Model-Potential Calculations of Phonon Energies in Aluminum

Abstract

The calculation of the lattice dynamics of simple metals to second order in a local model potential is discussed in terms of the real-space sum of Born-von Karman central-force constants. The real-space sum is found to converge faster than the more common reciprocal-space sum and to be more convenient for the calculation of thermal properties and integral properties of the electron-phonon interaction. The reciprocal-space sum is more suitable for the calculation of Kohn anomalies and elastic constants and may be generalized to more complicated models of the electron-ion interaction. These points are illustrated by a calculation of aluminum phonon energies throughout the Brillouin zone. Excellent agreement of the calculated dispersion relations along 10 symmetry lines, density of states, and specific heat with the experimental quantities are obtained by fitting the two parameter Harrison potential and using the Toigo-Woodruff susceptibility function. The results from this model are compared with those from the two models used by Wallace and with those of the eight-shell force-constant fit by Gilat and Nicklow. The predictions of the three models for band structure and for electrical resistivity of the liquid are discussed.