7 - Imaging of dispersive phonons

Summary

The previous chapters have dealt mainly with phonon-focusing patterns that are independent of phonon frequency. This nondispersive behavior is expected when the wavelengths of the phonons are long compared to the spacing between atoms in the crystal. For phonons with wavelengths of only a few lattice spacings, large changes are expected in the slowness surface, group velocities, and focusing pattern. In practice, however, it is quite difficult to observe the ballistic propagation of such short wavelength (large-k) phonons. As their wavelength approaches twice the lattice constant (i.e., k ≡ 2π/λ approaches π/a), the phonons become particularly sensitive to defects in the periodicity in the crystal: they scatter.

The crystalline defects can be impurity atoms or even atoms with different isotopic masses. The fractional difference in mass between two isotopes is usually small, but many elements have more than one isotope of large natural abundance. This implies a high density of weak-scattering centers, even in chemically pure crystals. For long-wavelength phonons, the rate of mass-defect scattering increases as the fourth power of the phonon frequency, similar to Raleigh scattering of light from particles in the atmosphere. For example, the mean free paths of 1-THz phonons in otherwise perfect Ge, InSb, and GaAs are limited to a fraction of a millimeter by isotope scattering.

In order to observe the ballistic propagation of large-wavevector phonons in such crystals, the experimenter must use thin samples of high chemical and structural purity.