Dynamical Theory of Electron Diffraction for a Finite Polyhedral Crystal I. Extension of Bethe's Theory

概要

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Bethe's dynamical theory of election diffraction has been extended by an approximate treatment first to the case of a wedge-shaped crystal, next to the case of a wedge-shaped crystal covered by opaque screens with an aperture and finally to the most general case of a polyhedral crystal of finite extension. If the incident wave, Ф_I=ψ_I exp j(K_<I・r>), impinges on the entrance surface, Se, and the transmitted and diffracted (interfracted) wave leave the erystal from the exit surface, Sa, their wave functions are given as a superposition of plane waves; the transimtted wave : [numerical formula] the diffracted wave : [numerical formula] Here, the amplitude functions, [numerical formula], are as follows; [numerical formula] where c^<(t.)> is the amplitude ratio of the primary and secondary (interfracted) waves in crystal which are related to the i-branch of the dispersion surface, and k_0^<(t)> and k^<(i)>=k_0^<(t)>+2πg are their wave vectors. The function L means the diffraction function due to an aperture S and expressed as [numerical formula] The most general expressions of the transmitted and diffracted waves for a finite polyhedral crystal are given as the sum of the waves mentioned above for every pair of the entrance and exit surface.
社団法人日本物理学会の論文
1952-08-25