The vibration spectra of crystals - Part I. Basic theory
The paper presents the author’s theory of the vibration spectra of crystals from a fresh point of view. It is shown that the nature of the spectra is necessarily different in the two regions of frequency in whioh they represent respectively the characteristic eigenvibrations of the crystal structure and the stationary wave-patterns of elastic vibration. The eigenvibrations repeat themselves in volume elements within the crystal having twice the linear dimensions and eight times the volume of the lattice cells. The number of modes of eigenvibration is (24p-3),p being the number of atoms in each lattice cell. The spectral frequencies which are (24p-3) in number (or less by reason of crystal symmetry) ate accordingly monochromatic. In relation to the entire crystal, they are highly degenerate. The three missing degrees of freedom are exactly accounted for when the possible elastic vibrations which give a quasi-continuous spectrum of frequencies are enumerated. The limiting elastie wave-lengths come out as four times the lattice spacings of the crystal. The effects of anharmonicity are also considered. It is shown that they result in lowering and spreading out the spectral frequencies of the crystal when its temperature is elevated.