Molecular Dynamics Calculation of Thermal Conductivity

Vibration of a 256 atom crystal of  face-centered cubic argon at 48K.

The calculated values of the thermal conductivity compared to previous numerical and experimental work.

Abstract

The thermal conducitvity of solid Lennard-Jones argon  is determined by analyzing the decay of the heat current auto-correlation function. Above 35 K there is good agreement with previous numerical work.

Introduction

Heat transfer in non-metallic crystals is realized through phonon transport. The thermal conductivity of a non-metallic crystal is an indication of the resistance phonons experience as they travel in the direction of a temperature gradient. Molecular dynamics simulations present an opportunity to 'observe' phonon transport.

Simulation

The simulations were run in the NVT ensemble using a Lennard- Jones potential and a time step of 2.14 fs. The temperature is controlled with a Nose-Hoover thermostat. The crystal consists of 256 atoms which make up 64 unit cells. Periodic boundary conditions are implemented in all directions. The upper figure shows the equilibrium vibration of the crystal at 48 K.

Data Analysis

The thermal conductivity is measured by integrating the heat-current auto-correlation function. The bottom figure plots the calculated thermal conductivity as a function of temperature along with previous numerical and experimental data. Previous authors have attributed the under-prediction of MDS to the failure of the Lennard Jones potential in the modeling of solid argon. The discrepancy between the current numerical data and previous work at temperatures below 35 K may be due to the ensemble used (NVT as opposed to NPT).

References

H. Kaburaki, J. Li and S. Yip, "Thermal conductivity of solid argon by classical molecular dynamics". Mat. Res. Soc. Symp. Proc. 538, 503 (1998).