Center Law of the Lattice Vibration Spectra

Abstract

The lattice vibration spectra of a solid, as a whole, can be characterized by one single frequency, defined as the frequency of "the center of gravity" of the infrared spectrum, simply called "center frequency." The data of this frequency have been determined for many nonconducting solids (compounds) from the experimental spectra of lattice vibrations in reflectance as well as in absorption. A striking experimental phenomenon is discovered: The center frequency, whether determined from the reflectance or from the absorption type spectrum, is found to be equivalent and identical with Debye's characteristic frequency. This phenomenon is exhibited for a large variety of nonconducting compounds covering almost the entire range of the vibrational spectra of solids. Moreover, the center frequency remains constant with varying temperature. The equality of the center frequency of the infrared spectrum and the characteristic frequency from specific heat constitutes the "center law of the lattice vibration spectra."