Thermal conductivity of an isotopically disordered harmonic crystal

Abstract

Using the Kubo formalism, an expression is obtained for the lattice thermal conductivity of a three-dimensional harmonic Bravais crystal, containing a certain number of randomly distributed isotopic impurities, by the method of double-time thermal Green's functions. It is shown that the total thermal conductivity can be separated into two contributions, namely, diagonal and nondiagonal contributions; the former in the case of small half-width of the phonons reduces to the expression obtained from the Boltzmann transport equation. An approximate expression for the dominant nondiagonal contribution to the conductivity is obtained.