Lattice Dynamics of White Tin

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Abstract
The theoretical lattice vibrational spectrum for white tin (body-centered tetragonal) is examined on the basis of the axially symmetric lattice dynamics model including fourth-nearest-neighbor interactions. The atomic force constants are derived using experimental data for the elastic constants, specific heat, Debye temperature, and the Debye-Waller factor at 100°K. The 6×6 dynamical matrix is diagonalized along the principal symmetry directions and the resulting dispersion curves are presented. The spectrum is characterized by low-lying optical modes which interact strongly with the acoustic modes, particularly near the surface of the first Brillouin zone. These optical modes give rise to a large density of states at intermediate acoustical frequencies and contribute significantly to both the specific heat and Debye-Waller factor at low temperature.