Cumulant expansion analysis of thermal disorder in face centred cubic copper metal by molecular dynamics simulation

Molecular dynamics, using a previously validated semi-empirical potential, are used to explore thermal disorder in face centred cubic copper over the temperature range 100 K to 1100 K. The mean-square displacement (MSD) of atoms from their mean positions has been extracted from the simulation. Results compare favourably with experiment and are consistent with the predictions of a range of theoretical lattice dynamics models. The temperature dependence of the first four cumulants of each probability distribution function (PDF) for the four nearest neighbour shells is compared with the predictions of a simple one-dimensional anharmonic oscillator model. With the exception of the third cumulant for the second shell, the behaviour of the simulated cumulants is consistent with this model. Where direct comparison of the simulation and experimentally derived cumulants is possible the two are found to be in good agreement except at low temperatures where quantum effects (neglected in the classical molecular dynam...