HEAT FLOW IN CRYSTAL LATTICES.
MASSACHUSETTS INST OF TECH CAMBRIDGE DEPT OF ELECTRICAL ENGINEERING
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A direct approach to the study of the lattice component of thermal conductivity in the classical temperature range is presented in terms of the mechanical energy transported. Both a mechanical Poynting vector and an Energy Flow Theorem, linking the power flow to the group velocity, are derived. Furthermore, these concepts are extended to include the manner in which both lattice imperfections and temperature gradients lead to a statistical steady-state energy distribution. In this phase of the work, statistical ensembles of normal modes with space- and time-dependent amplitudes are used in a classical second-order perturbation scheme to solve for the steady-state dynamics of the nonlinear lattice system. A linear energy i.e. temperature gradient, an unambiguous calculation of the accepted lattice relaxation times, and finally the evaluation directly from the mechanical power densities of the well-known anharmonic, mass-fluctuation, and force-fluctuation components of thermal conductivity are some of the more significant first-order results. All this work is based upon a completely general, 3-dimensional crystal. No need is found for restrictive assumptions as to lattice symmetry, number of atoms per unit cell, or nearness of interacting neighbors. Electronic contributions to heat flow, and size effects, however, have been omitted. No use is made of the Boltzmann Transport Equation, although the results are found to be wholly consistant with it. Author