Anharmonicity in Noble Metals; Higher Order Elastic Constants

Abstract

The third-order elastic constants of copper, silver, and gold have been measured at room temperature using high-purity single crystals. A sensitive ultrasonic interference method was employed to measure small changes of wave velocities in crystals deformed both uniaxially and hydrostatically at low stress levels. The results of the measurements were analyzed using finite elasticity theory to obtain the complete sets of six third-order constants. The values of $C_{111}$ are largest (of the order of ${10}^{13}$ dyn/${\mathrm{cm}}^2$), $C_{112}$ and $C_{166}$ are about half of $C_{111}$ in magnitude, and all are negative in sign. Almost all of the values of $C_{123}$, $C_{144}$, and $C_{456}$ are negative and small compared with the other constants. It is shown that the closed-shell repulsive interaction between nearest-neighbor atoms makes the dominant contribution to the higher order elastic constants in noble metals. In this sense, the anharmonic properties are simpler than the harmonic properties of these materials. The fourth-order elastic constants are also estimated on this basis.