Lattice Thermal Conductivity in Disordered Harmonic and Anharmonic Crystal Models

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Abstract
Results of numerical calculations of energy transport in one- and two-dimensional lattice models are reported. Nearest-neighbor harmonic or anharmonic forces were used in randomly disordered mixtures of two different atomic masses. Opposite ends of the lattices were in contact with thermal reservoirs, which transfer energy impulsively at random times to the end atoms. A computer was used to solve the equations of motion of the lattice and to compute the heat current and thermal gradient. The thermal conductivity obtained shows the expected dependence on alloy composition. Except for nearly monatomic lattices, the calculations give larger heat conductivities for anharmonic lattices than for harmonic ones. A qualitative interpretation of these results, dependent upon the nature of the normal modes of disordered crystals, is given.