Many-body forces in metals and the Brugger elastic constants

The method of homogeneous deformations is used to derive expressions for the first-, second- and higher-order elastic constants of a crystalline solid in which the energy density can be separated into contributions from many-body interactions of different order. Volume-dependent terms in the energy density such as those due to the conduction electrons in a metal are also considered. Emphasis is laid on casting all results into a form which is manifestly rotationally invariant and on treating the structure-dependent and structure-independent terms on the same footing. A comparison is made between the results obtained using Lagrangian and infinitesimal strain with particular reference to the symmetry properties of the elastic constants. A new and general condition for the Cauchy relation to hold is obtained.

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