On the Relation Between Grey and White Tin ($\alpha$-Sn and $\beta$-Sn)

A model capable of representing the structure of either grey or white tin and susceptible to lattice dynamical analysis has been studied. Values of atomic force constants for the models have been estimated and used in the appropriate secular equations to calculate frequency distributions of lattice modes for the two phases. From these distributions, thermodynamic quantities (in particular the specific heat and the vibrational contribution to the free energy) have been computed and the results are compared with observed data; fair agreement is found in view of the assumptions involved and the lack of any observed elastic constants for grey tin. The values of the force constants in relation to the phase change are discussed and a suggestion about the interpretation of the angular stiffnesses in terms of the interaction of the Fermi surface with Brillouin polyhedra is offered.