Probing the validity of the diffuse mismatch model for phonons using atomistic simulations

TL;DR

This study uses atomistic simulations to evaluate the diffuse mismatch model's validity for phonon transmission at solid-solid interfaces, revealing limitations in the model's assumptions especially at higher interdiffusion levels.

Contribution

It introduces a mode-by-mode analysis using an advanced simulation method to critically assess the DMM's applicability at atomistic interfaces.

Findings

Submonolayer interdiffusion increases transmission modes, aligning qualitatively with DMM.

Higher interdiffusion levels do not lead to convergence with DMM predictions.

Modes retain memory of initial polarization and wavevector, contradicting DMM assumptions.

Abstract

Due to it's simplicity the diffuse mismatch model (DMM) remains a popular description of phonon transmission across solid-solid boundaries. However, it remains unclear in which situations the DMM should be expected to be a valid model of the underlying physics. Here, its validity is investigated mode-by-mode using a 3-dimensional extension of the frequency domain, perfectly matched layer (FD-PML) method, to study the interface between face-centered cubic solids with interdiffused atoms. While submonolayer levels of interdiffusion are found to increase the number of available modes for transmission, consistent qualitatively with the DMM, we do not find quantitative or qualitative convergence toward the DMM at higher levels of interdiffusion. In particular, contrary to the fundamental assumption of the DMM, modes are not found to lose memory of their initial polarization and wavevector. The transmission coefficients of randomly interdiffused and smoothly-graded interfaces are also compared. While smoothly graded interfaces show strong anti-reflection properties, selection rules still prohibit transmission of many modes, whereas interdiffused interfaces are not subject to such rules and achieve similar thermal interface conductance by transmitting with lower probability but using a wider range of modes.