Perturbed Molecular Dynamics for Calculating Thermal Conductivity of Zirconia

Abstract

A perturbation method is modified to calculate the thermal conductivity of ionic crystals by molecular dynamics simulation. The energy flux and perturbation tensor are formulated so as to contain only phase space variables and a single convergence parameter. The characteristics of the perturbation method are studied using ZrO₂ as a model ionic crystal. The energy flux due to the perturbation is found to exhibit long time-scale oscillations due to the inclusion of long-range Coulombic interactions. In the linear response regime, the calculated thermal conductivity is independent of the external force field parameter, which is the only arbitrary parameter in the method. However, it is found that the external force field parameter plays an important role in minimizing thermal noise in the energy flux. An exponential relationship between thermal conductivity and the maximum external force field parameter is found, by which one can select an external force field parameter suitable for performing thermal conductivity calculations on different ionic materials without needing to carry out numerous preliminary simulations.

Keywords:

• Molecular dynamics
• Thermal conductivity
• Zirconia
• Perturbation
• Non-equilibrium

Acknowledgements

The authors wish to thank Prof. N. Ohtori and Dr K. Takase at Niigata University, Japan, and Dr B. Bernu at Université Pierre et Marie Curie and CNRS, France, for valuable discussions on heat flux in Coulombic system. Critical reading of the manuscript and useful suggestions by Dr C.A.J. Fisher (JFCC) are also gratefully acknowledged. This work was performed as a part of the Nanostructure Coating Project carried out by the New Energy and Industrial Technology Development Organization, Japan.