Phonon Conduction in Hexagonal Crystals Exhibiting Extreme Elastic Anisotrophy

Abstract

Striking differences (more than several orders of magnitude) are predicted in the intensity of phonons propagating ballistically along different directions to the c axis in hexagonal crystals exhibiting extreme elastic anisotropy. Calculations of the boundary-scattered phonon conductivity for long rods of square cross section predict anisotropy ratios λ₁₁/λ_⊥ due to phonon focusing of more than 70 for samples having the elastic constants of CAP graphite. Furthermore, the anisotropy ratio λ₁₁/λ_⊥ increased from less than unity to more than 100 as the sample dimension ratio d₁₁/d_⊥ was varied from 0.1 to 10. Corrections to Casimir’s theory generalized to include phonon focusing have been derived for samples in which a fraction of the phonons are specularly reflected from the side and end faces, and for samples in which a fraction of the phonons are specularly transmitted through domain walls. Calculations performed for CAP graphite near 1°K show little significant change in the anisotropy ratio λ₁₁/λ_⊥ if transmission of ballistic phonons occurs through grain boundaries, but reductions in λ₁₁/λ_⊥ by more than a factor of 20 can be realized if reflection rather than transmission occurs at grain boundaries perpendicular to the c axis.