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Protonic defects in yttria stabilized zirconia: incorporation, trapping and migration James A. Dawson,*a Hungru Chenb and Isao Tanakaa Both classical and quantum mechanical simulation techniques have been applied to investigate the incorporation, migration and potential binding of protonic defects in bulk yttria-stabilised zirconia (YSZ). The calculated redox reaction energies are found to be high, although the reduction energies are lower than those of bulk cubic ZrO2 and are shown to decrease further with increasing Y content. The hydration energies for YSZ are also lower than the values calculated for bulk ZrO2 and are found to be lowest when the oxygen ion is in close proximity to at least one Y ion. Strong binding (proton trapping) energies are observed between the protons and additional acceptor dopants including Sc, Yb and Gd.

Received 3rd January 2014, Accepted 22nd January 2014

These energies are found to vary significantly depending on local configuration and again are generally

DOI: 10.1039/c4cp00021h

energy barriers for proton transfers via neighbouring oxygen ions (Gro ¨ tthuss-type mechanism). Energy barriers of 0.32–0.42 eV are obtained for the pathways with the closest O–O interatomic distances and

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are found to be very comparable to well-established proton conducting materials.

lower than the values for ZrO2. Density functional theory (DFT) calculations are used to determine

1. Introduction In recent years the interest in yttria-stabilised zirconia (YSZ) as a potential proton conductor has increased significantly. Proton transport in polycrystalline YSZ at high temperatures was first studied by Wagner and was found to be negligible in comparison to the fast oxygen-ion conduction usually associated with YSZ.1,2 More recent papers have shown proton transport occurs at much lower temperatures (o150 1C) and that this transport is driven by the grain boundary structures in the material.2–6 In work by Kim et al.3 and Avila-Paredes et al.4 proton conduction is observed in nanocrystalline YSZ with grain boundary size between B13 and B100 nm at room temperature in humid atmospheres. Such works illustrate how samples with large grains exhibit very little protonic conduction leading to the conclusion that protonic conduction in YSZ is interfacially driven.2 This is further supported by Park et al.6 who used X-ray photoelectron spectroscopy (XPS) to confirm a higher proton concentration in YSZ thin films prepared by atomic layer deposition than in YSZ single crystals which also suggests proton diffusion occurs through grain boundaries in YSZ. Similar findings have also been found for Gd-doped CeO2 where the bulk defect chemistry does not significantly influence the protonic conductivity which occurs exclusively at the grain boundaries.7 a

Department of Materials Science and Engineering, Kyoto University, Sakyo, Kyoto, 606-8501, Japan. E-mail: [email protected] b Environmental Remediation Materials Unit, National Institute for Materials Sciences, Ibaraki, 305-0044, Japan

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These findings are contrary to the fact that YSZ grain boundaries are known to hinder oxygen-ion transport8,9 leading to the suggestion that the grain boundaries conduct ions selectively.2 It is noteworthy to add that there is ongoing debate over whether protonic conduction does occur primarily in the grain boundaries with Scherrer et al.10 observing no proton conductivity through grain boundaries in YSZ nanocrystalline, dense thin films. Proton conduction is, however, observed at low temperatures at the inner surface of the porous films. Additional studies by Raz et al.11,12 also support the conclusion that proton conductivity occurs at the YSZ surface and not its grain boundaries. It has also been suggested such conductivity in YSZ and CeO2 is actually a result of internal surfaces produced from cracks and pores.13–15 The data in the literature concerning the hydration enthalpy of YSZ is limited, however the value is generally considered to be ‘close to zero’ in the material and therefore the proton concentration is small.16 Information on the energies for proton trapping is equally limited, although there is a wealth of information for doped proton conducting perovskites17–20 with typical values ranging from 0.3–1.4 eV depending upon the dopant and the host material. As a result of its fast oxygen-ion conduction and application as a solid oxide fuel cell,2,21 the majority of both experimental and computational effort has been dedicated to the research of oxygen-ion migration in YSZ. However, an activation energy for mixed proton/oxygen conduction of between 0.4 eV and 1.1 eV in the temperature range of 120–400 1C has been found.10 The data available for proton migration in perovskites and in particular Y-doped BaZrO3 is far more substantial than that

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available for YSZ. Yamazaki et al.17 used a combined thermogravimetric and a.c. impedance study to calculate an activation energy of 0.17 eV and a proton trapping energy of 0.30 eV to produce an energy of 0.47 eV required for long-range proton transport. Density functional theory (DFT) calculations for proton migration in Y-doped BaZrO3 produce activation energies of 0.44–0.49 eV depending on whether the proton transfers are intraoctahedral or interoctahedral.22 Calculations by Kim et al.23 suggest that proton transport is hindered by the S5(310)/[001] grain boundary in Y-doped BaZrO3 with an energy barrier of 0.72 eV being calculated. Further DFT and molecular dynamics simulations focus on the local structures of protonated and unprotonated Y-doped BaZrO324 and the effects of Y clustering on the proton conduction.25 Recently we have shown using lattice statics calculations that both the hydration and redox reaction energies are significantly reduced in and around the S5(310)/[001] and S5(210)/ [001] grain boundaries of cubic ZrO2 when compared to the bulk structure.26 Furthermore the binding energies are also reduced at the grain boundaries suggesting that proton transport is more likely to occur at the grain boundaries in this material. To the best of our knowledge, there exists no lattice statics or DFT study on the incorporation and migration of protons in YSZ. The techniques applied in this work have also been used to investigate the defect chemistry, proton incorporation and dopant-proton association in a number of other potential proton conducting bulk materials.27–30 The present study focuses on the bulk structure of YSZ and its potential as a proton conducting material. This involves the use of classical and quantum mechanical atomistic simulation techniques to assess the redox properties, hydration energies, proton position and migration as well as any associated trapping energies. Direct comparison will be made between the results here and the results previously calculated for cubic ZrO2 in order to assess the consequences of the introduction of Y ions and O vacancies to the proton defect chemistry of the system. Further comparison with other proton conductors and experiment is made wherever possible. The results presented here will be used for the future comparison of similar properties of YSZ grain boundaries currently being calculated. It is the aim of this and future studies to provide a definitive answer to whether proton migration does primarily occur in the grain boundaries of YSZ and indeed similar materials.

2. Methods The majority of the results presented here hinge on well established simulation techniques based on the Born model for ionic solids. For the lattice statics calculations, the energy of the system is modelled from contributions of the long-range and short-range forces with respect to the atomic positions in the lattice. The long-range interactions are Coulombic and the short-range repulsive interactions are represented by Buckingham potentials: Vij ðrÞ ¼

n X iaj

   C A exp rij r  6 rij

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(1)

where the symbols have their usual meanings. Both the Zr and O ions are assumed to be fully ionic and therefore have formal charges. A cutoff of 10 Å was applied to all of the potentials. For this work we have used the ZrO2 potential model developed by Woodley et al.31 as this potential model has been shown to have the best agreement with experimental measurements.26 Comprehensive reviews of the methodology briefly described here are available elsewhere.32,33 The defect calculations are performed using the Mott–Littleton approximation.34 In this method defects are simulated at the infinitely dilute concentration limit. The lattice surrounding the defect is divided into two spherical regions; an inner region and outer region. In the inner region the interactions are calculated explicitly and ions are relaxed to positions of zero force. In the outer region, where the interactions are weaker, the polarisation energy and ionic positions are approximated using a dielectric continuum method. To ensure the inner region is properly bedded in the crystal, the interactions between ions of the inner region and the ions of the outer regions are calculated explicitly. Further details are again available elsewhere.32,33 All the lattice statics calculations in this work were completed using the General Utility Lattice Program (GULP).35 We use an attractive Morse potential to model the interactions of the proton. This potential was fitted using ab initio cluster calculations36 to describe the O–H interaction. A Buckingham potential is also used to describe the interactions between the OH group and the surrounding lattice.37 The Morse potential takes the form: V(r) = D{1  exp[b(r/r0)]}2

(2)

where D, b and r0 are the parameters obtained from ab initio quantum mechanical cluster calculations with a point charge representation of the surrounding lattice.36 The OH group is given the correct overall charge of 1 by distributing the dipole across both ions with an oxygen charge of 1.4263 and a hydrogen charge of +0.4263. This approach has been successfully applied to a wide range of materials including ZrO2,26 perovskites38–40 and Si/Ge-apatites.41 The proton migration calculations in this study were completed using DFT with the generalised gradient approximation Perdew–Burke–Ernzerhof (GGA-PBE) functional.42 The interactions between the core and valence electrons were treated using the projector augmented wave (PAW) approach.43 The cutoff energy for plane waves was set at 500 eV. The Brillouin zone was sampled with k-point spacing of less than 0.03 Å. Structural optimisation was performed until the forces were converged to less than 0.01 eV Å1 per ion. The proton migration paths and barriers were determined using the nudged elastic band (NEB) method.44 All calculations were performed using the Vienna ab initio simulation package (VASP).45 The proton was modelled in a 36 ion ZrO2 supercell, where one Zr ion was replaced with a Y ion to produce a YSZ cell with a 8 mol% Y concentration.

3. Bulk configurations For the proton defect calculations we used supercells consisting of 3  3  3 fluorite unit cells which contain between 316 and

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322 ions depending on the oxygen vacancy concentration as defined by the Y ion concentration. Five configurations for each Y ion concentration (4%, 8%, 11% and 15%) were constructed using a random number generator. The atomic coordinates of each cation site ion were assigned a random number and then sorted numerically. Zr ions placed first in the list were then replaced with the appropriate number of Y ions to produce unique, random configurations. The same procedure was adopted for the introduction of the oxygen vacancies. The lowest energy structure obtained for each Y ion concentration is shown in Fig. 1. This image clearly illustrates the increase in local disorder caused by increasing the concentration of Y ions and oxygen vacancies. The lattice energies and constants averaged for each set of five configurations are given in Table 1. The introduction of the larger Y ions (0.90 Å, ref. 46) compared to

Paper Table 1 Calculated average lattice energies and constants for YSZ with various Y mol% concentrations

Y mol%

Average lattice energies (eV)

Average lattice constants (Å)

4 8 11 15

12086.48 11884.03 11681.77 11484.50

a a a a

= = = =

15.26, 15.31, 15.37, 15.42,

b b b b

= = = =

15.26, 15.31, 15.37, 15.42,

c c c c

= = = =

15.26 15.32 15.38 15.42

the smaller host Zr ions (0.72 Å, ref. 46) causes the simulation cell to expand as well as reducing its lattice energy.

4. Redox properties The applications of proton conducting materials require them to be stable over a wide range of reducing and oxidising conditions. Therefore it is important to assess the redox properties of any potential proton conductors. For the reduction process, additional oxygen vacancies are formed in the system and are compensated for by electronic defects (e 0 ) represented as the reduction of Zr4+ to Zr3+: 1  0 O O ! VO þ O2ðgÞ þ 2e 2

(3)

For oxidation we fill the oxygen vacancies which are already present in the system because of the introduction of Y3+ acceptor dopants to produce electron holes (h ): 1   V O þ O2ðgÞ ! OO þ 2h 2

Fig. 1 Lowest energy structures for YSZ supercells with a range of Y mol% concentrations. (a) 4 mol% YSZ, (b) 8 mol% YSZ, (c) 11 mol% YSZ and (d) 14 mol% YSZ.

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(4)

This approach has previously been successfully applied to ZrO226 and other fluorite structured materials like CeO247,48 as well as CeO2–ZrO249,50 solid solutions. Both the electronic defects and electron holes are treated as small polarons localised at ion sites with holes modelled as O ions substituted at O2 sites and electronic defects are modelled as Zr3+ ions substituted at Zr4+ sites. The same interatomic potentials used for the Zr–O and O–O interactions are also used to model these interactions; however the ionic charge is changed by one. In order to assess the consequences of the Y dopant ions the redox properties have been calculated using oxygen ions in the closest proximity to a Y ion (i.e. where the local structure is the most perturbed) as well as using oxygen ions at the possible furthest distance away from the Y ions (i.e. where the local structure most resembles undoped ZrO2). This method ensures that the most extreme local environments are sampled in each configuration and it gives the clearest indication of the effects the Y ions have on the redox properties. A similar method has recently been applied to the calculation of diffusion energy barriers in Gd-doped BaCeO3.51 Illustrations of typical defect clusters used for the reduction calculations are given in Fig. 2. The calculated defect energies are combined with the contributions from the fourth ionization energy of Zr (34.34 eV, ref. 52), the first and second electron affinity of oxygen (7.29 eV, ref. 48) and the bond dissociation energy of an oxygen molecule (2.58 eV per oxygen atom53) to produce the

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Fig. 2 Illustrations of typical defect clusters used for the reduction calculations. (a) Defect cluster with oxygen vacancy in close proximity to Y ion and (b) defect cluster with oxygen vacancy unperturbed by Y ion. Ions surrounding the clusters have been omitted for clarity.

Table 2 Calculated average energies of redox reactions for YSZ with various Y mol% concentrations (eV per electronic defect). Close refers to data obtained in close proximity to a Y ion and far refers to data obtained not in close proximity to a Y ion

Y mol% 0 (ZrO2)

24

4

8

11

15

Redox reaction —

Close Far Close Far Close Far Close Far

Reductiona Oxidation

5.18 5.35 5.06 5.21 4.70 4.95 4.64 4.86 6.39 6.14 6.34 6.47 6.27 6.40 6.30 6.65

a

5.47 6.33



Zr The reduction energies are calculated using a bound Esub;Zr  V O 

Zr3þ Esub;Zr

defect cluster.

redox reaction energies. These energies were calculated for each configuration and then averaged and are presented in Table 2. Due to the uncertainties associated with such free-ion terms, caution must be given in drawing a detailed analysis. However, such calculations do provide an insight into the general trends and allow for comparison between materials. These results clearly show that the addition of Y to ZrO2 causes a decrease in the Zr4+/Zr3+ reduction energy and that this decrease continues to occur with increasing dopant concentration. A similar result has been confirmed both experimentally54–56 and computationally47–50 for CeO2 and the CeO2–ZrO2 solid solution. Balducci et al.48 used lattice statics calculations to show that the introduction of divalent (Ca, Mn, Ni and Zn) and trivalent dopants (Sc, Mn, Y, Gd and La) all reduced the reduction energy of CeO2 up to a defect concentration of 50%. The explanation proposed for this observation is that the oxygen vacancies generated by the acceptor dopants allow the cell to more easily accommodate the strain caused by forming the larger Ce3+ species and therefore decreases the reduction energy. It is highly likely that a similar phenomenon is also occurring for YSZ. The results also show that the reduction energy is lowest when a Y ion is in close proximity. This is unsurprising as the Coulombic repulsion between a Zr4+ ion and a positively charged oxygen vacancy has now been replaced by the Coulombic attraction between an Y3+ ion and the oxygen vacancy. It is noteworthy that Zr is also often added to CeO2 to decrease its reduction energy.49,50,57 Conversely, the oxidation energies seem relatively unaffected by the introduction of Y as they fluctuate around the value obtained for undoped ZrO2.

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It is clear that reduction in YSZ is preferential to oxidation which is to be expected given that YSZ is commonly used as a protective coating to reduce the oxidation rate of the substrate.58,59 The energies of reduction calculated for YSZ are significantly lower than those calculated for 10 mol% di- and tri-valent doped CeO248 and the perovskite structured proton conductor BaZrO3.27 It has been previously been shown that both the reduction and oxidation energies for ZrO2 are significantly smaller at the grain boundaries in comparison to the bulk material.26 It is interesting that the reduction energies calculated here for bulk YSZ are similar and in some cases lower than the values calculated for ZrO2 grain boundaries. The redox properties of YSZ grain boundaries are an important topic that is currently under investigation.

5. Proton incorporation Proton incorporation is achieved by replacing the existing oxygen vacancies produced from acceptor doping with protonic defects which are represented by hydroxyl ions. This process is achieved by treating the material with water vapour. The process is illustrated by the following equation:   H2 O þ O O þ VO ! 2OHO

(5)

Protonic conduction in YSZ and ZrO2 is attributed to the Grotthuss mechanism6,10,60 where protons ‘hop’ between neighbouring oxygen ions. Quantum mechanical computational studies on proton conduction in perovskites also suggest that rotational movement of the hydroxyl group and potential quantum effects are also important in the process.25,61,62 Assessment of the equilibrium O–H configuration is therefore crucial. Two examples of equilibrium O–H configurations for 4 mol% YSZ are given in Fig. 3. As was the case for ZrO2,26 the equilibrium proton position is towards the centre of the cell where the Coulombic repulsion with the surrounding Zr and Y cations is at a minimum. It is noteworthy that in Fig. 3(a) the proton is able to move closer to the centre of the cell compared to the proton in Fig. 3(b). This suggests that the reduced Coulombic repulsion between the Y3+ ions and the proton (when compared to the repulsion between a Zr4+ and a proton)

Fig. 3 Schematic of the lowest energy O–H configurations in two structures of 4 mol% YSZ. (a) Defect cluster with proton in close proximity to Y ions and (b) defect cluster with proton not in close proximity to Y ions.

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is important in influencing the equilibrium position of the proton. The position of the proton is between the centre of the bonded O ion and the centre of the cell in the majority of the configurations tested, however at higher Y mol% concentrations the local distortion is higher and in some cases this position is no longer the lowest energy option. An O–H distance of 0.98–0.99 Å is calculated for all configurations independent of the Y mol% concentration. This value is in agreement with ZrO2 and Zr-based perovskite proton conductors, BaZrO3 and BaPrO3.27 Using eqn (5), the hydration energy, (EH2O) can be calculated using:   EH2 O ¼ 2EOH  E V O þ EPT

(6)

where EOH is the energy associated with the substitution of an   O2 ion with an OH group, E V is the oxygen vacancy O energy and EPT is the energy of the gas phase reaction O2 + H2O = 2OH. This final term can be estimated from the difference between the proton affinity of O2 and OH and is taken to be 11.77 eV in this work.41 A more detailed explanation of this approach is available elsewhere.63,64 The averaged hydration energies and the additional terms used to calculate them are provided in Table 3. The same method used for the calculation of the redox properties is also applied here with energies being calculated at oxygen sites with the shortest and longest Y–O distances. With the exception of the 4 and 15 mol% Y concentrations taken at distances away from Y ions, the oxygen vacancy energies are lower than for bulk ZrO2. For the cases where the oxygen vacancies are neighbouring at least one Y ion, the vacancy energies are significantly reduced (>1.5 eV). This is similar to what was observed for the reduction energies of YSZ, where positively charged oxygen vacancies are more easily formed in the presence of Y3+ ions as opposed to the more Coulombically repulsive Zr4+ ions. Above a concentration of 4 mol% Y the oxygen vacancy energies remains constant when calculated close to Y ions, but for vacancies not close to Y ions the energies are more variable with Y mol% concentration. The EOH values are also lower for YSZ than for ZrO2 (with the exception of the far case for 4 mol% Y concentration). This strongly suggests the preferential substitution of the hydroxyl group in YSZ when compared with the undoped material.

Table 3 Calculated average hydration energies and additional values used in eqn (6) for YSZ with various Y mol% concentrations (eV). Close refers to data obtained in close proximity to a Y ion and far refers to data obtained not in close proximity to a Y ion

Although the EOH values are still high in comparison to the value of 0.68 eV recently calculated for CeO2.65 Similar to the oxygen vacancy energies, the lowest EOH values are obtained when the hydroxyl group substitutes close to Y ions. This is supported by Fig. 3(a) where, as previously discussed, the reduced Coulombic repulsion between the proton and the Y ion allows the proton to move further into the centre of the cell where repulsion with surrounding cations is at a minimum. DFT calculations23,24 have also confirmed that the lowest energy proton migration pathway is around the Y ion in Y-doped BaZrO3. The hydration energies for YSZ are high which suggests a low concentration of protons in the system. However, all the values calculated for YSZ are lower than those of undoped ZrO2 and this is especially true for the configurations where the proton is in close proximity to a Y ion. This shows that incorporation is preferred in YSZ whether the proton incorporates near a Y ion or not when compared to ZrO2. The fact that proton incorporation is energetically favoured near Y ions suggests that proton incorporation will be easier at higher Y mol% concentrations. It is noteworthy that although the hydration energies for bulk YSZ are lower than the values for bulk ZrO2, they are significantly higher than the values obtained for S5 grain boundaries of ZrO2. This again illustrates the necessity for a comprehensive study of proton incorporation and migration in YSZ grain boundaries.

6. Proton trapping Doping of YSZ is common and is usually done to increase ionic conductivity66,67 or to increase thermal stability for thermal barrier coating applications.68,69 In this work we feature doping with a range of trivalent ions common to the material, namely Sc, In, Yb and Gd. Additional doping of Y is also considered. In addition to the usual activation energy, protons must overcome any trapping that exists as a result of proton-dopant association if long-range transport in the system is to be achieved. Proton trapping energies can be estimated by calculating the binding energies between neighbouring hydroxyl groups and aliovalent dopants. Binding energies were calculated for the lowest energy ‘close’ and ‘far’ configuration at each concentration tested. For all configurations the closest Zr ion site to the proton was chosen as the dopant substitution site. In addition to the binding energies, the local structure around such defect pairs is also assessed. Examples of proton-dopant pairs in the eight configurations tested are given in Fig. 4. The binding energy (Ebind) between oppositely charged defects is defined as the difference between the total energy of the isolated defects and the energy when the same defects are simulated together in a cluster:70–72

Y mol% 0 (ZrO2)26 4

8

11

15



Close Far

Close Far

Close Far

EðV O Þ 14.77 EOH a 16.51 6.48 EH2O a

Close Far

14.20 15.30 13.14 14.20 13.12 13.94 13.11 14.80 15.94 16.71 15.47 16.13 15.42 15.96 15.19 16.35 5.91 6.35 6.03 6.29 5.95 6.21 5.50 6.13

Includes D of the Morse potential (7.05 eV).

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Ebind = E(X) + E(Y)  E(XY) where a negative value implies binding behaviour. Fig. 5 shows the calculated binding energies for each dopant ion in each of the configurations. The effect of the dopant ions on the local structure is assessed by measuring the interatomic distances between the dopant and the proton. These results are provided in Table 4.

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Fig. 5 Comparison of the dopant-proton binding energies for a range of dopant ion sizes in bulk ZrO2 with (a) YSZ configurations with Y ions close to the defect cluster and (b) YSZ configurations without Y ions close to the defect cluster.

Table 4 Dopant-proton (M–H) interatomic distances (Å) for the defect pairs in various YSZ configurations

Y mol% 0 (ZrO2)26 4

Fig. 4 Relaxed local structures of proton-dopant pairs. (a) Sc-doped 4 mol% YSZ (close), (b) In-doped 4 mol% YSZ (far), (c) Y-doped 8 mol% YSZ (close), (d) Yb-doped 8 mol% YSZ (far), (e) Gd-doped 11 mol% YSZ (close), (f) Sc-doped 11 mol% YSZ (far), (g) In-doped 15 mol% YSZ (close) and (h) Y-doped 15 mol% YSZ (far).

For all of the defect pairs calculated with the exception of Gd in the 8 mol% Y far configuration, the binding energies are negative which suggests the existence of proton trapping effects in proton-doped YSZ. As expected the strength of the binding is proportional to the ionic radii of the dopant ions. The smallest dopant ions with the highest charge density like Sc produce the largest binding energies and larger dopant ions with lower charge density like Gd produce the weakest binding energies. Sc-doped ZrO268 and Sc-doped YSZ66 receive considerable interest because of their superior ionic conductivity compared to YSZ. However, our results suggest that the addition of Sc to proton-doped YSZ

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8

11

15

Ionic Ion radius (Å)42 —

Close Far Close Far Close Far Close Far

Zr Sc In Yb Y Gd

2.46 2.46 2.29 2.39 2.44 2.49

0.72 0.75 0.80 0.87 0.90 0.94

2.25 2.15 2.18 2.20 2.21 2.25

2.43 2.29 2.33 2.37 2.40 2.44

2.32 2.22 2.25 2.29 2.31 2.35

2.29 2.02 2.02 2.03 2.02 2.03

2.27 2.20 2.21 2.26 2.27 2.30

2.25 2.16 2.18 2.20 2.20 2.24

2.42 2.30 2.34 2.37 2.40 2.44

2.16 2.08 2.46 2.53 2.41 2.34

would be detrimental to the protonic conductivity because of the large energy barrier that would have to be overcome to achieve long-range transport. It is noteworthy that as a result of its reasonably large ionic radius, Y has a relatively weak association in comparison to the smaller dopants. Perhaps the most overt feature of Fig. 5 is the significant spread of data and how the binding energy can vary dramatically depending on the particular configuration. This is especially true for Fig. 5(b) where the defect pairs are not in close proximity to Y ions. For example, the binding energy of Sc can vary by B1 eV depending on the cluster and the configuration. This variation caused by the local structure clearly illustrates the significant effect of the introduction of Y ions on the ZrO2 structure. This also makes direct

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comparison of the binding energies of YSZ and ZrO2 somewhat challenging. With the exception of one defect pair in both Fig. 5(a) and (b), the binding energies are weaker in YSZ compared to ZrO2. This is important as it suggests that protonic long-range transport is more likely when Y is incorporated into the fluorite structure. The weaker binding is also illustrated by the generally longer M–H distances in Table 4 for YSZ as well as some of the structures in Fig. 4 where local distortion prevents shorter M–H distances and therefore stronger binding energies. It is likely that this weaker binding is also a result of the partial loss of the attraction between Zr4+ and MZr0 ions due to the Y doping. It must be noted that the binding energies calculated here are still considerably larger than those obtained for the grain boundaries of ZrO2.26 Table 4 again shows the strong influence the local structure has on the defect-pairs. The variation in M–H distance is quite large and which dopant ions increase or decrease the M–H distance in comparison to the Zr–H distance is entirely dependent on the local structure around the defect pair. In the vast majority of cases, the incorporation of smaller dopants is met with a decrease in the M–H distance as a result of the strong binding. For larger dopants there is generally an increase in the M–H interatomic distance as the dopant ions perturb the local structure to the extent where the proton is hindered from moving close to the dopant ion. This is again well illustrated by Fig. 4 and a similar trend was also observed for S5 grain boundaries in ZrO2.26 There are a couple of exceptions to this trend, for example the M–H distances for 8 mol% Y far configuration remain constant regardless of the dopant ion size. As discussed, it is difficult to apply the same the explanation to each configuration because the local structure can be very different between configurations. It should be remarked that the intention of this study is only to provide an insight and examples that reflect the complex nature of these defect pairs and the surrounding local structures. It is unfeasible to consider all the potential doping sites in all of the configurations simulated.

Table 5 YSZ

Proton transfer energy barriers for each pathway calculated in

Transfer pathway

O–O distance (Å)

Transfer barrier (eV)

A–B A–C A–D B–E D–E

3.00 3.00 3.52 2.53 2.44

0.42 0.42 0.88 0.40 0.32

basis, we focus our investigation of proton transfer energy barriers on protons that are located in close proximity to a Y ion. Fig. 6 shows the supercell and the calculated proton migration pathways. From the starting oxygen ion (A), three pathways are considered for the migration of the proton to the closest oxygen ions (B–D). Two further paths are considered to investigate the energetics of longrange diffusion (B–E) and (D–E). The calculated energy barriers for each pathway are given in Table 5. An example energy barrier plots for the A–B pathway is also provided in Fig. 7. The NEB calculations produce energy barriers of 0.42 and 0.88 eV for the initial proton ‘hop’ to the nearest neighbouring oxygen ions. The smaller value is similar to computationally and experimentally obtained values for the perovskite proton conductors Y-doped BaZrO322,25,73 and Gd-doped BaCeO3.51 Merinov and Goddard22 calculated barriers for proton migration within ZrO6 and

7. Proton migration The previous calculations have shown that the energy of incorporation is lower when a Y is in the vicinity of the hydroxyl ion. On this

Fig. 6

Fig. 7 Energy profile for the A–B proton transfer pathway.

Illustration of proton transfer pathways calculated for YSZ.

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YO6 octahedra and showed that the energy was very dependent on the O–O edges of the octahedra. For the smaller values of O–O edge distance, energy barriers of 0.32–0.49 eV were calculated, in comparison to the experimental value of 0.44 eV.73 For Gd-doped BaCeO3,51 values of 0.16–0.50 eV were found for the proton hopping transfer. Proton migration energies have also been calculated for the S5(310)/[001] grain boundary of Y-doped BaZrO3,23 however these energies are significantly higher than those calculated for the bulk and our values for YSZ. The value of 0.88 eV obtained for the A–D pathway shows that even a relatively small increase in O–O distance can cause a dramatic increase in the energy barrier. The energy barriers for the second ‘hop’ (0.40 and 0.32 eV for B–E and D–E, respectively) are smaller than the values for the first ‘hop’ which is unsurprising given the reduced the O–O interatomic distance. These results strongly suggest the existence of long-range proton transport in bulk YSZ and that this transport occurs by the proton hopping between oxygen ions in close proximity. At this time, it is impossible to deduce whether such transport is easier or indeed even exists in the grain boundary structures of YSZ as this work is currently ongoing. However, on the basis of these results and comparison with other computational results, proton migration in bulk YSZ is certainly comparable with other well established proton conducting materials including doped BaZrO3 and BaCeO3 and that further calculations are crucial.

8. Summary Using a combination of classical and quantum mechanical computational techniques, we have successfully investigated various important aspects of proton incorporation and migration in YSZ. Through quantitative comparison with ZrO2, it is shown that the introduction of Y to the ZrO2 fluorite structure reduces the energy of reduction (similarly to cation-doped CeO2) as well as the energy required to incorporate protons when compared to undoped ZrO2. Both of these energies were found to be at a minimum when they were calculated in the proximity of Y ions. The proton-dopant binding energy is also reduced in YSZ for the majority of configurations tested, although it is clear that these energies vary significantly and are very configurationally dependant. Migration energies were calculated for various proton migration pathways and values of 0.32–0.42 eV were obtained for ‘hops’ with the shortest O–O distances. These energy barriers are comparable with those obtained for important perovskite proton conductors including Y-doped BaZrO3. This is the first computational study to consider these properties of proton-doped YSZ and in conjunction with ongoing grain boundary calculations will be essential in resolving the current debate as to whether proton incorporation and conduction is dominate in the bulk or in the grain boundaries.

Acknowledgements This research was supported by a Grant-in-Aid for Scientific Research on Innovative Areas, ‘‘Exploration of nanostructure– property relationships for materials innovation’’ from the

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Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan. The authors also thank the Japan Society for the Promotion of Science (JSPS) for funding.

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Protonic defects in yttria stabilized zirconia: incorporation, trapping and migration.

Both classical and quantum mechanical simulation techniques have been applied to investigate the incorporation, migration and potential binding of pro...
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