Thermodynamics and phonon dispersion of pyrope and grossular silicate garnets from ab initio simulations

Abstract

The phonon dispersion and thermodynamic properties of Mg 3 Al 2 Si 3 O 12 , pyrope, and Ca 3 Al 2 Si 3 O 12 , grossular, have been computed by using an ab initio quantum mechanical approach, an all-electron variational Gaussian type basis set and the B3LYP hybrid functional, as implemented in the CRYSTAL program. Dispersion effects in the phonon bands have been simulated by using supercells of increasing size, containing 80, 160, 320, 640, 1280 and 2160 atoms, corresponding to 1, 2, 4, 8, 16 and 27 k points in the first Brillouin zone. Phonon band structures, density-of-states and corresponding inelastic neutron scattering spectra are reported. Full convergence of the various thermodynamic properties, in particular entropy (S) and specific heat at constant volume (C V ), with the number of k points is achieved with 27 k points. The very regular behavior of the S(T ) and C V (T ) curves as a function of the number of k points, determined by high numerical stability of the code, permits extrapolation to an infinite number of k points. The limiting value differs from the 27-k case by only 0.40% at 100 K for S (the difference decreasing to 0.11% at 1000 K) and by 0.29% (0.05% at 1000 K) for C V . The agreement with the experimental data is rather satisfactory. We also address the problem of the relative entropy of pyrope and grossular, a still debated question. Our lattice dynamical calculations correctly describe the larger entropy of pyrope than grossular by taking into account merely vibrational contributions and without invoking "static disorder" of the Mg ions in dodecahedral sites. However, as the computed entropy difference is found to be larger than the experimental one by a factor of 2-3, present calculations can not exclude possible thermally-

Raman spectroscopic features of the neutral vacancy in diamond from ab initio quantum-mechanical calculations

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Thermodynamic and Elastic Properties of Grossular at High Pressures and High Temperatures: A First‐Principles Study

“…In contrast, Pavese et al () suggested that the pressure dependence of bulk modulus is lower than 3.0 from equation‐of‐state measurements. Some first‐principles studies also calculated the elasticity of grossular at static conditions (e.g., Erba, Mahmoud, et al, , Erba, Mahmoud, et al, ; Kawai & Tsuchiya, ; Mahmoud et al, ) and discussed some thermodynamics properties of grossular (Baima et al, ); nevertheless, the temperature effect on the elasticity is not available.…”

Thermal properties of the orthorhombic CaSnO3 perovskite under pressure from ab initio quasi-harmonic calculations

“…From the full phonon dispersion of a system, the phonon density-of-state (PDOS) can be determined, which is defined by the equation [58]:…”

“…The anisotropic elastic response of the system (in terms of elastic constants and directional seismic wave velocities) is investigated as a function of pressure [52][53][54][55][56]. Furthermore, the full phonon dispersion of the system is computed, which allows us to investigate other thermodynamic properties of the system and phonon density-of-states [57,58]. The Gibbs free energy of formation of CaSnO 3 from the two simple oxides CaO (cubic) and SnO 2 (tetragonal) is also evaluated as a function of temperature.…”