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A theory of inelastic scattering of fast electrons by thin crystals is developed. The inelastic scattering exciting plasma oscillation, exciting or quenching thermal vibration, or causing band transition is an object of application of the theory. Results of the theory are applied to interpretations of subsidiary maxima of Kikuchi pattern (R. Uyeda, Y. Fukano and T. Ichinokawa: Acta Cryst. 7 (1954) 217) and extinction fringes of electron micrograph produced by inelastically scattered electrons (Y. Kamiya and R. Uyeda: J. Phys. Soc. Japan 16 (1961) 1361, 17 (1962) Suppl. B-II, 191).
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Fujimoto et al. (1963) studied this question.
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