Morse-Potential Evaluation of Second- and Third-Order Elastic Constants of Some Cubic Metals

The second- and third-order elastic constants of Al, Cu, Ag, Au, Na, and K have been calculated in the framework of a central-force model. The interatomic potential was expressed in terms of the Morse potential. The parameters in the potential were determined by using the lattice parameter, bulk modulus, and cohesive energy. The range of the interatomic potential was cut off after 176 and 168 neighbors in the case of face-centered and body-centered cubic metals, respectively. The evaluated second- and third-order elastic constants were used to calculate the pressure derivatives of the second-order elastic constants. These pressure derivatives compare fairly well with the experimental values. The agreement between experimental values and theoretical values of third-order elastic constants is less satisfactory. Theory predicts ${\mathrm{C}}_{123}$ to be positive for all the fcc metals and negative for bcc metals. The available experimental data on the third-order elastic constants of Cu, Ag, and Au show that ${\mathrm{C}}_{123}$ is positive for Ag and negative for Cu and Au. The possible implications of this result are discussed.