A semi-analytical method to compute acoustic nonlinearity parameter of Cu, Ag and Au

Abstract

In this paper, a semi-analytical method was proposed to evaluate the acoustic nonlinearity parameter for single crystals of Cu, Ag and Au. The acoustic nonlinearity parameter can be derived analytically by general expressions in terms of the interatomic potentials with the distances between each pair of atoms in these transition metals. To evaluate the acoustic nonlinearity parameter, one needs to conduct one step molecular static simulation and obtain the equilibrium positions of all the atoms. Further, based on this method, numerical experiments with molecular dynamic code LAMMPS were given to compute the acoustic nonlinearity parameter of Cu, Ag and Au. To illustrate the validity of these expressions, comparison was made between calculation results and data in the literature. Reasonable agreement is observed. Because of the analytical nature of this method, it provides a fundamental understanding of the nonlinear elastic behavior of these transition metals. The second elastic constant and the third elastic constant can be computed with the proposed semi-analytical method. A reasonable agreement is found between the numerical calculations and the reported elastic constants for Cu, Ag and Au. The deviations might be due to the accuracy of the experimental processes and the microstructure factors like the grain structure, purity of the sample or the presence of impurities.