Article pubs.acs.org/JPCC
Study of Phase Stability and Hydride Diffusion Mechanism of BaTiO3 Oxyhydride from First-Principles Jiajia Zhang,†,‡ Gaoyang Gou,*,† and Bicai Pan‡ †
Frontier Institute of Science & Technology, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
‡
S Supporting Information *
ABSTRACT: First-principles calculations were performed to study structural, electronic and hydride diffusion properties of BaTiO3 oxyhydride. In agreement with experiment (Nat. Mater. 2012, 11, 507 and J. Am. Chem. Soc. 2012, 134, 8782), we find that the incoming H species occupy the anion vacancy sites left by oxygen, forming the stable hydride anions H−1. As a result of the electron doping introduced by H species, both interstitial H and hydride anion H−1 can induce metallicity and eliminate ferroelectricity in BaTiO3. We further clarify the role of the migration of the interstitial H in determining the hydrogen diffusion properties of the oxyhydrides. A low diffusion barrier was predicted, responsible for high hydrogen diffusion mobility observed in experiment. Based on our results, we demonstrate that BaTiO3 oxyhydride can be used as a mixed electron/hydride conductor, displaying the promising applications as the electrolytes for solid-oxide fuel cells.
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INTRODUCTION Perovskite BaTiO3 (BTO) is a prototypical ferroelectric material, which displays superior ferroelectric and dielectric properties.1 Ferroelectric BTO has wide applications as nonvolatile random access memories, ceramic capacitors, and electromechanical devices.2,3 Similar to many other perovskite oxides, various nonstoichiometry defects, such as oxygen vacancies or impurities always exist in as-grown BTO samples, creating diverse effects on material properties. For example, oxygen vacancy induced metal−insulator transition was reported in BaTiO3−δ.4,5 Hydrogen impurity of low concentration in BTO can lead to serious insulation degradation.6 Therefore, the defect properties in ferroelectric oxides have been studied extensively. A recent experimental work on BaTiO3 oxyhydride by Kobayashi et al.7 is another successful example in manipulating ferroelectric oxide properties through defects. After reducing reaction of BTO with CaH2, a large amount of hydrogen species were able to be incorporated into BTO lattice. The synthesized oxyhydride BaTiO3−xHx (x < 0.6) exhibits high electronic conductivity and its hydride ions are exchangeable with gaseous hydrogen at elevated temperature.7,8 Those properties indicate that oxyhydride BaTiO3−xHx can be an ideal mixed electron/hydride proton conductor, showing the potential as electrolyte materials for electrochemical applications.9−11 Despite some theoretical works that have been carried out to study the properties of H impurities in ferroelectric BTO,12,13 the critical questions in understanding experimental results about oxyhydride BaTiO3−xHx remain unclear. These questions include: (i) Under which condition would H species favorably incorporate into BTO lattice? (ii) Which lattice sites would H species occupy and how does © 2014 American Chemical Society
incorporated H affect the electronic and structural properties of BTO? (iii) How does hydrogen diffusion occur in BTO and what is the mechanism in determining hydride/hydrogen exchange process? To address the questions mentioned above, in this work we have performed first-principles calculations to explore the underlying physical properties of BaTiO3 oxyhydride. Hincorporated BaTiO3−δHx configurations have been proposed to simulate oxyhydride, where the interactions between H species and O vacancies are included. Based on our calculations, it is found that incorporated H atoms can stably occupy the vacancy sites left by oxygen, which can account for hydride anions H−1 observed in experiment. Hydride induced metallicity and structure change in oxyhydride are also reproduced in our simulations. Finally, using the predicted diffusion barriers obtained from different hydrogen migration trajectories, hydride diffusion mechanism for BaTiO3 oxyhydride has been proposed.
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COMPUTATIONAL METHODS Our first-principles density-functional calculations are performed within the local spin-density approximation (LSDA)14 as implemented in the Vienna ab initio simulation package (VASP).15,16 The projector-augmented wave method17 is used with the following valence-electron configurations: 5s25p66s2 for Ba, 3d24s2 for Ti, and 2s22p4 for O. A plane-wave basis set with a cutoff energy of 600 eV is used, and the Brillouin zone Received: March 27, 2014 Revised: July 11, 2014 Published: July 15, 2014 17254
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the possible van der Waals (vdW) interactions between incorporated H and BaTiO3 lattice, van der Waals density functional26,27 (vdW-DF) with Coopers exchange28 implemented in QE is used for test calculations for the selected BaTiO3 oxyhydride system. Calculations in QE code are performed using nonlocal optimized norm-conserving29,30 pseudopotentials, 60 Ry plane-wave cutoff and 6 × 6 × 6 Monkhorst−Pack k-point grid.
(BZ) integrations for BaTiO3 unit cell are performed using a 8 × 8 × 8 Monkhorst−Pack k-point grid.18 Our calculation predicts lattice parameter a = 3.934 Å and c/a = 1.014 for bulk tetragonal BaTiO3, in good agreement with both experimental and theoretical reports.19,20 BaTiO3 oxyhydride systems are simulated using the 40-atom supercell depicted in Figure 1, which is obtained by doubling
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RESULTS AND DISCUSSION Models and Phase Stability. In experiment, the synthesis of BaTiO3 oxyhydride requires highly reducing conditions, whereas the oxygen vacancies of a certain amount will be formed. Hydride with the concentration up to 20% can then be incorporated into the BaTiO3 lattice at the anionic sites.7,8 Therefore, to simulate experimental BaTiO3 oxyhydride, both oxygen vacancies and incorporated hydrogen species are included in our simulation. Figure 1 shows our supercell configuration BaTiO3−δHx in simulating BaTiO3 oxyhydride, where the formation of O vacancy (VO in Kröger-Vink notation31), incorporation of H species at the interstitial site (Hi), formation of hydrides at anionic sites (filling the O vacancy sites by H: HO and [HO]I+[HO]II), as well as the coexistence of interstitial and hydride anion (HO+Hi) respectively are considered for simulation. It is noted that for VO and HO we consider both apical and equatorial anion sites to remove O or incorporation of H. After structural optimization, the apical and equatorial configurations are relaxed into the same structure with identical energy and crystal structure. The BaTiO3−δHx configurations we choose contain H species with maximum concentration of 8%, which is lower than the experimental H concentration. But these configurations are still informative enough to study the intrinsic properties of BaTiO3 oxyhydride. BaTiO3−δHx in charge neutral state are simulated first. To evaluate phase stability of BaTiO3−δHx oxyhydride, we calculated both incorporation energy and solution energy for the formation of H species in BaTiO3 lattice. The incorporation energy (Einc) is defined by Grimes et al.32 as
Figure 1. Supercell model composed of 2 × 2 × 2 BaTiO3 unit cells used in simulation of BaTiO3−δHx oxyhydride. Following configurations are considered: formation of oxygen vacancy (VO); incorporation of H atom at anionic site (HO); interstitial of a single H atom (Hi); incorporation of two H atoms at anionic site I and II ([HO]I+[HO]II); incorporation of H atom at anionic site together with the other H occupies at interstitial site (HO+Hi). Ba, Ti, O, and H atoms are in green, blue, red, and black, respectively.
BaTiO3 unit cell structure along the three Cartesian directions. Such a supercell could capture the structural distortions and substitutional disorder existing in BaTiO3 oxyhydride. Atomic positions and lattice parameters for BaTiO3 oxyhydride are fully optimized until residual Hellmann−Feynman forces on the atoms are smaller than 0.01 eV/Å and the stresses are less than 0.1 kbar. The optimized BaTiO3 oxyhydride configurations are confirmed to be energy minima by double checking their stability against randomized atomic and cell distortions. A 6 × 6 × 6 Monkhorst−Pack k-point grid is used for supercell calculations. Hydride diffusion properties were evaluated by simulating the minimum energy path (MEP) trajectory for diffusion of hydrogen species in BaTiO3 oxyhydride phases using the nudged elastic band (NEB) method.21,22 For a better treatment of the electron correlation effect from partially occupied Ti-3d states in BaTiO3 oxyhydride, the rotationally invariant LSDA+U method23 implemented in quantum espresso (QE) code24 is also used for electronic structure calculations. Within such LSDA+U method, a selfconsistent Hubbard term U for a localized orbital can be determined from linear response calculations.25 To account for
⎛ ⎞ 1 E inc = E[BaTiO3 − δ Hx] − ⎜E[BaTiO3 − δ ] + xμH ⎟ 2⎠ ⎝ 2
(1)
where E[BaTiO3−δHx] and E[BaTiO3−δ] are total energies for oxyhydride BaTiO3−δHx and pure/defective BaTiO3. μH2 is chemical potential of H2 molecule (enthalpy and entropy for H2 at a given temperature are obtained from the JANAF table33). Incorporation energy does not account for the formation of the trap sites (oxygen vacancy or interstitial sites in our case) of BaTiO3 lattice, by assuming there are always excess sites available. To compensate for limitations of incorporation energy, solution energy (Esol) is considered:32
Table 1. Calculated Incorporation Energy (Einc in eV) and Solution Energies (Esol in eV) under Both BaTiO3 and BaTiO3−δ Stoichiometries for Fully Optimized BaTiO3−δHx Oxyhydride Configurationsa
Einc 3 EBaTiO sol BaTiO3‑δ Esol a
HO
Hi
[HO]I + [HO]II
HO + Hi
BaTiO2.875H0.125
BaTiO3H0.125
BaTiO2.75H0.25
BaTiO2.875H0.25
−1.59 1.92 −1.59
0.58 0.58 0.58
−1.62 1.89 −1.62
−0.39 1.37 −0.39
For [HO]I + [HO]II and HO + Hi, Einc and Esol correspond to the formation energy per H atom. 17255
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Figure 2. Calculated orbital-resolved density of states for (a) pure BaTiO3 and charge neutral BaTiO3−δHx oxyhydrides, (b) negatively charged (BaTiO3−δHx)−1 from LSDA. The vertical line corresponds to the Fermi level. Both charge neutral and negatively charged BaTiO3−δHx systems are metallic with partially filled Ti-t2g orbitals. As LSDA predicts both BaTiO3−δHx and (BaTiO3−δHx)−1 as spin-degenerate paramagnetic metals, only one spin component is given in their PDOS plots.
Esol = E inc + Etrap
We show in Figure 2a the electronic DOS for BaTiO3 and charge-neutral BaTiO3−δHx. Ferroelectric BaTiO3 is a band gap insulator, whose conduction band is mainly contributed by the empty Ti-t2g states, while the O-2p states are distributed throughout the entire valence band. There is pronounced hybridization between Ti-3d and O-2p, which was reported crucial for the ferroelectricity in BaTiO3.34 Contrary to insulating BaTiO3, LSDA predict all BaTiO3−δHx oxyhydrides as paramagnetic metals: Fermi energy levels (EF) are located above the energy minima of BaTiO3 conduction bands, making the original empty Ti-t2g as the partial filled orbital.12 Specifically, for interstitial H atom, Bader charge analysis indicates interstitial H has the electron charge of 0.7 e, where the rest 0.3 e from H will occupy the conduction band of BaTiO3. After H occupies anionic (oxygen vacancy) site, its 1s orbital will be fully occupied. Bader charge for H at anionic site is 1.58, indicating H species exist at anionic sites as negatively charged hydride H−1.13 As anionic H only compensates 0.58 of two electrons released from Ovac, the uncompensated 1.42 e will once more occupy the conduction band. Therefore, formation of both interstitial H and hydride anion can introduce electron doping into BaTiO3, leading to the increase on electron occupations on Ti-3d orbital (Figure S2) and decrease of oxidation state of Ti cation.7 Considering the highly reducing experimental condition, it is likely that BaTiO3−δHx oxyhydrides can be further reduced by accepting electrons from the outside environment. Without losing generality, BaTiO3−δHx oxyhydrides in negative charge state are also simulated. Figure 2b displays orbital-revolved DOS for negatively charged (BaTiO3−δHx)−. It is found that (BaTiO3−δHx)− are still in metallic ground states, with electronic DOS similar to charge-neutral BaTiO3−δHx. Therefore, in the remainder of this paper, we will focus on chargeneutral BaTiO3−δHx oxyhydrides for detailed analysis. We further study the electronic structure of BaTiO3−δHx using LSDA+U method. A self-consistent Hubbard U term of 4.49 eV (Figure S3, computational details for calculating selfconsitent U in ref 35) is applied to Ti-3d orbitals. Oxyhydrides remain in metallic ground states after including the on-site
(2)
where Etrap is the trap site formation energy. Etrap depends on the stoichiometry of the system. For example, for oxygen vacancy site, Etrap is zero under BaTiO3−δ stoichiometry (defective BaTiO3 with VO). While under BaTiO3 stoichiometry, EVo trap = 3.51 eV, which is the half of the oxygen Frenkel pair 32 (OO× → Oi″ + V•• O ) formation energy. Etrap of interstitial site is zero for all stoichiometries. Our calculated incorporation and solution energies for various BaTiO3−δHx configurations are given in Table 1. The 3 large solution energy EBaTiO for HO, [HO]I + [HO]II, and HO + sol Hi indicate the direct incorporation of H species into the BaTiO3 anionic sites are energetic unpreferable. Anionic hydride in BaTiO3 occurs preferentially after the oxygen vacancies are formed, as H can fill the anionic sites left by 3−δ < 0). Therefore, oxygen vacancy exothermically (EBaTiO sol oxygen vacancies are crucial for the formation of hydride anion, which explains why synthesis of BaTiO3 oxyhydride requires the highly reducing conditions in the experiment.7 Moreover, the HO configuration is energetic more stable than Hi under BaTiO3−δ stoichiometry, indicating the hydrogen species in BaTiO3 oxyhydride mostly exist at anionic sites, instead of interstitial sites. We also perform calculations on H i configuration using van der Waals functional (vdW-DF). vdW-DF predicted hydrogen incorporation energy (Einc = 0.54 eV) and local structure (Figure S1 of the Supporting Information) for Hi are similar to LSDA results, indicating LSDA can provide convincing structural and energetic results for BaTiO3−δHx. Electronic and Structural Properties. Compared to insulating BaTiO3, oxyhydride BaTiO3−δHx exhibits good electronic conductivity.8 After hydride reducing reaction, BaTiO3 also exhibits a structural change from tetragonal to cubic symmetry.7 To obtain the atomic-level understanding of these experimental findings, we carried out theoretical study on the electronic and structural properties of pure BaTiO3 and oxyhydride BaTiO3−δHx. 17256
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Figure 3. Contour plots of local density of states around Fermi level for charge neutral BaTiO3−δHx obtained from LSDA calculations. The contours are linearly spaced, ranging from 0.00 to 0.02 e/Å3, with the interval of 0.001 e/Å3.
Coulomb interaction, except that LSDA+U predicts BaTiO3−δHx as ferromagnetic metals with nonzero magnetic moments (Figure S4). Similar electronic structures have been found in other Perovskite paramagnetic metal LaNiO3, where LSDA predicts LaNiO3 as paramagnetic metal, while LSDA+U predicts as ferromagnetic metal.36 Therefore, it is confirmed metallic states are intrinsic ground states for BaTiO3−δHx oxyhydrides. To obtain insight into metallicity in BaTiO3−δHx, we examine their local density of states around the Fermi level in more detail. Figure 3 shows the projection of these metallic states (LSDA results) along the planar Ti−O plane. All BaTiO3−δHx oxyhydrides have the metallic states spatially distributed around Ti cations and O anions, exhibiting Ti-dxz (dyz) and O-px (py) hybridization features. The delocalized nature of these metallic states indicates BaTiO3−δHx oxyhydrides are electronically conductive in experimental transport measurements.8 As metallicity occurs in BaTiO3−δHx, how does it affect the structural properties, especially the tetragonality of the BaTiO3 lattice? Figure 4a shows the change of the tetragonality induced
Therefore, with the incorporated H species, the tetragonality of the BTO lattice will be reduced. Such a trend is well reproduced in our simulation (Figure 4). Moreover, we also investigate the local structures of our simulated BaTiO3−δHx oxyhydride. Shown in Figure 4 are average off-center cation displacements for BaTiO3 and BaTiO3−δHx. Tetragonality as well as ferroelectricity in BaTiO3 come from the large polar cation displacement, but there are neglected cation displacement in BaTiO3−δHx. Therefore, ferroelectricity should be almost absent in metallic oxyhydrides.38,39 Hydride Diffusion Mechanism. After treatment of oxyhydride with hydrogen gas, the exchange of the hydrogen species in BaTiO3−δHx with the gaseous environment was observed in experiment.7,8 In this subsection, we will investigate the hydride diffusion kinetics in BaTiO3−δHx and reveal the mechanism responsible for the hydride/hydrogen exchange in the oxyhydride. Simulation of the hydride/hydrogen exchange in oxyhydride is computationally challenging, as the complex process including the adsorption and dissociation of the H2 molecule at the BaTiO3 oxyhydride surface are involved. Study of such a surface reaction is out of the scope of our first-principles calculations on periodic bulk systems. In our work, we focus on the migration of the incorporated hydrogen species “inside” the oxyhydride bulk and investigate the most likely intrinsic hydride diffusion scenario by simulating the minimum energy path (MEP) for three independent migration trajectories: (i) diffusion of a hydrogen atom between two adjacent interstitial sites; (ii) migration of a H atom from the interstitial site into the O vacancy site; and (iii) replacing of a H atom at the anionic site by interstitial H. Figure 5 illustrates our calculated hydrogen migration pathways and the energy profiles along the MEP. Diffusion of the interstitial H along MEP involves the migration of H atom between the adjacent octahedral sites along the edge of Ti−O6 octahedral, separated by a energy barrier of 0.18 eV (Figure 5a). Such a barrier is comparable with the activation energy for H transfer in oxide proton conductor BaZrO3.9,40,41 Once the oxygen vacancy is formed in the BaTiO3 lattice, it acts as the trapping site for the interstitial H. Migrating H atom occupies the vacancy site left by O and transforms into a more stable hydride anion with very small (
