Anharmonicity in Noble Metals: Some Thermal Properties

The room-temperature Grüneisen parameters of copper, silver, and gold have been calculated within the quasiharmonic approximation, using the anisotropic-continuum model and values of the third-order elastic constants recently determined. The agreement between the calculated and the experimental values is good for copper and silver, but only fair (12%) for gold. Expressions for the temperature dependences of the three second-order elastic constants have been derived using the continuum model. These depend upon the second-, third-, and fourth-order elastic constants. The fourth-order elastic constants of copper, silver, and gold have been computed using these expressions, and it was found that they are positive in sign and of the order of ${10}^{14}$ dyn/${\mathrm{cm}}^2$ in magnitude. Only the closed-shell repulsive interaction between nearest-neighbor ions was taken into account in computing the fourth-order constants. Previous work has indicated that this might be a good approximation for noble metals. The two parameters in the Born-Mayer potential expressing the repulsive interaction were evaluated, and reasonable values were obtained for copper and silver. Anomalous results for gold indicate that contributions to the higher order elastic constants from other than ion-core repulsion cannot be ignored in that metal.