Lattice thermal conductivity of disordered binary alloys : a formulation

TL;DR

This paper introduces a new formulation for calculating the lattice thermal conductivity in disordered alloys using augmented-space theorem and diagrammatic techniques, accounting for disorder effects.

Contribution

It presents a novel theoretical framework combining augmented-space theorem and diagrammatic methods to compute thermal conductivity in disordered alloys.

Findings

Disorder scattering affects phonon propagators and heat currents.

The formalism includes vertex corrections in a ladder diagram approximation.

Initial numerical results align with experimental data for NiPd alloys.

Abstract

We present here a formulation for the calculation of the configuration averaged lattice thermal conductivity in random alloys. Our formulation is based on the augmented-space theorem, introduced by one of us, combined with a generalized diagrammatic technique. The diagrammatic approach simplifies the problem of including effects of disorder corrections to a great extent. The approach allows us to obtain an expression for the effective heat current in case of disordered alloys, which in turn is used in a Kubo-Greenwood type formula for the thermal conductivity. We show that disorder scattering renormalizes the phonon propagators as well as the heat currents. The corrections to the current terms have been shown to be related to the self-energy of the propagators. We also study the effect of vertex corrections in a simplified ladder diagram approximation. A mode dependent diffusivity $D_{\gamma}$ and then a total thermal diffusivity averaged over different modes are defined. Schemes for implementing the said formalism are discussed. A few initial numerical results on the frequency and temperature dependence of lattice thermal conductivity are presented for NiPd alloy and are also compared with experiment. We also display numerical results on the frequency dependence of thermal diffusivity averaged over modes.