Crystal Structures of the Tetragonal Ceria−Zirconia Solid Solutions

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J. Phys. Chem. C 2009, 113, 12658–12662

Crystal Structures of the Tetragonal Ceria-Zirconia Solid Solutions CexZr1-xO2 through First Principles Calculations (0 e x e 1) Masatomo Yashima* Department of Materials Science and Engineering, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Nagatsuta-cho 4259, Midori-ku, Yokohama-shi, Kanagawa 226-8502, Japan ReceiVed: March 18, 2009; ReVised Manuscript ReceiVed: May 23, 2009

Crystal structures of metastable tetragonal CexZr1-xO2 have been studied through first principles calculations (0 e x e 1). Unit-cell parameters a, c, and atomic coordinates of 24 atoms were optimized for all the occupational configurations of Ce and Zr atoms by using the constraints for cell parameters: a ) b and R ) β ) γ ) 90°. Axial ratio and oxygen displacement from the regular position of the optimized structures of ground states decrease with increasing CeO2 content, which is consistent with diffraction experiments in the literature. The tetragonal (t”) form with axial ratio of unity is strongly suggested to be stable in Ce0.875Zr0.125O2, compared with the tetragonal (t’) form with axial ratio larger than unity and the cubic phase. This work also demonstrates that the ground state of CexZr1-xO2 (x e 0.75) is the t’ form. The phase stability of the t’ and t” forms are discussed by comparing the ground states with experimental data in the literature. Introduction Fluorite-related solid solutions as CexZr1-xO2 and Zr1-xYxO2-x/2 have extensively been studied, since they are useful materials in current technologies with many applications, as in solid electrolytes for fuel cells, oxygen gas sensors, and automobile exhaust catalysts.1-6 The zirconia-based materials exhibit a cubic-tetragonal structural phase transition.7-19 The ideal fluorite-type structure has the space group Fm3jm, while the tetragonal phase belongs to P42/nmc and has the oxygen displacement d(O) from an ideal Fm3jm fluorite 8c position (arrows in Figure 1). One of the most important keys to make clear the formation mechanism of the tetragonal (t’) phase is the study on the diffusionless cubic-tetragonal (c-t’) phase transition where t’ emphasizes a metastable tetragonal phase. Thus, the t’ form can be distinguished from the stable t that forms diffusionally. This transition has extensively been studied by diffraction experiments;9-19 however, its mechanism is not understood satisfactorily. An internal distortion feature has been suggested where the lattice distortion does not induce the cubictetragonal phase transition, but the oxygen displacements along the c axis from the ideal fluorite positions do.7,9,15,17-19 A notable feature is the existence of a tetragonal CexZr1-xO2 phase having an axial ratio c/aF of unity and oxygen displacements. Here, the aF denotes the unit-cell a parameter in the pseudo-fluorite cell. However, it is unknown whether the t” form is thermodynamically stable or not in the compositionally homogeneous CexZr1-xO2. Density functional theory (DFT)-based calculations are useful to examine the ground state. Although a number of researchers have applied the DFT technique to the CeO2, CexZr1-xO2 solid solutions, and ZrO2,20-30 the formation of the t” form has not been confirmed yet by this method. In the cubic CexZr1-xO2 phase, Rodriguez et al.20 studied the compositional dependence of crystal structure by the DFT method. The tetragonal CexZr1-xO2 phase is much more important for automobile * To whom correspondence should be addressed. E-mail: yashima@ materia.titech.ac.jp.

Figure 1. (a) Optimized structure and (b) yellow isosurface of valence electron density at 0.0133 Å-3 with valence electron density distributions on the (100), (010), and (001) planes of the supercell (2 × 2 × 1) of tetragonal zirconia ZrO2. (c) Optimized structure and (d) yellow isosurface of valence electron density at 0.0133 Å-3 with valence electron density distributions on the (100), (010), and (001) planes of the supercell (2 × 2 × 1) of tetragonal ceria CeO2. The optimized structure of CeO2 was cubic. Yellow and green spheres are Ce and Zr atoms, respectively. The pink sphere is an oxygen atom. The arrow along the c axis in both (a) and (b) indicates the direction of the oxygen displacement from the ideal fluorite 8c position. 0 and 100% of the color scale for the valence electron density correspond to 0.0133 and 0.148 Å-3, respectively.

exhaust catalysts. However, in the tetragonal CexZr1-xO2 solid solutions, the compositional dependence of the unit-cell parameters and oxygen displacement d(O) has not been investigated yet by the DFT calculations. The purpose of the present study is to investigate the unitcell parameters and oxygen displacement of tetragonal ceriazirconia solid solutions CexZr1-xO2 (x ) 0, 1/8, 1/4, 3/8, 1/2, 5/8, 3 /4, 7/8, and 1) through the DFT technique. The phase stability

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Crystal Structures of CexZr1-xO2 and ground state were studied in the tetragonal and cubic phases to examine the compositionally (x) induced tetragonal-cubic phase change of CexZr1-xO2. Here, the ZrO2-CeO2 system was chosen to investigate the composition-induced t’-c phase change by the DFT calculations, because in this system, the t” form appears in a wide compositional region as shown by the diffraction experiments.10-19 The present study of CexZr1-xO2 indicates that the axial ratio c/aF and the oxygen displacement from the fluorite position decrease with an increase in CeO2 content. Furthermore, this work demonstrates that the t” form is not stable in the compositions x of x e 0.75 but stable at x ) 0.875, in comparison with the t’ form. Calculations and Data Processing. The generalized gradient approximation (GGA) electronic calculations were performed with the Vienna ab initio simulation package (VASP)31 to examine the ground state and optimized crystal structure of tetragonal CexZr1-xO2 (x ) 0, 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8, and 1). Calculations were performed for all the occupational configurations of Zr and Ce atoms in the 2 × 2 × 1 tetragonal supercell using projector augmented-wave (PAW) potentials32 for Ce, Zr, and O atoms. One configuration for Ce0.5Zr0.5O2 is shown in Figure 2. There exist one, one, three, three, nine, three, three, one, and one independent occupational configurations of Ce and Zr atoms for compositions of x ) 0, 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8, and 1, respectively. The 2 × 2 × 1 supercells contain eight CexZr1-xO2 formula units. The reference configurations for valence electrons were 4f1, 5d1, and 6s2 for Ce, 4s2, 4p6, 4d2, and 5s2 for Zr, and 2s2 and 2p4 for O. A plane-wave basis set with a cutoff of 500 eV was used. The Perdew-Burke-Ernzerhof (PBE) GGA was employed for the exchange and correlation functionals. We have not used the DFT+U scheme that has been applied to the oxygen deficient CexZr1-xO2-δ in the literature23-26,28 because this work focuses on non-deficient CexZr1-xO2 materials (δ ) 0 in CexZr1-xO2-δ). Sums over occupied electronic states were performed using the MonkhorstPack scheme33 on a 3 × 3 × 3, 4 × 4 × 4, 5 × 5 × 5, and 6 × 6 × 6 sets of a k-point mesh. Unit-cell parameters and atomic coordinates were optimized with the convergence condition of 0.02 eV/Å for all the occupational configurations of Ce and Zr atoms. The positions of all atoms were relaxed in the space group P1. Cell parameters a and c were optimized with the constraints of a ) b = 2(2)1/2 aF and R ) β ) γ ) 90°. Initial unit-cell and positional parameters used in the optimization were referred from the literature.10,11,18,19 It was confirmed that the optimized unit-cell parameters of CexZr1-xO2 for the 5 × 5 × 5 sets of a k-point mesh are equaled to those for the 6 × 6 × 6 sets. Thus, the final calculations to draw the figures and table were performed based on the 5 × 5 × 5 sets using the most stable occupational configuration for each composition. Crystal structures and valence electron density distributions were drawn with a computer program VESTA.34 Results and Discussion Optimized Structure and Valence Electron Density of ZrO2. Figures 1(a) and 1(b) show the optimized crystal structure and isosurface of the corresponding valence electron density distribution of tetragonal zirconia (Zr8O16), respectively. The optimized unit-cell parameters (a ) 3.64 Å; c ) 5.30 Å) agree with the experimental values (a ) 3.591 Å; c ) 5.167 Å).35 The average value of the calculated z coordinate of the oxygen atom (0.195) also agrees with the experimental z value (0.204).35 The oxygen atoms are displaced from the regular position (z ) 1 /4) (Figure 1). The oxygen displacement yields longer and shorter cation-oxygen interatomic distances. Covalent bonds

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Figure 2. (a) Optimized structure and (b) yellow isosurface of valence electron density at 0.0133 Å-3 with valence electron density distributions on the (100), (010), and (001) planes of the supercell (2 × 2 × 1) of the tetragonal (t’) ceria-zirconia solid solution Ce0.5Zr0.5O2. In (a), yellow and green spheres are Ce and Zr atoms, respectively. The pink sphere with an arrow is an oxygen atom in (a). The arrow along the c axis in both (a) and (b) indicates the direction of the oxygen displacement from the ideal fluorite 8c position. The Ce atom is more ionic while the Zr atom is more covalent. 0 and 100% of the color scale for the valence electron density correspond to 0.0133 and 0.148 Å-3, respectively. See the Supporting Information for other compositions CexZr1-xO2.

between Zr and O atoms are observed for the shorter Zr-O bond in the calculated valence electron density map (Figure 1(b)). These features from the DFT calculations are consistent with the crystal structure and electron density of zirconium oxides obtained through diffraction experiments.36 Optimized Structure and Valence Electron Density of CeO2. Figures 1(c) and 1(d) show the optimized crystal structure and isosurface of the corresponding valence electron density distribution of ceria (Ce8O16), respectively. The optimized unitcell parameters were a ) 3.862 Å and c ) 5.4623 Å ) (2)1/2 a, which agree with the experimental value (c ) (2)1/2 a ) 5.41129 Å: NIST reference material ceria). The relation c ) (2)1/2 a and optimized atomic coordinates (see the Supporting Information) indicate that the ceria has the cubic fluorite-type structure. Compared with the Zr-O bonds in zirconia (Figure 1(b)), the Ce-O bond is more ionic (Figure 1(d)). Optimized Structure and Valence Electron Density of Ce0.5Zr0.5O2 and CexZr1-xO2. Figure 2 shows the optimized crystal structure with the second most stable occupational configuration of Ce and Zr atoms and isosurface of corresponding valence electron density distribution of tetragonal (t’) ceria-zirconia solid solution Ce0.5Zr0.5O2. The most stable configuration was excluded because its weight was low. Calculated tetragonal unit-cell parameters (a ) 3.78 Å; c ) 5.39 Å) agree with experimental values (a ) 3.7191 Å; c ) 5.3057 Å).14 Table 1 shows the optimized atomic coordinates of the ground state of Ce0.5Zr0.5O2. The average value of the calculated z coordinate of the oxygen atom (0.214) also agrees with the experimental z value (0.2190).14 The oxygen atoms are displaced from the regular position (z ) 1/4) (Figure 2). The oxygen displacement yields longer and shorter cation-oxygen atomic distances. Covalent bonds between Zr and O atoms in Ce0.5Zr0.5O2 are observed for the shorter Zr-O bond in the

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Yashima

TABLE 1: Atomic Coordinates of the Optimized Structure of (CeZrO4)4 with the Second Most Stable Occupational Configuration in the Supercell (2 × 2 × 1) of the Crystallographic Tetragonal Unit Cella fractional coordinate atom

x

y

z

Ce Ce Ce Ce Zr Zr Zr Zr O O O O O O O O O O O O O O O O Ce Ce

0.0000 0.25000 0.75000 0.50000 0.25000 0.0000 0.50000 0.75000 0.23532 0.98539 0.020347 0.27039 0.26468 0.014610 0.97965 0.22961 0.76468 0.51461 0.47965 0.72961 0.73532 0.48539 0.52035 0.77039 0.0000 0.25000

0.0000 0.75000 0.25000 0.50000 0.25000 0.50000 0.0000 0.75000 0.020347 0.27039 0.23532 0.98539 0.47965 0.72961 0.76468 0.51461 0.97965 0.22961 0.26468 0.014610 0.52035 0.77039 0.73532 0.48539 0.0000 0.75000

0.0000 0.50000 0.50000 0.0000 0.50000 0.0000 0.0000 0.50000 0.28596 0.21407 0.71404 0.78593 0.28596 0.21407 0.71404 0.78593 0.28596 0.21407 0.71404 0.78593 0.28596 0.21407 0.71404 0.78593 0.0000 0.50000

a

All the fractional coordinates were varied in the structural optimization. Atomic coordinates of the optimized structure for other compositions are described in the Supporting Information.

Figure 4. Reduced unit-cell parameters (a) and unit-cell volume (b) of ceria-zirconia solid solutions CexZr1-xO2 as a function of CeO2 content x, which were obtained by the present DFT calculations. In (a), the red inverted triangle and blue triangle denote the aF- and c-lengths, respectively.

Figure 3. Partial density of states (PDOS) of Zr3 and O12 atoms in (CeZrO4)4, which indicates the overlap of the Zr 3d and the O 2p orbitals. The positions of Zr3 and O12 atoms are shown in Figure 2.

calculated valence electron density map (Figure 2(b)) as well as in ZrO2 (Figure 1(b)). The covalent bond is formed by the overlap of the Zr 3d and the O 2p orbitals as shown in the partial density of states (Figure 3). These features are also obtained for other compositions CexZr1-xO2 (x ) 1/8, 1/4, 3/8, 5/8, and 3/4; see the details in the Supporting Information). Unit-Cell Parameters of CexZr1-xO2. Figure 4 shows the compositional dependence of unit-cell parameters of aF and c and unit-cell volume in the ground states of CexZr1-xO2, which were obtained by structural optimization in the DFT calculations. The aF and c parameters increase with an increase in CeO2 composition x. The unit-cell volume also increases with x, which is attributable to the larger size of the Ce4+ cation compared to that of the Zr4+ ion. These theoretical results are consistent with experimental ones reported in the literature.10,13,17-19 Axial Ratio and Oxygen Displacements of CexZr1-xO2. Figure 5(a) and (b) shows the compositional dependences of axial ratio c/aF - 1 and oxygen displacement d(O) from the ideal fluorite 8c position, respectively, in the ground states of

Figure 5. Axial ratio c/aF - 1 (a) and the average value of oxygen displacement from the ideal fluorite 8c position (b) of ceria-zirconia solid solutions CexZr1-xO2 as a function of CeO2 content x.

CexZr1-xO2. The d(O) was estimated from the equation d(O) ) c(1/4 - 〈z〉) where the c and 〈z〉 are unit-cell parameter c and average atomic coordinate z of the pseudo-tetragonal cell,

Crystal Structures of CexZr1-xO2

J. Phys. Chem. C, Vol. 113, No. 29, 2009 12661 phases from the present first principles study are consistent with those from the diffraction experiments for the ceria-zirconia samples through the high-temperature processing.18 Conclusions

Figure 6. Relationship between the energy from the ground state and axial ratio c/aF for Ce0.75Zr0.25O2. Blue open and red filled circles were results with 3 × 3 × 3 and 5 × 5 × 5 sets of a k-point mesh, respectively.

respectively.14,18 In the compositional range from x ) 0 to x ) 0. 75, both c/aF - 1 and d(O) are larger than 0, which indicate that the ground states are identified to be the tetragonal t or t’ form. The axial ratio c/aF - 1 and displacement d(O) decrease with x, which is consistent with the experimental data in the literature.18 Theoretical Evidence of the t” Form in Ce0.875Zr0.125O2. At the composition x ) 0.875, the oxygen displacements of 0.021 Å from an ideal fluorite position are observed, although the c/aF value is 1.000, identifying the optimized structure to be the t” form. This result is the theoretical evidence for the existence of the t” form in Ce0.875Zr0.125O2. In the diffraction and Raman experiments,17,18 Ce0.875Zr0.125O2 was also identified to be the t” form at room temperature; however, researchers were not sure whether the t” form (c/aF ) 1) is more stable than the t’ form (c/aF > 1) or not. The present DFT calculations have strongly suggested that the t” form is more stable than t’ in Ce0.875Zr0.125O2 for the first time. Phase Stability of t” and t’ Forms in CexZr1-xO2. In the compositions of x ) 0.625 and x ) 0.75, the present DFT calculations indicate the t’ form, while the experiments showed the t” form.17,18 One reason for the difference could be the energy barrier between the t’ and t” forms due to the strain energy caused by the lattice mismatch between the tetragonal domains when the c axis length increases and the aF axis length decreases in the t” matrix. In the chemical energy obtained by the DFT calculations, no energy barrier was observed between t’ and t” forms (Figure 6). The other reason could be the extremely small energy difference between the t’ and t” forms (e.g., less than 0.05 meV/atom for Ce0.75Zr0.25O2), which indicates much less driving force for the t”-to-t’ transformation. As shown in Figure 6, the energy of Ce0.75Zr0.25O2 was almost unchanged with an axial ratio c/aF in the range from 1.000 to 1.006, showing the flat minimum. The metastable t’ and t” ceria-zirconia solid solutions can be prepared by either the low-temperature process or the hightemperature process. The diffraction profile from the ceria-zirconia samples prepared by the low-temperature process exhibits broad peaks due to the small crystallite sizes; thus, it is difficult to determine the phase boundaries among the t’, t”, and cubic phases.37,38 On the contrary, the diffraction peaks of samples through the high-temperature processing have narrow peak widths; therefore, they enable exact determination of the phase boundaries.18 The phase boundaries among the t’, t”, and cubic

Crystal structures of metastable tetragonal CexZr1-xO2 have been studied through first principles calculations (0 e x e 1). Unit-cell parameters a, c, and atomic coordinates of 24 atoms were optimized for all the occupational configurations of Ce and Zr atoms by using the constraints for cell parameters: a ) b and R ) β ) γ ) 90°. The present theoretical results have demonstrated that the axial ratio and oxygen displacement from the regular position of the optimized structures of ground states decrease with increasing CeO2 content, which is consistent with diffraction experiments from the ceria-zirconia solid solutions prepared by the high-temperature process in the literature. The tetragonal t” form with axial ratio of unity is strongly suggested to be stable in Ce0.875Zr0.125O2, compared with the tetragonal t’ form with axial ratio larger than unity and the cubic phase. This work has also demonstrated that the ground state of CexZr1-xO2 (x e 0.75) is the t’ form. The phase stability of the t’ and t” forms are discussed by comparing the ground states with experimental data in the literature. The difference in the t”-t’ phase boundary between the present theoretical calculations and experiments in the literature is attributable to the strain energy caused by the lattice mismatch between the tetragonal domains when the c axis length increases and aF axis length decreases in the t” matrix. The other reason for the difference could be the extremely small energy difference between the t’ and t” forms (e.g., less than 0.05 meV/atom for Ce0.75Zr0.25O2), which indicates much less driving force for the t”-to-t’ transformation. Supporting Information Available: Optimized structures and valence electron density for all the compositions. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Subbarao, E. C. Science and Technology of Zirconia. In AdVances in Ceramics; Heuer, A. H., Hobbs, L. W., Eds.; American Ceramic Society: Westerville, OH, 1981; Vol 3, pp 1-24. (2) Ozawa, M.; Kimura, M.; Isogai, A. J. Alloys Compd. 1993, 193, 73. (3) Yashima, M.; Kakihana, M.; Yoshimura, M. Solid State Ionics 1996, 86-88, 1131. (4) Balducci, G.; Kassˇpar, J.; Fornasiero, P.; Graziani, M.; Islam, M. S.; Gale, J. D. J. Phys. Chem. B 1997, 101, 1750. (5) Kasˇpar, J.; Fornasiero, P.; Graziani, M. Catal. Today 1999, 50, 285. (6) Trovarelli, A. Catalysis by Ceria and Related Materials; Imperial College Press: London, 2002; p 257. (7) Faber, J., Jr.; Mueller, M. H.; Cooper, B. R. Phys. ReV. B 1978, 17, 4884. (8) Teufer, G. Acta Crystallogr. 1962, 15, 1187. (9) Yashima, M.; Sasaki, S.; Kakihana, M.; Yamaguchi, Y.; Arashi, H.; Yoshimura, M. Acta Crystallogr. B 1994, 50, 663. (10) Yashima, M.; Morimoto, K.; Ishizawa, N.; Yoshimura, M. J. Am. Ceram. Soc. 1993, 76, 1745. (11) Yashima, M.; Morimoto, K.; Ishizawa, N.; Yoshimura, M. J. Am. Ceram. Soc. 1993, 76, 2865. (12) Yashima, M.; Takashina, H.; Kakihana, M.; Yoshimura, M. J. Am. Ceram. Soc. 1994, 77, 1869. (13) Torng, S.; Miyazaki, K.; Sakuma, T. Ceram. Int. 1996, 22, 309. (14) Wakita, T.; Yashima, M. Acta Crystallogr. B 2007, 63, 384. (15) Acuna, L. M.; Fuentes, R. O.; Lamas, D. G.; Fabregas, I. O.; Walsoe de Reca, N. E.; Craoevocj, A. F. Powder Diff. 2008, 23, S70. (16) Wakita, T.; Yashima, M. Appl. Phys. Lett. 2008, 92, 101921. (17) Yashima, M.; Arashi, H.; Kakihana, M.; Yoshimura, M. J. Am. Ceram. Soc. 1994, 77, 1067.

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(18) (a) Yashima, M.; Sasaki, S.; Yamaguchi, Y.; Kakihana, K.; Yoshimura, M.; Mori, T. Appl. Phys. Lett. 1998, 72, 182. (b) Yashima, M.; Wakita, T. Appl. Phys. Lett. 2009, 94, 171902. (19) Lamas, D. G.; Fuentes, R. O.; Fabregas, I. O.; Fernandez de Rapp, M. E.; Lascalea, G. E.; Casanova, J. R.; Walsoe de Reca, N. E.; Craievich, A. F. J. Appl. Crystallogr. 2005, 38, 867. (20) Rodriguez, J. A.; Hanson, J. C.; Kim, J.-Y.; Liu, G.; Iglesias-Juez, A.; Fernandez-Garcia, M. J. Phys. Chem. B 2003, 107, 353. (21) Conesa, J. J. Phys. Chem. B 2003, 107, 8840. (22) Tibiletti, D.; Amieiro-Fonseca, A.; Burch, R.; Chen, Y.; Fisher, J. M.; Goguet, A.; Hardacre, C.; Hu, P.; Thompsett, D. J. Phys. Chem. B 2005, 109, 22553. (23) Yang, Z.; Fu, Z.; Wei, Y.; Lu, Z. J. Phys. Chem. C 2008, 112, 15341. (24) Yang, Z.; Fu, Z.; Wei, Y.; Hermansson, K. Chem. Phys. Lett. 2008, 450, 286. (25) Nolan, M.; Fearon, J. E.; Watson, G. W. Solid State Ionics 2006, 177, 3069. (26) Castleton, C. W. M.; Kullgren, J.; Hermansson, K. J. Chem. Phys. 2007, 127, 244704. (27) Da Silva, J. L. F.; Veronica Ganduglia-Pirovano, M.; Sauer, J. Phys. ReV. 2007, 75, 045121.

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