Structural Stability of La2Ce2O7

Article pubs.acs.org/JPCC

Structural Stability of La2Ce2O7 as a Proton Conductor: A FirstPrinciples Study Qingping Zhang,† Xiao Zheng,*,‡,§,∥ Jun Jiang,§,∥ and Wei Liu†,*,⊥ †

CAS Key Laboratory of Materials for Energy Conversion, Department of Material Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China ‡ Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China § Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China ∥ Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Institute of Applied Physics, Guizhou Normal College, Guiyang, Guizhou 550018, China ⊥ Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei, Anhui 230031, China S Supporting Information *

ABSTRACT: As a promising candidate of a proton conductor under reducing atmosphere, La2Ce2O7 has attracted considerable research interest. However, the thermodynamically stable structure of bulk La2Ce2O7 has remained rather unclear. In this paper, first-principles calculations are carried out to resolve this issue. It is found that the lattice of La2Ce2O7 is substantially stabilized by the formation of anion Frenkel defects, i.e., oxygen atoms displaced from their original sites to interstitial regions. Consequently, the bulk La2Ce2O7 favors disordered fluorite configurations over pyrochlore structure. Our calculation results are consistent with the previously reported neutron diffraction patterns. In addition, partial disordering of cations is also likely under experimental conditions. We then explore the possible proton transfer pathways inside bulk La2Ce2O7. It is revealed that the partial disordering in La2Ce2O7 increases the energy barriers of proton transfer pathways.

1. INTRODUCTION Hydrogen energy has aroused great attention over the decades. Given the high cost of H2 generation directly by renewable energy, effective technologies are demanding the separation of hydrogen from gaseous products of fuel reforming.1 It is desirable to find a proper proton conductor material which reaches a balance among cost, stability, and performance. Various ceramic proton conductors have already been extensively studied for their lower expense than noble metals such as Pd alloys.1 Among these materials, La2Ce2O7 (50% Lanthanum doped ceria) has demonstrated appreciable proton conductivity under reducing atmosphere as well as satisfactory stability in the presence of CO2.2 These virtues have made La2Ce2O7 a potentially promising electrolyte for solid oxide fuel cells3 and a possible outstanding candidate as a hydrogen separation membrane.4 The thermodynamically stable structure determines critically the physical and chemical properties of a material. Despite extensive studies,6−9,45−48 it had remained an open question on the stable structure of bulk La2Ce2O7 under experimental conditions. The inconsistency in the literature basically concerns the uncertainty between two structural models: the distorted pyrochlore structure and the disordered fluorite structure.47 Here, the distorted pyrochlore indicates that, while all of the cations reside precisely at the pyrochlore lattice sites, © 2013 American Chemical Society

the oxygen atoms near the vacancies are slightly shifted from their original positions.10 In the pyrochlore structure (A2B2O7, space group Fd3m, which is a derivative of fluorite), the 16d ̅ and 16c sites are occupied by +IIIA and +IVB cations, the 48f and 8b sites are occupied by oxygen anions (O48f and O8b), and the 8a sites remain vacant, respectively. An O48f site is surrounded by a tetrahedron of two trivalent and two quadrivalent ions, an O8b site is wrapped by a tetrahedron of four trivalent ions, and an O8a site is enclosed by a tetrahedron of four quadrivalent ions.5 The disordered fluorite structure (space group Fm3̅m) of La2Ce2O7 can be viewed as 50% La doped CeO2 with displaced atoms, where La/Ce cations and oxygen anions/vacancies are distributed with a certain level of randomness. The distorted pyrochlore structure can be represented by a primitive cell consisting of 22 atoms, or by a cubic supercell of 88 atoms (L4, as it is four times the size of the primitive cell). The L4 cubic supercell is illustrated schematically in Figure 1a. Recently, Vanpoucke et al. predicted that La2Ce2O7 has the structure of pyrochlore rather than the disordered fluorite by comparing the total energies of both structures with densityReceived: April 14, 2013 Revised: September 4, 2013 Published: September 16, 2013 20379

dx.doi.org/10.1021/jp403660y | J. Phys. Chem. C 2013, 117, 20379−20386

The Journal of Physical Chemistry C

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pyrochlore La2Ce2O7 lies right at the boundary of the stable pyrochlore region. Panero et al. carried out first-principles calculations on defect formation energies of Y2B2O7 (B = Ti, Sn, and Zr).14 They concluded that cation defect formation energy does not depend simply on the cation radius, but is sensitive to other aspects of the electronic structure. Hess et al. performed spectroscopic investigations on the pyrochlore-tofluorite structural transition of Gd2(Ti1‑yZry)2O7.19 They concluded that the composition-driven transition involves both anion and cation disorder, while the irradiation-driven transition is dominated by cation disorder. Lian et al. showed that cation and anion disorder occur independently in A2Ti2O7 (A = Gd, Er, and Lu) under ion irradiation.15 Through selected area electron diffraction (SAED) measurements, they found an intermediate structure with substantial disordering of the anions and pyrochlore ordered cations before a fully disordered fluorite structure is reached. This was confirmed by the disappearance of characteristic diffraction maxima associated with the ordering of oxygen sublattice. To summarize, numerous efforts have been made to exploit the mechanism of structural disorder in various A2B2O7-type materials. However, to the best of our knowledge, studies on the structural properties of La2Ce2O7 have remained rather scarce. Investigation on the microscopic processes of proton migration is essential to gain insights into ceramic proton conductors. The proton mobility in BaZrO3 has been studied by kinetic Monte Carlo simulations,20 and the effects of acceptor dopants have been explored.21,22 Proton migrations in LaBaGaO4,23 doped CaZrO3,24−27 SrTiO3,28 La2Zr2O7,29,30 and LaP3O931 have also been investigated. However, theoretical studies on the proton transfer pathways, particularly the calculations on energy barriers of relevant microscopic processes, were rather scarce. Moreover, the influence of the structural aspects of La2Ce2O7 on the proton migration has remained largely unexplored. To investigate the properties and applications of La2Ce2O7, in this paper we first study the stable structure of La2Ce2O7 by carrying out first-principles calculations, based on which a mechanism leading to the prediction of a partial disordered structure is proposed. We then explore the stable proton sites and proton transfer pathways in La2Ce2O7. The influence of partial structural disorder on the proton migration is also elaborated. The remainder of the paper is organized as follows. In section 2, computational methods are described. In section 3.1, we discuss the energetically stable structure (distorted pyrochlore versus disordered fluorite) of the material and propose a possible mechanism resulting in the disorder tendency. In sections 3.2 and 3.3, stable proton sites and proton migration pathways are calculated respectively. Concluding remarks are finally given in section 4.

Figure 1. Schematic diagrams showing the pyrochlore structure of La2Ce2O7: (a) a cubic supercell (L4) consisting of 88 atoms and (b) a supercell (L2) with 44 atoms. The smaller balls in red, green, and purple represent O48f and O8b sites and O8a vacancies, respectively; and the larger balls in blue and gray represent the La and Ce cations, respectively. The hollowed squares mark the positions of oxygen vacancies. [211], [121], and [112] directions are marked by arrows.

functional theory (DFT) methods.6 They also argued that the pyrochlore structure cannot be excluded from the X-ray diffraction pattern. In contrast, Besikiotis et al. declared that no evidence of the stabilized pyrochlore structure was found for La2Ce2O7 in either XRD or neutron diffraction patterns.7 They thus concluded that La2Ce2O7 is unlikely to be in the pyrochlore structure. At almost the same time, Reynolds et al.42 performed neutron diffraction and X-ray absorption nearedge structure (XANES) analyses and arrived at the same conclusion as ref 7. Besides, some earlier experimental studies8,9,45 were also in favor of disordered fluorite structure. Aside from the controversy on what the stable structure of La2Ce2O7 is, there are diversified opinions and arguments on the underlying mechanisms which would cause the disorder in pyrochlore solids. A variety of mechanisms have been proposed for different materials in the literature.5,10−16,19 For instance, Jiang et al.10 introduced a concept of disordering energy, which is the difference between the total energy of a special quasirandom structure (SQS)17,18 and that of a pyrochlore structure. The disordering energy was proposed to indicate the tendency toward structural disorder for pyrochlore materials. With an estimated mix entropy, a quantitative relation was established between the disordering energy and an order−disorder transition temperature (TO−D). The pyrochlore structure is considered to be unstable at a temperature higher than TO−D. Based on the calculations of a series of materials using the Buckingham potential form, a contour map on defect formation energy versus the radii of cations A and B was proposed.13 The map was expected to measure the relative stability of a material which assumes the pyrochlore structure. Intriguingly, the

2. COMPUTATIONAL METHODS The electronic structure calculations are carried out at the density functional theory (DFT) level with the Vienna Ab initio Simulation Package (VASP).32 The projector augmented wave (PAW) approach is employed to treat the core−valence interactions. A generalized gradient approximation (GGA) developed by Perdew, Burke, and Ernzerhof (PBE) is used for the exchange-correlation functional. 33 Under the PAW pseudopotentials, the reference configurations of valence electrons are (5s2 5p6 6s2 5d1 4f0) for La, (5s2 5p6 6s2 5d1 4f1) for Ce, (2s2 2p4) for O, and (1s1) for H. The on-site 20380



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Coulomb-U correction34 is adopted for Ce 4f electrons. The magnitude of UCe was suggested to be 5.0 eV,44 which leads to a band gap of 2.50 eV for La2Ce2O7. Such a band gap is comparable to the reported gap of 2.70 eV for Sm2Ce2O735 and seems to be reasonable. A Coulomb-U correction on the O 2p orbitals has been used for calculations of the La doped ceria surface.49 We have examined the effect of a +U correction on the O 2p orbitals. Several configurations (x0y0, x0y1 and x0y2α) listed in Figure 2 are studied. It turns out that the

considered to be sufficiently large to reflect its disordering nature. An SQS is also constructed, which is based on the cubic L4 supercell of 88 atoms, with some rearrangement of the atomic positions.10 Crystal structures are visualized by VESTA.43 The positively charged protons play the role of charge carriers in the ceramic proton conductor.23 To investigate the proton transfer pathways inside the bulk ceramic material, two structural configurations are examined. The two configurations without and with antisites are represented by an L2 supercell and a F2 supercell, respectively. They both have the stoichiometry of La8Ce8O28 and contain four oxygen vacancies; see the Supporting Information for their detailed structures. To search for the stable proton sites in La2Ce2O7, an additional proton is added to each supercell. In the VASP calculations, the excess positive charges are neutralized by homogeneous compensating background to avoid divergence of Coulomb energy.31 The cutoff for kinetic energy is set at 400 eV for structural optimizations and 480 eV for single-point self-consistent-field calculations at fixed geometries. The lattice constant of La2Ce2O7 is calculated to be 11.24 Å for the L4 supercell, which agrees reasonably with the experimental value of 11.14 Å.38 Such a lattice constant is then fixed in the subsequent calculations. The 4 × 4 × 4 and 2 × 2 × 2 Monkhorst-Pack39 kpoints are used to sample the Brillouin zones of L2 and SQS supercells, respectively. The energy cutoff and k-point sampling for single-point calculations are confirmed to be sufficient to yield converged energies (with a residual uncertainty of energy less than 0.5 meV per atom). The geometric optimizations are considered to complete once the residual forces on all atoms are less than 0.03 eV/Å. In the search for transition states, eight images are interpolated between initial (reactant) and final (product) configurations, and all images are relaxed in the energy surface perpendicular to the reaction coordinate, until the maximum residual force is found less than 0.03 eV/Å.

Figure 2. Relative energies of various structural configurations of La2Ce2O7 resulting from different combinations of cation antisite(s) and anion Frenkel defect(s). The energy of the distorted pyrochlore structure (x0y0) is taken as the reference. The number of structural configurations explicitly studied for each class is given in parentheses.

resulting energetic properties are almost the same with and without the +U correction for O 2p orbitals. Therefore, we conclude that the +U correction on oxygen atoms does not affect the structural stability of La2Ce2O7, and it thus can be safely neglected from the calculations. In addition, we have verified that the magnetizations on all atoms are found to be zero even when spin polarization is explicitly considered. Thus spin polarization is not considered in this work. The climbing image-nudged elastic band (CI-NEB) method36 is adopted to calculate the proton transfer pathways and the associated energy barriers. The NEB calculations are performed using the GGA+U method. The screened hybrid Heyd−Scuseria− Ernzerhof functional (HSE06)37 is used to verify the energy barrier calculated with the GGA-PBE. Note that the experiments are done at finite temperatures and pressures while the first-principles calculations assume zero temperature and pressure. The difference in external conditions may have some effect on the comparison between experimental and theoretical findings. To evaluate the relative stabilities between distorted pyrochlore and disordered fluorite, structural configurations with anion or cation antisites are constructed, and their energies are calculated and compared with each other. Here, antisite means exchange of positions between a pair of ions. The antisite structural models have been utilized in the literature.16 A supercell of 44 atoms in pyrochlore structure (L2) is used as reference configuration (i.e., x0y0 in Figure 2). The [112], [211], and [121] directions of the cubic CeO2 unit cell are taken as the lattice vectors of the L2 supercell, as shown in Figure 1b. Since experiments have discovered an appreciable level of disorder in La2Ce2O7,7 the size of L2 supercell is

3. RESULTS AND DISCUSSIONS 3.1. Comparison between Distorted Pyrochlore and Disordered Fluorite Structures of La2Ce2O7. The disordering of La2Ce2O7 concerns the formation of anion Frenkel defects and/or cation antisites in the distorted pyrochlore structure. In this section, the energy changes associated with cation antisites and anion Frenkel defects are calculated by exchanging the positions of cations and/or oxygen anions in the pyrochlore configuration, followed by relaxation of the entire supercell. An anion Frenkel defect is formed with an oxygen anion transferring from an O8b or O48f site to occupy a nearby O8a vacancy, leaving the originally occupied O8b or O48f site vacant. The corresponding Kröger−Vink representations are × OO(48f) → V •• O(48f) + O″ i(8a)

(1)

× OO(8b) → V •• O(8b) + O″ i(8a)

(2)

In the following, the structural configuration free of anion Frenkel defect is denoted by y0, the configuration with one (two) Frenkel defect(s) of eq 1 in the L2 supercell is labeled by y1 (y2), and that with one Frenkel defect of eq 2 in the L2 is represented by y′1, respectively. The structural configurations with cation antisites are constructed by exchanging pairs of La 20381



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disordered fluorite structure.7,15 Our calculation results are consistent with the neutron diffraction patterns of ref 7 and the SAED measurements on A2Ti2O7 (A = Gd, Er, and Lu) materials which have identified the intermediate structure with disordered anion matrix and pyrochlore-arranged cation sublattice under ion irradiation.15 To justify our approach of predicting the structural stability of mixed-valent metal oxides, we also investigate the distorted pyrochlore and disordered fluorite configurations in bulk La2Zr2O7 as a direct comparison. During the relaxation of the x0y1 configuration, the oxygen anion designated to occupy an O8a vacancy tends to move back to its original position (the O48f site).14 To avoid this, a larger tolerance of maximal force is adopted. The total energy of the x0y1 configuration is calculated to be 0.80 eV higher than the distorted pyrochlore structure (x0y0), and the x1y0 resulting from cation antisite is 1.53 eV higher in energy than x0y0. The calculation results thus indicate that, unlike the La2Ce2O7 case, either anion or cation disorder is energetically rather unfavorable for La2Zr2O7. Therefore, La2Zr2O7 is predicted to be most stable in the distorted pyrochlore structure, as suggested by experiments.40 The distinct difference between La2Zr2O7 and La2Ce2O7 again indicates that the formation of the O48f-O8a Frenkel defect is responsible for the disorder tendency in La2Ce2O7. The SQS structure had been used to characterize the disorder inclination in pyrochlore-fluorite transition,6,10 which has been introduced in section 1. The energy difference between the SQS and the distorted pyrochlore structure is calculated to be 0.40 eV per La2Ce2O7 unit, which is consistent with the reference value of 0.50 eV.6 Although it is positive, its magnitude is comparable to the empirical threshold of about 0.50 eV per A2B2O7 as deduced from ref 10. Such a positive energy difference does not guarantee the pyrochlore structure be favorable. For instance, for compounds A2B2O7 which are found to be of disordered fluorite structures by experiment (see ref 10), the SQS energies may be even higher than the energies of pyrochlore structures. Only when the SQS energy is significantly higher than the pyrochlore counterpart (by as large as 0.50 eV per A2B2O7 unit) can the pyrochlore structure be deemed probable. From this aspect, the La 2 Ce 2 O 7 compound lies on the boundary between pyrochlore and disordered fluorite structures. Since the energy difference is not significantly large, partial disordering is expected, which is also consistent with the results above. It is concluded that the oxygen vacancy is stabilized by Cesurrounding in ref 6. As the number of surrounding La atoms increases, the vacancies become less stable. However, such a trend no longer applies in the presence of Frenkel defects. This is because the vacancy surrounded by 4Ce tends to be filled by an oxygen atom, leaving a neighboring oxygen site enclosed by 2La2Ce vacant. It seems that there is no direct and simple relation between the vacancy stability and the number of surrounding Ce/La atoms. Vanpoucke et al.’s work considered three different structures but all with ordered cation arrangement (LZO, L1, and L11, see ref 6) and a special quasi-random structure (SQS). Among these configurations, the pyrochlore structure is found to be the most stable one. However, Vanpoucke et al.’s work did not explore the possible presence of antisite defects. If the antisite defects are considered, the pyrochlore structure is no longer the most stable one, since the anion Frenkel defect could further lower the total energy of La2Ce2O7. Moreover, the relative energy of the SQS structure cannot be taken as a direct or

and Ce cations surrounding O48f sites. The Kröger−Vink representation of such an antisite is × La ×La + CeCe → La′Ce + Ce•La

(3)

The configuration with one La/Ce cation antisite in the L2 supercell is denoted as x1, and the structure free of cation antisite is labeled by x0. Following the above notations, the combinations of {y0, y1, y2, y′1} and {x0, x1} give a variety of possible structural configurations for the bulk La2Ce2O7 at different levels of disorder. In particular, the distorted pyrochlore structure is denoted by x0y0. The atomic geometries of a number of representative structural configurations are optimized with the DFT method. Those configurations with total energies comparable to the distorted pyrochlore (x0y0) are presented in Figure 2, with the energy of x0y0 taken as the reference value. Note that the y2 class actually consists of multiple configurations, since the two anion Frenkel defects may take place at different relative positions in the L2 supercell. Here, two possible structures of y2 class are selected and marked as y2α and y2β respectively. Each x1 class also has multiple configurations because the La/ Ce cations can also exchange around different O48f sites. The number of configurations studied explicitly for each class is given in the parentheses in Figure 2. The detailed structures of all representative configurations listed in Figure 2 are demonstrated in Figure S1 of Supporting Information. The zero-point energy is found to be rather insensitive to the pyrochlore-fluorite transition considered here (as verified by frequency analysis) and is thus safely neglected. Figure 2 shows that the distorted pyrochlore configuration (x0y0) is apparently not the lowest in energy. The configurations x0y1 and x0y2, which have O48f-O8a Frenkel defects and pyrochlore ordered cation sublattice are more than 0.50 eV lower in energy than that of x0y0. Moreover, the formation of O8b vacancy (x0y′1 configuration) is not favored in the pyrochlore structure. In general, the cation antisite (x1) increases the total energy. However, the increase in energy due to cation antisite is largely reduced with the formation of O48fO8a Frenkel defects. For instance, in the absence of anion Frenkel defect (y0), one pair of La/Ce antisite (x1y0) leads to a configuration whose total energy is 0.97 eV higher than that of the distorted pyrochlore (x0y0). In contrast, with the presence of two O48f-O8a anion Frenkel defects in the L2 supercell (y2α), the increase in energy due to the cation antisite (i.e., the energy difference between x1y2α and x0y2α configurations) is significantly compromised (the increase in energy ranges from 0.09 to 0.46 eV). Some configurations of the x1y2α class are lower in energy than the x0y0 structure and only slightly higher than the x0y2α counterparts. Furthermore, the experimental synthesis of La2Ce2O7 involves thermal treatment processes (such as annealing), and hence those structural configurations with cation antisites accessed during the synthesis may be retained in the final product. Therefore, the cation antisites are likely to be present in bulk La2Ce2O7 at room temperature, from both thermodynamic and dynamic perspectives. It is concluded from the energetic distribution of local minima configurations displayed in Figure 2 that the formation of O48f-O8a type anion Frenkel defects tends to stabilize the La2Ce2O7 and is thus the primary source of disordering. The cation disorder is also possible to some extent, but not as prominent as the disordering of anions. This thus advocates the previous studies in the literature which were in favor of 20382



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critical criterion to determine the favorable structure of La2Ce2O7. As mentioned earlier, the prediction of the pyrochlore structure is considered reliable only when the disordering energy is significantly larger than 0.50 eV. These lead to the different conclusions regarding the energetically most stable structures between Vanpoucke et al.’s work and ours. The SQS is apparently not the most effective way to model the structural disordering. A more reasonable way of modeling the defect fluorite structure is based on the analysis of Figure 2. Since the disordered fluorite admits numerous possible cation/ anion arrangements, the disordering features could be characterized in a statistical manner. Therefore, instead of having a single representative configuration, a series of configurations with different cation/anion antisites are constructed. The energetic properties of these representative configurations are then explored. The level of structural disordering and thermodynamic features of the fluorite are determined by taking the average over all of the involving configurations as those resolved in Figure 2. 3.2. Stable Proton Sites in Bulk La2Ce2O7. The pyrochlore supercell (L2, La8Ce8O28) and the most energetically stable configuration in x1y2α class (F2, La8Ce8O28) are adopted in the calculation of stable proton sites and proton transfer pathways. Note that the supercell of La8Ce8O28H corresponds to the proton uptake under the temperature of about 250 °C,7 and it thus provides a reasonable structural model to account for the experimental condition. In the L2 configuration with pyrochlore structure, four energetically stable proton sites are found as local minima through geometric optimizations. Two proton sites (denoted as HA1 and HA2) are in the vicinity of O8b, while the other two (HB1 and HB2) are located near O48f. The O−H bond lengths in the four stable configurations are listed in Table 1, along with

Figure 3. Stable proton sites predicted by structural optimizations in L2 structure: (a) HA1, (b) HA2, (c) HB1, and (d) HB2. The smaller balls in red and green represent O48f and O8b sites, respectively; while the larger balls in blue and gray represent the La and Ce cations, respectively.

In the disordered F2 configuration, more stable proton sites are found around oxygen atoms due to the more diversified chemical environment. Although the disordered structure is more complex, the general features observed in the L2 configuration remain valid in the F2 configuration. For instance, the H−O bonds are about 1 Å and the distance between two neighboring oxygen atoms is shortened with the presence of an interstitial proton. 3.3. Proton Transfer Pathways and Energy Barriers. Proton migration in a ceramic proton conductor has been described with a jump-diffusion model.23 The migration of a proton through the bulk material involves an enormous amount of consecutive transfer processes. The proton may transfer by jumping between two adjacent oxygen atoms or rotating toward another direction around its nearest oxygen. To elucidate the underlying mechanism of proton migration, we perform first-principles calculations to search for the energetically most favorable proton transfer pathways. The structural configurations with stable proton sites in both L2 and F2 configurations are adopted as initial and final states in the CINEB calculations. In the L2 case, six representative proton transfer processes are investigated: four rotation processes (HA1-HA2, HA1HA1′, HB1-HB1′, and HB1-HB2) and two jumping processes (HA1-HB2 and HB1-HB′1). Here, the prime symbol labels a same type of proton/oxygen site but of different position in the L2 supercell. A and B represent O8b and O48f oxygen sites, and their positions in L2 supercell are marked in Figure S2 of Supporting Information. Since the rotation process HA1-HA1′ can be split into two symmetric rotation steps (HA1-HA2 and HA2-HA1′) after NEB calculation, only five processes are examined explicitly. Table 2 lists the energy barriers associated with the five proton transfer processes calculated with GGA-PBE for L2 configuration, where the numbers in parentheses are the barriers for the backward processes. The forward and backward processes are defined so that the reaction barriers of forward

Table 1. Relative Potential Energies and Optimized O−H Bond Lengths of the Four Local Minima Structures in the L2 Case As Shown in Figure 3a HA1 HA2 HB1 HB2 a

O−H (Å)

E − Eref (eV)

1.02 0.99 1.02 1.00

0.17 0.18 0.00 0.15

The energy of HB1 (Eref) is taken as the reference.

the relative energies by taking HB1 as reference. Figure 3 depicts schematically the atomic structures around the interstitial protons. The HA1, HB1, and HB2 sites are almost on the lines connecting two adjacent oxygen atoms (O8b-O48f, O48f-O48f ,and O48f-O8b respectively), while HA2 is located approximately on the plane bisecting the angle of O48f-O8b-O48f. From Table 1, the distances between protons and their nearest oxygen atoms are about 1 Å, which are the typical OH bond lengths, indicating the formation of OH bonds. The proton sites close to O48f are energetically more stable than those near O8b. Moreover, it is important to note that the distance between two nearest oxygen atoms is shortened with the presence of an interstitial proton. For instance, the distance between two neighboring O48f is 2.85 Å in the pristine L2 supercell, while it reduces to 2.55 Å in the HB1 configuration. This is because the electrostatic repulsion between the two oxygen anions is effectively screened by the interstitial proton. 20383



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In the case of the F2 configuration, four proton rotation/ jump processes around two neighboring oxygen atoms are examined as representatives. These two oxygen atoms are surrounded by two La and two Ce ions, and they are denoted as C and D, respectively. Their positions in the supercell are marked in Figure S2 of the Supporting Information. The associated energy barriers are listed in Table 2. Figure 4c,d depicts the reaction pathways of HC2-HD1 and HC1-HC2, respectively. Apart from the low-barrier (less than 0.2 eV) pathways, pathways with higher energy barriers (0.59 eV for HD1-HC2 and 0.42 eV for HC2-HC1) are also found in such a disordered configuration. From the kinetic point of view, only those pathways with lower barriers actually contribute to the proton conduction. The calculated energy barriers in both configurations are significantly lower than the reported formal activation energy of 0.84 eV obtained by fitting the experimentally measured total conductivity in wet O2.7 It is possible to exclude the contribution of oxygen vacancy transfer from the total conductivity and leave the contribution of proton transfer. In doing so, Sun et al. have obtained the formal activation energy for proton conduction, which is 0.68 eV and changes little under various temperatures and air humidities.41 Noting that the typical formal activation energy for ceramic proton conductors is around 0.4−0.6 eV, the value of 0.84 eV in ref 7 might be somewhat overestimated. Nevertheless, the calculated barriers for proton transfers are still significantly

Table 2. Calculated Energy Barriers for Various Proton Transfer Steps in Distoted Pyrochlore (L2) and Representative Disordered Fluorite (F2) Configurationsa pathway distorted pyrochlore configuration, L2

disordered fluorite configuration, F2

HB1HB′1 HB1HB1′ HB1-HB2 HB2-HA1 HA1-HA2 HC4HC5 HD1HC2 HC2HC1 HC3HC1

type

energy barrier (eV)

jump

0.06 (0.06)

rotation

0.10 (0.10)

rotation jump rotation rotation

0.17 0.11 0.06 0.12

jump

0.59 (0.04)

rotation

0.42 (0.14)

rotation

0.12 (0.11)

(0.03) (0.09) (0.05) (0.08)

a

The numbers in parentheses are the corresponding energy barriers for the backward transfer reactions.

directions are not lower than the backward ones. Figure 4a,b depict the reaction pathways of HB2-HB1 and HB1-HB1′, respectively. The calculated energy barriers are below 0.20 eV, which are similar to the estimated barrier of 0.20 eV for another proton conductor material, the undoped BaZrO3.21

Figure 4. Potential energy profiles for proton transfer reaction pathways in both L2 and F2 structures: (a) HB1-HB2 in L2 structure, (b) HB1-HB1′ in L2 structure, (c) HC2-HD1 in F2 structure, and (d) HC1-HC2 in F2 structure. The insets depict the local atomic structures of the initial, transition, and final states. 20384



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Notes

lower than the formal activation energies obtained experimentally. To verify the calculated energy barriers, the screened hybrid functional HSE06 is used to recalculate the energies of the initial and transition configurations of the HB1-HB2 rotation process. The HSE06 functional gives an energy difference of 0.13 eV, which is close to the PBE result of 0.17 eV. This indicates that the calculated energy barrier is not very sensitive to the choice of exchange-correlation functional, and the large deviation from experimental activation energy is not due to the intrinsic error of density functional approximation. The low calculated barriers may imply that the proton transfer processes inside the bulk La2Ce2O7 is not the rate-determining step of proton migration, while the interfacial processes such as adsorption and decomposition of hydrogen molecules at the solid surface may be responsible for the large formal activation energy. Further investigations are necessary for understanding the interfacial processes, which are however outside the scope of this paper. The above proton transfer pathways are for the pyrochlore (L2) and a representative disordered fluorite (F2) configuration. The discussions can be extended to general disordered fluorite structures. The impact of structural disordering on the proton migration is evident by comparing these two cases. As indicated by Table 2, the protons in a disordered fluorite structure will experience somewhat higher energy barriers for their conduction. Therefore, the structural disorder may disfavor the proton migration process.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support from the National Science Foundation of China (Grant Nos. 21103157, 21233007, and 21322305), the Anhui Natural Science Foundation, the Ministry of Science and Technology of China (Grant No. 2012CB215403), the Fundamental Research Funds for the Central Universities of China (Grant Nos. 2340000034 and 2340000025), and the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB01020000) is gratefully appreciated. We are also grateful for the Supercomputing Center of USTC for providing computational resources.

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(1) Phair, J. W.; Badwal, S. P. S. Review of proton conductors for hydrogen separation. Ionics 2006, 12, 103−115. (2) Fang, S. M.; Bi, L.; Yan, L. T.; Sun, W. P.; Chen, C. S.; Liu, W. CO2-resistant hydrogen permeation membranes based on doped ceria and nickel. J. Phys. Chem. C 2010, 114, 10986−10991. (3) Tao, Z. T.; Bi, L.; Fang, S. M; Liu, W. A stable La1.95Ca0.05Ce2O7−δ as the electrolyte for intermediate-temperature solid oxide fuel cells. J. Power Sources 2010, 195, 3481−3484. (4) Zhu, Z. W.; Yan, L. T.; Liu, H. W.; Sun, W. P.; Zhang, Q. P.; Liu, W. A mixed electronic and protonic conducting hydrogen separation membrane with asymmetric structure. Int. J. Hydrogen Energy 2012, 37, 12708−12713. (5) Chartieer, A.; Meis, C.; Weber, W. J.; Corrales, L. R. Theoretical study of disorder in Ti-substituted La2Zr2O7. Phys. Rev. B 2002, 65, 134116. (6) Vanpoucke, D. E. P.; Bultinck, P.; Cottenier, S.; Speybroeck, V.; Driessche, I. V. Density functional theory study of La2Ce2O7 disordered fluorite versus pyrochlore structure. Phys. Rev. B 2011, 84, 054110. (7) Besikiotis, V.; Knee, C. S.; Ahmed, I.; Haugsrud, R.; Norby, T. Crystal structure, hydration and ionic conductivity of the inherently oxygen-deficient La2Ce2O7. Solid State Ionics 2012, 228, 1−7. (8) Cao, X. Q.; Vassen, R.; Fischer, W.; Tietz, F.; Jungen, W.; Stöver, D. Lanthanum-Cerium oxide as a thermal barrier-coating material for high-temperature applications. Adv. Mater. 2003, 15, 1438−1442. (9) Yamamura, H.; Nishino, H.; Kakinuma, K.; Nomura, K. Crystal phase and electrical conductivity in the pyrochlore-type composition system, Ln2Ce2(Ln=La, Nd, Sm, Eu, Gd, Y and Yb)O7. J. Ceram. Soc. Jpn. 2003, 111, 902−906. (10) Jiang, C.; Stanek, C. R.; Sickafus, K. E.; Uberuaga, B. P. Firstprinciples prediction of disordering tendencies in pyrochlore oxides. Phys. Rev. B 2009, 79, 104203. (11) Moon, P. K. Electrical Conductivity and Structural Disorder in Gd2Ti2O7-Gd2Zr2O7 and Y2Ti2O7-Y2Zr2O7 Solid Solutions. Ph.D. Thesis; Massachusetts Institute of Technology: Cambridge, MA, 1988. (12) Dijk, M. P. V.; Burggraaf, A. J.; Cormack, A. N.; Catlow, C. R. A. Defect structures and migration mechanisms in oxide pyrochlores. Solid State Ionics 1985, 17, 159−167. (13) Minervini, L.; Grimes, R. W. Disorder in pyrochlore oxides. J. Am. Ceram. Soc. 2000, 83, 1873−1878. (14) Panero, W. R.; Stixrude, L. First-principles calculation of defectformation energies in the Y2(Ti,Sn,Zr)2O7 pyrochlore. Phys. Rev. B 2004, 70, 054110. (15) Lian, J.; Wang, L.; Chen, J.; Sun, L.; Ewing, R. C; Farmer, J. M. The order−disorder transition in ion-irradiated pyrochlore. Acta Mater. 2003, 51, 1493−1502. (16) Zhu, X. T.; Li, N.; Gao, F. First principle study of structural and energetic properties of A2Hf2O7 (A=Dy, Ho, Er) compounds. J. App. Phys. 2008, 104, 043517. (17) Zunger, A.; Wei, S. H.; Ferreira, L. G.; Bernard, J. E. Special quasirandom structures. Phys. Rev. Lett. 1990, 65, 353−356.

4. CONCLUSIONS To summarize, in this work we investigated the structural stability of bulk La2Ce2O7, which is a promising proton conductor. First-principles calculations are performed to explore the stable structure by comparing between pyrochlore-distorted and fluorite-disordered configurations. It is found that the pyrochlore-distorted structure is not the lowest in energy. The formation of O48f-O8a type anion Frenkel defects tends to stabilize the La2Ce2O7 and is the primary source of disordering. Since the rise in energy due to cation antisite is significantly compromised after the O48f-O8a type anion Frenkel defects, the cation antisites are also likely to be present in bulk La2Ce2O7 at room temperature, from both thermodynamic and dynamic perspectives. This is consistent with the previously reported neutron diffraction pattern. Moreover, stable proton sites and proton transfer pathways in La2Ce2O7 are calculated under both distorted pyrochlore (L2) and representative disordered fluorite (F2) configurations. The distance between two nearest oxygen atoms is shortened with the presence of an interstitial proton. It is likely that the partial structural disorder disfavors the proton migration because of the existence of higher energy barriers.

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ASSOCIATED CONTENT

S Supporting Information *

Structural configurations listed in Figure 2 and the positions of the various oxygen atoms denoted by A, B, C, and D in Table 2. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. 20385



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(18) Wei, S. H.; Ferreira, L. G.; Bernard, J. E.; Zunger, A. Electronic properties of random alloys: Special quasirandom structures. Phys. Rev. B 1990, 42, 9622. (19) Hess, N. J.; Begg, B. D.; Conradson, S. D.; McCready, D. E.; Gassman, P. L.; Weber, W. J. Spectroscopic investigations of the structural phase transition in Gd2(Ti1‑yZry)2O7 pyrochlores. J. Phys. Chem. B 2002, 106, 4663−4677. (20) Bjorketun, M. E.; Sundell, P. G.; Wahnstrom, G.; Engberg, D. A kinetic Monte Carlo study of proton diffusion in disordered perovskite structured lattices based on first-principles calculations. Solid State Ionics 2005, 176, 3035−3040. (21) Björketun, M. E.; Sundell, P. G.; Wahnström, G. Effect of acceptor dopants on the proton mobility in BaZrO3: A density functional investigation. Phys. Rev. B 2007, 76, 054307. (22) Bjorketun, M. E.; Sundell, P. G.; Wahnstrom, G. Structure and thermodynamic stability of hydrogen interstitials in BaZrO3 perovskite oxide from density functional calculations. Faraday Discuss. 2007, 134, 247−265. (23) Kendrick, E.; Kendrick, J.; Knight, K. S.; Islam, M. S.; Slater, P. R. Cooperative mechanisms of fast-ion conduction in gallium-based oxides with tetrahedral moieties. Nat. Mater. 2007, 6, 871−875. (24) Islam, M. S.; Davies, R. A.; Gale, J. D. Proton migration and defect interactions in the CaZrO3 orthorhombic perovskite: A quantum mechanical study. Chem. Mater. 2001, 13, 2049−2055. (25) Bilic, A.; Gale, J. D. Proton mobility in the In-doped CaZrO3 perovskite oxide. Chem. Mater. 2007, 19, 2842−2851. (26) Bilić, A.; Gale, J. D. Simulation of proton diffusion in In-doped CaZrO3. Solid State Ionics 2008, 179, 871−874. (27) Islam, M. S.; Daviesa, R. A.; Gale, J. D. Hop, skip or jump? Proton transport in the CaZrO3 perovskite oxide. Chem. Commun. 2001, 7, 661−662. (28) Shimojo, F.; Hoshino, K. Microscopic mechanism of proton conduction in perovskite oxides from ab initio molecular dynamics simulations. Solid State Ionics 2001, 145, 421−427. (29) Björketun, M. E.; Knee, C. S.; Nyman, B. J.; Wahnström, G. Protonic defects in pure and doped La2Zr2O7 pyrochlore oxide. Solid State Ionics 2008, 178, 1642−1647. (30) Nyman, B. J.; Björketun, M. E.; Wahnström, G. Substitutional doping and oxygen vacancies in La2Zr2O7 pyrochlore oxide. Solid State Ionics 2011, 189, 19−28. (31) Amezawa, K.; Takahashi, H.; Kuwabara, A.; Unemoto, A.; Kawada, T. Local structural arrangements around oxygen and hydrogen-related defects in proton conducting LaP3O9 investigated by first principles calculations. Int. J. Hydrogen Energy 2012, 37, 7995− 8003. (32) Kresse, G.; Furthmuller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169. (33) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (34) Anisimov, V. I.; Zaanen, J.; Andersen, O. K. Band theory and Mott insulators: Hubbard U instead of Stoner I. Phys. Rev. B 1991, 44, 943. (35) Vishnu, V. S.; George, G.; Reddy, M. L. P. Effect of molybdenum and praseodymium dopants on the optical properties of Sm2Ce2O7: Tuning of band gaps to realize various color hues. Dyes Pigm. 2010, 85, 117−123. (36) Henkelman, G.; Jonsson, H. Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J. Chem. Phys. 2000, 113, 9978−9985. (37) Heyd, J.; Scuseria, G. E. Efficient hybrid density functional calculations in solids: Assessment of the Heyd-Scuseria-Ernzerhof screened Coulomb hybrid functional. J. Chem. Phys. 2004, 121, 1187− 1192. (38) Ma, W.; Gong, S.; Xu, H.; Cao, X. Q. On improving the phase stability and thermal expansion coefficients of lanthanum cerium oxide solid solutions. Scr. Mater. 2006, 54, 1505−1508. (39) Monkhorst, H. J.; Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 1976, 13, 5188−5192.

(40) Lian, J.; Zu, X. T.; Kutty, K. V. G.; Chen, J.; Wang, L. M.; Ewing, R. C. Ion-irradiation-induced amorphization of La2Zr2O7 pyrochlore. Phys. Rev. B 2002, 66, 054108. (41) Sun, W.; Fang, S.; Yan, L.; Liu, W. Investigation on proton conductivity of La2Ce2O7 in wet atmosphere: dependence on water vapor partial pressure. Fuel Cells 2012, 12, 457−463. (42) Reynolds, E.; Blanchard, P. E. R.; Zhou, Q. D.; Kennedy, B. J. Structural and spectroscopic studies of La2 Ce2 O7: Disordered fluorite versus pyrochlore structure. Phys. Rev. B 2012, 85, 132101. (43) Momma, K.; Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 2011, 44, 1272−1276. (44) Nolan, M.; Grigoleit, S.; Sayle, D. C.; Parker, S. C.; Watson, G. W. Density functional theory studies of the structure and electronic structure of pure and defective low index surfaces of ceria. Surf. Sci. 2005, 576, 217−229. (45) Brisse, F.; KNOP, O. Pyrochlores. II. An investigation of La2Ce2O7 by neutron diffraction. Can. J. Chem. 1967, 45, 609−614. (46) Baea, J. S.; Chooa, W. K.; Lee, C, H. The crystal structure of ionic conductor LaxCe1‑xO2‑x/2. J. Eur. Ceram. Soc. 2004, 24, 1291− 1294. (47) Narayanan, V.; Lommens, P.; Buysser, K. D; Vanpoucke, D. E. P.; Huehne, R.; Molina, L.; Tendeloo, G. V.; Voorta, P. V. D.; Driessche, I. V. Aqueous CSD approach for the growth of novel, lattice-tuned LaxCe1‑xOδ depitaxial layers. J. Mater. Chem. 2012, 22, 8476−8483. (48) Chambonnet, D.; Keller, D.; Belouet, C. Control of the 2D/3D transition of the growth mechanism in the YBCO/Ce1‑xLaxO2‑x/2/ SrTiO3 system. Physica C 1998, 302, 198−206. (49) Yeriskin, I.; Nolan, M. Doping of ceria surfaces with lanthanum: a DFT+U study. J. Phys., Condens. Matter 2010, 22, 135004.

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Structural Stability of La2Ce2O7

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