Debye-Waller factors for incommensurate structures

Abstract

Overhauser has predicted that thermal fluctuations in the phase of the modulation wave will give rise to large $Q$-independent Debye-Waller factors for incommensurate diffraction satellites. We show that a key to understanding this surprising result is a spatial modulation of the fluctuation of atomic positions in an incommensurate solid. The range of validity of Overhauser's assumptions is discussed and an alternate calculation which should be valid over a larger range of relative fluctuation amplitude is presented. This new calculation predicts the existence of fluctuation- and displacement-dominated regimes, in which higher-order diffraction satellites display qualitatively different behavior.