Premium
The Critical Voltage Effect in Transmission Electron Microscopy. I. Eigenvalue Degeneracy in the Three‐Beam Case
Author(s) -
Gevers R.,
Serneels R.,
David M.
Publication year - 1974
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220660209
Subject(s) - degeneracy (biology) , reflection (computer programming) , eigenvalues and eigenvectors , physics , beam (structure) , intensity (physics) , absorption (acoustics) , diffraction , optics , quantum mechanics , bioinformatics , computer science , biology , programming language
Given an orientation where only one reflection h is nearly in exact Bragg condition, the others being far from the Ewald sphere, the various physical processes are discussed which may lead to an anomalously low intensity of the reflection h . It is found that exact eigenvalue degeneracy is neither a sufficient nor a necessary condition for an anomalous intensity reduction. Absorption effects being neglected, a general three beam case 0, h , g is discussed. It is shown that a reflection being far from the Ewald sphere may induce a weak intensity for a reflection ft close to the Ewald sphere. The necessary conditions are discussed. The usual linear second order critical voltage effect follows as a particular case. Then it is shown that for the linear three beam case, absorption effects taken into account, particular diffraction conditions exist, i.e. voltage and orientation conditions, for which two complex eigenvalues are equal.