Fourth order nonlinear elastic coefficients of hexagonal close packed lattice

Abstract

The expressions for the fourth-order elastic constants of a hexagonal close packed lattice is derived using the sublattice displacements to the second order in strains. These expressions together with the expressions for the second- and third-order elastic constants have been used to obtain the higher order nonlinear elastic coefficients in some hexagonal metals. These expressions are used to find the second-order, third-order and fourth-order elastic constants of cadmium. The pressure derivatives of their elastic constants are also obtained. The results obtained are compared with the available experimental results.