Article pubs.acs.org/Langmuir
Significant Reduction in Hydration Energy for Yttria Stabilized Zirconia Grain Boundaries and the Consequences for Proton Conduction James A. Dawson* and Isao Tanaka Department of Materials Science and Engineering, Kyoto University, Sakyo, Kyoto 606-8501, Japan ABSTRACT: Using well-established atomistic techniques, we investigate the defect chemistry, structural effects, and energetics of proton incorporation at the Σ5(310)/[001] and Σ5(210)/[001] symmetrical tilt grain boundaries of yttria-stabilized zirconia. Building upon past work, we consistently show a dramatic decrease (∼4−5 eV) in the proton incorporation and hydration energies in and around the grain boundary structures compared to values obtained for the bulk material and undoped ZrO2 grain boundaries. This decrease is prevalent in both Y segregated grain boundaries and grain boundaries where the distribution of Y is completely random. The results presented here strongly support the argument that proton conduction in this system is primarily interfacially driven, as reported by numerous experimental studies. Redox properties are also presented for grain boundaries structures both with and without defect segregation. The methodology and results presented here can also be applied to a wide range of proton conductors and will prove essential in any future assessment of the effects of grain boundaries on the defect chemistry of protons in these systems.
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Alternatively, Scherrer et al.10 reports that the proton conduction mechanism at temperatures between 120 and 400 °C is due to proton transport via chemisorbed water at the inner surface of the material. It is reported that, from room temperature to 120 °C, proton conduction is due to physisorbed water at the inner surface. It is also stated that grain boundaries are not permeable to protons for dense nanocrystalline YSZ samples. Studies by Raz et al.11,12 also support these findings. Recent studies also suggest such conductivity in YSZ, and CeO2 is actually a result of internal surfaces produced from cracks and pores.13−15 The work presented here builds upon our two recent studies, where lattice statics calculations are used to investigate various aspects of proton defect chemistry in undoped bulk and grain boundary structures of ZrO216 and bulk YSZ.17 For ZrO2, it was discovered that both the hydration and redox reaction energies are significantly reduced in and around the Σ5(310)/[001] and Σ5(210)/[001] grain boundaries when compared to the bulk structure. The proton trapping or proton-defect binding energies are also reduced at the grain boundaries, suggesting that any potential trapping effects will be less significant at the grain boundaries, meaning reduced hindrance of protonic transport. The calculations for bulk YSZ show that the introduction of Y to the system significantly reduces both the reduction energy and hydration energy. These energies were found to be at a minimum when the proton is in close
INTRODUCTION The need for solid electrolytes for solid oxide fuel cells (SOFCs) with operating temperatures lower than those based on the conventional oxygen-ion conductor YSZ is essential in avoiding the problems usually associated with material degradation at such high temperatures (>800 °C). 1,2 Considerable effort has been given to the study of nanosolid electrolytes with potential application in lower temperature SOFCs in the hope that the high density of grain boundaries will act as fast conduction paths.1 This is despite the fact that grain boundaries in YSZ ceramics have been shown to be highly resistive to oxygen diffusion.3−5 Since the discovery of high protonic conduction at low temperatures in YSZ ceramics,1,6 there has been much debate over whether this conduction primarily occurs in the bulk, grain boundaries, or even the internal surfaces of the material. Numerous studies support the argument that proton conduction is interfacially driven. Two examples are the work of Kim et al.6 and Avila-Paredes et al.,7 where proton conduction is observed in nanocrystalline YSZ with grain boundary size between ∼13 and ∼100 nm at room temperature in humid atmospheres and that samples with large grain sizes exhibited very little protonic conduction. Park et al.8 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. It has also been found that the bulk defect chemistry of Gd-doped CeO2 (a material with the same fluorite structure as YSZ) plays no significant role in controlling the protonic conductivity, which again primarily occurs at the grain boundaries.9 © 2014 American Chemical Society
Received: May 15, 2014 Revised: August 6, 2014 Published: August 8, 2014 10456
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material that relaxes harmonically based on its dielectric constant and structure beyond the inner region. Of course, this is not the case for grain boundaries. One method for solving this problem is discussed by Duffy and Tasker33 and uses planar integrals to calculate the outer region summations. However, this approach only works for diagonally cubic systems and becomes far more complicated for lower symmetry systems.34 Fortunately, this error is small in our cubic system, and energy convergence with region size can be easily achieved, as illustrated by Figure 1. We used Mott−Littleton radii sizes of 13 and 21 Å for the inner and outer regions, respectively.
proximity to one or more Y ions. Low proton trapping and migration energies were also calculated for bulk YSZ structures. This work represents the final part of this study of proton incorporation in these materials. Using classical atomistic methods, we address the question of whether proton incorporation is truly preferred at the grain boundaries or the bulk, and from this we deduce the implications for proton conduction. We consider grain boundaries both with defect segregation and with a completely random distribution of defects. Grain boundary segregation in YSZ has received considerable attention18,19 and in particular its effect on GB resistance.20−22 For these grain boundaries, the preferred proton positions are established and the energies of hydration calculated for a range of Y mol % concentrations. Redox energies are also considered for both grain boundary and bulk regions of the simulation cell. Comparisons to previous calculations and experiment are made wherever possible. In addition to providing essential information on protons in YSZ, it is hoped that this study will stimulate many other studies of grain boundaries in solid-state proton conductors, a research area where currently the literature is very limited with regard to simulation.
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METHODS
Figure 1. Illustration of the defect energy convergence with Mott− Littleton inner region size for an oxygen vacancy at the Σ5(210)/ [001] YSZ grain boundary.
All calculations presented here were performed using the General Lattice Utility Program (GULP).23 For the simulation of the YSZ structure, a force field described with a Born model is used. Atoms are treated as charged spheres with attractive and repulsive short-range interactions being accounted for by interatomic potentials. In the static limit, lattice vibrations are ignored and the structure is determined by the static contributions to the internal energy as well as lattice vectors and atomic positions. The methods discussed in this section are well established, and comprehensive reviews are available elsewhere.24 As with the previous studies, we use the ZrO2 potential model developed by Woodley et al.25 because of its excellent agreement with experimental measurements.16 All the short-range interactions are calculated using Buckingham interatomic potential, and 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 the protonic interactions, we use an attractive Morse potential developed using ab initio cluster calculations26 to describe the O−H interaction as well as a Buckingham potential to describe the interactions between the OH group and the surrounding lattice.27 The Morse potential takes the form
V (r ) = D{1 − exp[− β(− r /r0)]}2
Grain Boundary Models. In this work we focus on two symmetric tilt grain boundaries, namely Σ5(310)/[001] and Σ5(210)/[001]. These grain boundaries were formed using CSL theory where two individual grains are tilted by a given angle (36.8° for Σ5(310)/[001] and 53.2° for Σ5(210)/[001]) until their surface planes ((310) or (210)) coincide. Both of the grain boundary supercells are longest in the z direction in order to minimize the interactions between the equivalent grain boundary planes at the center and edges of the supercells. In between these two equivalent grain boundaries, the supercell maintains the bulk structure, albeit with the influence of the nearby grain boundary planes. The unoptimized initial pure ZrO2 grain boundary structures are given in Figure 2. One issue with the initial grain boundaries structures is that there are ions with the same charge in close proximity at the interfaces, as shown by the ellipses in Figure 2. This of course causes significant Coulombic repulsion and instability at the grain boundary. In order to reduce the repulsion, we follow the approach of Yoshiya et al.,35 where vacancies are introduced across the grain boundary to halve the atom density. Vacancies are introduced in a zigzag manner along the y axis, leaving the atomic columns within the ellipses with half the atom density of other columns. As also reported by Yoshiya et al., for undoped ZrO2 these half-occupied columns remain separate after structural optimization. However, for the case of the defect segregated YSZ grain boundaries, the half-occupied columns merge and form one fully occupied column, in agreement with experiment.36 The formation of this one fully occupied column for the nonsegregated (i.e. random defect introduction) YSZ grain boundaries is entirely dependent on the individual configuration. While some configurations do form the fully occupied column, others do not and remain separate, leaving large unoccupied areas (this is especially true for Σ5(210)/[001]) at the grain boundary, as observed for previous calculations of ZrO2 grain boundaries.16 Examples of these “closed” and “open” grain boundary structures are given in Figures 3 and 4. The properties of the two undoped grain boundaries are presented in Table 1. All our grain boundary calculations were completed using supercells with between 316 and 348 ions, depending on the oxygen vacancy concentration, as defined by the Y ion concentration. Convergence with grain boundary separation was tested and achieved using a selection of supercells with fewer atoms and smaller z cell dimensions. The grain boundary energies are calculated using
(1)
where D, β, and r0 are the parameters obtained from ab initio quantum mechanical cluster calculations with a point charge representation of the surrounding lattice.26 To ensure the OH group has the correct overall charge of −1, the dipole is distributed across both ions with an oxygen charge of −1.4263 and a hydrogen charge of +0.4263. All other oxygen ions have the usual charge of −2. In addition to our previous studies, this approach has been successfully applied to a wide range of proton conducting solid state materials.28−31 Both point defects and proton incorporation are simulated at the infinitely dilute limit using the Mott−Littleton method.32 The crystal structure surrounding the defect is divided into two spherical regions: an inner and an outer region. In the inner region, explicit relaxations of the atoms occur, whereas in the outer region (where the interactions are weaker) an approximation based on a dielectric continuum method is made. The total energy, E, can be written as E = E1(x) + E12(x , η) + E2(η)
(2)
where E1 and E2 are the energies of the inner and outer regions, respectively, and E12 is the energy of the interactions between them. Atomic displacements are denoted by x and η for the inner and outer regions, respectively. The Mott−Littleton method assumes a uniform 10457
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Figure 4. Example unoptimized and optimized configurations for the (a) 3.5 mol % YSZ Σ5(310)/[001], (b) 7 mol % YSZ Σ5(210)/[001], (c) 10.5 mol % YSZ Σ5(310)/[001], and (d) 14 mol % YSZ Σ5(210)/ [001] grain boundaries with randomly distributed defects. Figure 2. Initial structures for the (a) Σ5(310)/[001] and (b) Σ5(210)/[001] undoped ZrO2 grain boundaries. The arrows indicate the position of the grain boundary in the supercell. The ellipses show the ions with the same charge in close proximity at the grain boundaries.
Table 1. Lowest Grain Boundary Energies for the Two Structures and the Respective Energies, Cell Dimensions, and Grain Boundary Separations
EGB − E bulk 2A
Energy (J m−2)
Cell dimensions (x, y, z) (Å)
Grain boundary separation (Å)
Σ5(310)/[001] Σ5(210)/[001]
3.03 3.07
5.07, 16.03, 48.10 5.07, 11.34, 63.49
24.20 31.75
− 2.52 J/m2 and Σ5(210)/[001] − 2.69 J/m2). Fisher and Matsubara5 used molecular dynamics to calculate a value between 2.7 and 2.9 J m−2 for the Σ5(310)/[001] boundary at temperatures between 1273 and 2673 K. For the defect segregated grain boundaries, one configuration was considered for each of the Y ion concentrations considered (3.5 mol %, 7 mol %, 10.5 mol %, and 14 mol %). For these configurations, the Y ion concentration simply refers to the overall cell concentration. Y dopants and the compensating oxygen vacancies were placed at and as close as possible to the grain boundary, so the actual interface Y ion concentration is much higher. In order to avoid any potential confusion, it must also be stated that, for these segregated grain boundaries, there is no depletion of the interior grain structure, as can be observed for grain sizes of only a few nanometers. For grain boundaries with a random distribution of Y ions and oxygen vacancies, a total of 20 configurations were considered: five for each Y ion concentration. The defect locations 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 creation of configurations with random Y ions and oxygen vacancies at the bulk-like structure (i.e. grain interior) allows for direct comparison with the segregated configurations. Figure 3 shows an example of an optimized and unoptimized segregated YSZ grain boundary configuration for each Y concentration. Figure 4 shows the same for YSZ grain boundaries with random defect locations. Our optimized YSZ grain boundaries are generally in good agreement with previous transition electron microscopy (TEM)37 and high resolution electron microscopy (HREM)38 experiments. More details on the structural comparison
Figure 3. Unoptimized and optimized configurations for the (a) 3.5 mol % YSZ Σ5(310)/[001], (b) 7 mol % YSZ Σ5(210)/[001], (c) 10.5 mol % YSZ Σ5(310)/[001], and (d) 14 mol % YSZ Σ5(210)/ [001] defect segregated grain boundaries.
σGB =
Grain boundary
(3)
where EGB and Ebulk are the energies of the grain boundary and the bulk supercell, respectively, and A is the area of the interface. The area of the interface is doubled to account for the presence of the two equivalent grain boundaries in the supercell. The ZrO2 grain boundary energies calculated using the Woodley et al. potential model are slightly higher than those calculated by Yoshiya et al. (Σ5(310)/[001] 10458
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Figure 5. Examples of the different structural environments used for the reduction and oxidation energy calculations in (a) a defect segregated Σ5(310)/[001] grain boundary and (b) a nonsegregated Σ5(310)/[001] grain boundary. The triangles represent example defect clusters used for the reduction calculations, and the circles show the typical oxygen locations for the oxidation calculations. The labels signify each of the three environments: O1 is the center of the grain boundary, O2 is directly next to the center of the grain boundary, and O3 is the bulk-like environment with Y ions in close proximity (where possible).
where h• is an electron hole. Both the electronic defects and electron holes are treated as small polarons localized at ion sites, meaning holes (h•) are modeled as O‑ ions substituted at O2− sites and electronic defects (e′) are modeled as Zr3+ ions substituted at Zr4+ sites. The same Zr−O and O−O potentials are used to model these interactions also, albeit with the ionic charge changed by one. The same approach has been used for our previous work on ZrO216 and bulk YSZ17 as well as other fluorite structured materials, such as CeO239,40 and CeO2− ZrO241,42 solid solutions. For the segregated YSZ grain boundaries, the reduction energy is only calculated for the bulk-like environment, as the calculation requires Zr ions which have been replaced by Y ions at the segregated grain boundaries. The oxidation energies are calculated for oxygen ions in the center of the grain boundary, the next adjacent column to the center of the grain boundary, and the bulk-like environment. For the nonsegregated grain boundaries, both reduction and oxidation energies are calculated for representative sites at three different locations: at the grain boundary, at the next adjacent column, and in close proximity to a Y ion away from the grain boundary (i.e. the bulk structure). This method ensures that the most extreme local environments are sampled in each configuration, and it gives
and open/closed grain boundaries in ZrO2 are available in our earlier work.16
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RESULTS AND DISCUSSION Redox Reactions. Reduction and oxidation are important in proton conductors because of the need for them to remain stable and work over a wide range of chemical environments. By calculating and comparing the energetics of these processes at different locations in the simulation cell and for both segregated and nonsegregated grain boundaries, the influence of these grain boundaries on the redox properties of the material can be assessed. For reduction, oxygen vacancies are formed in the system and are compensated for by electronic defects (e′) represented as the reduction of Zr4+ to Zr3+: OOx → V •• O +
1 O2(g) + 2e′ 2
(4)
For oxidation we assume oxygen vacancies are already present in the system as a result of Y acceptor doping: V •• O +
1 O2(g) → OOx + 2h• 2
(5) 10459
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Table 2. Calculated Redox Reaction Energies for the Segregated Σ5(310)/[001] and Σ5(210)/[001] YSZ Grain Boundaries with Various Y mol % Concentrationsa Redox energies (eV) Σ5(310)/[001] 3.5 mol % Y Redox reaction Reductionb Oxidation
O1 6.34
7 mol % Y
O2
O3
5.95
5.33 6.16
O1 6.02
3.5 mol % Y Redox
reaction
Reductionb Oxidation a
O1 4.88
10.5 mol % Y
O2
O3
O1
5.28 5.76 5.98 Σ5(210)/[001]
6.05 7 mol % Y
O2
O3
5.87
5.39 6.25
O1 4.94
14 mol % Y
O2
O3
6.16
5.53 5.93
O1 6.29
10.5 mol % Y
O2
O3
5.74
5.49 6.01
O1 5.10
O2
O3
6.25
5.33 5.97
14 mol % Y
O2
O3
5.17
5.47 6.30
O1 4.76
O2
O3
5.65
5.38 5.89 3+
•• The structural environments labeled O1, O2, and O3 are as defined in Figure 5. bThe reduction energies are calculated using a bound EZr sub,Zr − Vo 3+
− EZr sub,Zr defect cluster.
Table 3. Calculated Average Redox Reaction Energies for the Nonsegregated Σ5(310)/[001] and Σ5(210)/[001] YSZ Grain Boundaries with Various Y mol % Concentrationsa Redox energies (eV) Σ5(310)/[001] 3.5 mol % Y
7 mol % Y
Redox reaction
O1
O2
O3
O1
O2
Reductionb Oxidation
4.39 6.18
4.44 6.27
4.94 6.24
4.37 6.39
4.60 6.17
3.5 mol % Y Redox
reaction
Reductionb Oxidation a
10.5 mol % Y O3
14 mol % Y
O1
O2
O3
O1
O2
O3
4.50 4.88 6.43 6.33 Σ5(210)/[001]
4.82 6.47
4.41 6.72
4.73 6.03
4.97 6.31
4.35 6.36
7 mol % Y
10.5 mol % Y
14 mol % Y
O1
O2
O3
O1
O2
O3
O1
O2
O3
O1
O2
O3
4.57 5.74
4.73 5.70
5.13 6.63
4.55 5.44
5.04 5.19
4.87 6.55
4.46 5.16
4.31 5.50
4.64 6.17
4.45 5.39
4.61 5.65
4.60 5.69 3+
•• The structural environments labeled O1, O2, and O3 are as defined in Figure 5. bThe reduction energies are calculated using a bound EZr sub,Zr − Vo 3+
− EZr sub,Zr defect cluster.
grain boundary nor the Y mol % has any major influence on the oxidation energies. For some cases, the energy is lower at the grain boundary core, but in other cases, it is lower in the bulk. Similar small fluctuations in the energy were also observed for bulk structures of YSZ.17 When compared to the values obtained for undoped ZrO2 grain boundaries,16 the oxidation values here are higher, suggesting that in some cases the presence of Y hinders oxidation. This is interesting, considering that YSZ is commonly used as a protective coating to reduce the oxidation rate of the substrate.46,47 Alternatively, the oxidation energies for the Σ5(210)/[001] grain boundary show a far stronger dependence on the interface. The energies are significantly reduced at the grain boundary core and also to a lesser extent at the adjacent grain boundary layer when compared to the bulk structure. This clearly shows that the ease of oxidation varies depending on the particular grain boundaries. The Y mol % concentration again does not seem to strongly affect the oxidation energies. Unlike for the segregated cases, the nonsegregated grain boundaries show a trend of deceasing reduction energy with Y mol % concentration for the bulk-like environment calculations (close Y proximity). This was also earlier confirmed for bulk YSZ configurations17 and has been observed in both CeO2 and CeO2−ZrO2 solid solutions.39−41,48,49 It is noteworthy that no such trend exists at the grain boundary core or the adjacent
the clearest indication of the effects the grain boundaries and defects have on the redox properties. Illustrations of all these different structural environments are given in Figure 5. The calculated defect energies are combined with the contributions from the fourth ionization energy of Zr (34.34 eV43), the first and second electron affinity of oxygen (7.29 eV44), and the bond dissociation energy of an oxygen molecule (2.58 eV per oxygen atom45) to produce the redox reaction energies. The calculated energies for the segregated and nonsegregated grain boundaries are presented in Tables 2 and 3, respectively. For the nonsegregated grain boundaries, the energies are averaged for each configuration and then again for the five configurations per Y mol % concentration. The reduction energies for the segregated grain boundaries are reasonably constant over the Y mol % concentration range, which is unsurprising given that they are calculated at the bulklike regions of the cell (and therefore there is minimum influence from the grain boundaries and Y ions). The results agree with our previous calculations on ZrO 2 grain boundaries,16 where reduction energies of 5.53 and 5.02 eV were calculated for the bulk-like regions of the Σ5(310)/[001] and Σ5(210)/[001] simulation cells, respectively. For the oxidation energies, however, there are distinct differences between the two types of segregated grain boundary structures. For Σ5(310)/[001], it would seem that neither the 10460
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layer for Σ5(310)/[001], although this trend (albeit weak) can be seen for the grain boundary core of Σ5(210)/[001]. Another illustration of the differences between the results for the two grain boundaries is that, for Σ5(310)/[001], at high Y concentrations the bulk reduction energies are lower than those calculated at the grain boundary. This suggests that, in some cases, the proximity of Y ions to the oxygen site of interest is more important in determining its redox properties than the grain boundary. This is not true for Σ5(210)/[001] grain boundaries where the reduction energies at the grain boundary are considerably lower than the bulk-like values. Our values are similar to those calculated for undoped ZrO216 grain boundaries and generally smaller than those calculated for bulk YSZ.17 Oxidation energies for the nonsegregated grain boundaries are all high, especially for the Σ5(310)/[001] grain boundary. The lower values are observed at the grain boundary core and the adjacent layer of the grain boundary. As is true for the segregated cases, there seems to be no trend with Y concentration. Again, the calculated oxidation energies here are generally higher than those calculated for undoped ZrO2 grain boundaries,16 but they are lower than those calculated for bulk YSZ.17 This also supports the arguments that the introduction of the Y to the system increases the oxidation energies and that these energies are usually at a minimum near the grain boundary. Proton Incorporation. Proton incorporation in such materials is usually achieved through treatment with water vapor. The oxygen vacancies produced to compensate the negative charge formed from acceptor doping are replaced by the protonic defects2,50 as illustrated by • H 2O + OOx + V •• O → 2OH O
(6) Figure 6. Illustrations of Mott−Littleton defect regions for the lowest energy O−H configurations in the 10.5 mol % Y defect segregated Σ5(310)/[001] grain boundary at (a) the grain boundary core, (b) the first adjacent layer grain boundary layer, and (c) the bulk-like region.
where the protonic defect is described as a hydroxyl ion. Protonic conduction in YSZ is attributed to the Grotthuss mechanism51,52 where protons “hop” between neighboring oxygen ions. Quantum mechanical studies on proton conduction in perovskites also suggest that rotational movement of the hydroxyl group and potential quantum tunneling effects may also be important in the transport process.53,54 It is clearly essential, therefore, to determine the lowest energy O− H configurations. Figures 6 and 7 show examples of Mott−Littleton defect regions and local structures for the lowest energy O−H configurations in each simulation cell environment for both types of grain boundary. It is clear that the position of the proton varies significantly depending on the grain boundary and the local structure. For simple bulk ZrO2 and YSZ structures, the equilibrium proton position lies directly between the bonded oxygen ion and the central point of the cell.16,17 In this position Coulombic repulsion between the proton and the surrounding Zr ions is minimized. However, for complicated grain boundary structures and local structures strongly perturbed by the introduction of Y ions and oxygen vacancies, this is not always possible. Whenever possible the proton resides in the spaces formed at the grain boundary; this is evident from both Figures 6 and 7, where for both the segregated and nonsegregated cases the proton sits at the closest possible free area to minimize repulsion from nearby Zr and Y ions. As was the case for undoped ZrO2 grain boundaries,16 the proton is often capable of slightly displacing the attached oxygen ion. Figure 7c shows that protons are more likely to reside near Y ions rather than Zr ions, which is
unsurprising given the smaller positive charge density of a Y3+ ion when compared to a Zr4+ ion. As with previous work, O−H distances of 0.98−1.00 Å are observed, in agreement with typical values for solid-state proton conductors.2 The hydration energy (EH2O) is based on eq 6 and is calculated using E H2O = 2EOH − E(V •• o ) + E PT
(7)
where EOH is the energy associated with the substitution of an O2− ion with an OH− group, E(V•• o ) is the oxygen vacancy energy, and EPT is the energy of the gas phase reaction O2− + H2O = 2OH−. This final term is estimated from the difference between the proton affinities of O2− and OH− and is taken to be −11.77 eV in this work.55 This approach is described in more detail elsewhere.56,57 The hydration energies and the additional terms used to calculate them are provided in Tables 4 and 5 for the segregated and nonsegregated grain boundaries, respectively. These results clearly illustrate the substantial reduction in hydration energy at and around the grain boundary for all types of grain boundary simulated. This reduction is far greater than what has been observed for ZrO2 grain boundaries16 and bulk YSZ.17 For the segregated grain boundaries the decrease in hydration energy at the core compared to the bulk is ∼4-5 eV. 10461
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as the presence of only one of these criteria produces far higher hydration energies.16,17 The high energies calculated for the bulk-like environment are in good agreement with our previous calculations16,17 and suggest a very low proton concentration. The most important feature of these results is that they strongly suggest a far higher concentration of protons at the grain boundaries in YSZ compared to the bulk structure and therefore the strong likelihood that proton conduction in YSZ primarily occurs at the interfaces and not the bulk. With the exception of the bulk-like environment in the nonsegregated Σ5(310)/[001] grain boundary, there again appears to be no trend between the hydration energy and the Y concentration. This leads to the conclusion, that at least for the grain boundary, the concentration of Y does not have a significant effect on the proton concentration. For the majority of examples, the hydration energy is lowest at the grain boundary core; however, this is not true for the nonsegregated Σ5(210)/[001] grain boundary, where the hydration energy of the oxygen ions at the adjacent layer is consistently lower. Figure 7 shows that protons in this grain boundary reside in the large spaces of the grain boundary. This was also observed previously for the Σ5(210)/[001] ZrO2 grain boundary and is the result of strain from the unfavorable threefold coordination and the two short Zr−O interatomic distances of the grain boundary core oxygen ions.16 Tables 4 and 5 also show the large spread of oxygen vacancy and EOH energies calculated and that these energies are very configurationally dependent. This is especially true for the segregated cases where energies can vary by more than 5 eV and almost 5 eV for oxygen vacancies and EOH values, respectively. This is perhaps unsurprising given the extreme differences in structural environments for where the energies are calculated. Again, there is no strong trend with Y concentration for these results. Generally, both the oxygen vacancy and EOH values are lower at the grain boundary than at the bulk-like environment, as a result of the unfavorable oxygen threefold coordination and the large free spaces available at the grain boundaries. As discovered previously, for the nonsegregated Σ5(210)/[001] grain boundary, these energies are mostly higher than for Σ5(310)/[001].16 The bulk oxygen vacancy and EOH values are in good agreement with our previous work.16,17
Figure 7. Illustrations of Mott−Littleton defect regions for the lowest energy O−H configurations in, for example, the 10.5 mol % Y nonsegregated Σ5(210)/[001] grain boundary configuration at (a) the grain boundary core, (b) the first adjacent layer grain boundary layer, and (c) the bulk-like region in Y ions in close proximity.
For the nonsegregated grain boundaries the decrease is not quite as dramatic, but is still ∼3-4 eV. This strongly suggests that it is both the introduction of Y ions to the system and the presence of grain boundaries that produces such low energies,
Table 4. Calculated Hydration Energies and Additional Values (eV) Used in Eq 7 for the Segregated Σ5(310)/[001] and Σ5(210)/[001] YSZ Grain Boundaries with Various Y mol % Concentrationsa Σ5(310)/[001] 3.5 mol % Y E(V•• o ) EOHb EH2O
7 mol % Y
10.5 mol % Y
14 mol % Y
O1
O2
O3
O1
O2
O3
O1
O2
O3
O1
O2
O3
10.76 12.17 1.81
15.63 14.62 1.84
15.29 16.77 6.48
12.08 12.48 1.11
14.53 14.05 1.80
16.22 17.05 6.11
13.68 13.36 1.27
14.96 14.40 2.07
16.02 16.91 6.03
12.01 13.02 2.26
13.67 13.76 2.08
15.89 16.91 6.28
Σ5(210)/[001] 3.5 mol % Y E(V•• o ) EOHb EH2O a
7 mol % Y
10.5 mol % Y
14 mol % Y
O1
O2
O3
O1
O2
O3
O1
O2
O3
O1
O2
O3
15.74 14.14 0.77
13.67 13.91 2.38
14.87 16.52 6.40
13.68 12.99 0.53
12.34 13.09 2.07
15.85 17.02 6.42
13.58 13.26 1.17
13.77 13.57 1.60
14.67 16.31 6.18
14.36 13.50 0.87
12.60 12.91 1.45
16.36 17.29 6.45
The structural environments labeled O1, O2, and O3 are as defined in Figure 5. bIncludes D of the Morse potential (7.05 eV). 10462
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Table 5. Calculated Average Hydration Energies and Additional Values (eV) Used in Eq 7 for the Nonsegregated Σ5(310)/ [001] and Σ5(210)/[001] YSZ Grain Boundaries with Various Y mol % Concentrationsa Σ5(310)/[001] 3.5 mol % Y E(V•• o ) EOHb EH2O
7 mol % Y
10.5 mol % Y
14 mol % Y
O1
O2
O3
O1
O2
O3
O1
O2
O3
O1
O2
O3
12.60 12.91 1.45
12.76 13.90 3.26
14.26 15.43 4.84
13.19 13.19 1.35
12.35 13.22 2.33
13.41 14.85 4.53
12.97 13.08 1.42
13.05 13.89 2.96
11.51 13.79 4.30
13.28 13.18 1.32
12.73 13.91 3.31
13.33 14.65 4.21
Σ5(210)/[001] 3.5 mol % Y E(V•• o ) EOHb EH2O a
7 mol % Y
10.5 mol % Y
14 mol % Y
O1
O2
O3
O1
O2
O3
O1
O2
O3
O1
O2
O3
14.67 14.25 2.06
14.74 14.19 1.87
12.31 14.26 4.44
16.39 15.05 1.93
16.79 15.14 1.72
12.93 14.62 4.54
16.08 15.04 2.23
15.78 14.73 1.93
13.67 15.01 4.58
14.94 14.36 2.01
13.70 13.62 1.78
15.08 15.65 4.45
The structural environments labeled O1, O2, and O3 are as defined in Figure 5. bIncludes D of the Morse potential (7.05 eV).
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SUMMARY Through the use of atomistic simulation techniques and by extending our previous studies, we have successfully shown that hydration energies in and around the grain boundaries are dramatically lower than the bulk values, and as a result a far higher concentration of protons exists at the grain boundaries in YSZ compared to the bulk structure. It must therefore be concluded that proton conduction in YSZ is not primarily a bulk phenomenon, but is indeed an interface phenomenon. In this comprehensive study, we have considered both defect segregated and nonsegregated Σ5(310)/[001] and Σ5(210)/ [001] grain boundaries. All of the example structures simulated show this reduction in hydration energy, regardless of segregation, structure, and Y mol % concentration. Redox reaction energies have also been calculated and are also lower at the grain boundary. Our results are in good agreement with previous work. The importance of local coordination environments, defect structure, and distance from grain boundaries on the oxidation, reduction, and hydration properties of YSZ has clearly been illustrated. All of the results that have been presented show that the grain boundaries and the introduction of Y ions and oxygen vacancies to the system both have a dramatic effect on the defect chemistry of protons in this system and undoubtedly other solid-state proton conducting systems. Currently, the literature concerning the effect of grain boundaries on proton defect chemistry in solid state materials is limited, and this is especially true for modeling studies. We hope the work described here will inspire further studies on other solid-state proton conductors so that the true impact of such interfaces on proton incorporation, trapping, and migration can be assessed.
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(Grant No. 25106005) and for (b) a JSPS fellowship (Grant No. 2503370).
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REFERENCES
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank the Japan Society for the Promotion of Science (JSPS) for (a) funding through Grants-in-Aid for Scientific Research on Innovative Areas “Nano Informatics” 10463
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