Sound Wave Propagation and Anharmonic Effect in Solid 3He and 4He
In the treatment of lattice dynamics of quantum solids at low temperatures the harmonic approximation is not applicable because the zero-point motion of such an atom is a large fraction of the near-neighbor distance. Various theoretical models which take anharmonicity into consideration have been proposed to study thermal and elastic properties of rare gas solids. Theoretical calculations of the second-order elastic constants (SOEC)1 and velocity contours of sound wave propagation in bcc 3He2 and hcp 4He3 crystals have been reported. Experimental determination of SOEC of these crystals4 through sound velocity measurements yielded results which in varying degrees are in agreement with the theoretical ones. However, the verification of the anisotropic behavior of sound waves in these solids became possible when the recently improved techniques for growing large single crystals were achieved. In view of this advancement, this paper is primarily concerned with the information which may be obtained about the effect of anharmonicities on the physical properties of these crystals through the study of the third-order elastic constants (TOEC).
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