggest that these potentials are well suited to this present study. The

DL_POLY code [

33] was used in this study to perform the molecular dynamics (MD) simulations.

Table 1 Potential parameters of the form V(r)=Aexp(-r/) –Cr-6

A C Reference

Ce4+

-O2-

1986.83 0.351 20.40 [4]

Ce3+

-O2-

1731.62 0.364 14.43 [4]

Zr4+

-O2-

985.87 0.376 0.00 [34

]

Y3+

-O2-

1345.10 0.349 0.00 [35

]

O2-O

2- 22764.30 0.149 27.89 [

35]

Amorphisation and Recrystallisation (A&R)

The generation of a realistic atomistic model for CeO2/YSZ heterolayers is not a trivial undertaking. In

particular, the Miller indices of the surfaces exposed by the CeO2 and YSZ at the interface are required.

Next, the lattice misfit needs to be accommodated, which can be achieved by proposing a particular near

coincidence site lattice (NCSL) [22

23

] and then applying a strain to either the CeO2 or YSZ or both to

accommodate the misfit associated with the particular NCSL. For example, the lattice parameters for

CeO2 and YSZ are 5.41Å and 5.14Å respectively. Using a NCSL theory, one can calculate epitaxial

configurations with low associated lattice misfits (there are many): for example, 18 repeat units of CeO2

(18 5.41 = 97.4Å) is well (lattice) matched with 19 repeat units of YSZ (19 5.14 = 97.7Å). The small

residual strain can then be applied to the materials to accommodate the misfit. However, HRTEM images

reveal that the misfit between CeO2 and YSZ is accommodated by misfit dislocations [36

]. The inclusion

5

of dislocations will increase further the complexity because inevitably a misfit dislocation will influence

the particular NCSL. Next, the point defect concentrations at or near the interfacial region need to be

considered. These may include vacancies and substitutionals – the latter perhaps arising from intermixing

across the interfacial plane. Indeed, calculations performed by Harris et al. suggested that heteroepitaxial

ionic systems with similar structure could not grow without intermixing across the interface because the

diffusion of ions deposited onto the substrate proceeds via an exchange mechanism involving the surface

layer of the substrate [27

]. The situation is so complex that it is probably intractable to generate a model

with this rich microstructural detail ‘by-hand’. Accordingly, we use an evolutionary method:

Amorphisation and Recrystallisation (A&R) to capture the complex structural features associated with a

heteroepitaxial system.

Fabrication of a material experimentally involves inevitably some kind of crystallisation process, whether

recrystallisation from solution, vapour deposition, molecular beam epitaxy, ball milling etc. Clearly, the

ideal way of capturing, within an atomistic model, the structural complexity observed experimentally, is

to simulate the crystallisation process itself. This is what we have endeavoured to do in this study. We do

not claim that the A&R approach is able model the recrystallisation process accurately or indeed that the

approach is very realistic in comparison with real crystallisation; the details of the microstructure and the

kinetics are highly dependent on the method of preparation and we are still a long way from treating

laboratory time-scales. However, the method has been able to generate complex microstructural features

observed experimentally including, for example, epitaxial configurations, dislocation core structures,

grain-boundary configurations, point defects and nanoparticle morphologies and all within a single

simulation cell [9 32

29

]. Accordingly, we suggest that the simulated crystallisation process we show in this

present study must, at least in part, reflect crystallisation that occurs in nature and therefore the atomistic

models generated are likely to be realistic.

The A&R procedure, which has been developed over the past five years [28

], attempts to avoid the

inherent limitations of Molecular Dynamics when applied to crystalline solids, which, owing to the

barrier heights for ionic mobility, cannot explore configurational space for the system within the

timescales accessible. Conversely, in a liquid, the ions are highly mobile because the barrier heights are

much lower and A&R exploits this high ionic mobility. In particular, an amorphous/liquid configuration

is generated in which the ions have high mobility. The system is then allowed to recrystallise, during

which time the ions have sufficiently high mobilities to allow them to move into low energy

6

configurations within the timescales (typically nanoseconds) accessible to the simulation. The CeO2/YSZ

system, as it recrystallises, will evolve microstructural features observed experimentally, including, for

example, interfacial and epitaxial configurations, grain-boundaries, dislocations and point defects. A

powerful attribute of the A&R strategy is that it does not require one to propose and generate a realistic

atomistic structure that includes all the microstructural features, prior to simulating with dynamical or

static methods.

We have generated interface models for CeO2/YSZ in previous sumulations [32

]. However, in this

study we have introduced two important extensions (in addition to constructing a multi-layered

system).

(i) Many simulations of interfaces involve placing one solid block on top of another. Using this approach,

the epitaxial configuration has to be specified – and remains fixed. Amorphisation and recrystallisation

enables one to specify a substrate only. The overlayer is then amorphised and allowed to recrystallise and

in doing so the system explores the particular epitaxial configuration that is of low-energy. Moreover,

A&R will introduce dislocations automatically if desired by the system. In this study, we remove the

‘constraint’ of holding the substrate fixed. In particular, the CeO2 and YSZ films are both amorphised and

then recrystallised. In this way both the CeO2 and YSZ are able to evolve their own microstructural

features.

(ii) In a previous simulation of CeO2/YSZ, we amorphised then recrystallised a CeO2 film on top of ZrO2.

The ZrO2 was then changed to yttrium stabilised ZrO2 by introducing Y3+

species, randomly substituting

for Zr4+

, together with the appropriate number of charge balancing oxygen vacancies. Here, we introduce

Y3+

and oxygen vacancies into the ZrO2 lattice and then amorphise and recrystallise the system. In this

way the oxygen vacancies and Y3+

species are able to explore more of the potential energy surface and

move into low energy configurations resulting in a more realistic model.

Extentions (i) and (ii) are not as trivial as they might at first appear. First, with an amorphous

substrate, the recrystallisation is problematic because there is no crystalline substrate acting as a

template in directing the crystallisation of the overlayer. Consequently, it is more difficult to get the

system to recrystallise. Second, oxygen vacancies are ‘smeared out’ when the system is amorphised,

which again makes recrystallisation of the system within a reasonable time more difficult. The A&R

7

procedure is slightly different from previous studies, and may appear contrived, but we report below

a successful approach in that it led to a realistic crystalline model structure for CeO2/YSZ

heterolayers.

Generating atomistic Models for CeO2/YSZ

A block of CeO2, comprising 6144 Ce4+

and 12288 O2-

, was placed on top of a block of ZrO2 comprising

6144 Zr4+

and 12288 O2-

. The interface was constructed initially to conform to CeO2(111)/ZrO2(111) for

ease of construction. However, because the system is amorphised, this starting configuration will change

when the system recrystallises. The CeO2 was then doped with Ce3+

. In particular, 6.25% of the Ce4+

ions

were replaced with Ce3+

, which corresponds to 384 Ce4+

lattice sites exchanged for Ce3+

and to

compensate for the resulting charge imbalance, 192 oxygen vacancies were introduced by removing 192

O2-

species. The Ce3+

and O2-

species were introduced at random positions within the CeO2 lattice. To

change the ZrO2 into yttrium stabilized zirconia (YSZ), 12.5% of the Zr4+

ions were exchanged for Y3+

. In

particular, 768 Zr4+

species were exchanged for Y3+

together with 384 charge compensating oxygen

vacancies. The whole system was then compressed by 31% and placed in a 3D periodic cell with a void

introduced perpendicular to the interfacial plane between the xxx

OCeCe

2

3

2

4

21(x = 0.0625) and underlying

YSZ substrate. The atom positions (cations only) and simulation cell depicting this configuration is

shown in fig. 1(a). Constant volume MD simulation was then run, for 62ps at 3400K, with velocity

scaling to the simulation temperature performed at every step. Under MD, the ions started to accelerate

immediately into the void, fig. 1(b), and, in so doing, the crystalline structure of the system was quickly

perturbed resulting in a rapid amorphisation of the thin films.

Trial simulations, performed with constant pressure and temperature, failed to generate amorphous thin

films. This is because the interfacial area can change under MD performed at constant pressure,

consequently, the thin films simply expanded back to their natural lattice parameters whilst retaining the

fluorite structure.

8

Figure 1 Amorphisation of the CeO2/YSZ system. The images show sphere model representations of the atom positions. (a):

starting configuration with an YSZ thin film on top of CeO2 with the whole system compressed by 31%; (b): the system after

0.5ps of MD simulation showing the ions accelerating into the vacuum gap; (c): after 62ps of MD simulation in which the

atoms have filled the vacuum gap completely and the whole system is amorphous. Ce4+

is coloured white, Ce3+

is orange, Zr4+

is blue and Y3+

is yellow.

Finally, after 62ps, the ions have filled the simulation cell completely, fig. 1(c). The size of the void was

chosen carefully such that once the 31% compression had been completely relieved, the simulation cell

would be fully populated. Close inspection of fig. 1(c) reveals that both the CeO2 and YSZ are, as desired,

fully amorphous.

The next step was to recrystallise the thin films. To this end, MD simulation was performed on the

configuration, fig. 1(c), for about 3000ps at 3400K. In contrast to the amorphisation step, the MD

simulation was run under constant pressure rather than constant volume. Running the simulation under

constant pressure enables the simulation cell size and in particular the interfacial area to change during

the simulation. Accordingly, the system is free to explore different interfacial epitaxial configurations. A

(constant) pressure of 20GPa was imposed upon the system to help eliminate any voids that might evolve

during the recrystallisation. After 3000ps of MD simulation the thin film had recrystallised fully. The

configurational energy of the system during the (high pressure) recrystallisation is shown in fig. 2.

a b c

9

-1.255

-1.25

-1.245

-1.24

0 1000 2000 3000

Time (ps)

En

erg

y

Figure 2 Configurational energy (106 eV) of the CeO2/YSZ heterolayered system, calculated during the recrystallisation.

The configurational energy becomes more negative (which corresponds to a more stable system)

during the simulation and plateaus after about 2000ps. The energy released during the

recrystallisation (latent heat of crystallisation) is extracted from the system by velocity scaling to the

simulation temperature every step. It is interesting to note that the energy drop from about 500 to

1500ps is shallower compared with the energy drop from 1500ps to 2000ps.

The structure of the simulation cell after 845ps and 2955ps is shown in fig. 3(a) and 3(b)

respectively. Detailed inspection of 3(a), using molecular graphics, reveals that the CeO2 and YSZ

are polycrystalline and comprise a wealth of grain-boundaries and triple juctions between the

component CeO2 and YSZ materials. Conversely, the CeO2 and YSZ thin films in fig. 3(b) are single

crystals. Clearly, the MD simulation at 3400K has led to the ‘annealing out’ or sintering of the grain -

boundary structures. (We note that if one quenched (MD, 0K) the system after 845ps, Fig. 3(a), then a

model for a heterolayered system with nanopolycrystalline grains would be generated.)

10

Fig 3 Structure of the heterolayered CeO2/YSZ simulation cell shown during the recrystallisation step after: (a) 845ps and

(b) 2955ps. A sphere model representation of the cations are shown; the anions are not shown to preserve clarity. Ce4+

is

coloured white, Ce3+

is orange, Zr4+

is blue and Y3+

is yellow.

Inspection of the system after 845ps (fig.3(a)) revealed no amorphous regions remain. However, the

configurational energy, fig. 2, still shows a significant drop in energy until 2000ps. This indicates that

the polycrystalline structure is of a higher energy compared with the single crystal, and, as the grain-

boundaries anneal out, energy is released. By observing animations of the system during the

recrystallisation, the structural mechanism for this annealing process can be followed. For example,

the drop in configurational energy from 1500ps to 2000ps corresponds to the agglomeration of a

single missoriented crystallite within the surrounding crystal. The structure of this missoriented

crystallite is shown in fig. 4(a). Inspection of the CeO2 component of this grain reveals that, either it

does not conform to the fluorite structure, or, it is so heavily defective that it is difficult to

characterise – although it is certainly crystalline. Conversely, the CeO2 and YSZ surrounding this

grain is fluorite-structured.

After a further 50ps of MD, the size of the crystallite has reduced significantly, fig. 4(b). Finally, at

2100ps, the missoriented grain has fully dissolved, fig. 4(c). It is interesting to note that the transition

from fig. 4(a) to 4(c) is associated with a 1% increase in the simulation cell volume.

a b

11

Figure 4 Illustration showing the dissolution of a missoriented grain within the heterolayered CeO2/YSZ system. The images

correspond to snapshots of the system taken during the recrystallisation of the system after: (a) 1850ps, (b) 1900ps and (c)

2100ps. The grain-boundary region between the encapsulated missoriented crystallite is highlighted by the white trace in (a)

and (b). However, in (c) the crystallite has dissolved fully. Ce4+

is coloured white, Ce3+

is orange, Zr4+

is blue and Y3+

is

yellow; oxygen ions are shown as red dots (small – hardly visible).

The final step was to relieve the pressure. In particular, MD simulation was run at 3400K for about

2500ps under (constant) zero pressure. The structure of the system at the end of this step is shown in fig.

5. We note that the simulation cell volume increased by about 10% after the pressure had been relieved.

Figure 5 Sphere model representation of the simulation cell after zero pressure MD. Only the cations have been shown to

ensure clarity. Ce4+

is coloured white, Ce3+

is orange, Zr4+

is blue and Y3+

is yellow.

a b c

12

Finally, the system was cooled to 0K. In particular, MD (constant, zero pressure) was performed for

375ps @ 3000K; 60ps @ 2500K; 50ps @ 2000K; 50ps @ 1500K; 995ps @1000K; 50ps @ 500K and

320ps @ 0K, which acts effectively as a pseudo energy minimisation.

Atomic Transport Properties

Ionic self diffusion, conductivity and the associated activation energies can be determined using the

atomistic model and calculating the Mean Square Displacements (MSD) of the ions at a particular

temperature (Appendix).

Once a realistic model for CeO2/YSZ had been generated, MD simulation was applied to this system,

for 500ps at 1000, 1175, 1335, 1500, 1700, 2000K and 2500K. Each simulation included a

preliminary 250ps equilibration to the simulation temperature. The simulations were performed

within a (zero pressure) NPT ensemble with thermostat and barostat relaxation times of 1ps. The

MSDs of the ions were then calculated as a function of time.

In addition, the MSDs of the component YSZ and CeO2 were calculated and used as a comparison.

The stoichiometry of the parent materials matched exactly the stoichiometry of the thin films

comprising the heterolayered system, In particular, the YSZ parent material comprised: 1728 Zr4+

and

3456 O2-

. 216 Zr4+

were then replaced at random by Y3+

(12.5%) together with 108 Oxygen

vacancies. The CeO2 parent comprised 1728 Ce4+

and 3456 O2-

. 108 Ce4+

were then replaced at

random by Ce3+

(6.25%) together with 54 oxygen vacancies. MSDs were calculated for these systems

(500ps production run with a 250ps equilibration step) at 2500, 2000, 1700, 1500 and 1335K. To

ensure reproducibility, the YSZ cell was run with two different random positionings of the Y3+

and O

vacancies and the MSDs were identical thereby validating the control systems.

Results The first part of the results describes the structural features that have evolved within the heterolayered

CeO2/YSZ system, together with experimental data taken from HRTEM to compare. In the second part

we report on the calculated oxygen self diffusion and compare with diffusion data obtained from tracer

experiments.

13

Structural features

The atom positions comprising the final 0K structure is shown in fig. 6. A slice, cut through this structure,

perpendicular to the interfacial plane, is shown in fig. 7 and the ion density, calculated as a function of

depth perpendicular to the interface, is shown in fig. 8. Inspection of figures 6, 7 and 8 reveal the system

to be fully dense with no voids as desired. Layers of CeO2, about 3nm thick, are sandwiched between

layers of YSZ of similar thickness. The interfacial regions are not atomically sharp; rather they exhibit

about 4 atomic layers of interfacial roughening, which corresponds to an interfacial region spanning about

1 nm (fig. 8). The Y3+

ions (yellow) and Ce3+

species (orange) are well dispersed within the ZrO2 and

CeO2 thin films respectively. Both the CeO2 and YSZ recrystallised into the cubic fluorite structure.

Figure 6 Structure of the final, OK, simulation cell. Four cells periodic in the interfacial plane are shown. The ion

positions are represented by spheres: Ce4+

is coloured white, Ce3+

is orange, Zr4+

is blue and Y3+

is yellow. Oxygen is not

shown to ensure clarity.

14

Fig. 7. (a) sphere model representation of the atom positions within a slice cut through the CeO2/YSZ

system. Three unit cells are shown to illustrate the heterolayered structure. Ce4+

is coloured white, Ce3+

is

orange, Zr4+

is blue and Y3+

is yellow. (b) HRTEM taken from [15

] for illustration.

a

b

15

0 50 100 150 200

Distance (Angstroms)

De

nsity

O2- Zr4+ Y3+ Ce4+ Ce3+

YSZYSZ YSZCeO2 CeO2

Fig. 8 Calculated ion density as a function of depthe within the heterolayered CeO2/YSZ system. Just over 2.5 periodic

repeats are shown to help demonstrate graphically the layered nature of the system.

Fig. 8 also reveals the thickness of the CeO2 thin film to be about 3nm, YSZ = 2.5nm and the interfacial

region, 1nm. The periodicity of the CeO2/YSZ heterolayers is therefore about 6.5nm.

Inspection of the final structure, using molecular graphics, revealed that misfit dislocations, with

approximately 7nm periodicity, have evolved within the system, fig. 9. The evolution of dislocations

within the structure is expected because of the lattice misfit between the CeO2 and YSZ. In particular, the

lattice parameters of CeO2 and YSZ are 5.41Å and 5.14Å respectively and therefore to accommodate the

misfit, an extra atomic plane is introduced on the YSZ side. Specifically, if one counts the number of

planes between dislocations in fig. 9 there are 23 atomic planes comprising YSZ and 22 comprising

CeO2.

16

The lattice misfit, F, is given by:

(1)

where n is the number of lattice planes of CeO2 and m, the number of lattice planes of YSZ. The

configuration that has evolved, together with the misfit dislocation is associated with a 0.7% misfit (n=22;

m=23). This compares with 5.1% for the bulk materials (n=1; m=1). A reduction of 4.4% in the

interfacial misfit associated with this configuration is high - the resulting reduction in the strain energy

required to accommodate this (n=22, m=23, F=0.7%) configuration compared with a fully coherent (n=1,

m=1, F=5.1%) configuration provides a significant driving force to evolve this particular NCSL

configuration together with dislocation formation. Moreover, this provides support to the A&R method in

that it is capable of evolving structurally realistic configurations.

In fig. 9(a), an enlarged segment, cut through the CeO2/YSZ system, is presented to illustrate the structure

of the misfit dislocations, which have evolved. In 9(b) a high resolution transmission electron micrograph

(Fourier filtered) of a CeO2/YSZ interface with a 30-nm thick YSZ layer is presented, and taken with

permission from the study of Chen and co-workers [36

]. An enlarged section, showing more clearly the

individual ions comprising the dislocation core, is shown in fig. 10

2/)(2

2

YSZCeO

YSZCeO

mana

manaF

17

Fig 9 (a) graphical representation of a side view of the CeO2/YSZ model system (top: CeO2 layer, bottom: YSZ layer) showing

the misfit dislocations. (b) HRTEM of a CeO2 film supported on YSZ, reproduced, with permission, from Chen and co-

workers [36

].

YSZ

CeO2

YSZ

CeO2

a

b

18

Fig. 10 (a) Enlarged view of a dislocation (circled) within the model CeO2/YSZ system. Ce4+

is coloured white, Ce3+

is orange,

Zr4+

is blue and Y3+

is yellow. (b) Fourier filtered HRTEM image showing the interfacial and internal dislocations within ZrO2

and CeO2, taken with permission, from Wang and co-workers [15

].

In addition to the dislocations, various other factors are integral in helping accommodate the lattice

misfit. These include point defects, lattice strain and ionic relaxation. In particular, cation vacancies

are observed to have evolved within both the YSZ and CeO2 lattices – the highest concentration of

which are within dislocation core regions. We note that for each cation vacancy, two oxygen

vacancies must evolve to quench the charge imbalance.

Fig. 11 sphere model representation of: (a) full simulation cell, (b) enlarged region to show more clearly the disorder within the

oxygen sublattice in the YSZ layers compared with the oxygen in the CeO2 layers. Ce4+

is coloured white, Ce3+

is orange, Zr4+

is blue, Y3+

is yellow and oxygen is red.

YSZ

CeO2

a b

a b

19

In fig. 11, the simulation cell, which includes the oxygen ions, is shown. Close inspection of the figure

reveals that the oxygen ions are highly ordered within the CeO2; inspection of the structures using

graphical techniques reveals the Ce4+

and Ce3+

ions to be predominantly 8-coordinated. Conversely,

considerable oxygen ion disorder can be seen within the YSZ thin film with Zr4+

and Y3+

ions being

predominantly 6 or 7 coordinated with only a very few ions coordinated to 8 oxygen.

In fig. 12, the calculated cation-anion Radial Distribution Functions (RDF) for the CeO2 and YSZ layers

are shown. The Ce4+

-O2-

and Ce3+

-O2-

RDF are sharp as far as 10Å indicating long-range crystalline order

within the system. Conversely, the Zr4+

-O2-

and Y3+

-O2-

RDF are broader, signifying a higher structural

disorder within the YSZ film as compared with the CeO2. However, peaks are still evident as far as 10Å

indicating that the YSZ accommodates long-range crystallinity and is not amorphous. The RDFs show

that the nearest neighbour peak for Ce4+

-O2-

compared with Ce3+

-O2-

(12(a)) and Zr4+

-O2-

compared with

Y3+

-O2-

(12(b)) differ by 0.15 and 0.3Å respectively. This is to be expected because of the larger size of

the Ce3+

ion compared with Ce4+

and Y3+

compared with Zr4+

. However, inspection of the higher order

peaks further from the nearest neighbour peak reveals that all the additional peaks are superimposed. This

shows that the Ce3+

and Y3+

dopants are well dispersed and occupy Ce4+

and Zr4+

lattice positions rather

than existing as separate phases such as Ce2O3 or Y2O3. If the latter were true, then higher order peaks

would not be superimposed.

0

10

20

30

0 2 4 6 8 10

Interionic Separation (r)

g(r

)

0

2

4

6

8

0 2 4 6 8 10

Interionic Separation (r)

g(r

)

Fig. 12 Calculated cation-anion RDFs. (a) Ce4+

-O2-

(thick line) and Ce3+

-O2-

(thin line), (b) Zr4+

-O2-

(thick line) and Y3+

-

O2-

(thin line).

a b

20

A slice cut through the CeO2 thin film is shown in fig. 13 to illustrate the atomistic structure of point

defects that have evolved within the CeO2 layer. In this figure, for illustration, four defect clusters have

been identified (A-D). In cluster “A” one can observe from the figure an oxygen vacancy. However,

directly above and below this vacancy there exist Ce3+

species (not shown). The vacancy cluster can

therefore be described, using Kroger Vink notation, as: ]2,[ '

CeO CeV . Inspection of cluster B reveals an

oxygen vacancy together with a Ce3+

ion next to the vacancy. In addition, there is another Ce3+

ion that

lies just underneath the vacancy (not shown). The cluster is therefore ]2,[ '

CeOCeV . Cluster C comprises

an oxygen vacancy (shown) together with an associated Ce3+

lying below this vacancy (not shown)

giving: ],[ '

CeO CeV . Finally, cluster D can be described as ]3,2[ '

CeO CeV . Clusters “A” and “B” are

charge neutral, whereas clusters “C” and “D” are locally charged. Because the whole system is charge

neutral additional defects are present to compensate for locally charged defect clusters - such as cation

vacancies. These structures are illustrative and typical of the point defects that have evolved within the

CeO2 layer, which range from isolated vacancies and substitutionals to complex defect clusters

comprising four or more species. Similar defect structures, including cation and anion vacancies, are

present within the YSZ layer. However, these are more difficult to identify and characterize structurally

because of the considerable disorder of the oxygen sublattice within this layer (fig. 11).

Fig. 13 Representations depicting the atomistic structure of isolated and associated point defects that have evolved within the

CeO2/YSZ system. (a) Sphere model representation of the atom positions within a slice, cut through the CeO2 thin film; (b) as

(a) but with a stick model representation. Ce4+

is coloured white, Ce3+

is purple, Zr4+

is blue and Y3+

is yellow.

A B

C

D

a b

21

Experimental Comparison/Validation

Multi-layer nanometer films of pure ZrO2 and CeO2 have been grown, using oxygen plasma assisted

molecular beam epitaxy, on yttrium stabilised zirconia [15

]. High-resolution microscopy and

spectroscopy were used to explore the microstructural features of these thin films. The deposited pure

CeO2 layers were found to exist in the cubic fluorite structure, with a distorted oxygen sublattice.

Moreover, the ZrO2 layers were also found to accommodate the cubic fluorite structure. The authors

attributed the distorted oxygen sublattice to the nanometer thickness of the ZrO2 layers together with

the constraints imposed by the laminating CeO2 layers. The system also includes misfit dislocations

and the authors suggest that the critical thickness for misfit dislocation evolution for the system is

less than 11nm; our dislocated films are about 3-4nm. The cross-sectional structure of the

experimental multilayered CeO2/ZrO2 films on YSZ is reproduced, with permission, in fig. 7(b).

Double CeO2/YSZ layers have been prepared by pulsed laser deposition on Si(001) substrates [36

].

The authors observed that misfit dislocations evolve within the films to help accommodate the lattice

misfit associated with the YSZ and CeO2 films. The structure is reproduced with permission in fig. 9

and compared with our atomistic model.

Ionic Diffusion, Conductivity and Activation Energy

In this section we present both pictorially and graphically, the calculated ionic diffusion within the

CeO2/YSZ system. Further details explaining how self diffusion, conductivities and associated

activation energies can be found in the appendix.

Fig 14 shows the cation sublattice of the CeO2/YSZ system, generated in the previous section; the

cation positions are depicted as ‘dots’. In addition, those cations within three ‘slices’ cut through the

system parallel with the interfacial plane are highlighted by using a sphere model represention of the

atom positions. Fig. 14(a) shows the structure for the system at the start of a production run,

performed to measure ionic self diffusion at 2500K, and 14(b), the same system after 500ps of MD

performed at 2500K. Comparison between figures 14(a) and 14(b) reveal the structures (cation

positions) to be almost identical. In particular there is no observable cation mobility during this

simulation.

22

Fig. 14 representation of the cation positions within the CeO2/YSZ system. Cations are depicted as dots apart from three

regions, for which a sphere model representation is used to depict the cation positions. The top region in each figure (a and b)

shows a slice through the YSZ film; middle: through the interfacial region; bottom: through the CeO2 film. (a) at the start of

the production run; (b) after 500ps of MD, performed at 2500K. Ce4+

is white, Ce3+

is orange, Zr4+

is blue and Y3+

, yellow.

Fig. 15(a), similar to 14(a), shows the positions of the oxygen ion sublattice at the start of the

production run. After 500ps of MD performed at 2500K, fig. 15(b), the oxygen ions have moved a

considerable distance in comparison to their starting positions. Moreover, it is clear from the figure

that the oxygen ions in the YSZ layer have moved further compared with oxygen ions within the

CeO2 layer. In addition, fig. 15(b) reveals there is no enhancement in the oxygen mobility within the

interfacial region. Indeed, there appears a slight cusp in the oxygen distribution as indicated by the

arrows on fig. 15(b) - we suggest, tentatively, a reduced oxygen mobility within the interfacial

region.

CeO2

YSZ

a b

23

Fig. 15 representation of the oxygen anion positions within the CeO2/YSZ system. (a) at the start of the production run –

analogous to 14(a) above. Oxygen anions are depicted as red dots apart from a thin slice in the middle of each figure for which

a sphere model representation (oxygen coloured yellow) is shown; (b) after 500ps of MD, performed at 2500K The figure thus

indicates the mobility of the oxygen ions during the MD.

To explore the mobility of the ions within various regions, for example, within the CeO2 layers, the YSZ

layers or the interfacial region, the MSD’s were calculated within each of 20, equally spaced, slices,

which were parallel with the interfacial plane. In fig. 17, the calculated MSDs of the oxygen anions

comprising a slice within the YSZ layer are shown (for illustration) for temperatures spanning 1335 to

2000K; the ionic self diffusion coefficients, Di, can be extracted from these MSDs by calculating 1/6th

of

the gradient (see appendix). Analogous cation MSDs (not shown) revealed no mobility even at 2000K.

CeO2

YSZ

a b

24

0

10

20

30

40

50

60

70

80

250 350 450 550 650 750

Time (ps)

MS

D 2000K

1700K

1500K

1335K

Fig 17 MSDs calculated for oxygen anions contained in a slice within the YSZ layer. MSD are

calculated in Å2.

The diffusion coefficients, calculated as a function of temperature, fig. 18, were used to determine the

activation energies associated with ionic diffusion within each of the 20 slices. Fig 18 shows the results of

three such slices: one within the YSZ thin film, one within the CeO2 and the third within the interfacial

region. These three traces are illustrative of the three regions comprising the heterolayered CeO2/YSZ

system. The activation energy barriers to ionic diffusion, calculated from these traces, together with data

for the parent CeO2 and YSZ materials and experimental data for YSZ are also presented in the figure.

25

-21

-19

-17

-15

-13

-11

0.3 0.5 0.7 0.9 1.1 1.3

1000/T

ln(D

i)

YSZ (0.74 eV) Interface (0.80 eV) CeO2 (0.84 eV)

CeO2 pure (0.75 eV) YSZ pure (0.46 eV) YSZ expt. (1.0 eV)

Fig. 18 Calculated oxygen anion diffusion coefficients, Di, calculated as a function of temperature. The traces are calculated

within a slice, parallel to the interfacial plane through the YSZ film, through the CeO2 film and through the interfacial region.

The calculated diffusion coefficients for ‘pure YSZ’ and ‘pure CeO2’ are also presented as a comparison. The Y3+

/Oxygen

vacancy content and Ce3+

/Oxygen vacancy content in the pure YSZ and CeO2 respectively is commensurate with those of the

corresponding YSZ and CeO2 thin films. Experimental diffusion coefficients, taken from [37

] are also presented on the same

figure as a comparison. Activation energies, calculated from the respective gradients, are included in the legend.

Finally, the ionic conductivity, calculated within each of the 20 slices at 2500K, is presented, as a

function of depth in fig. 19. Approximately two unit cells are shown to illustrate the periodic nature of the

CeO2/YSZ heterolayered system. The ionic densities, from fig. 8, are also superimposed to enable the

conductivity to be easily correlated with the particular region of the CeO2/YSZ system from which it was

26

calculated. The ionic densities, calculated for the parent materials CeO2 (0.12 siemens/cm) and YSZ (0.91

siemens/cm), are included for comparison.

50 100 150 200

Distance

Density

0

0.2

0.4

0.6

0.8

1

Conductivity

Zr4+ Y3+ Ce4+ Ce3+ Conductivity

Fig. 19 Ionic conductivities, calculated as a function of distance within the CeO2/YSZ system at 2500K. The density of ions,

fig. 8, are superimposed on the figure. The dotted black lines correspond to ionic conductivity within the perfect parent YSZ

(top line) and CeO2 (bottom line) materials. The conductivity is calculated in siemens/cm and distance is in angstroms.

Discussion

In a previous study, on BaF2/CaF2 heterolayers [29

], we calculated that the ionic conductivity in the

BaF2/CaF2 heterolayered system was considerably higher compared with the parent BaF2 and CaF2

materials (in accord with earlier experimental findings [19

]). This is in contrast to the present system in

which the ionic conductivity of the CeO2/YSZ heterolayered system is calculated to be slightly lower

compared with the parent materials. Clearly, to aid the design of new materials with increased ionic

27

conductivity, it is desirable to understand why the conductivities change with respect to the parent

materials.

There are two central factors that influence the conductivity: the activation energies associated with ions

moving through the material and the number of charge carriers. For the BaF2/CaF2 system, considered

previously, we calculated that the activation energy for ionic conduction was reduced from 1.1 eV (BaF2)

and 1.2 eV (CaF2) for the parent materials to 0.5 eV for the heterolayered BaF2/CaF2 system. When we

observed movies (generated using molecular graphics) showing the trajectories of the ions, we could see

that the fastest diffusing ions, and therefore those that contributed most to the conductivity, were ions

diffusing along grain-boundary regions. Clearly, the reduction in the activation energy can be attributed to

the relative ease that ions move through interfacial/grain-boundary regions compared with the bulk

material. In addition, the number of charge carriers was deemed to have increased.

Conversely, for the CeO2/YSZ heterolayered system, the activation energy was calculated to have

increased from 0.46 eV for the YSZ parent to 0.74 eV (YSZ thin film) and from 0.74 eV (CeO2 parent) to

0.84 eV (CeO2 thin film). Neither is there a reduction in activation energy at the interfacial region, which

at 0.80 eV, lies mid-way between that for the CeO2 and YSZ thin films. In addition, figs. 15, 18 and 19

suggest that the ionic conductivity is not enhanced at the interfacial region and therefore the transport of

oxygen ions remains predominantly vacancy driven (as opposed to grain-boundary diffusion)

commensurate with the parent materials. Indeed, we suggest that the changes in structure associated with

fabricating heterolayered thin films is deleterious to the ionic self diffusion.

It is now worth commenting upon the quality of the interatomic potentials: Literature values for the

activation energy barrier associated with oxygen diffusion for YSZ are 0.8-1.0 eV [37

]; 0.8-0.9 [38

].

Our value of 0.46 eV for the pure YSZ is lower than experiment, which, as suggested by Khan an co -

workers [39

] may be attributed to a ‘binding energy term which arises from the trapping of oxygen

vacancies by Y3+

dopants to form associated clusters’. An MD study [40

] by Li and Hafskjold found

that the calculated diffusion coefficients yielded activation energy barriers in the range 0.2 – 0.8 eV.

For pure CeO2 the activation energy barrier for oxygen diffusion was measured to be about 0.9 eV

[41

], which compares to 0.75 eV for our model. Activation energy barriers calculated in this present

study are therefore in reasonable accord with previous experimental and theoretical values.

28

An experimental study by Azad et al. on gadolinia-doped ceria and zirconia heterolayers [16

] revealed an

increase in the oxygen ion conductivity compared with the parent materials. The authors also found that

when the thickness of the individual layers was reduced below 15 nm, the conductivity decreased. This is

echoed in the study of Sata et al, on BaF2/CaF2 heterolayers [19

] who found that the conductivity reduced

when the heterolayer thicknesses was reduced to below 5nm. Our heterolayers are about 3-4 nm and this

may perhaps explain why we did not observe an increase in the conductivity. Conversely, previous

calculations on the BaF2/CaF2 system, with heterolayers thinner than 5nm, did suggest a considerable

increase in the ionic conductivity compared with the parent materials [29

]. At present simulating

CeO2/YSZ heterolayers with thicknesses larger than 15nm would result in simulation cells far larger than

could be accommodated within the available computational resources. However, with the explosive

increase in computational power, simulating films of 15nm and above will likely become routine. In

addition, the simulation strategy presented in this study can be used to introduce a range of other dopants

– such as Gd3+

- into heterolayered systems to determine whether defects or heterolayer thicknesses (or

both) are key to the increased conductivity.

We have used a rigid ion model approximation for all the simulations performed in this study and

therefore our description does not include the polarisability of the oxygen anion, which may influence the

ionic transport properties (although we note that our results were similar to experiment). The most

important aspect of this study is the calculated change in diffusivity/conductivity for the heterolayered

system compared with the parent materials rather than absolute values and therefore we suggest that even

without the shell model we would still observe differences in the diffusivity as a consequence of the

configuration and microstructure. At present a shell model description is prohibitively expensive

computationally; a typical point on fig. 18 required about 2000 hours using a SunFire galaxy-class

supercomputer. We recommend that future studies, which have access to increased computational

resources, incorporate a shell model description of the ions into their simulations.

Otsuka and co-workers observed that dislocations within YSZ enhanced the ionic conductivity [42

]. They

attributed this to fast diffusion of oxygen vacancies along dislocation lines. Our model comprises

dislocations however animations of the oxygen self diffusion did not reveal any obvious enhanced self

diffusion along dislocation lines.

Microstructural features such as defects, dislocations, grain-boundaries and heterointerfaces are

associated with a volume change compared with the perfect parent material. For example, a grain-

29

boundary will be associated with a relatively large volume increase, which reflects the lower density of

ions at the boundary regions. This ‘excess volume’ may lead to an enhancement of ionic conductivity by

enabling ions to migrate more freely along grain-boundary regions [26

], which, in some cases, comprise

relatively open channels. Conversely, Fisher and Matsubara determined using MD simulation that tilt

grain-boundaries within YSZ decrease the overall conductivity of YSZ by trapping vacancies within the

boundary region [43

]. The ‘excess volume’ for our CeO2/YSZ system, compared with the component

materials, was calculated to be +1.2% at 2000K. This low value indicates dense interfacial regions

between heterolayers (also evidenced by fig. 7b) that prohibit ionic mobility other than via a vacancy

mechanism. We therefore recommend that future models include a more open channel system at

boundary regions.

Conclusion An evolutionary simulation strategy (A&R) has been used to generate an atomistic model for a

heterolayered CeO2/YSZ system. Our model is structurally realistic in that it comprises all the important

microstructural features, observed experimentally, that are likely to influence the oxygen anion

diffusivity. These include epitaxial interfacial configurations with low associated misfit, grain-boundaries,

misfit dislocations, point defects such as vacancies and substitutionals including clustering, intermixing

(roughening) of ions across the interfacial plane.

Using this model we have calculated ionic transport properties, including oxygen anion self diffusion

coefficients, ionic conductivities and associated activation energies within the CeO2 and YSZ layers

and within the interfacial regions. Our calculations suggest that the oxygen diffusivity is lower in the

CeO2 and YSZ comprising the heterolayered system compared with the component CeO2 and YSZ

materials and that conductivity in this system proceeds primarily via a vacancy mechanism as

opposed to interfacial or grain-boundary diffusion, which was the preferred transport mechanism for

BaF2/CaF2 heterolayers. In addition, this study describes a framework simulation proceedure that can

be used to aid experiment explore the diffusivity/conductivity of interfacial or heterolayered systems.

In particular, it can be used to determine and predict those factors that might enhance (or inhibit) the

diffussivity/conductivity such as intrinsic or extrinsic dopant ions or other interfacial configurations.

With the explosive growth in computational power coupled with grid computing, such simulations are

likely to become routine in future to help complement and reduce the number of expensive

experiments that need to be performed in the search for improved materials.

30

31

Appendix Molecular Dynamics simulation can be used to extract important atomistic transport properties. In

particular, the ionic self diffusion can be determined from calculated mean square displacements

(MSDs) following:

N

iiirtr

NtrMSD

1

22 )0()(1

)( (A1)

The diffusion coefficient, Di, can then be derived from the MSDs following:

BDtrii 6)(2

(A2)

where B is the Debye-Waller factor. From the diffusion coefficient, the ionic conductivity, σ, can be

estimated using the Nernst-Einstein equation:

Tfk

DNq

B

i

2

(A3)

where N is the density of charge carriers per unit volume, q is the charge on the charge carrier (-2 for

Oxygen anion), f, the Haven Ratio, kB, Boltzman constant (8.63 x 10-5

eVK-1

), and T, the temperature

(Kelvin). There is much debate over the Haven Ratio in the literature, for example see [44

], and because,

in this study, the particular value for the Haven ratio does not change the general conclusions (from fig.

19) we have, for simplicity, chosen a value of 1.

The activation energy barriers, EAct, associated with the ionic diffusion can be calculated using the

standard Arrhenious equation:

Tk

EAD

B

Act

iexp (A4)

32

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