Phonons in disordered alloys : a multiple scattering approach

TL;DR

This paper develops a detailed multiple scattering theoretical framework to analyze how disorder affects phonon Green functions and thermal transport in substitutional random alloys, with explicit diagrammatic calculations up to fourth order.

Contribution

It introduces a comprehensive diagrammatic approach combining the augmented space theorem and Edwards-Langer technique to analyze phonon scattering in disordered alloys, including self-energy and vertex corrections.

Findings

Disorder renormalizes phonon propagators and heat currents.

Explicit scattering diagrams up to fourth order are derived.

The approach links disorder scattering to thermal response properties.

Abstract

In this paper we shall discuss the effect of disorder induced configuration fluctuations on single particle and two-particle phonon Green functions in substitutional random binary alloys. The randomness of the system will be dealt within the augmented space theorem, introduced by one of us [J. Phys. C : Solid State Phys. 6, L205(1973)]. This will be combined with a generalized Edwards-Langer diagrammatic technique to extract various useful results in the form of mathematical expressions. The purpose of present manuscript will be to describe the scattering diagrams in full detail. This will form the basis of the calculational algorithms which we had used in an earlier paper on NiPd and NiPt alloys [J. Phys.: Condens. Matter 18, 4589-4608 (2006)]. We shall show the structure of all possible scattering diagrams up to the 4-th order and subsequently illustrate how to obtain Dyson's equation from a re-summation of the diagrammatic series. We shall also study how disorder scattering affects two-particle Green functions associated with thermal response. We shall show that disorder scattering renormalizes both the phonon propagators as well as the heat currents. These renormalized heat currents will be shown to be related to the self-energy of the propagators. We shall also study a different class of scattering diagrams which are not related to the self-energy but rather to the vertex corrections.