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- W1985655992 abstract "The lattice thermal conductivity is studied for monatomic crystal structures in the framework of the theory of linear response functions. The lattice anharmonicity is treated by three phonon-processes only and the simplest nontrivial self-consistent expression for the phonon self-energy is used. This approximation which corresponds to a generalized Peierls-phonon-Boltzmann equation, where repeated random phase approximation is not assumed, is used in a self-consistent evaluation of the energy-current autocorrelation function. Summing an infinite set of ladder-type diagrams, an expression for the conductivity is obtained in terms of a “transport lifetime” replacing the “single-mode relaxation time” commonly used as an approximate description for transport phenomena. This transport lifetime is found to be a modification of the single-mode relaxation time in two ways. Firstly, it describes the relaxation of an energy current rather than a particle density and secondly, it takes explicitly into account the lifetime of the scattered phonons. For temperatures T large compared with Debye temperature θ, this modification does not alter the 1T behavior of the conductivity. However for temperatures T ⪡ θ a sharp rise in the conductivity is obtained as a result of this modification. For a spectrum with two Debye branches the temperature behavior of the conductivity in this regime varies like 1T(1 − α(θT)3), where α decreases monotonically with T. In the limit corresponding to Peierls's-phonon-Boltzmann equation based on a spectrum consisting in a single Debye branch, the transport lifetime is found to diverge for N-processes." @default.
- W1985655992 created "2016-06-24" @default.
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- W1985655992 date "1967-12-01" @default.
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- W1985655992 title "Thermal conductivity in nonconducting crystals" @default.
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- W1985655992 doi "https://doi.org/10.1016/0003-4916(67)90060-7" @default.
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