Ab initio study of the elastic properties of single and polycrystalTiO2,ZrO2 and HfO2 in the cotunnite structure

Abstract

In this work, we study theoretically the elastic properties of the orthorhombic(Pnma) high-pressure phase of IV-B group oxides: titania, zirconia and hafnia. By means of theself-consistent SIESTA code, pseudopotentials, density functional theory in the LDA and GGAapproximations, the total energies, hydrostatic pressures and stress tensor components arecalculated. From the stress–strain relationships, in the linear regime, the elastic constantsCij are determined. Derived elastic constants, such as bulk, Young’s and shearmodulus, Poisson coefficient and brittle/ductile behavior are estimated with thepolycrystalline approach, using Voigt–Reuss–Hill theories. We have found thatC11,C22 and C33 elastic constants of hafnia and zirconia show increased strengthwith respect to the experimental values of the normal phase,P 21/c. A similar situation applies to titania if these constants are comparedwith its normal phase, rutile. However, shear elastic constantsC44,C55 and C66 are similar to the values found in the normal phase. This fact increasesthe compound anisotropy as well as its ductile behavior. The dependenceof unit-cell volumes under hydrostatic pressures is also analyzed.P–V data, fitted to third-order Birch–Murnaghan equations of state, provide the bulk modulusB0 and its pressurederivatives B′0. In this case, LDA estimations show good agreement with respect to recent measured bulk moduliof ZrO2 and HfO2.Thermo-acoustic properties, e.g. the propagation speed of transverse, longitudinal elasticwaves together with associated Debye temperatures, are also estimated.