Ab initio and shell model studies of structural, thermoelastic and vibrational properties of SnO2 under pressure.

The pressure dependences of the structural, thermoelastic and vibrational properties of SnO2 in its rutile phase are studied, as well as the pressure-induced transition to a CaCl2-type phase. These studies have been performed by means of ab initio (AI) density functional theory calculations using the localized basis code SIESTA. The results are employed to develop a shell model (SM) for application in future studies of nanostructured SnO2. A good agreement of the SM results for the pressure dependences of the above properties with the ones obtained from present and previous AI calculations as well as from experiments is achieved. The transition is characterized by a rotation of the Sn-centered oxygen octahedra around the tetragonal axis through the Sn. This rotation breaks the tetragonal symmetry of the lattice and an orthorhombic distortion appears above the critical pressure P(c). A zone-center phonon of B1g symmetry in the rutile phase involves such rotation and softens on approaching Pc. It becomes an Ag mode which stabilizes with increasing pressure in the CaCl2 phase. This behavior, together with the softening of the shear modulus (C11-C12)/2 related to the orthorhombic distortion, allows a precise determination of a value for Pc. An additional determination is provided by the splitting of the basal plane lattice parameters. Both the AI and the experimentally observed softening of the B(1g) mode are incomplete, indicating a small discontinuity at the transition. However, all results show continuous changes in volume and lattice parameters, indicating a second-order transition. All these results indicate that there should be sufficient confidence for the future employment of the shell model.

Ab initio study of the elastic properties of single and polycrystal TiO(2), ZrO(2) and HfO(2) in the cotunnite structure.

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 the self-consistent SIESTA code, pseudopotentials, density functional theory in the LDA and GGA approximations, the total energies, hydrostatic pressures and stress tensor components are calculated. From the stress-strain relationships, in the linear regime, the elastic constants C(ij) are determined. Derived elastic constants, such as bulk, Young's and shear modulus, Poisson coefficient and brittle/ductile behavior are estimated with the polycrystalline approach, using Voigt-Reuss-Hill theories. We have found that C(11), C(22) and C(33) elastic constants of hafnia and zirconia show increased strength with respect to the experimental values of the normal phase, P 2(1)/c. A similar situation applies to titania if these constants are compared with its normal phase, rutile. However, shear elastic constants C(44), C(55) and C(66) are similar to the values found in the normal phase. This fact increases the compound anisotropy as well as its ductile behavior. The dependence of unit-cell volumes under hydrostatic pressures is also analyzed. P-V data, fitted to third-order Birch-Murnaghan equations of state, provide the bulk modulus B(0) and its pressure derivatives B'(0). In this case, LDA estimations show good agreement with respect to recent measured bulk moduli of ZrO(2) and HfO(2). Thermo-acoustic properties, e.g. the propagation speed of transverse, longitudinal elastic waves together with associated Debye temperatures, are also estimated.

Ab initio localized basis set study of structural parameters and elastic properties of HfO2 polymorphs.

The SIESTA approach based on pseudopotentials and a localized basis set is used to calculate the electronic, elastic and equilibrium properties of P 21/c, Pbca, Pnma, Fm3m, P42nmc and Pa3 phases of HfO2. Using separable Troullier-Martins norm-conserving pseudopotentials which include partial core corrections for Hf, we tested important physical properties as a function of the basis set size, grid size and cut-off ratio of the pseudo-atomic orbitals (PAOs). We found that calculations in this oxide with the LDA approach and using a minimal basis set (simple zeta, SZ) improve calculated phase transition pressures with respect to the double-zeta basis set and LDA (DZ-LDA), and show similar accuracy to that determined with the PPPW and GGA approach. Still, the equilibrium volumes and structural properties calculated with SZ-LDA compare better with experiments than the GGA approach. The bandgaps and elastic and structural properties calculated with DZ-LDA are accurate in agreement with previous state of the art ab initio calculations and experimental evidence and cannot be improved with a polarized basis set. These calculated properties show low sensitivity to the PAO localization parameter range between 40 and 100 meV. However, this is not true for the relative energy, which improves upon decrease of the mentioned parameter. We found a non-linear behaviour in the lattice parameters with pressure in the P 21/c phase, showing a discontinuity of the derivative of the a lattice parameter with respect to external pressure, as found in experiments. The common enthalpy values calculated with the minimal basis set give pressure transitions of 3.3 and 10.8 GPa for [Formula: see text] and [Formula: see text], respectively, in accordance with different high pressure experimental values.