The effect of a long range oscillatory interaction on the stability of alloys

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Abstract
If a long range oscillatory interaction having an asymptotic form proportional to cos(2kFr+ phi )/(2kFr)3 is assumed to hold for electron phases in alloys then there occur infinite singularities in the long range contributions to the second order elastic constants at certain critical values of the valence. The problem is analysed by the method of homogeneous deformation and results are given for body centred and face centred cubic alloys. A value of phi fairly near pi /2 seems to be a prerequisite for the existence of fcc phases, based on noble metals, with orderly elastic behaviour yet well defined phase boundaries at an effective valence near 1.36.