Anharmonicity and symmetry in crystals

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Abstract
A number of investigators have observed anharmonic (i.e. non-linear) behaviour in stress-strain curves of metallic whiskers: For f.c.c. metals, in general, the non-linearities are ordered according to l″100 > 0 > l″111 > l″110, where l″ is the second derivative of stress with respect to strain and the subscripts indicate the axial, crystallographic direction of loading. (It is of particular interest to note that the stress-strain curve is concave upward in [100] loading.) In the present work, this behaviour is explained in terms of the influence of crystal symmetries occurring on the primary loading paths (specifically, in terms of the existence of multiple zeros—or unstressed states—and bifurcations or branchings among paths of different symmetry). Theoretical computations for lattice models of Ni and Cu in [100], [110] and [111] loading are presented as examples. The agreement between the results of theory and experiment is excellent. It is suggested that such symmetry considerations may be valuable in the study of other anharmonic phenomena.