Analysis of multiple inelastic scattering of electrons incident on crystalline specimens

Abstract

An approximate expression is given for describing Bloch-wave amplitudes of electrons which undergo multiple inelastic scattering in crystalline specimens. The expression is derived from differential equations of inelastic scattering given by Howie [Proc. R. Soc. London Ser. A (1963), 271, 268-2871 In the course of the derivation, the differential equations are reduced to a transport equation which has been applied to the analysis of multiple inelastic scattering in noncrystalline specimens. The identity between them is discussed, including the approximations employed. The expression was used to analyze Bloch-wave amplitudes of transmitted electrons at various thicknesses of copper and silicon crystals. It was found that the values of the amplitudes were sensitive to the shape of the interaction potential resulting from the excitation of core electrons. An accurate estimate of the potential will be required in future studies.

Phase dependence of Kikuchi patterns. I. Theory

“…Many of the earlier O 1989 International Union of Crystallography papers discussed two-beam theory (e.g. Kainuma, 1955;Fukuhara, 1963;Fujimoto & Kainuma, 1963;Ishida, 1970Ishida, , 1971Okamoto, Ichinokawa & Ohtsuki, 1971;Chukhovskii, Alexanjan & Pinsker, 1973), this giving way to more general single scattering theories (Gj0nnes, 1966;Gj0nnes & H0ier, 1971;Rez, Humphreys & Whelan, 1977;Rossouw, 1985;Rossouw & Bursill, 1985) and analysis of the relationship between single and multiple diffuse scattering (H0ier, 1973;Yamamoto, 1980). In two recent papers Taft0 (1983Taft0 ( , 1987 has revived interest in two-beam theory by showing that structural and even phase information is retained in two-beam inelastic scattering.…”