A comparison of differential equations that control transmission of strained, non-centrosymmetric crystals by fast electrons

Electron transmission of non-centrosymmetric crystals is treated by matrix notation of the dynamical many-beam theory consistently applied to conventional and modified Bloch waves, correlated plane waves, and column models. Attributed known and supplementary differential equations are shown to be derivable and transformable into each other in a systematic way. Also two integration procedures are generalised. Besides, an explicite expression is derived that describes the physics of scattering of modified Bloch waves in the many-beam case. It is also shown how those Bloch wave transitions forbidden under Bragg orientation at centrosymmetry, arise due to non-centrosymmetry. (author)