Microscopic theory of the second- and third-order elastic constants of cobalt in a thermodynamic module

The total potential energy of a crystal is presented as an expansion by irreducible interactions in clusters containing pairs of atomic triplets and quadruplets. The potential energy of the clusters in the adiabatic approximation is a function of vectors connecting the centers of atoms in the clusters. Arguments (basic functions) affecting the potential energy of clusters are found using the model with allowance for the exchange symmetry of atoms and the irreducibility of the considered energies of doublet, triplet, and quadruplet atoms and interactions. This allows us to present arguments of the potential energy in the form of summed integral numbers (latticed sums) multiplied by a fixed value of the crystal unit cell parameter, and to set the numerical values of the potential energy arguments as a function of vectors . A potential corresponding to the thermodynamic additivity concept of crystal energy is selected as the model potential of pairwise interaction. Secondand third-order moduli of the rigidity of Co crystals with A 1, A 2, and HCP structures are calculated using this model of multiatom interactions.