Optimum-model-potential lattice dynamics of β-Sn

Shaw and Harrison's optimized form of the model potential of Heine, Abarenkov, and Animalu has been employed for the calculation of energy wave-number characteristics and phonon dispersion relations in β-Sn. A good fit with experimental dispersion relations can be obtained by using the electron effective mass m* as a free parameter with the value m*=1.4. For this value of m*, the calculated dispersion relations display a certain fine structure which is observed experimentally. The quality of fit of the model to experimental data depends sensitively on m*. It is also deduced that, unless m* is suitably adjusted, Shaw's method of including exchange and correlation in the model potential does not produce low enough phonon frequencies in the case of β-Sn. Nonlocal contributions to the model potential play a significant role in accounting for phonon data. This model is also employed to calculate g(ω), which is compared with data of coherent scattering of neutrons from polycrystalline β-Sn. © 1972 The American Physical Society.