Perspectives on spatial dispersion in cubic crystals provided by neutron scattering, phonon imaging, picosecond laser ultrasound and lattice dynamics models

Abstract

This paper treats spatial dispersion as an extension to continuum elasticity, by incorporating third and fourth order spatial derivatives of the displacement field in the elastic wave equation. The coefficients of these derivatives, the dispersive and non-dispersive elastic constants, are extracted for InSb and GaAs from published neutron scattering data on the phonon dispersion relations of these crystals, and their values are compared with values reported elsewhere, that have been obtained from laser ultrasound measurements and from lattice dynamics models. It is further demonstrated in this paper how modified continuum elastodynamics is able to account well for the observed dispersive phonon images of these crystals. © 2008 Acoustical Society of America.