Thermo-chemical and thermo-physical properties of stishovite: An ab-initio all-electron investigation

Abstract

Ab-initio thermo-chemical and thermo-physical properties of stishovite, the high pressure polymorph of SiO 2, were computed with the hybrid B3LYP density functional method. First, investigation of static properties through a symmetry preserving relaxation procedure was carried out and then, on the equilibrium structure, harmonic vibrational modes were computed at the long-wavelength limit corresponding to the center of the Brillouin zone ( k → 0 ). While optic modes are the eigenvectors of the Hessian matrix, acoustic modes at Γ point are obtained by solving the non-zero components of the strain matrix. Acoustic branches were then assumed to follow a sine wave dispersion when traveling within the Brillouin zone (Kieffer model). The quasi-harmonic mode-gamma analysis of volume effects on vibrational frequencies allowed computation of all vibrationally dependent thermodynamic properties (isochoric and isobaric heat capacity, thermal expansion, thermal derivative of the bulk modulus, thermal correction to internal energy, enthalpy and Gibbs free energy, thermal pressure, elastic and calorimetric Debye temperature) with sufficient accuracy. Moreover, the conformation of the strain tensor allowed satisfactory reproduction of known thermo-physical properties, viz. transverse and longitudinal wave velocities, shear modulus, Young’s modulus and Poisson’s ratio.