Motions of Molecules in Condensed Systems: V. Classification of Motions and Selection Rules for Spectra According to Space Symmetry

TLDR

The paper classifies crystal motions using space symmetry and Born‑Karman boundary conditions, and describes the corresponding space‑group character tables. The authors relate unit‑cell and site analyses, showing that unit‑cell results can be obtained through the simpler site method. They demonstrate that the selection rules for fundamental transitions match those of Bhagavantam and Venkatarayudu, and establish a space‑symmetry criterion predicting composite transitions and their expected effects.

Abstract

A classification of the motions of a crystal is made on the basis of space symmetry, with the aid of the Born-Karman boundary conditions. It is shown that the selection rules for fundamentals arising from this classification are the same as those derived by the unit cell analysis of Bhagavantam and Venkatarayudu. A relation between the unit cell and site analyses is investigated which makes it possible to obtain the unit cell results by means of the usually simpler site method. A space symmetry criterion for the appearance of composite transitions is established, and some of the effects expected on the basis of this criterion are discussed. The character tables for space groups are described.