An ab initio study of ZrO2-HfO2 solid solution with cotunnite structure

Goryaeva, A.M.; Vinograd, V.L.; Winkler, B.; Eremin, N.N.; Urusov, V.S.

Авторы: Goryaeva A.M., Vinograd V.L., Winkler B., Eremin N.N., Urusov V.S.
Журнал: Acta Crystallographica Section A: Foundations of Crystallography
Том: 67
Номер: A1
Год издания: 2011
Издательство: Blackwell Publishing Inc.
Местоположение издательства: United Kingdom
Первая страница: C710
Последняя страница: C710
DOI: 10.1107/S0108767311082031
Аннотация: Previous experimental and theoretical studies [1], [2], [3], [4] suggested that cotunnite-type zirconia and hafnia, as well as their solid solutions, could be candidates for superhard materials due to their high bulk moduli. Another possible application of cotunnite-type ZrO2 and HfO2 as waveguide materials is discussed here. An investigation of these questions requires knowledge of the elastic stiffness tensor as a function of chemical composition. According to the results of ab initio calculations [2, 4 and this study] the elastic stiffness coefficients of the HfO2 polymorphs are significantly larger than those of the corresponding ZrO2 polymorphs, while the volumes of the ZrO2 polymorphs are consistently smaller. It is not obvious whether the contraction of the HfO2 structure due to the incorporation of a smaller, but more compressible cation causes an increase in the bulk modulus, or how the incorporation of the larger, but less compressible Hf cation changes the elastic stiffness properties of ZrO2. We have computed the elastic stiffness tensors of ZrO2 and HfO2 polymorphs with baddeleyite-type (P21c), Pbca and cotunnite-type (Pnma) structures in order to obtain the anisotropy of sound wave phase velocities and have calculated the thermodynamic mixing properties of HfO2-ZrO2 solid solutions with the cotunnite structure. The calculations were based on density functional theory within the generalized gradient approximation (GGA) with PBE and PBEsol functionals [5, 6]. The calculations were carried out with the program CASTEP [7] using high-performance computers at the University of Frankfurt and at the Moscow State University. The anisotropic sound wave phase velocities were determined using the Christoffel tensor [8]. Despite the lower stiffness, the calculated speeds of sound wave propagation are generally higher for ZrO2 polymorphs because of their lower density. Cotunnite-type ZrO2 has rather high longitudinal acoustic wave velocities (about 8 km/s) which are not strongly dependent on direction and thus could be considered for applications as a solid acoustic waveguide material. The solid solution is characterized by unusual negative enthalpy and volume of mixing. The ordering energies corresponding to the reaction ZrZr + HfHf = 2ZrHf were calculated for 9 interatomic distances within a 2x2x1 supercell. These energies are very small (< 1 kJ/mol). This suggests that any intermediate ordered compound can be used as a probe for the elastic stiffness of the solid solution at intermediate compositions. The calculations of elastic stiffness tensors of ordered compounds within the HfO2-ZrO2 binary are currently underway. [1] J. Haines et al. J. Am. Ceram. Soc. 1997, 80, 1910. [2] M.A. Caravaca et al., J. Phys. Condens. Matter. 2009, 21, 015501 (1-11). [3] S. Desgreniers, K. Lagarec, Phys. Rev. B, 1999, 59, 8467–8472. [4] J.E. Jaffe, R.A. Bachorz, M. Gutowski, Phys. Rev. B. 2005, 72, 144107 (1-9). [5] J.P Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Let. 1996, 77, 3865-3868. [6] J.P Perdew et al., Phys. Rev. Let. 2008, 100, 136406-136409. [7] S.J. Clark et al., Z. Kristallogr. 2005, 220,567–570. [8] A.G. Every, Phys. Rev. B. 1980, 22, 1746-1760
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An ab initio study of ZrO2-HfO2 solid solution with cotunnite structureстатья

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