Analysis of multiple inelastic scattering of electrons incident on crystalline specimens

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, 268-287]. 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 non-crystalline 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.