X-ray study of crystal dynamics: An historical and critical survey of experiment and theory

Abstract

An outline is given of the reciprocal-lattice method of relating x-ray reflections to the density distribution in the crystal. The experimental work of Laval, Preston, Zachariasen, Raman and Nilakantan, Lonsdale and Smith, and others, is described in some detail, and it is shown that a spreading of the reflecting power outside the reciprocal-lattice points is proved. The main features of this extension of reflecting power are (1) that it is markedly dependent upon temperature, (2) that the surfaces of equal reflecting power are not spherical, (3) that the intensity of extra reflection is weak even in the neighbourhood of the reciprocal-lattice points, and falls off rapidly with distance from the lattice points. The simple diffraction theory, the Fax?n-Waller theory and the Raman theory are briefly sketched and related to recent experimental work, and the necessity for distinguishing effects due to dynamic and static disorder of the crystal structure is emphasized. A description is given of the anomalous effects found for diamond, and finally it is shown that only the Fax?n-Waller theory, which explains the spread of reflecting power as due, in the main, to the thermal (elastic) vibrations of the atoms and molecules, can account satisfactorily for the results observed for crystals of all kinds, and especially for single crystals of metals. The limitations of the theory, especially in respect to its assumption of small amplitudes of vibration, are indicted, and possible future developments are outlined.