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First-principles molecular dynamics simulations of proton diffusion in cubic BaZrO $$_3$$ 3 perovskite under strain conditions

First-principles molecular dynamics simulations of proton diffusion in cubic BaZrO $$_3$$ 3... Mater Renew Sustain Energy (2016) 5:14 DOI 10.1007/s40243-016-0078-9 ORIGINAL PAPER First-principles molecular dynamics simulations of proton diffusion in cubic BaZrO perovskite under strain conditions 1,2 1 3 4 • • • • Marco Fronzi Yoshitaka Tateyama Nicola Marzari Michael Nolan Enrico Traversa Received: 19 April 2016 / Accepted: 7 August 2016 / Published online: 29 August 2016 The Author(s) 2016. This article is published with open access at Springerlink.com Abstract First-principles molecular dynamics simulations Introduction have been employed to analyse the proton diffusion in cubic BaZrO perovskite at 1300 K. A non-linear effect on The development of highly ionic conductive materials is of the proton diffusion coefficient arising from an applied particular importance for the fabrication of high-perfor- isometric strain up to 2 % of the lattice parameter, and an mance solid oxide fuel cells (SOFCs) operating at inter- evident enhancement of proton diffusion under compres- mediate temperatures (550–900 K). State-of-the-art SOFC sive conditions have been observed. The structural and technology requires the cell to operate at temperatures electronic properties of BaZrO are analysed from Density between 1000 and 1300 K, which makes both fabrication Functional Theory calculations, and after an analysis of the and operation costly because expensive materials need to electronic structure, we provide a possible explanation for be used for sealing and for inter-connectors [1, 2]. There- an enhanced ionic conductivity of this bulk structure that fore, to encourage widespread adoption of SOFCs, the can be caused by the formation of a preferential path for development of highly conductive materials that can proton diffusion under compressive strain conditions. By operate at intermediate temperatures is imperative. means of Nudged Elastic Band calculations, diffusion BaZrO , similar to several other compounds that crys- barriers were also computed with results supporting our tallize in a perovskite structure, shows high proton con- conclusions. ductivity and is, therefore, a good candidate for an electrolyte material capable of operation at the desired Keywords First principles calculations  Proton operating temperature [3]. Ideally, in a perfect perovskite conduction  Strain effect  Fuel cells structure, a proton forms an O–H bond with one of the oxygen atoms, where the O–H group is characterized by its vibrational and rotational motion. The proton conduction mechanism has been described in terms of proton jumps from one oxygen site to another by H transfer and O–H reorientation [4, 5]. Because of the lattice geometry, the & Marco Fronzi marco.fronzi@mail.xjtu.edu.cn possible jumps are classified as intra-octahedral or inter- octahedral [6]. At its stable site, the hydrogen atom inter- International Center for Materials Nanoarchitectonics acts strongly with the surrounding atoms; this interaction (MANA), National Institute for Materials Science (NIMS), deforms the lattice by shortening the distance between the Tsukuba, Japan proton and the neighbouring oxygen. Migration occurs State Key Laboratory of Multiphase Flow in Power through a series of transitions between sites coordinated to Engineering, International Research Center for Renewable Energy, Xi’an Jiaotong University, Xi’an, Shaanxi, China different oxygens and sites coordinated to the same oxygen [7, 8]. The proton jump and O–H reorientation are ´ ´ Ecole Polytechnique Federale de Lausanne (EPFL), schematically illustrated in Fig. 1. Lausanne, Switzerland It is also well known that ionic conductivity can be Tyndall National Institute, University College Cork, Cork, higher in doped perovskites where one or more cations of Ireland 123 14 Page 2 of 10 Mater Renew Sustain Energy (2016) 5:14 diffusion to develop a new class of electrolyte materials with good chemical stability and high ion conductivity in the intermediate-/low-temperature range. In this work, we analysed the effect of external strain on proton diffusion in the cubic perovskite crystal structure of BaZrO to estimate the conditions under which proton conduction might be enhanced. Here, we considered only isotropic strains to avoid the existence of a preferential diffusion direction. We use a first-principles molecular dynamics approach, within the Car–Parrinello approxima- tion, with a temperature of 1300 K. The choice of the temperature has been made to facilitate the diffusion pro- Fig. 1 Schematic representation of proton diffusion, highlighting cess if compared to the typical intermediate temperature of proton reorientation and proton transfer movements. The H atom a SOFC. For temperature between 550 and 1300 K, the bonded to the O atom migrates to the next oxygen atom, breaking a physical properties of the lattice and proton diffusion O–H bond and forming a new one. The proton can reorient on an would differ quantitatively, but there will be no difference oxygen site to facilitate the next jump. The picture shows the octahedron polyhedrons formed by oxygen atoms, and paths for in the mechanism. The elevated temperature was also proton diffusion through intra- and inter-octahedral jumps chosen to increase the computational efficiency of the simulations, due to the increase in ion mobility and proton the host crystal is substituted with lower valence cations diffusion at this temperature, without affecting the signif- [2, 9]. A charge redistribution occurs after doping to bal- icance of the results. In practical applications, barium zir- ance the different oxidation states of the dopant and the conate is doped to facilitate the formation of the oxygen substituted atom. This can create oxygen vacancies in the vacancies, which are necessary to allow proton incorpo- lattice. If the crystal is in contact with a humid environ- ration and diffusion. However, in the present work, we ment, water molecules occupy the vacancies and dissoci- analyse only the pure BaZrO crystal because we focus on ate, increasing the concentration of interstitial protons in analysing the effect of strain on proton diffusion. We focus the lattice and thereby the conductivity. This may, how- in this study on the trapping-free conductivity by investi- ever, be reduced by traps produced by the dopants, as gating undoped BaZrO . Specifically, we want to analyse described by Yamazaki et al. [10] in Ref. 10. Furthermore, the effect of strain on the proton diffusivity, independently an additional and non-negligible effect of doping is a local from trapping. Work on doped BaZrO forms the basis of a distortion and the breaking of the lattice symmetry. This separate study outside the scope of this paper. effect contributes to the creation of new oxygen transport pathways; the local distortion stretches the bond, affecting Calculation methods the activation barriers and the diffusivity of the species. First-principles molecular dynamics simulations have been Conditions for electronic states calculations widely used to calculate and predict the ion conduction properties of several bulk crystal structures, confirming this We used plane-wave basis density functional theory (DFT) migration mechanism [11, 12]. as implemented in the Car–Parrinello code of the Quan- In addition to describing a new class of compounds, the tum-ESPRESSO distribution [16]. We used a Perdew– latest studies highlight the significant increase in conduc- Burke–Ernzerhof functional for the exchange-correlation tivity that can be achieved by coupling metal oxide mate- term [17]. Ultrasoft pseudo-potentials were used to simu- rials having different lattice parameters. This would create late the effect of the core electrons. Eight and twelve a so-called semi-coherent interface at which the two 2 6 2 2 2 6 2 valence electrons in the 6s 5p 5s and 5s 4d 4p 4s con- compounds are subjected to strain, although the role of figurations were considered for barium and zirconium strain on the ionic conductivity has been recently ques- 4 2 atoms, respectively, and six electrons in 2p 2s were con- tioned [13, 14, 15]. A semi-coherent interface preserves the crystal structure of the original compound while creating a sidered for oxygen atoms. C point sampling of the Brillouin deformation of the cell, which, however, preserves its zone was employed, while for Nudged Elastic Band cal- culation a (2  2  2) grid has been employed, and the original volume. In the cubic perovskite structure, the deformation would result in an interface strain (epitaxial cutoff energies for the wave function and charge density were 27.0 and 240 Ry, respectively [18]. strain) that would produce a tetragonal structure with the same volume as the original cubic one. Within this The calculation was considered to be converged when framework, it is essential to study the effect of strain on ion the force on each ion was less than 10 eV/A with a 123 Mater Renew Sustain Energy (2016) 5:14 Page 3 of 10 14 Fig. 2b. The separation between the ionic and wave func- convergence in the total energy of 10 eV, while for tion kinetic energies in Fig. 2b indicates a good approxi- Nudged Elastic Band calculation value of the norm of the mation for the fictitious electron mass. We discarded from forces orthogonal to the path is less than 10 eV/A. each trajectory the initial 4 ps, during which the ions reached their target kinetic energy. To calculate the Conditions for dynamics calculations BaZrO average lattice constant at T ¼ 1300 K, variable cell simulations were performed in a 135-atom super-cell We performed Car–Parrinello molecular dynamics simu- in isothermal–isobaric ensemble, with an external pressure lations. The simulations were performed in super-cells of imposed at 10 kbar. BaZrO with 40 and 135 atoms (symmetry group Pm3m) and in the canonical ensemble. To simulate the target Hydrogen charge treatment temperature a Nose´–Hoover thermostat at 1300 K has been used. The runs, each lasting between 40 and 50 ps, were Bjo¨rketun et al. studied the charge state of the hydrogen performed using a fictitious electron mass m = 150 a.u. atom [19]. Using DFT calculations, they estimated the and a time step dt ¼ 0.21 fs. These choices allow for interstitial hydrogen atom formation energy as a function excellent conservation of the constant of motion (Fig. 2 a of the Fermi energy. Their results showed that the hydro- shows negligible dissipation during a typical 46 ps simu- gen atom is stable in the charge state ?1 (the proton) for lation) and negligible drift in the fictitious kinetic energy of every value of the Fermi energy within the band gap range the electrons for simulations of that duration. In addition, [19]. Therefore, in this work we considered only the dif- the ratio between the kinetic energies of ions and electrons fusion of the positive charge state of the hydrogen (the was R \ 1/20 for the entire simulation time, as shown in proton), and a compensating jellium background was inserted in the calculations to remove divergences due to -40 the positive charged cell in the calculations. We calculate Pot. energy the hydrogen defect formation energy as follows: Const. of mot. bulk bulk DE ¼ E  E  l þ ql ; ð1Þ H e bulk bulk where E and E are the energy of the hydrogenated -60 and stoichiometric BaZrO , respectively, while q is the charge of the system, l is the chemical potential of the hydrogen atom, l is the chemical potential of the electrons (Fermi energy). We obtained a value of 0.18 eV in a relaxed super-cell (40 atoms) calculated when the Fermi level is at -80 0 10203040 the valence band maximum, whereas l is defined as one time (ps) half of the total energy of a hydrogen molecule in vacuum. For BaZrO cubic perovskite, this value has been calculated in Ref. [19] in relaxed super-cells to be 0.05 eV (in a Ionic KE 2  2  2 super-cell) and 0.21 eV (in a 3  3  3 super- Wavefunction KE cell). Thus, our results are consistent with Ref. [19]. Results We obtained a value of 4.21 A for the relaxed lattice constant of the stoichiometric BaZrO bulk by cell opti- mization at T = 0 K; this is consistent with other DFT ˚ ˚ studies (4.20 A) and with the experimental value (4.19 A) 0 10203040 time (ps) [20, 21]. After a proton is introduced into the relaxed bulk 40-atom super-cell and for the cell under tensile strain and Fig. 2 The top and the bottom panels represent, respectively, the compression, relaxation yields an O–H bond distance of potential energy and constant of motion (blue and green lines, respectively), and the ionic and wave function kinetic energy (red and 0.98 A. The positively charged region surrounding the black lines). The simulation was performed in a 40-atom super-cell proton produces a structural distortion compared to the where the temperature of the simulations was maintained at 1300 K stoichiometric BaZrO bulk with a Zr–O–Zr angle of by a Nose–Hoover thermostat. The fictitious electron mass is 150 a.u. 162.55 (180.00 in the stoichiometric bulk). and the time step dt ¼ 0.21 fs Energy (eV) Energy (eV) 14 Page 4 of 10 Mater Renew Sustain Energy (2016) 5:14 4.5 MSD 7000 MSD 9000 4.4 MSD 10000 MSD 11000 4.3 4.2 4.1 0 2000 4000 6000 8000 0246 8 10 12 14 16 18 20 Iteration (n) time (ps) Fig. 3 Lattice constant of BaZrO super-cell as a function of Fig. 4 Mean square displacement of the proton during self-diffusion simulation iterations calculated at 1300 K calculated in the fully relaxed BaZrO bulk at 1300 K averaged over different time steps We analysed the effect of temperature on the lattice calculated that the Haven ratio by averaging the MSD over parameter expansion by calculating the average change in 10,000 time steps is 1.46 times that by averaging over 7000 the cell parameter as a function of time at T = 1300 K, as time steps, which increases significantly the precision of illustrated in Fig. 3. We simulated the BaZrO stoichio- the calculations. The Haven ratio calculated by averaging metric bulk allowing a variable cell size, starting with a over 11,000 time steps is 1.04 times of that calculated from thermally expanded lattice parameter, as reported by 10,000 time steps. experimental measurements, to estimate the effect of the Next, we calculated the self-diffusion coefficient (D) temperature on the lattice parameter and the relative from the MSD using the Einstein relation: expansion coefficient [22]. The calculated average lattice DE constant in a variable cell simulation at T = 1300 K was 6D ¼ lim jr ðtÞ r ð0Þj ; ð3Þ i i 4.236 A, and the calculated expansion coefficient was t!1 dt 6 1 Ec = 5.4  10 K ; experimental data in the literature where r is the position of the proton at each time step t. In 6 1 report a value of 7.8  10 K , suggesting a 0.04 A the relaxed bulk, the calculated diffusion coefficient was expansion of the lattice parameter [22]. To simulate an 5 2 2.3 ± 0.3  10 cm /s. This value can be compared with applied external strain (either tensile or compressive), we other computational work in the literature [26, 10]. applied a variation of ±2 % (0.10 A) to the thermally Although no explicit evaluation at 1300 K has been done, expanded lattice parameters, which corresponds to a pres- Ref. [10] uses a reactive force field approach to a calcu- sure of ca. ±5 Gpa. The simulations for proton diffusion 5 2 lated diffusion coefficient of ca. 1.5  10 cm /s for the were run at a constant lattice parameter for the relaxed bulk relaxed bulk at 1300 K [10]. Yamazaki et al. measured and under compressive or tensile strain. proton diffusion in yttrium-doped BaZrO by impedance For each condition, we calculated the mean square dis- spectroscopy and thermogravimetric analysis and they placement (MSD) of the proton during simulations of 40– found a trapping mechanism, due to the yttrium atoms, to 50 ps [23]. The MSD can be calculated from a single tra- coexist with a trap-free diffusion mechanism. They were jectory by only performing a time average. Each curve is, able to extrapolate the trap-free proton diffusion coefficient therefore, a time-average calculation over a single trajec- 5 2 and they reported it to be 3 ± 2  10 cm /s at 1000 K, tory. Here, we considered the average value of the MSD of 5 2 which can be extrapolated to 1.0 ± 2.0  10 cm /s at the proton during self-diffusion over different time lengths, 1300 K, in line with our results [10]. as shown in Fig. 4 for the relaxed bulk. An average over The D values, calculated by extracting the coefficient of N = 11,000 time steps yields a linear relationship between a linear regression of the MSD curves shown in Fig. 5, the MSD and time, which is consistent with other works in 5 5 2 were 2.2 ± 0.3 10 and 3.5 ± 0.3 10 cm /s, the literature [24, 25]. To have a measure of the accuracy respectively, for the bulk under tensile and compressive when MSD averages were calculated, we compute the strain. Given the accuracy of the calculation of D, this Haven ratio (H ) for MSD averages over different time change is significant, and the proton diffusivity under length, where H is defined as follows: compressive strain is enhanced compared with the other H ¼ D =D ðr Þ; ð2Þ R i i i two conditions, resulting in a total path-length of 9.16  10 cm after 40 ps, where the same value is Here, D is the tracer diffusion coefficient and D ðr Þ the i i i 7.43  10 cm under relaxed conditions. These results conductivity diffusion coefficient of particle i. We lattice parameter (Å) MSD (Å ) Mater Renew Sustain Energy (2016) 5:14 Page 5 of 10 14 relax. cond. tens. cond comp. cond. 01 2 3 4 time (ps) Fig. 5 Mean square displacement of the proton during diffusion Fig. 6 Power spectrum of calculated proton diffusion in the fully calculated in bulk BaZrO under fully relaxed, isometric tensile relaxed BaZrO bulk. The spectrum was obtained by Fourier strain, and compressive strain conditions at 1300 K (black, red, and transform of the velocity–velocity correlation function. The high blue lines, respectively). Dotted lines represent linear regressions of wave number peak is consistent with that of the O–H bond in water at the MSD curves around 3600 cm , while the peak at low wave number resembles that measured by Karlsson et al in similar systems [28] show that the change in the lattice parameter under uniform compressive strain does not result in a linear variation of the proton diffusivity. By way of explanation, when a relax. cond. tens. cond. tensile strain is applied to the relaxed bulk, D does not comp. cond. change significantly, whereas a compression of the same length clearly increases D. To understand the origin of this effect, we analysed the 10 typical vibration frequencies of the proton, the typical O–H distances, and the electronic structure of the system under different strain conditions. We analysed the typical vibra- tion frequency of the proton by performing a Fourier transform of the velocity–velocity correlation function 23 4 5 6 7 (ACF), which was calculated in the x–y–z coordinates r(Å) (Fig. 6). While the diffusion coefficient extrapolated from Fig. 7 Calculated oxygen–oxygen pair correlation function atoms in the MSD gives insights into the total displacement, the the BaZrO bulk under relaxed, tensile strain, and compressive strain Fourier transform of the ACF shows two distinct peaks conditions (red, blue, and black lines, respectively) clearly corresponding to distinct diffusion mechanisms, which are attributed to rotation and transfer. The peak at oxygen–oxygen radial distribution, with a clear peak ˚ ˚ 700–900 cm represents the frustrated reorientation of the around 3.00 A and a second peak around 4.10–4.30 A O–H axis, while that at 3500–3700 cm represents the O– (Fig. 7). We observe only minor differences in the peak H stretching vibration (see Fig. 1). Interestingly, the frus- positions arising from the effect of the applied strain that trated reorientation peak splits into two parts, consistent slightly modifies atomic distances. On the other hand, in with the crystal symmetry. Both peaks are in good agree- the proton–oxygen distribution, a clear peak appears at ment with infrared spectroscopy and inelastic neutron around 1.00 A, indicating binding of the proton to oxygen; scattering analysis (see Refs. [29, 28, 30]), and in line with a second peak appears at different distances in the three the one calculated with the same methodology in similar cases. When the bulk is fully relaxed, the pair correlation perovskites by Shimojo et al. (see Ref. [12]); however, no function shows a broad peak around 3.12–3.16 A, and this substantial change in the power spectrum was observed peak is reduced under tensile strain. Under compressive under tensile or compressive strain. strain, a pronounced peak appears around 3.12–3.16 A, We calculated the pair correlation function (g(r)) to with a new peak appearing around 2.40 A (Fig. 8). Since evaluate how the probability of finding an oxygen atom this feature is broad and shows a higher intensity, it indi- changes with the distance from the proton and with the cates an enhanced probability of finding a second oxygen distance from another oxygen atom. Considering the sta- atom close to the proton, suggesting that there is a further tistical error, which results in a broadening of the peaks, the interaction of the proton with a second oxygen atom (O in three cases do not show qualitative differences in the Fig. 9) in addition to the original O–H bond (O in Fig. 9), MSD (Å ) g(r) 14 Page 6 of 10 Mater Renew Sustain Energy (2016) 5:14 as supposed in experimental works [31]. In Ref. [31], it is contribution to the upper valence band appears. When the stated that since the hopping rate decreased rapidly as the bulk is under compressive strain, the PDOS shows the O–O separation is increased, the reduced diffusion of interaction of the H with a second (next-nearest O in 1s B protons across the grain boundary may arise from the Fig. 10c) oxygen atom around 7:9 eV, suggesting the increased average distances between oxygen atoms in the origin of a hybridization of the proton with another oxygen interface. This confirm our results that link the magnitude atom, consistent with the pair correlation function of the of proton diffusion with the O–O, and the O–H distances proton. In the bulk under tensile strain, this type of calculated from the pair correlation function. hybridization does not appear (Fig. 10d). This analysis We found a substantial difference in the electronic suggests that lattice compression induces an interaction structure of the relaxed, compressed, and strained bulk between H and a second O that is not present in the original BaZrO . In the absence of a proton, all oxygen atoms are structure or with the tensile strain. The electronic structure structurally and chemically identical. The introduction of analysis, together with the analysis of the g(r), suggests the the proton then breaks the local symmetry of the oxygen formation of a favourable path for proton diffusion under sites, giving a modified electronic structure when compared compressed conditions that facilitates proton migration. to pure BaZrO . The projected density of states (PDOS) The appearance a proton–oxygen interaction is also shows a strong O –H bond (Fig. 10b) formed by suggested by the O –H distances for the next-nearest A B hybridization of the H and O states that peaks around oxygen atom O in the relaxed, compressed and strained 1s 2p B -8.3 eV. In addition, a second peak representing the structures. Using GGA-DFT calculations, we optimized oxygen 2p state of O around -6.3 eV and some these structures and found an O –H distance of 2.13 A in A B the fully relaxed bulk and in the bulk under tensile strain. Thus, the geometry of the structure under tensile strain is relax. cond. qualitatively similar to that of the relaxed bulk. The same tens. cond. comp. cond. distance is 1.63 A under compression, which is comparable to the typical O–H hydrogen bond distance in liquid water and appears due to the compressive strain allowing an interaction between proton and O . In addition, under compression, the two oxygen atoms O and O show a A B shorter O–O distance (of 2.51 A) if compared with the other two conditions. However, this is a purely local effect due to the positive charge of the proton, which is not 0 1 23 4 5 6 7 reflected in the average O–O distance shown in Fig. 7. r(Å) Finally, we analysed the charge redistribution after pro- tonation of the bulk structures. We calculated the charge Fig. 8 Calculated proton–oxygen pair correlation function atom in redistribution by taking the difference between the charge the BaZrO bulk under relaxed, tensile strain, and compressive strain conditions (red, blue, and black lines, respectively) distributions of the stoichiometric and protonated bulk. In Fig. 9 a Schematic representation of proton equilibrium position before diffusion. During diffusion, the H atom bonded to the O atom migrates to the next oxygen atom, breaking the O –H bond and forming a new O –H bond. b, c Energy configuration during proton diffusion, calculated by using the Nudged Elastic Band method, as a function of the reaction coordinate under tensile and compressed conditions, respectively. For these calculations, the 40-atom super-cell has been used g(r) Mater Renew Sustain Energy (2016) 5:14 Page 7 of 10 14 bFig. 10 Projected density of states (PDOS) of BaZrO a under relaxed stoichiometric conditions, b after introduction of a proton under relaxed conditions, and after introduction of a proton under c compressive and d tensile strain. In the plots, the Fermi energy is positioned at 0 eV. The valence band maximum lies below E and conduction band minimum lies above E the compressed bulk, we found a quasi-symmetric charge distribution around the proton in the direction of two neighbouring oxygens, suggesting the presence of a second (weaker) O–H interaction discussed above, in addition to the structural O–H bond (Figs. 11b, d). The quasi-sym- metrical charge distribution and the resemblance of the O – H to the O –H bond did not appear in the relaxed or tensile strained structure (Figs. 11a, c) and confirm the formation of a natural pathway in the compressed structure that facili- tates proton diffusion. The change of the electronic struc- ture and the appearance of a new O–H interaction suggests a lower activation energy of the proton jump if compared with the tensile or no strain conditions. Our calculated activation barriers (E ) for proton migration (O –H to O –H in Fig. 9 a), whose correlation A B with the bond length has been confirmed in other compu- tational works (see Refs. [32, 33, 34]), support these find- ings: under relaxed condition E ¼0.60 eV, while under tensile strain condition E ¼0.62 eV and compressive stain conditions E ¼0.50 eV (Fig. 9b, c). The diffusion barrier measured by Yamazaki et al. at low temperature is 0.46 eV, while the extrapolated value at indefinitely high tempera- ture (associated to a trap-free diffusion) is 0.17 eV [10]. Our calculated trap-free diffusion barriers are relatively higher then the one extrapolated by Yamazaki et al.; however, here we intend to show the relative change in proton diffusion under different conditions; therefore, the main focus is the relative change rather than the absolute value. In addition, the proton migration barrier values calculated for the relaxed conditions in the present work lie in the range of values found in the literature, with reported values between 0.20 and 0.83 eV [35, 6, 8, 20, 20]. Such a large range might be due to the different setup used in different works (e.g. Bjo¨rketun et al. in Ref. [35] use a different GGA func- tional), to which NEB calculations are very sensitive. We also calculate the barriers for a 90 rotation of the proton around oxygen ions, and we find these to be 0.06, 0.04 and 0.12 eV for the relaxed, tensile strained and compressed conditions, respectively. While these barriers do show an opposite trend compared to the trend for proton migration, their magnitude is significantly lower and they will not result in any significant decrease in proton diffusion. Our conclusion may appear to contradict the experi- mental evidence of Chen et al., which shows an enhanced 123 14 Page 8 of 10 Mater Renew Sustain Energy (2016) 5:14 Fig. 11 Induced charge density due to introduction of a proton in the relaxed (a, c) and compressed (b, d) BaZrO bulk. Red areas indicate charge accumulation; blue areas indicate charge depletion proton mobility in hydrated conditions, where a strain and compressive strain conditions. The analysis of BaZr Y O shows larger lattice parameter due to the the MSD indicates that an applied external strain has a non- 0:9 0:1 3 hydrostatic pressure induced by the syntheses route [36]. linear effect on the proton diffusion constant, and we found The discrepancies may be due to several differences in the that there is an evident enhancement of proton diffusion system and the environmental conditions, such as the under compressive strain, whereas there is no difference hydrated conditions, under which the experiment has been between the relaxed bulk crystal and that under tensile performed, which means that water is present and strain. The power spectrum obtained by a Fourier transform hydroxyls can form, do not resemble our simulated con- of the velocity–velocity autocorrelation function showed ditions [37, 38]. However, Ottochan et al. analysed proton two main peaks, one of which (ca. 3600 cm ) is likely to conduction in Yttrium-doped BaZrO under biaxial com- indicate the O–H stretching mode, while the other (ca. pressive conditions through the use of reactive molecular 700–900 cm ) indicates the frustrated rotational mode. dynamics simulations. They conclude that compressive However, no obvious differences appeared under either pressure should lead to an increase in the proton diffusion tensile or compressive strain. coefficient by shortening the oxygen–oxygen distance, We calculated the oxygen–oxygen and proton–oxygen which confirm our results supporting our conclusions [39]. pair correlation functions and found a significant difference in the latter under compression compared to the other two conditions, which suggests the origin of a second O–H Conclusions interaction, in addition to the original O–H bond. The PDOS show a significant difference between the electronic We applied Car–Parrinello Molecular Dynamics to inves- structure of the protonated compressed bulk when com- tigate proton diffusion in the undoped BaZrO cubic per- 3 pared to other systems, where there is an evident overlap of ovskite bulk crystal under fully relaxed, isometric tensile the H with two neighbouring O confirming the 1s 2p 123 Mater Renew Sustain Energy (2016) 5:14 Page 9 of 10 14 15. Pergolesi, D., Fabbri, E., Cook, S., Roddatis, V., Traversa, E., formation of a second O–H interaction. Finally, the anal- Kilner, J.: Tensile lattice distortion does not affect oxygen ysis of the charge redistribution after the introduction of a transport in yttria-stabilized zirconia-CeO . ACS Nano 6, 10524 proton into the structures also supports this hypothesis (2012) indicating the formation of a pathway that facilitates proton 16. 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Cammarata, A., Ordejon, P., Emanuele, A., Duca, D.: Y:BaZrO Bagdassarov, N.: Hydrostatic pressure decreases the proton Perovskite compounds I: DFT study on the unprotonated and mobility in the hydrated BaZr Y O . Appl. Phys. Lett. 97, protonated local structures. Chem. Asian J. 7, 1827 (2012) 0:9 0:1 3 041902 (2010) 39. Ottochian, A., Dezanneau, G., Gilles, C., Raiteri, P., Knight, C., 37. Shu, D.-J., Ge, S.-T., Wang, M., Ming, N.-B.: Interplay between Gale, J.: Influence of isotropic and biaxial strain on proton con- external strain and oxygen vacancies on a rutile TiO (110). Phys. duction in Y-doped BaZrO : a reactive molecular dynamics 2 3 Rev. Lett. 101, 116102 (2008) study. J. Mater. Them. A 2, 3127 (2014) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Materials for Renewable and Sustainable Energy Springer Journals

First-principles molecular dynamics simulations of proton diffusion in cubic BaZrO $$_3$$ 3 perovskite under strain conditions

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Materials Science; Materials Science, general; Renewable and Green Energy; Renewable and Green Energy
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Mater Renew Sustain Energy (2016) 5:14 DOI 10.1007/s40243-016-0078-9 ORIGINAL PAPER First-principles molecular dynamics simulations of proton diffusion in cubic BaZrO perovskite under strain conditions 1,2 1 3 4 • • • • Marco Fronzi Yoshitaka Tateyama Nicola Marzari Michael Nolan Enrico Traversa Received: 19 April 2016 / Accepted: 7 August 2016 / Published online: 29 August 2016 The Author(s) 2016. This article is published with open access at Springerlink.com Abstract First-principles molecular dynamics simulations Introduction have been employed to analyse the proton diffusion in cubic BaZrO perovskite at 1300 K. A non-linear effect on The development of highly ionic conductive materials is of the proton diffusion coefficient arising from an applied particular importance for the fabrication of high-perfor- isometric strain up to 2 % of the lattice parameter, and an mance solid oxide fuel cells (SOFCs) operating at inter- evident enhancement of proton diffusion under compres- mediate temperatures (550–900 K). State-of-the-art SOFC sive conditions have been observed. The structural and technology requires the cell to operate at temperatures electronic properties of BaZrO are analysed from Density between 1000 and 1300 K, which makes both fabrication Functional Theory calculations, and after an analysis of the and operation costly because expensive materials need to electronic structure, we provide a possible explanation for be used for sealing and for inter-connectors [1, 2]. There- an enhanced ionic conductivity of this bulk structure that fore, to encourage widespread adoption of SOFCs, the can be caused by the formation of a preferential path for development of highly conductive materials that can proton diffusion under compressive strain conditions. By operate at intermediate temperatures is imperative. means of Nudged Elastic Band calculations, diffusion BaZrO , similar to several other compounds that crys- barriers were also computed with results supporting our tallize in a perovskite structure, shows high proton con- conclusions. ductivity and is, therefore, a good candidate for an electrolyte material capable of operation at the desired Keywords First principles calculations  Proton operating temperature [3]. Ideally, in a perfect perovskite conduction  Strain effect  Fuel cells structure, a proton forms an O–H bond with one of the oxygen atoms, where the O–H group is characterized by its vibrational and rotational motion. The proton conduction mechanism has been described in terms of proton jumps from one oxygen site to another by H transfer and O–H reorientation [4, 5]. Because of the lattice geometry, the & Marco Fronzi marco.fronzi@mail.xjtu.edu.cn possible jumps are classified as intra-octahedral or inter- octahedral [6]. At its stable site, the hydrogen atom inter- International Center for Materials Nanoarchitectonics acts strongly with the surrounding atoms; this interaction (MANA), National Institute for Materials Science (NIMS), deforms the lattice by shortening the distance between the Tsukuba, Japan proton and the neighbouring oxygen. Migration occurs State Key Laboratory of Multiphase Flow in Power through a series of transitions between sites coordinated to Engineering, International Research Center for Renewable Energy, Xi’an Jiaotong University, Xi’an, Shaanxi, China different oxygens and sites coordinated to the same oxygen [7, 8]. The proton jump and O–H reorientation are ´ ´ Ecole Polytechnique Federale de Lausanne (EPFL), schematically illustrated in Fig. 1. Lausanne, Switzerland It is also well known that ionic conductivity can be Tyndall National Institute, University College Cork, Cork, higher in doped perovskites where one or more cations of Ireland 123 14 Page 2 of 10 Mater Renew Sustain Energy (2016) 5:14 diffusion to develop a new class of electrolyte materials with good chemical stability and high ion conductivity in the intermediate-/low-temperature range. In this work, we analysed the effect of external strain on proton diffusion in the cubic perovskite crystal structure of BaZrO to estimate the conditions under which proton conduction might be enhanced. Here, we considered only isotropic strains to avoid the existence of a preferential diffusion direction. We use a first-principles molecular dynamics approach, within the Car–Parrinello approxima- tion, with a temperature of 1300 K. The choice of the temperature has been made to facilitate the diffusion pro- Fig. 1 Schematic representation of proton diffusion, highlighting cess if compared to the typical intermediate temperature of proton reorientation and proton transfer movements. The H atom a SOFC. For temperature between 550 and 1300 K, the bonded to the O atom migrates to the next oxygen atom, breaking a physical properties of the lattice and proton diffusion O–H bond and forming a new one. The proton can reorient on an would differ quantitatively, but there will be no difference oxygen site to facilitate the next jump. The picture shows the octahedron polyhedrons formed by oxygen atoms, and paths for in the mechanism. The elevated temperature was also proton diffusion through intra- and inter-octahedral jumps chosen to increase the computational efficiency of the simulations, due to the increase in ion mobility and proton the host crystal is substituted with lower valence cations diffusion at this temperature, without affecting the signif- [2, 9]. A charge redistribution occurs after doping to bal- icance of the results. In practical applications, barium zir- ance the different oxidation states of the dopant and the conate is doped to facilitate the formation of the oxygen substituted atom. This can create oxygen vacancies in the vacancies, which are necessary to allow proton incorpo- lattice. If the crystal is in contact with a humid environ- ration and diffusion. However, in the present work, we ment, water molecules occupy the vacancies and dissoci- analyse only the pure BaZrO crystal because we focus on ate, increasing the concentration of interstitial protons in analysing the effect of strain on proton diffusion. We focus the lattice and thereby the conductivity. This may, how- in this study on the trapping-free conductivity by investi- ever, be reduced by traps produced by the dopants, as gating undoped BaZrO . Specifically, we want to analyse described by Yamazaki et al. [10] in Ref. 10. Furthermore, the effect of strain on the proton diffusivity, independently an additional and non-negligible effect of doping is a local from trapping. Work on doped BaZrO forms the basis of a distortion and the breaking of the lattice symmetry. This separate study outside the scope of this paper. effect contributes to the creation of new oxygen transport pathways; the local distortion stretches the bond, affecting Calculation methods the activation barriers and the diffusivity of the species. First-principles molecular dynamics simulations have been Conditions for electronic states calculations widely used to calculate and predict the ion conduction properties of several bulk crystal structures, confirming this We used plane-wave basis density functional theory (DFT) migration mechanism [11, 12]. as implemented in the Car–Parrinello code of the Quan- In addition to describing a new class of compounds, the tum-ESPRESSO distribution [16]. We used a Perdew– latest studies highlight the significant increase in conduc- Burke–Ernzerhof functional for the exchange-correlation tivity that can be achieved by coupling metal oxide mate- term [17]. Ultrasoft pseudo-potentials were used to simu- rials having different lattice parameters. This would create late the effect of the core electrons. Eight and twelve a so-called semi-coherent interface at which the two 2 6 2 2 2 6 2 valence electrons in the 6s 5p 5s and 5s 4d 4p 4s con- compounds are subjected to strain, although the role of figurations were considered for barium and zirconium strain on the ionic conductivity has been recently ques- 4 2 atoms, respectively, and six electrons in 2p 2s were con- tioned [13, 14, 15]. A semi-coherent interface preserves the crystal structure of the original compound while creating a sidered for oxygen atoms. C point sampling of the Brillouin deformation of the cell, which, however, preserves its zone was employed, while for Nudged Elastic Band cal- culation a (2  2  2) grid has been employed, and the original volume. In the cubic perovskite structure, the deformation would result in an interface strain (epitaxial cutoff energies for the wave function and charge density were 27.0 and 240 Ry, respectively [18]. strain) that would produce a tetragonal structure with the same volume as the original cubic one. Within this The calculation was considered to be converged when framework, it is essential to study the effect of strain on ion the force on each ion was less than 10 eV/A with a 123 Mater Renew Sustain Energy (2016) 5:14 Page 3 of 10 14 Fig. 2b. The separation between the ionic and wave func- convergence in the total energy of 10 eV, while for tion kinetic energies in Fig. 2b indicates a good approxi- Nudged Elastic Band calculation value of the norm of the mation for the fictitious electron mass. We discarded from forces orthogonal to the path is less than 10 eV/A. each trajectory the initial 4 ps, during which the ions reached their target kinetic energy. To calculate the Conditions for dynamics calculations BaZrO average lattice constant at T ¼ 1300 K, variable cell simulations were performed in a 135-atom super-cell We performed Car–Parrinello molecular dynamics simu- in isothermal–isobaric ensemble, with an external pressure lations. The simulations were performed in super-cells of imposed at 10 kbar. BaZrO with 40 and 135 atoms (symmetry group Pm3m) and in the canonical ensemble. To simulate the target Hydrogen charge treatment temperature a Nose´–Hoover thermostat at 1300 K has been used. The runs, each lasting between 40 and 50 ps, were Bjo¨rketun et al. studied the charge state of the hydrogen performed using a fictitious electron mass m = 150 a.u. atom [19]. Using DFT calculations, they estimated the and a time step dt ¼ 0.21 fs. These choices allow for interstitial hydrogen atom formation energy as a function excellent conservation of the constant of motion (Fig. 2 a of the Fermi energy. Their results showed that the hydro- shows negligible dissipation during a typical 46 ps simu- gen atom is stable in the charge state ?1 (the proton) for lation) and negligible drift in the fictitious kinetic energy of every value of the Fermi energy within the band gap range the electrons for simulations of that duration. In addition, [19]. Therefore, in this work we considered only the dif- the ratio between the kinetic energies of ions and electrons fusion of the positive charge state of the hydrogen (the was R \ 1/20 for the entire simulation time, as shown in proton), and a compensating jellium background was inserted in the calculations to remove divergences due to -40 the positive charged cell in the calculations. We calculate Pot. energy the hydrogen defect formation energy as follows: Const. of mot. bulk bulk DE ¼ E  E  l þ ql ; ð1Þ H e bulk bulk where E and E are the energy of the hydrogenated -60 and stoichiometric BaZrO , respectively, while q is the charge of the system, l is the chemical potential of the hydrogen atom, l is the chemical potential of the electrons (Fermi energy). We obtained a value of 0.18 eV in a relaxed super-cell (40 atoms) calculated when the Fermi level is at -80 0 10203040 the valence band maximum, whereas l is defined as one time (ps) half of the total energy of a hydrogen molecule in vacuum. For BaZrO cubic perovskite, this value has been calculated in Ref. [19] in relaxed super-cells to be 0.05 eV (in a Ionic KE 2  2  2 super-cell) and 0.21 eV (in a 3  3  3 super- Wavefunction KE cell). Thus, our results are consistent with Ref. [19]. Results We obtained a value of 4.21 A for the relaxed lattice constant of the stoichiometric BaZrO bulk by cell opti- mization at T = 0 K; this is consistent with other DFT ˚ ˚ studies (4.20 A) and with the experimental value (4.19 A) 0 10203040 time (ps) [20, 21]. After a proton is introduced into the relaxed bulk 40-atom super-cell and for the cell under tensile strain and Fig. 2 The top and the bottom panels represent, respectively, the compression, relaxation yields an O–H bond distance of potential energy and constant of motion (blue and green lines, respectively), and the ionic and wave function kinetic energy (red and 0.98 A. The positively charged region surrounding the black lines). The simulation was performed in a 40-atom super-cell proton produces a structural distortion compared to the where the temperature of the simulations was maintained at 1300 K stoichiometric BaZrO bulk with a Zr–O–Zr angle of by a Nose–Hoover thermostat. The fictitious electron mass is 150 a.u. 162.55 (180.00 in the stoichiometric bulk). and the time step dt ¼ 0.21 fs Energy (eV) Energy (eV) 14 Page 4 of 10 Mater Renew Sustain Energy (2016) 5:14 4.5 MSD 7000 MSD 9000 4.4 MSD 10000 MSD 11000 4.3 4.2 4.1 0 2000 4000 6000 8000 0246 8 10 12 14 16 18 20 Iteration (n) time (ps) Fig. 3 Lattice constant of BaZrO super-cell as a function of Fig. 4 Mean square displacement of the proton during self-diffusion simulation iterations calculated at 1300 K calculated in the fully relaxed BaZrO bulk at 1300 K averaged over different time steps We analysed the effect of temperature on the lattice calculated that the Haven ratio by averaging the MSD over parameter expansion by calculating the average change in 10,000 time steps is 1.46 times that by averaging over 7000 the cell parameter as a function of time at T = 1300 K, as time steps, which increases significantly the precision of illustrated in Fig. 3. We simulated the BaZrO stoichio- the calculations. The Haven ratio calculated by averaging metric bulk allowing a variable cell size, starting with a over 11,000 time steps is 1.04 times of that calculated from thermally expanded lattice parameter, as reported by 10,000 time steps. experimental measurements, to estimate the effect of the Next, we calculated the self-diffusion coefficient (D) temperature on the lattice parameter and the relative from the MSD using the Einstein relation: expansion coefficient [22]. The calculated average lattice DE constant in a variable cell simulation at T = 1300 K was 6D ¼ lim jr ðtÞ r ð0Þj ; ð3Þ i i 4.236 A, and the calculated expansion coefficient was t!1 dt 6 1 Ec = 5.4  10 K ; experimental data in the literature where r is the position of the proton at each time step t. In 6 1 report a value of 7.8  10 K , suggesting a 0.04 A the relaxed bulk, the calculated diffusion coefficient was expansion of the lattice parameter [22]. To simulate an 5 2 2.3 ± 0.3  10 cm /s. This value can be compared with applied external strain (either tensile or compressive), we other computational work in the literature [26, 10]. applied a variation of ±2 % (0.10 A) to the thermally Although no explicit evaluation at 1300 K has been done, expanded lattice parameters, which corresponds to a pres- Ref. [10] uses a reactive force field approach to a calcu- sure of ca. ±5 Gpa. The simulations for proton diffusion 5 2 lated diffusion coefficient of ca. 1.5  10 cm /s for the were run at a constant lattice parameter for the relaxed bulk relaxed bulk at 1300 K [10]. Yamazaki et al. measured and under compressive or tensile strain. proton diffusion in yttrium-doped BaZrO by impedance For each condition, we calculated the mean square dis- spectroscopy and thermogravimetric analysis and they placement (MSD) of the proton during simulations of 40– found a trapping mechanism, due to the yttrium atoms, to 50 ps [23]. The MSD can be calculated from a single tra- coexist with a trap-free diffusion mechanism. They were jectory by only performing a time average. Each curve is, able to extrapolate the trap-free proton diffusion coefficient therefore, a time-average calculation over a single trajec- 5 2 and they reported it to be 3 ± 2  10 cm /s at 1000 K, tory. Here, we considered the average value of the MSD of 5 2 which can be extrapolated to 1.0 ± 2.0  10 cm /s at the proton during self-diffusion over different time lengths, 1300 K, in line with our results [10]. as shown in Fig. 4 for the relaxed bulk. An average over The D values, calculated by extracting the coefficient of N = 11,000 time steps yields a linear relationship between a linear regression of the MSD curves shown in Fig. 5, the MSD and time, which is consistent with other works in 5 5 2 were 2.2 ± 0.3 10 and 3.5 ± 0.3 10 cm /s, the literature [24, 25]. To have a measure of the accuracy respectively, for the bulk under tensile and compressive when MSD averages were calculated, we compute the strain. Given the accuracy of the calculation of D, this Haven ratio (H ) for MSD averages over different time change is significant, and the proton diffusivity under length, where H is defined as follows: compressive strain is enhanced compared with the other H ¼ D =D ðr Þ; ð2Þ R i i i two conditions, resulting in a total path-length of 9.16  10 cm after 40 ps, where the same value is Here, D is the tracer diffusion coefficient and D ðr Þ the i i i 7.43  10 cm under relaxed conditions. These results conductivity diffusion coefficient of particle i. We lattice parameter (Å) MSD (Å ) Mater Renew Sustain Energy (2016) 5:14 Page 5 of 10 14 relax. cond. tens. cond comp. cond. 01 2 3 4 time (ps) Fig. 5 Mean square displacement of the proton during diffusion Fig. 6 Power spectrum of calculated proton diffusion in the fully calculated in bulk BaZrO under fully relaxed, isometric tensile relaxed BaZrO bulk. The spectrum was obtained by Fourier strain, and compressive strain conditions at 1300 K (black, red, and transform of the velocity–velocity correlation function. The high blue lines, respectively). Dotted lines represent linear regressions of wave number peak is consistent with that of the O–H bond in water at the MSD curves around 3600 cm , while the peak at low wave number resembles that measured by Karlsson et al in similar systems [28] show that the change in the lattice parameter under uniform compressive strain does not result in a linear variation of the proton diffusivity. By way of explanation, when a relax. cond. tens. cond. tensile strain is applied to the relaxed bulk, D does not comp. cond. change significantly, whereas a compression of the same length clearly increases D. To understand the origin of this effect, we analysed the 10 typical vibration frequencies of the proton, the typical O–H distances, and the electronic structure of the system under different strain conditions. We analysed the typical vibra- tion frequency of the proton by performing a Fourier transform of the velocity–velocity correlation function 23 4 5 6 7 (ACF), which was calculated in the x–y–z coordinates r(Å) (Fig. 6). While the diffusion coefficient extrapolated from Fig. 7 Calculated oxygen–oxygen pair correlation function atoms in the MSD gives insights into the total displacement, the the BaZrO bulk under relaxed, tensile strain, and compressive strain Fourier transform of the ACF shows two distinct peaks conditions (red, blue, and black lines, respectively) clearly corresponding to distinct diffusion mechanisms, which are attributed to rotation and transfer. The peak at oxygen–oxygen radial distribution, with a clear peak ˚ ˚ 700–900 cm represents the frustrated reorientation of the around 3.00 A and a second peak around 4.10–4.30 A O–H axis, while that at 3500–3700 cm represents the O– (Fig. 7). We observe only minor differences in the peak H stretching vibration (see Fig. 1). Interestingly, the frus- positions arising from the effect of the applied strain that trated reorientation peak splits into two parts, consistent slightly modifies atomic distances. On the other hand, in with the crystal symmetry. Both peaks are in good agree- the proton–oxygen distribution, a clear peak appears at ment with infrared spectroscopy and inelastic neutron around 1.00 A, indicating binding of the proton to oxygen; scattering analysis (see Refs. [29, 28, 30]), and in line with a second peak appears at different distances in the three the one calculated with the same methodology in similar cases. When the bulk is fully relaxed, the pair correlation perovskites by Shimojo et al. (see Ref. [12]); however, no function shows a broad peak around 3.12–3.16 A, and this substantial change in the power spectrum was observed peak is reduced under tensile strain. Under compressive under tensile or compressive strain. strain, a pronounced peak appears around 3.12–3.16 A, We calculated the pair correlation function (g(r)) to with a new peak appearing around 2.40 A (Fig. 8). Since evaluate how the probability of finding an oxygen atom this feature is broad and shows a higher intensity, it indi- changes with the distance from the proton and with the cates an enhanced probability of finding a second oxygen distance from another oxygen atom. Considering the sta- atom close to the proton, suggesting that there is a further tistical error, which results in a broadening of the peaks, the interaction of the proton with a second oxygen atom (O in three cases do not show qualitative differences in the Fig. 9) in addition to the original O–H bond (O in Fig. 9), MSD (Å ) g(r) 14 Page 6 of 10 Mater Renew Sustain Energy (2016) 5:14 as supposed in experimental works [31]. In Ref. [31], it is contribution to the upper valence band appears. When the stated that since the hopping rate decreased rapidly as the bulk is under compressive strain, the PDOS shows the O–O separation is increased, the reduced diffusion of interaction of the H with a second (next-nearest O in 1s B protons across the grain boundary may arise from the Fig. 10c) oxygen atom around 7:9 eV, suggesting the increased average distances between oxygen atoms in the origin of a hybridization of the proton with another oxygen interface. This confirm our results that link the magnitude atom, consistent with the pair correlation function of the of proton diffusion with the O–O, and the O–H distances proton. In the bulk under tensile strain, this type of calculated from the pair correlation function. hybridization does not appear (Fig. 10d). This analysis We found a substantial difference in the electronic suggests that lattice compression induces an interaction structure of the relaxed, compressed, and strained bulk between H and a second O that is not present in the original BaZrO . In the absence of a proton, all oxygen atoms are structure or with the tensile strain. The electronic structure structurally and chemically identical. The introduction of analysis, together with the analysis of the g(r), suggests the the proton then breaks the local symmetry of the oxygen formation of a favourable path for proton diffusion under sites, giving a modified electronic structure when compared compressed conditions that facilitates proton migration. to pure BaZrO . The projected density of states (PDOS) The appearance a proton–oxygen interaction is also shows a strong O –H bond (Fig. 10b) formed by suggested by the O –H distances for the next-nearest A B hybridization of the H and O states that peaks around oxygen atom O in the relaxed, compressed and strained 1s 2p B -8.3 eV. In addition, a second peak representing the structures. Using GGA-DFT calculations, we optimized oxygen 2p state of O around -6.3 eV and some these structures and found an O –H distance of 2.13 A in A B the fully relaxed bulk and in the bulk under tensile strain. Thus, the geometry of the structure under tensile strain is relax. cond. qualitatively similar to that of the relaxed bulk. The same tens. cond. comp. cond. distance is 1.63 A under compression, which is comparable to the typical O–H hydrogen bond distance in liquid water and appears due to the compressive strain allowing an interaction between proton and O . In addition, under compression, the two oxygen atoms O and O show a A B shorter O–O distance (of 2.51 A) if compared with the other two conditions. However, this is a purely local effect due to the positive charge of the proton, which is not 0 1 23 4 5 6 7 reflected in the average O–O distance shown in Fig. 7. r(Å) Finally, we analysed the charge redistribution after pro- tonation of the bulk structures. We calculated the charge Fig. 8 Calculated proton–oxygen pair correlation function atom in redistribution by taking the difference between the charge the BaZrO bulk under relaxed, tensile strain, and compressive strain conditions (red, blue, and black lines, respectively) distributions of the stoichiometric and protonated bulk. In Fig. 9 a Schematic representation of proton equilibrium position before diffusion. During diffusion, the H atom bonded to the O atom migrates to the next oxygen atom, breaking the O –H bond and forming a new O –H bond. b, c Energy configuration during proton diffusion, calculated by using the Nudged Elastic Band method, as a function of the reaction coordinate under tensile and compressed conditions, respectively. For these calculations, the 40-atom super-cell has been used g(r) Mater Renew Sustain Energy (2016) 5:14 Page 7 of 10 14 bFig. 10 Projected density of states (PDOS) of BaZrO a under relaxed stoichiometric conditions, b after introduction of a proton under relaxed conditions, and after introduction of a proton under c compressive and d tensile strain. In the plots, the Fermi energy is positioned at 0 eV. The valence band maximum lies below E and conduction band minimum lies above E the compressed bulk, we found a quasi-symmetric charge distribution around the proton in the direction of two neighbouring oxygens, suggesting the presence of a second (weaker) O–H interaction discussed above, in addition to the structural O–H bond (Figs. 11b, d). The quasi-sym- metrical charge distribution and the resemblance of the O – H to the O –H bond did not appear in the relaxed or tensile strained structure (Figs. 11a, c) and confirm the formation of a natural pathway in the compressed structure that facili- tates proton diffusion. The change of the electronic struc- ture and the appearance of a new O–H interaction suggests a lower activation energy of the proton jump if compared with the tensile or no strain conditions. Our calculated activation barriers (E ) for proton migration (O –H to O –H in Fig. 9 a), whose correlation A B with the bond length has been confirmed in other compu- tational works (see Refs. [32, 33, 34]), support these find- ings: under relaxed condition E ¼0.60 eV, while under tensile strain condition E ¼0.62 eV and compressive stain conditions E ¼0.50 eV (Fig. 9b, c). The diffusion barrier measured by Yamazaki et al. at low temperature is 0.46 eV, while the extrapolated value at indefinitely high tempera- ture (associated to a trap-free diffusion) is 0.17 eV [10]. Our calculated trap-free diffusion barriers are relatively higher then the one extrapolated by Yamazaki et al.; however, here we intend to show the relative change in proton diffusion under different conditions; therefore, the main focus is the relative change rather than the absolute value. In addition, the proton migration barrier values calculated for the relaxed conditions in the present work lie in the range of values found in the literature, with reported values between 0.20 and 0.83 eV [35, 6, 8, 20, 20]. Such a large range might be due to the different setup used in different works (e.g. Bjo¨rketun et al. in Ref. [35] use a different GGA func- tional), to which NEB calculations are very sensitive. We also calculate the barriers for a 90 rotation of the proton around oxygen ions, and we find these to be 0.06, 0.04 and 0.12 eV for the relaxed, tensile strained and compressed conditions, respectively. While these barriers do show an opposite trend compared to the trend for proton migration, their magnitude is significantly lower and they will not result in any significant decrease in proton diffusion. Our conclusion may appear to contradict the experi- mental evidence of Chen et al., which shows an enhanced 123 14 Page 8 of 10 Mater Renew Sustain Energy (2016) 5:14 Fig. 11 Induced charge density due to introduction of a proton in the relaxed (a, c) and compressed (b, d) BaZrO bulk. Red areas indicate charge accumulation; blue areas indicate charge depletion proton mobility in hydrated conditions, where a strain and compressive strain conditions. The analysis of BaZr Y O shows larger lattice parameter due to the the MSD indicates that an applied external strain has a non- 0:9 0:1 3 hydrostatic pressure induced by the syntheses route [36]. linear effect on the proton diffusion constant, and we found The discrepancies may be due to several differences in the that there is an evident enhancement of proton diffusion system and the environmental conditions, such as the under compressive strain, whereas there is no difference hydrated conditions, under which the experiment has been between the relaxed bulk crystal and that under tensile performed, which means that water is present and strain. The power spectrum obtained by a Fourier transform hydroxyls can form, do not resemble our simulated con- of the velocity–velocity autocorrelation function showed ditions [37, 38]. However, Ottochan et al. analysed proton two main peaks, one of which (ca. 3600 cm ) is likely to conduction in Yttrium-doped BaZrO under biaxial com- indicate the O–H stretching mode, while the other (ca. pressive conditions through the use of reactive molecular 700–900 cm ) indicates the frustrated rotational mode. dynamics simulations. They conclude that compressive However, no obvious differences appeared under either pressure should lead to an increase in the proton diffusion tensile or compressive strain. coefficient by shortening the oxygen–oxygen distance, We calculated the oxygen–oxygen and proton–oxygen which confirm our results supporting our conclusions [39]. pair correlation functions and found a significant difference in the latter under compression compared to the other two conditions, which suggests the origin of a second O–H Conclusions interaction, in addition to the original O–H bond. The PDOS show a significant difference between the electronic We applied Car–Parrinello Molecular Dynamics to inves- structure of the protonated compressed bulk when com- tigate proton diffusion in the undoped BaZrO cubic per- 3 pared to other systems, where there is an evident overlap of ovskite bulk crystal under fully relaxed, isometric tensile the H with two neighbouring O confirming the 1s 2p 123 Mater Renew Sustain Energy (2016) 5:14 Page 9 of 10 14 15. Pergolesi, D., Fabbri, E., Cook, S., Roddatis, V., Traversa, E., formation of a second O–H interaction. Finally, the anal- Kilner, J.: Tensile lattice distortion does not affect oxygen ysis of the charge redistribution after the introduction of a transport in yttria-stabilized zirconia-CeO . ACS Nano 6, 10524 proton into the structures also supports this hypothesis (2012) indicating the formation of a pathway that facilitates proton 16. 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