Computing lattice sums for calculating the elastic moduli of bcc metals via cluster decomposition

The complete potential energy of a crystal E(r→ ik) is presented in the form of an expansion in irreducible interactions in clusters containing pairs, triplets, and quadruplets of atoms, situated on A2 lattice sites. The full set of invariants {Ij (r →ik)}, on which {Ij (r →ik)} can depend is found. Vectors r →ik are presented in the form of an expansion of the base of a Brave lattice. This allows us to {Ij (r →ik)} in the form of integers (lattice sums) multiplied by τ m, where τ is half of an elementary cell rib, and m = const is determined by the model. The sum of the Lenard-Jones potential and the potentials of tri- and tetra-atomic interactions was chosen as the model potential. Within this model, elastic moduli of the second and third order were calculated for crystals with A2-type structure. © 2013 Allerton Press, Inc.