Nonequilibrium distribution function in the presence of a heat flux at the interface between two crystals

TL;DR

This paper investigates the non-equilibrium phonon distribution caused by heat flux at a crystal interface using a harmonic chain model, deriving conditions for distribution matching and generalizing the Enskog--Chapman method for Kapitza conductance.

Contribution

It introduces a generalized approach for calculating phonon distribution functions and Kapitza conductance at crystal interfaces, improving upon previous models.

Findings

Derived conditions for phonon distribution matching at interfaces

Generalized the Enskog--Chapman method for Kapitza conductance

Obtained a precise relation under simplified assumptions

Abstract

A one-dimensional harmonic chain model is used to study the non-equilibrium distribution function of phonons induced by a heat flux across the interface between two crystals. Conditions are derived which govern the matching of distribution functions on both sides of the interface. A generalization of the Enskog--Chapman method for calculating the Kapitza conductance is introduced. A precise relation is obtained under some simplifications. This version contains improved translation, modernized notation, and corrects one mistake, that does not affect the final formulae.