Abstract
In an earlier communication by Foldy and Witten, indications were given that "mirror" pairs of alkali halide crystals in which the positive and negative ions of one are replaced, respectively, in the other by the negative and positive ions having the identical isoelectronic structure and nearly the same mass (NaCl-KF, NaBr-RbF, NaI-CsF, and KBr-RbCl) showed very similar crystal phonon properties. The present paper explores the degree to which a more general mirror-symmetry principle, namely that the ion-dynamic properties of mirror alkali halides in both the crystal and melt state are very similar, can be verified by available data. For the crystalline state of the mirror pairs, the dispersion curves along certain symmetry directions and the data available over an extended range of temperatures on specific heats are directly compared, and the infrared reflection data on the RbCl and KBr pair are compared with each other and with that for the pair RbBr and KCl. In addition more than a score of other properties, ion-dynamic and electronic, are analyzed for symmetry by a number of methods specifically developed to give an objective but quantitative measure of this symmetry. The conclusion reached is that indeed ion-dynamic properties of both crystal and melt forms of the alkali halides show quite a high degree of mirror symmetry which is broken in part by the mass differences of homologous ions and in part by the interposition of electronic excitation effects (which do not show this symmetry) into some of the ion-dynamic properties at the higher frequencies. The results also lend credence to the extended symmetry hypothesis proposed by Foldy and Witten to explain certain phonon near degeneracies found in the isobaric crystals but not predicted by the space-group symmetry of these crystals. If mirror symmetry is established it implies near equalities of various other properties of mirror pairs, e.g., viscosity, heat conductivity, thermal diffusivity, self-diffusion coefficients, and x-ray diffraction patterns of melts all as functions of temperature, and corresponding applicable properties of crystals.
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