Long-Wavelength Elastic Interactions in Complex Crystals

The long-wavelength (LWL) limit of the elastic interactions in complex non-Bravais lattices is investigated on the basis of microscopic elasticity theory. The conceptual simplicity of our approach enables large-scale simulations in materials with complex crystalline structures. We demonstrate the method by calculating the LWL elastic energy of hcp-based Mg binary alloys for a variety of impurities. Our results show that for large coherent precipitates, the strain-induced interactions control the shape along the hexagonal axis, whereas the surface energy dictates the basal growth. The present formalism enables a straightforward treatment of the long-range elastic interactions in the cluster expansion method for complex crystals.