The contrast, breadths and relative intensities of electron diffraction rings

Abstract

A theoretical expression for the contrast of transmission electron diffraction patterns is developed, assuming kinematical conditions. The effects of the accelerating voltage, the specimen thickness, crystallite size and amorphous content are discussed. Experimental measurements of the contrast of diffraction patterns obtained with iron specimens are compared with the theoretical predictions. Theory and experiment show that the highest contrast is obtained in single scattering conditions and that the contrast is then independent of specimen thickness and accelerating voltage. In plural scattering conditions the contrast rapidly diminishes with increasing thickness and decreasing voltage. However, the reduced contrast remains constant if the ratio of the specimen thickness over the electron mean free path is kept constant. The experimental variation of the contrast with this ratio agrees with that predicted, and has the same form for all rings. Results obtained with other materials by previous workers are shown to agree with the present theory and results. The effect of plural electron scattering on ring breadths and intensities has been measured. It is shown that broadening is caused by very small angle scattering of diffracted electrons, and that true estimates of crystallite size can be made only in single scattering conditions. The relative ring intensities are, however, unaffected even when the proportion of scattered electrons within the ring profiles is large. The effect of accelerating voltage on the extent of dynamical diffraction conditions is compared with that predicted by Blackman (1939). The experiments indicate that dynamical conditions arise with crystallites six times smaller than those predicted by Blackman.