Spatial dispersion in phonon focusing

• Main Author: Jakata, Kudakwashe
• Format: Others
• Language: en
• Published: 2009
• Online Access: http://hdl.handle.net/10539/6617

The ballistic phonon flux emanating from a point–like heat source in a crystal shows strong directional dependence. This effect is called phonon focusing and is measured using a technique called phonon imaging. In situations where long wavelength phonons are involved, the observations can be explained on the basis of classical continuum elasticity theory. Dispersion i.e. the variation of velocity with wavelength, sets in when the phonon wavelengths become comparable to the natural scale of length of the material, the lattice constant. This has a significant effect in the phonon focusing pattern and causes shorter wavelength phonons to lag behind longer wavelength ones and the dispersion relation i.e. the relation between angular frequency ω and wave number k becomes non-linear. A number of studies have used lattice dynamics models to explain the observed dispersive phonon images. Measured phonon images are not entirely satisfactorily reproduced by any of these lattice dynamics models and the different models tend to predict somewhat different focusing patterns. In this thesis, we set out to explain the observed dispersive phonon focusing patterns of cubic crystals by using a modification of continuum elasticity theory. This is done by including third and fourth order spatial derivatives of the displacement field in the wave equation. The coefficients of these higher order terms are the dispersive elastic constants. They are determined through optimized fitting to frequency versus wave vector data extracted from neutron scattering experiments for the acoustic modes in symmetry directions of a number of cubic crystals. Our approach is limited to the first onset of spatial dispersion and does not apply to near Brillouin zone boundary phonons. It is also applicable to crystals of any symmetry but in this thesis we focus on crystals of cubic symmetry. We report results on two crystals with a centre of inversion, Ge and Si, and two crystals without a centre of inversion, InSb and GaAs.