Elastic constants of the central force model for cubic structures: Polycrystalline aggregates and instabilities

The central force theory is extended to predict the elastic properties of polycrystalline aggregates of crystallites of the NaCl, ZnS, CsCl, and CaF2 lattices, from zero pressure up to the point of a phase transition. Poisson's ratio at zero pressure is always equal to or greater than 0.25, according to the central force model. dVs/dP is negative for crystallites of the ZnS lattice, positive for the CsCl lattice, and may be negative or positive for the NaCl and CaF2 lattice, depending on the details of the model. The point of phase transition is determined by the vanishing of a shear elastic constant. In the transition from the NaCl to the CsCl structure, the central force model predicts a jump of about 35% in Vs, and about 8% in Vp.