Internal relaxation in the HCP lattice

There are two atoms per primitive unit cell in a monoatomic HCP lattice. Internal relaxations within the unit cell when a homogeneous strain is applied to the overall HCP crystal structure have been investigated with a short-range embedded-atom method (EAM) model both by computer energy minimization and by analytic expansions. Relaxation displacements proportional to the strain occur for shear strains in the basal plane, i.e., for (C 11 -C 12 )/2- and C 66 -type strains, and these two constants remain equal after relaxation. The internal displacement is comparable in magnitude to the relative displacement of neighbouring atoms arising from the homogeneous applied strain and the decrease in this elastic constant due to relaxation is about 10%, with both results independent of model parameters. Another relaxation effect was found to C 44 -type shears, but the displacements were proportional to the square of the strain. While this does not affect the value of this elastic constant in equilibrium, i.e., in the limit of small displacements, it does yield a softening with large strains. There are no relaxation effects for strains independent of these two.