Determination of the dispersive elastic constants of the cubic crystals Ge, Si, GaAs, and InSb

The first onset of spatial dispersion, i.e., the variation of velocity of an elastic wave when its wavelength approaches the natural scale of length of a medium, can be accommodated within continuum elasticity theory by the incorporation of third and fourth order spatial derivatives of the displacement field in the elastic wave equation. This paper is concerned with the access to the coefficients of these higher order derivatives in gradient elasticity provided by inelastic neutron scattering, ballistic phonon imaging, and picosecond laser ultrasound measurements. Numerical values of the dispersive elastic constants of the four cubic crystals, germanium, silicon, gallium arsenide, and indium antimonide, are obtained by fitting to available near zone center symmetry direction acoustic mode phonon dispersion relations of these crystals, measured by inelastic neutron scattering. Ballistic phonon transport calculations using these values, account well for available dispersive phonon images of these crystals. For Ge, Si, and GaAs, comparison is made with values of dispersion coefficients reported elsewhere in literature, which have been obtained from laser ultrasound measurements and from empirical and ab initio lattice dynamics models.