Normal Frequencies of a Simple Cubic Lattice. III

Abstract

For a simple cubic crystal, with forces resisting displacement along and perpendicular to the connecting line between closest neighbors, the secular equation for the internal motions is rigorously broken down to ultimate factors of the formν2=νx2+α(νy2+νz2),in which νx, etc., are the normal frequencies of the one‐dimensional crystal.The corresponding frequency distribution shows no indication of the ``infinities'' found by Montroll for a model with central forces between first and second neighbors.