Thermal Expansion and Phonon Frequency Shifts in Nonprimitive Lattices

Abstract

Expressions have been derived in the quasiharmonic approximation for the change in normal-mode frequencies associated with thermal expansion in a nonprimitive lattice. The work is formulated in terms of coupling parameters for an undistorted lattice with cubic anharmonicity. Symmetric finite-strain parameters and appropriate internal strains are introduced in such a manner that the formulation exhibits explicitly the invariance of the crystal potential energy and normal-mode frequencies under rigid-body rotations. As a numerical application, the coefficient of linear expansion and the phonon frequency distributions at 300 and 800 \ifmmode^\circ\else\textdegree\fi{}K have been calculated for zirconium hydride with a short-range central-force model including third-nearest-neighbor forces.