High pressure elastic properties of minerals from ab initio simulations: The case of pyrope, grossular and andradite silicate garnets

Abstract

A computational strategy is devised for the accurate ab initio simulation of elastic properties of crystalline materials under pressure. The proposed scheme, based on the evaluation of the analytical stress tensor and on the automated computation of pressure-dependent elastic stiffness constants, is implemented in the CRYSTAL solid state quantum-chemical program. Elastic constants and related properties (bulk, shear and Young moduli, directional seismic wave velocities, elastic anisotropy index, Poisson's ratio, etc.) can be computed for crystals of any space group of symmetry. We apply such a technique to the study of high-pressure elastic properties of three silicate garnet end-members (namely, pyrope, grossular, and andradite) which are of great geophysical interest, being among the most important rock-forming minerals. The reliability of this theoretical approach is proved by comparing with available experimental measurements. The description of high-pressure properties provided by several equations of state is also critically discussed.

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

“…A fully automated implementation in the Crystal program of the calculation of the stiffness tensor B (and of S = B −1 , the compliance tensor) under pressure has recently been presented [53,54]. A two-index representation of the elastic stiffness tensor is obtained (B ijkl → B vu ) by exploiting Voigt's notation, according to which v, u = 1, .…”

“…[59] harmonic (without the need for an explicit anharmonic description of the system, then). 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].…”

Structural and elastic anisotropy of crystals at high pressures and temperatures from quantum mechanical methods: The case of Mg2SiO4 forsterite

“…(3) is replaced by the equilibrium volume V (P) at pressure P. An implementation in the C program of the calculation of the stiffness tensor C (and of S = C −1 , the compliance tensor) under pressure has recently been presented. 15,68,69 A two-index representation of the elastic stiffness tensor is obtained (…”

“…The effectiveness of DFT-based methods in describing structural and elastic properties of solids under pressure is well-known; 7 several techniques are available such as fitting energy-volume data to analytical expressions of the equation-of-state (EOS) of the system, 8,9 computing the analytical stress tensor and performing pressure-constrained geometry optimizations, 10,11 and correcting the fourth-rank elastic tensor according to its Lagrangian or Eulerian strain tensor formulation. [12][13][14][15] The description of thermal structural and elastic properties of crystals requires to go beyond the standard harmonic approximation to the lattice potential, whose limitations (including but not limited to zero thermal expansivity and temperature independence of elastic constants and bulk modulus) are wellknown. 16,17 In this respect, due to its formal simplicity and relatively low computational cost, an effective method of a) Electronic mail: alessandro.erba@unito.it choice is the so-called quasi-harmonic approximation (QHA), which introduces the missing volume dependence of phonon frequencies by retaining the harmonic expression for the Helmholtz free energy of the system.…”

“…The effect of the particular choice of the exchange-correlation functional, within the DFT, on computed properties is explicitly investigated and documented by considering three different levels of approximation, corresponding to three rungs of the well-known "Jacob's ladder." 33 A development version of the C14 program 6 is used for all calculations where some of the present authors have recently implemented fully automated algorithms for the calculation of quasi-harmonic, 28,34,35 photo-elastic, 36 piezoelectric, 37,38 and elastic 15,39 properties of crystals.…”