Lattice Fringe Visibility after Tilt

Abstract

Abstract Factors that affect the visibility of lattice fringes include crystal orientation and thickness, as well as instrument response. As a crystal gets smaller, lattice fringes stay visible for larger deviations from the Bragg condition. Hence the persistence of fringes under tilt affects the abundance and range of lattice spacings (and angles) that one sees in an image of randomly-oriented crystals. A subset of the fringes in an image are “still-visible” after large (e.g. 35°) single or double axis tilts. If one is looking for “new-fringes” from the same crystal (e.g. to analyze it's 3D lattice parameters), rules for recognizing redundant fringes might also help out. Here we examine a semi-empirical model for predicting the visibility of lattice fringes after tilt, by connecting the visibility to intersection of the corresponding crystal reciprocal-lattice spot with the illuminating Ewald sphere.