A new force-constant model for graphite

Earlier force-constant models of graphite either assume the lattice vibrations parallel and perpendicular to the basal plane to be independent, which leads to a zero value for the shear modulus C44, or require an external pressure to be applied for a finite value of C44 to be obtained. In order to avoid these difficulties, and to account for the elastic constants, it was found necessary to consider a model allowing for general interactions out to third-nearest neighbours in the plane and second-nearest neighbours in adjacent planes. The best fit obtained to experimental data uses a model which consists of eight pairwise potential constants and three many-body valence constants. This model gives an exact fit to all five elastic constants and a good fit to the phonon dispersion data. The combination of pairwise potential and valence constants would make the model suitable for predicting the displacement fields of vacancy clusters using the lattice statics method.