CUMULANT EXPANSION ANALYSIS OF THERMAL DISORDER IN FACE-CENTERED-CUBIC COPPER METAL BY MOLECULAR-DYNAMICS SIMULATION

Molecular dynamics, using a previously validated semi-empirical potent ial, are used to explore thermal disorder in face centred cubic copper over the temperature range 100 K to 1100 K. The mean-square displacem ent (MSD) of atoms from their mean positions has been extracted from t he simulation. Results compare favourably with experiment and are cons istent with the predictions of a range of theoretical lattice dynamics models. The temperature dependence of the first four cumulants of eac h probability distribution function (PDF) for the four nearest neighbo ur 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 con sistent 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 (ne glected in the classical molecular dynamics simulation) are most signi ficant. The simulated PDF profiles are reproduced well across the temp erature range by a reconstruction formula employing only the first fou r cumulants. The linear expansivitity calculated from the cumulants is in only modest agreement with experimental data. Analysis of the PDF of a shell in the high r limit is consistent with essentially uncorrel ated isotropic vibration of the atoms, but demonstrates the difficulty of extracting MSD values from extended X-ray absorption fine structur e (EXAFS) spectroscopy and correlating EXAFS and X-ray diffraction the rmal parameters.