Elastic constants of the central force model for three cubic stuctures: Pressure derivatives and equations of state

The case of the generalized repulsive potential in the central force approximation is used in Born's lattice theory to derive the elastic constants versus pressure for the NaCl, CsCl, and ZnS structures. The equations are rearranged so that cij is a function of K and P, the bulk modulus and pressure. The isothermal equation of state relates K, P, and the density ρ, so that the elastic constants are specific functions of the relation between K and P, and ρ and P. As a special case of the theory, the parameter in the repulsive potential n is evaluated by the measured value Ko′. The theory shows that the simple repulsion v (r) = b/rn accounts for the experimental results, except for a small term due to noncentral binding.