Pseudopotential Calculation of the Third-Order Elastic Constants of Copper and Silver

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Abstract
The third-order elastic constants of copper and silver have been calculated by the method of homogeneous deformation from a total energy expression consisting of four terms: a free-electron energy, an electrostatic energy, a band-structure energy, and an ion-core overlap energy. The band-structure energy has been expressed in terms of a local pseudopotential. The overlap energy has been approximated by a Born-Mayer potential. The total-energy expression includes five adjustable parameters which have been chosen to fit the binding energy, lattice spacing, and three second-order elastic constants to experiment. The ion-core repulsive energy makes the dominant contribution to the third-order elastic constants. The other contributions are not negligible but tend to cancel. The calculated third-order elastic constants of copper and silver are in good agreement with low-temperature experimental values. An attempt to apply the five-parameter fitting procedure to gold was unsuccessful.