Fourth-order elastic constants of nonideal hcp crystal Mg and Er

The expressions for the 19 fourth-order elastic constants of an hcp crystal with nonideal axial ratio have been derived with interactions extending up to second neighbors and using sublattice displacements to the second degree in strains. These formulas have been used to evaluate the fourth-order elastic constants of magnesium and erbium. The results reveal higher-order elastic anisotropy in erbium. The second pressure derivatives of the effective second-order elastic constants of magnesium and erbium have been obtained using their fourth-order elastic constants and are positive. The magnitudes of the second pressure derivatives of C112, C133, and C111 in magnesium and that of C112 in erbium are extremely large, lending support to the phase changes that occur in these metals when subjected to hydrostatic pressure.