Higher-order elastic constants and megabar pressure effects of bcc tungsten:Ab initiocalculations

Abstract

The general method for the calculation of $n\mathrm{th}$ ($n\ensuremath{\ge}2$) order elastic constants of the loaded crystal is given in the framework of the nonlinear elasticity theory. For the crystals of cubic symmetry under hydrostatic compression, the two schemes of calculation of the elastic constants of second, third, and fourth order from energy--finite strain relations and stress--finite strain relations are implemented. Both techniques are applied for the calculation of elastic constants of orders from second to fourth to the bcc phase of tungsten at a 0--600 GPa pressure range. The energy and stress at the various pressures and deformations are obtained ab initio in the framework of projector augmented wave+generalized gradient approximation (PAW+GGA) method, as implemented in Vienna Ab initio Simulation Package (VASP) code. Using the obtained results, we found the pressure dependence of Gr\uneisen parameters for long-wave acoustic modes in this interval. The Lam\'e constants of second and third order were estimated for polycrystalline tungsten. The proposed method is applicable for crystals with arbitrary symmetry.