Mechanical Energy Flow in Crystal Lattices

Abstract

A detailed study of the mechanical energy transported through a completely general crystal lattice in the classical temperature range is presented. Both a mechanical "Poynting" vector and the corresponding mechanical "Poynting" theorem are established for an arbitrary, 3-dimensional, anisotropic, anharmonic crystal lattice, containing many atoms per cell, inclusive of substitutional impurities, and possessing an arbitrary range of atomic interactions. The extension of the energy-flow procedures to a quantum treatment is discussed, and the resulting quantum-mechanical form of the mechanical "Poynting" vector is given. In addition, a mechanical energy theorem, linking the average mechanical energy flow to the group velocity for the restricted case of a perfectly periodic and harmonic but otherwise completely general, crystal is derived for the classical temperature range.