Abstract
Abstract As a crystal gets smaller, diffraction spots stay visible for larger deviations from the Bragg condition. The upper limit of such deviations is connected to the threshold for getting lattice fringes in TEM images. This in turn allows one to quantify the probability of seeing cross lattice fringes along a certain zone axis. In this abstract we examine a simple semi-empirical model for the probability of detecting (001) zone cross-fringes of a spherical crystal of cubic lattice. The upper limit for the deviation of crystal orientation from the exact Bragg condition, without losing cross fringes down a given zone, is expressed as the maximum half-angle θ1 between the zone and the electron beam. The solid angle σ subtended by a cone with this half-angle is proportional to the probability px that a randomly-oriented crystal will show the cross-fringes associated with that zone. A schematic, illustrating the principle used to calculate the probability of seeing cross-fringes, is given in Figure 1.
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