Spatial dispersion in phonon focusing
Files
Date
2009-03-05T06:42:09Z
Authors
Jakata, Kudakwashe
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
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.