Group-Theoretical Analysis of Lattice Vibrations in Metallicβ−Sn

A group-theoretical method of analyzing lattice-vibrational properties, which is applicable to both symmorphic and nonsymmorphic space lattices, is presented. The method consists of the determination of the explicit transformation matrices of the polarization vectors under the general space-group operations and the construction of the projection operators, which are then used to project out the required polarization vectors. Different branches of the dispersion curves at symmetry points and along symmetry directions are then classified according to their symmetry species, and the dynamical matrix block diagonalized. The usefulness and practicality of the method is then demonstrated by applying it to to $\beta -\mathrm{S}\mathrm{n}$ lattice vibrations in detail, and the result is compared with the experimentally determined dispersion curves to be described in the following paper.