Ab initiocalculations of second-, third-, and fourth-order elastic constants for single crystals

Abstract

We present a general scheme to calculate the second-, third-, and fourth-order elastic constants of single crystals with arbitrary symmetry by employing ab initio density-functional theory. The method utilizes a series of homogeneous deformation strains applied to a crystalline system to obtain the internal energy-strain relations. From the nonlinear least-squares fitting, we obtain the elastic constants from the coefficients of the fitted polynomials of the internal energy functions. We applied this method first to four fcc metal crystals, Cu, Al, Au, and Ag. The calculated second-, third-, and fourth-order elastic constants are compared with the available experimental data and other theoretical calculations and found very good agreement. Since accurate determination of higher-order elastic constants, in particular, the fourth-order elastic constants from experiment, is still a challenge, the theoretical approach presented here is certainly of a great help to fill the gap.