Relationship between the Macroscopic and Microscopic Theory of Crystal Elasticity. II. Nonprimitive Crystals

A recent microscopic elasticity formalism is generalized to nonprimitive, nonpiezoelectric crystals, and extended to treat long-range electrostatic interactions explicitly. Its relationship with the macroscopic theory of crystal elasticity is established for this type of crystal up to, and including, third order. The long-range Coulomb interactions are treated in a convenient new way in this theory, which involves readily convergent lattice sums. The problem of rotational invariance and noncentral nearest-neighbor forces is considered, and an explanation of the disagreements encountered in the literature is proposed.