Article pubs.acs.org/JPCC
Proton Distribution and Dynamics in Y- and Zn-Doped BaZrO3 Naoto Kitamura,*,†,‡,§ Jaakko Akola,§,∥ Shinji Kohara,⊥,# Kenjiro Fujimoto,†,‡ and Yasushi Idemoto†,‡ †
Department of Pure and Applied Chemistry, Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan ‡ Division of Ecosystem Research, Research Institute for Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan § Department of Physics, Tampere University of Technology, P.O. Box 692, FI-33101 Tampere, Finland ∥ Centre of Excellence in Computational Nanoscience, Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland ⊥ Research and Utilization Division, Japan Synchrotron Radiation Research Institute/SPring-8, Sayo-cho, Sayo-gun, Hyogo 679-5198, Japan # Schools of Materials Science, Japan Advanced Institute of Science and Technology, Nomi, Ishikawa 923-1291, Japan ABSTRACT: Proton diffusion in Y- and Zn-doped BaZrO3 has been studied by performing molecular dynamics (MD) simulations, where the forces acting on atoms have been computed by the density functional theory (DFT). Special attention has been paid for the dopant effect on the proton conduction. The atomic configuration of 338 atoms obtained by the simulations has been verified by infrared absorption spectroscopy and neutron and synchrotron X-ray total scattering techniques. It is found from the DFT-based MD simulation that protons tend to get localized around Zn but not Y in significant amounts even at elevated temperature. Such a trapping is also indicated by change in the infrared absorption spectra by temperature, and the atomic configuration optimized by the DFT is consistent with that refined by the reverse Monte Carlo simulation using the Bragg reflections and structure factors. From DFT calculations, it can be concluded that the differences in the effective charges between Zr and the dopants explain the reason for the strong proton trapping by Zn.
1. INTRODUCTION In recent decades, the solid oxide fuel cell (SOFC) has drawn much attention as an energy source because of the high efficiency, low environmental load, and fuel flexibility. These benefits originate from the high operating temperature, that is, 800−1000 °C, compared with other electrochemical energy sources, but such a severe condition limits the wide commercialization of SOFC at the same time. Taking both of these advantages and disadvantages into account, much research has tried to make the operating temperature lower to around 500−800 °C.1,2 To realize SOFC working at this temperature range, which is the so-called intermediate-temperature SOFC (IT-SOFC), there are some problems to be resolved. One of them is to develop a novel ion conductor which can be applied for the electrolyte because yttria-stabilized zirconia, which is widely utilized as the electrolyte, exhibits low ion conductivity at the intermediate temperature. Here, BaZrO3-based materials in which Zr is partially replaced by other elements can be regarded as promising candidates.3−15 Although various elements have been investigated as dopants, it is well-known that Y-doped BaZrO3, that is, Ba(Zr, Y)O3, shows the highest proton conductivity.3−6,9−11 However, the preparation process of dense ceramics of this material requires an extremely high temperature around 1600 °C. According to previous work,12,13 Zn-doping improves the sinterability and results in a lower sintering temperature below 1400 °C, but © 2014 American Chemical Society
simultaneously, the Zn-doped material exhibits a lower proton conductivity in the crystal compared to Ba(Zr, Y)O3. Such an effect of the dopant on the proton behavior has been discussed empirically from the viewpoint of ionic sizes and nominal charges,11,12 but theoretical calculations are expected to provide a deeper understanding of the nature of the dopant effect. As a theoretical approach to study proton diffusion in BaZrO3-based materials, computational simulations at atomistic level can be considered as one of the most significant techniques. In fact, some previous investigations studied the proton diffusion in BaZrO3 by the density functional theory (DFT) and the molecular dynamics (MD) calculations and discussed the proton diffusion coefficients and the activation energies.14−19 However, these works did not consider effects of dopant species although the protonic conduction in the BaZrO3-based materials depends on the dopant species considerably. In this work, we have investigated crystalline samples of Ba(Zr, Y, Zn)O3 with protons by means of MD simulations where the electronic structure and forces acting on atoms have been evaluated by the density functional theory (DFT), that is, we have performed DFT-based MD calculations. The atomic configuration obtained from the Received: March 11, 2014 Revised: July 24, 2014 Published: July 25, 2014 18846
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reverse Monte Carlo (RMC) simulation as described below. We also performed a high-energy X-ray diffraction experiment with an incident beam of 61.5 keV by BL04B2 at SPring-8, Japan.30 The incident X-ray intensity was monitored by an ionization chamber filled with Ar gas, and the scattered beam was detected by a Ge detector. The obtained data was corrected using a standard program.30 These structure factors and the Bragg peaks recorded with HIPPO were analyzed simultaneously by the RMC method using the RMCProfile program.31 In the analysis, the experimentally corrected structure factors were degraded by convolution in order to take the finite cell size for the analysis into account. The RMC simulation was performed by using the DFT-optimized atomic configuration as an initial cell under a constraint for minimum interatomic distances which were determined on the basis of the DFToptimized cell. Infrared absorption spectra were measured with a diffuse reflectance mode (Cray 660 FT-IR, Agilent Technologies). The measurements were carried out at room temperature and at 400 °C under N2 condition.
DFT-MD calculation was verified by experimental results of the infrared absorption and neutron and synchrotron X-ray total scatterings. On the basis of these results, we discuss the effects of the Y- and Zn-doping on the proton conductivity in BaZrO3.
2. CALCULATION AND EXPERIMENTAL METHODS 2.1. DFT-MD Simulations. The DFT simulations were performed with the CP2K program which combines the localized Gaussian basis set and plane waves for a dual GPW basis set.20,21 A library of DZVP basis sets was used as the Gaussian localized expansion of Kohn−Sham orbitals,22 and the cutoff energy of the plane waves was set to 400 Ry for the expansion of electron density. The valence electron−ion interaction was represented by norm-conserving and scalarrelativistic pseudopotentials derived by Goedecker et al.23 The generalized gradient approximation of Perdew, Burke, and Ernzerhof (PBE) was adopted as the exchange-correlation energy functional.24 A simulation cell for a system of Ba64Zr52Y6Zn6O192H18 was constructed on the basis of the refined crystal structure by the Rietveld method using neutron diffraction measurements described below, and the cell size and the atomic configuration were optimized by DFT calculations. To investigate proton diffusion in the Y- and Zn-doped BaZrO3, we performed DFT-based MD calculations, where the time step was set to 0.5 fs, and the NVT ensemble was adopted. The temperature was controlled at 800 °C by using canonical sampling through the velocity rescaling (CSVR) thermostat,25 and the system was simulated for 50 ps. Before starting the simulation, we performed a preannealing simulation for 15 ps without the CSVR thermostat in order to stabilize the structure. The electron density distribution was calculated and analyzed for the optimized atomic configuration by using the Bader and Voronoi methods for effective charge.26,27 The electronic valence states were transformed by using the maximally localized Wannier functions.28 In addition, harmonic oscillations with infrared absorptions were computed via finite differences for the optimized structure. 2.2. Atomic Configuration Analysis Using Spectroscopic Data. BaZr0.8Y0.1Zn0.1O3 was prepared by a conventional solid-state method using BaCO3, ZrO2, Y2O3, and ZnO as starting materials. These materials were mixed in appropriate proportions and then were calcined at 1100 °C for 12 h in air. The obtained powder was sintered at 1450 °C for 12 h in air after a uniaxial pressing. Post annealing at 650 °C overnight under a H2O-moisturized condition was carried out for infrared absorption measurement, and that under a D2O-moisturized condition was also performed for neutron and synchrotron Xray total scattering measurements. A metal composition of the sample was analyzed by the inductively coupled plasma (ICP) spectroscopy. For the purpose of a phase identification and preliminary atomic configuration determination, a neutron total scattering pattern was measured at room temperature with HIPPO installed at Los Alamos Neutron Science Center (LANSCE), U.S.A. The recorded Bragg reflection was analyzed by the Rietveld method using the EXPGUI-GSAS,29 and the initial structure of BaZr0.8Y0.1Zn0.1O3 with protons was generated for the DFT-MD calculation. In principle, it is not possible to get information about local atomic arrangements from Bragg peaks because such an analysis reflects only a crystallographic periodicity. Therefore, the measured structure factor was normalized by using data of an empty can, a vanadium rod, and an instrument background and then was used for the
3. RESULTS AND DISCUSSION 3.1. Initial Atomic Configuration for DFT-MD Calculation. From Bragg reflections of a neutron diffraction pattern, it was confirmed that the protonated BaZr0.8Y0.1Zn0.1O3 synthesized in this work had a single phase of the cubic perovskite structure with a lattice parameter of 4.20653(3) Å. An ICP measurement also demonstrated that a metalcomposition ratio of Ba:Zr:Y:Zn in the specimen was 0.98:0.81:0.10:0.11 and was essentially the same as the nominal value. Taking these results into account, an initial cell for the DFT calculations with 338 atoms, that is, Ba64Zr52Y6Zn6O192H18, was constructed by multiplying the experimentally refined unit cell 4 times in each direction. It was assumed that protons existed at interstitial positions in the crystal and that the concentration satisfied the charge neutrality condition. Figure 1 shows the atomic configuration after a geometry optimization by DFT. As shown in this figure, Zr, Y, and Zn are located at octahedral sites, and Ba is in a 12coordinated site, indicating that the perovskite structure of the protonated BaZr0.8Y0.1Zn0.1O3 is stable also from the theoretical viewpoint. The optimized size of the cubic cell is 17.09 Å,
Figure 1. Atomic configuration of protonated BaZr0.8Y0.1Zn0.1O3 after DFT optimization. The cell comprises 338 atoms (Ba64Zr52Y6Zn6O192H18) with a cubic box size of 17.09 Å. Color code: Ba, dark green; Zr, light green; Y, orange; Zn, purple; O, red; and H, light blue. 18847
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which is very close to the experimental value of 16.83 Å (1.5% deviation). It is also found that all the protons are bound to oxygen in the crystal structure. 3.2. Proton Diffusion at Elevated Temperature. To investigate proton dynamics in the BaZrO3-based material, we simulated proton diffusions at 800 °C by the DFT-based MD and then calculated the mean square displacements, MSD, of protons by eq 1 MSD = |r(t ) − r0|2
(1)
in which t, r, and r0 represent the simulation time, the simulated position at t, and the initial position for the proton, respectively. The logarithm values as a function of logarithm of simulation time are given in Figure 2. This figure demonstrates that the
Figure 3. Examples of the mean-square displacements, MSD, for individual protons as a function of time. (a, b) Free protons and (c−e) trapped protons.
Figure 2. Logarithm mean-square displacements, MSD, averaged over all protons as a function of logarithm simulation time. A broken line has a slope of 1.
the negative influence of the Zn-doping on the protonic conduction property of BaZrO3-based protonic conductors.12,13 Figure 4a shows a typical diffusion path of free protons in the material. It is demonstrated that the protons diffuse via interstitial sites in the crystal structure. The magnified diffusion path images in Figure 4b and c show that the proton-diffusion mechanism can be divided into rotation and hopping processes. The conducting proton forms a hydrogen bond with oxygen, and it can diffuse via forming a new hydrogen bond and breaking the old one by the hopping process (Figure 4b). Then, the proton breaks the hydrogen bond and forms a new hydrogen bond with another oxygen by the rotation mode (Figure 4c). By these two processes, the free protons can diffuse through the crystal and exhibit larger MSD values as shown in Figure 3. This result is consistent with the expected conduction mechanism in previous works.1,14−16,18 The trapped protons (Figure 4d) can also diffuse via both hopping and rotation, but their diffusion routes are restricted only around Zn. In other words, hopping to other oxygens outside the particular Zn coordination seems to be prohibited at least at the temperature and time scale studied. These results highlight that the 3D proton-diffusion pathways are determined by the host cation species and their distribution in the crystal although all the protons can move with the hopping and rotation mechanism. Correspondingly, we discuss the electronic properties of the cations in detail in the subsection 3.4. 3.3. Optimized Atomic Configuration. To verify the atomic configuration obtained by the theoretical calculation from the viewpoint of experiments, we performed neutron and synchrotron X-ray total scattering measurements, and we carried out RMC simulations using their structure factors and the neutron Bragg reflections. Figure 5a−c shows the simulation results by using one of the atomic configuration snapshots obtained by the DFT-based MD calculation as the
slope of this plot becomes unity with the simulation time, indicating proton diffusion based on the Fick’s low. This means that the diffusion coefficient, D, can be calculated from the MSD at the longer simulation time, according to the following equation:
D = MSD/6t
(2)
The average diffusion coefficient for all the protons, which was evaluated from the linear fit of the MSD against the simulation time for the last 20 ps, is 1.3 × 10−5 cm2·sec−1. This value is close to previous results for protons in pure and Y-doped BaZrO3.18 This indicates that the DFT-MD simulations reported in this work can describe the proton dynamics in the Ba(Zr,Y,Zn)O3-based protonic conductor at least at 800 °C for the last 20 ps, although longer MD simulation time is preferable as in some previous works,17,18 especially at lower temperature for IT-SOFC, for example, 500 °C. To estimate the effects of the dopants in detail, we investigated the distances between protons and dopants, and then we labeled protons which remained localized in Y−O−H or Zn−O−H configurations during the MD simulation during the last 20 ps as “trapped protons”. As a result, it was found that the protons could be divided into the trapped or free protons, and all the trapped protons existed around Zn. Figure 3a−e presents some examples of MSD for the trapped and free protons at 800 °C. The result shows that MSD of the trapped protons is at smaller values and that the apparent diffusion is 3.4 × 10−6 cm2·sec−1 on average. In contrast, an average diffusion coefficient of the free protons is 3.9 × 10−5 cm2·sec−1 and is higher than that of all the protons mentioned above because of the Zn trapping contribution. Taking these results into account, it can be concluded that Zn reduces proton diffusion by trapping part of the protons, and this explains well 18848
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Figure 5. (a) X-ray and (b) neutron structure factors S(Q) and (c) neutron Bragg reflection of deuterated BaZr0.8Y0.1Zn0.1O3. The red plus marks and the blue solid line represent the experimental data and the DFT-RMC model, respectively.
where Isample and Ireference mean the raw intensities of the sample and the reference, respectively. Figure 6 shows the spectra
Figure 4. Diffusion path of (a) a free proton and (b, c) magnified images in the protonated BaZr0.8Y0.1Zn0.1O3. (d) Proton behavior of a trapped proton is also presented. Dark green, light green, orange, purple, and red spheres represent Ba, Zr, Y, Zn, and O, respectively. Blue objects stand for the proton location at different times.
Figure 6. Infrared diffusive reflectance spectra in the OH-vibration region for protonated BaZr0.8Y0.1Zn0.1O3. Blue and red solid lines represent reflectance at room temperature and at 400 °C, respectively. The dips denoted by the asterisk are caused by CO2, and the sharp feature is due to an instrumental noise.
initial structure. The fittings could be carried out successfully by this strategy, and further DFT calculations confirmed that the energy difference between the fitted configuration and the DFT-MD configuration (base structure) was below 0.14 eV·atom−1, which is very small. We conclude that the atomic configuration determined by the DFT-based MD is in good agreement with the experimentally observed spectra. For the purpose of a more detailed investigation on proton dynamics, we also measured infrared absorption spectra of the protonated BaZr0.8Y0.1Zn0.1O3 as a function of temperature by a diffuse reflection mode. According to previous works,32,33 we normalized the diffuse reflectance spectra, Rd, by using pure BaZrO3 without protons as a reference in the following way:
R d = Isample/Ireference
recorded at room temperature and at 400 °C. At room temperature, we observe a strong reflectance at 3300 cm−1 and broad peaks around 2850 and 2350 cm−1 in the protonated BaZr0.8Y0.1Zn0.1O3. The strong peak at 3300 cm−1 becomes weaker and broader with increasing temperature whereas the others are almost unchanged. To attribute these absorption peaks to vibration modes, we calculated the infrared absorption spectrum of the material on the basis of harmonic oscillations of atoms in the DFToptimized cell. The spectrum and the typical vibration modes are presented in Figure 7a−c. This figure demonstrates that the OH vibration around Zn should be observed at a wide range of
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Figure 8. Electronic densities of states projected onto elements (PDOS) via atomic orbitals for protonated BaZr0.8Y0.1Zn0.1O3: (a) all atoms and (b) Y, Zn, and H. The P-DOS distributions are plotted with a Gaussian broadening of σ = 0.1 eV for each state. The color code is as in Figure 1.
the electronic density of states, DOS, of the DFT-optimized BaZr0.8Y0.1Zn0.1O3 with projections onto different elements (PDOS). There is a large band gap of over 3 eV between the valence and the conductance bands, indicating that electronic conduction is negligible in this material. As we focus on Y, Zn, and H (Figure 8b), we can see that the P-DOS of H has a significant overlap with that of Zn in comparison to Y. This is coupled to the fact that protons in BaZr0.8Y0.1Zn0.1O3 prefer to be associated with Zn. We have also computed the maximally localized Wannier f u n c t i o n s ( W F , lo c a l i z e d c h e m i c a l o r b i t a l s ) in BaZr0.8Y0.1Zn0.1O3. The WFs have been produced from the occupied Kohn−Sham (KS) orbitals by a unitary transformation where the spatial extension (spread) of the WF orbitals has been minimized. Each WF function is characterized by the WF center (location, bond) and spread (extent), and the results for WF centers are visualized in Figure 9a. Most WF centers are located around non-hydrogen atoms except for OH bonds where the centers are along the bonds highlighting the covalent character of chemical binding. On the other hand, the chemical bonding between metals and oxygen (M−O bonds) is of ionic character in doped barium zirconates, and the corresponding WF centers have been shifted to oxygen (charge transfer). In Figure 9b, the WF centers with larger spreads are denoted with a different color from the other WF centers. The WFs around oxygens which are coordinated with Zr or Y tend to have larger spreads. Because the proton hopping presented in Figure 4a can be regarded as a bond-reforming process, such a flexible electronic structure around Zr or Y is preferable for protonic conduction, in comparison to Zn−O surroundings. We have estimated the effective charges of the host cations and oxygens with and without proton in the barium zirconatebased material from electron density by means of the Bader method.26,27 Table 1 lists the effective charges, and it also presents the Voronoi charges (from electron density) and nominal charges as references. Although Zr, Y, and Zn occupy the same crystallographic site in the perovskite structure, Zn has a much smaller positive charge than the others, whereas the difference between Y and Zr is rather small. Because proton has a positive charge, a lower positive charge can be regarded preferable for proton localization from the viewpoint of
Figure 7. Calculated infrared absorption spectrum (a) of protonated BaZr0.8Y0.1Zn0.1O3. Typical vibration modes in region 1 and region 2 are also presented: (b) region 1 and (c) region 2. In the figure, dark green, light green, orange, purple, red, and blue spheres represent Ba, Zr, Y, Zn, O, and H, respectively.
the wavenumbers from 2000 to 3200 cm−1 (region 2) and that around Zr or Y should be detected at 3000−3800 cm−1 (region 1) in the case of the protonated BaZr0.8Y0.1Zn0.1O3. Taking this calculated result into account, the experimentally observed intense absorption around 3300 cm−1 is supposed to be attributable to OH groups coordinating with Zr or Y, and the absorption becomes broader at higher temperature as protons are able to escape these atoms more readily than Zn. This result provides further support that the conductive protons in the crystal are ascribed to Zr or Y. On the other hand, the peaks at the lower wavenumbers have a significant contribution from the vibrational modes of OH groups around Zn, and these groups are stable even at the high temperature. This provides evidence that a proton around Zn is strongly trapped, and such a tendency has a good agreement with the proton dynamics in the DFT-MD simulations. 3.4. Electronic Structure. As discussed above, the DFToptimized atomic configuration of the protonated BaZr0.8Y0.1Zn0.1O3 is in good agreement with the experimental infrared absorption spectra and with the neutron and synchrotron X-ray total scattering measurements. These results indicate that there is a significant proton trapping around the Zn dopant, and we have performed electronic structure analysis in order to investigate the underlying reasons. Figure 8a shows 18850
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4. CONCLUSIONS The protonated form of crystalline BaZr0.8Y0.1Zn0.1O3 was studied by means of the density functional theory (DFT) and molecular dynamics (MD) simulations, and then proton dynamics was discussed on the basis of optimized proton sites and the diffusion coefficient. These results indicate that the apparent diffusion coefficients of proton are 1.3 × 10−5 cm2·sec−1 at 800 °C, and some protons tend to get trapped by Zn dopants considerably. From the reverse Monte Carlo modeling using the neutron and synchrotron X-ray total scattering data, it is found that the atomic configuration with the protons trapped by Zn can explain well the experimentally obtained structure factors, S(Q), as well as Bragg reflection. Such a trapping is also suggested by interpreting the experimentally collected diffuse reflectance infrared spectra on the basis of the computed harmonic oscillations. The charge analysis of this configuration based on the Bader method demonstrates that a charge difference among Zr, Y, and Zn plays an important role in the proton-trapping mechanism, and the Bader charges (effective charges) can be regarded as a better index for the trapping capacity compared with the nominal charge values.
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AUTHOR INFORMATION
Corresponding Author
*Tel: +81-4-7124-1501. Fax: +81-4-7123-9890. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
Figure 9. Atomic configuration of protonated BaZr0.8Y0.1Zn0.1O3 with centers of the maximally localized Wannier functions: (a) all WF centers are denoted as gray spheres and (b) WF centers with larger spreads are denoted with pink. Otherwise, the color code is as in Figure 1.
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ACKNOWLEDGMENTS The DFT-MD simulations were performed with the Cray XT4/ XT5 supercomputers at CSC - IT Center for Science Ltd., Espoo, Finland, and Cray XC30 in Japan Advanced Institute of Science and Technology, Japan. The authors acknowledge Dr. Sven C. Vogel at Los Alamos National Laboratory, U.S.A., for his help on the neutron total scattering measurement. The authors also appreciate Prof. David A. Keen and Matthew G. Tucker at ISIS Facility, Rutherford Appleton Laboratory, U.K., for their support on the structure analysis. J.A. acknowledges financial support from the Academy of Finland through its Centres of Excellence Program (Project 251748).
Table 1. Electronic Charges of the Host Cations and Oxygens with and without Proton Estimated by the Bader Method of Electron Densitya ion
nominal
Bader
Voronoi
Ba Zr Y Zn O OH group
+2 +4 +3 +2 −2 −1
+1.57 +2.39 +2.03 +1.17 −1.32 −0.76
+1.90 +2.63 +2.31 +1.17 −1.56 −1.16
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a
Those by the Voronoi charge analysis and nominal values are also given as references.
REFERENCES
(1) Malavasi, L.; Fisher, C. A. J.; Islam, M. S. Oxide-Ion and Proton Conducting Electrolyte Materials for Clean Energy Applications: Structural and Mechanistic Features. Chem. Soc. Rev. 2010, 39, 4370− 4387. (2) Jacobson, A. J. Materials for Solid Oxide Fuel Cells. Chem. Mater. 2010, 22, 660−674. (3) Bohn, H. G.; Schober, T. Electrical Conductivity of the HighTemperature Proton Conductor BaZr0.9Y0.1O2.95. J. Am. Ceram. Soc. 2000, 83, 768−772. (4) Schober, T.; Bohn, H. G. Water Vapor Solubility and Electrochemical Characterization of the High Temperature Proton Conductor BaZr0.9Y0.1O2.95. Solid State Ionics 2000, 127, 351−360. (5) Kreuer, K. D.; Adams, St.; Münch, W.; Fuchs, A.; Klock, U.; Maier, J. Proton Conducting Alkaline Earth Zirconates and Titanates for High Drain Electrochemical Applications. Solid State Ionics 2001, 145, 295−306. (6) Gorelov, V. P.; Balakireva, V. B.; Kleshchev, Y. N.; Brusentsov, V. P. Preparation and Electrical Conductivity of BaZr1−xRxO3−α (R = Sc, Y, Ho, Dy, Gd, In). Inorg. Mater. 2001, 37, 535−538.
electrostatic repulsion. This kind of electrostatic effect has been discussed in the literature on the basis of the difference in nominal charges of cations,12 but the effect should be considered in practice by using the Bader charges (or equivalent, e.g., Voronoi) because this method takes the electron density distribution around all atoms into account. In fact, the difference in the Zn and Zr charges is more than twice larger than that of Y and Zr. A simple comparison of nominal charges underestimates the effect of Zn doping in the protonated BaZr0.8Y0.1Zn0.1O3, and we consider the Bader charge analysis as a better method to gain insight of the protontrapping mechanism. 18851
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Article
Maximally Localized Wannier Functions. Phys. Rev. B 2000, 61, 10040−10048. (29) Toby, B. H. EXPGUI, a Graphical User Interface for GSAS. J. Appl. Crystallogr. 2001, 34, 210−213. (30) Kohara, S.; Itou, M.; Suzuya, K.; Inamura, Y.; Sakurai, Y.; Ohishi, Y.; Takata, M. Structure Studies of Disordered Materials Using High-Energy X-Ray Diffraction from Ambient to Extreme Conditions. J. Phys.: Condens. Matter 2007, 19, 506101. (31) Tucker, M. G.; Keen, D. A.; Dove, M. T.; Goodwin, A. L.; Hui, Q. RMCProfile: Reverse Monte Carlo for Polycrystalline Materials. J. Phys.: Condens. Matter 2007, 19, 335218. (32) Omata, T.; Noguchi, Y.; Otsuka-Yao-Matsuo, S. Infrared Study of High-Temperature Proton-Conducting Aliovalently Doped SrZrO3 and BaZrO3. J. Electrochem. Soc. 2005, 152, E200−E205. (33) Omata, T.; Noguchi, Y.; Otsuka-Yao-Matsuo, S. Infrared Study of High Temperature Proton Conducting Sr(Zr0.95MIII0.05)O3−δ; Formation of MIIIO6-Cluster Depends on Dopant Species. Solid State Ionics 2005, 176, 2941−2944.
(7) Ahmed, I.; Eriksson, S.-G.; Ahlberg, E.; Knee, C. S.; Berastegui, P.; Johansson, L.-G.; Rundlöf, H.; Karlsson, M.; Matic, A.; Börjesson, L.; et al. Synthesis and Structural Characterization of Perovskite Type Proton Conducting BaZr1−xInxO3−δ (0.0 ≤ x ≤ 0.75). Solid State Ionics 2006, 177, 1395−1403. (8) Ahmed, I.; Eriksson, S.-G.; Ahlberg, E.; Knee, C. S.; Götlind, H.; Johansson, L.-G.; Karlsson, M.; Matic, A.; Börjesson, L. Structural Study and Proton Conductivity in Yb-Doped BaZrO3. Solid State Ionics 2007, 178, 515−520. (9) Nomura, K.; Kageyama, H. Transport Properties of Ba(Zr0.8Y0.2)O3−δ Perovskite. Solid State Ionics 2007, 178, 661−665. (10) Babilo, P.; Uda, T.; Haile, S. M. Processing of Yttrium-Doped Barium Zirconate for High Proton Conductivity. J. Mater. Res. 2007, 22, 1322−1330. (11) Imashuku, S.; Uda, T.; Nose, Y.; Taniguchi, G.; Ito, Y.; Awakura, Y. Dependence of Dopant Cations on Microstructure and Proton Conductivity of Barium Zirconate. J. Electrochem. Soc. 2009, 156, B1− B8. (12) Babilo, P.; Haile, S. M. Enhanced Sintering of Yttrium-Doped Barium Zirconate by Addition of ZnO. J. Am. Ceram. Soc. 2005, 88, 2362−2368. (13) Tao, S.; Irvine, J. T. S. Conductivity Studies of Dense YttriumDoped BaZrO3 Sintered at 1325 °C. J. Solid State Chem. 2007, 180, 3493−3503. (14) Münch, W.; Seifert, G.; Kreuer, K. D.; Maier, J. A Quantum Molecular Dynamics Study of the Cubic Phase of BaTiO3 and BaZrO3. Solid State Ionics 1997, 97, 39−44. (15) Kreuer, K. D. Aspects of the Formation and Mobility of Protonic Charge Carriers and the Stability of Perovskite-Type Oxides. Solid State Ionics 1999, 125, 285−302. (16) Münch, W.; Kreuer, K.-D.; Seifert, G.; Maier, J. Proton Diffusion in Perovskites: Comparison between BaCeO3, BaZrO3, SrTiO3, and CaTiO3 Using Quantum Molecular Dynamics. Solid State Ionics 2000, 136−137, 183−189. (17) van Duin, A. C. T.; Merinov, B. V.; Han, S. S.; Dorso, C. O.; Goddard, W. A., III. ReaxFF Reactive Force Field for the Y-Doped BaZrO3 Proton Conductor with Applications to Diffusion Rates for Multigranular Systems. J. Phys. Chem. A 2008, 112, 11414−11422. (18) Raiteri, P.; Gale, J. D.; Bussi, G. Reactive Force Field Simulation of Proton Diffusion in BaZrO3 Using an Empirical Valence Bond Approach. J. Phys.: Condens. Matter 2011, 23, 334213/1−334213/13. (19) Merinov, B.; Goddard, W., III. Proton Diffusion Pathways and Rates in Y-Doped BaZrO3 Solid Oxide Electrolyte from Quantum Mechanics. J. Chem. Phys. 2009, 130, 194707−1−6. (20) Hutter, J.; Iannuzzi, M.; Schiffman, F.; VandeVondele, J. CP2K: atomistic simulations of condensed matter systems. WIREs Comput. Mol. Sci. 2014, 4, 15−25. (21) VandeVondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. QUICKSTEP: Fast and Accurate Density Functional Calculations Using a Mixed Gaussian and Plane Waves Approach. Comput. Phys. Commun. 2005, 167, 103−128. (22) VandeVondele, J.; Hutter, J. Gaussian Basis Sets for Accurate Calculations on Molecular Systems in Gas and Condensed Phases. J. Chem. Phys. 2007, 127, 114105/1−114105/9. (23) Goedecker, S.; Teter, M.; Hutter, J. Separable Dual-Space Gaussian Pseudopotentials. Phys. Rev. B 1996, 54, 1703−1710. (24) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (25) Bussi, G.; Donadio, D.; Parrinello, M. Canonical Sampling through Velocity Rescaling. J. Chem. Phys. 2007, 126, 014101/1− 014101/7. (26) Henkelman, G.; Arnaldsson, A.; Jónsson, H. A Fast and Robust Algorithm for Bader Decomposition of Charge Density. Comput. Mater. Sci. 2006, 36, 254−360. (27) Tang, W.; Sanville, E.; Henkelman, G. A Grid-Based Bader Analysis Algorithm without Lattice Bias. J. Phys.: Condens. Matter 2009, 21, 084204. (28) Berghold, G.; Mundy, C. J.; Romero, A. H.; Hutter, J.; Parrinello, M. General and Efficient Algorithms for Obtaining 18852
dx.doi.org/10.1021/jp502455v | J. Phys. Chem. C 2014, 118, 18846−18852
