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Perturbation theory in transmission electron diffraction I. The perturbing matrix is constant and hermitian
Author(s) -
Serneels R.,
Gevers R.
Publication year - 1972
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.2220500112
Subject(s) - hermitian matrix , eigenvalues and eigenvectors , physics , perturbation (astronomy) , perturbation theory (quantum mechanics) , constant (computer programming) , mathematical analysis , matrix (chemical analysis) , amplitude , classical mechanics , quantum mechanics , mathematical physics , mathematics , materials science , computer science , composite material , programming language
Instead of using the usual Schrodinger equation perturbation theory is directly applied to the system of Howie and Whelan. According to the nature of the perturbing dynamical matrix generally three different types of perturbation are distinguished. The perturbing dynamical matrix may be a) constant and hermitian, b) constant but not hermitian, c) not constant but depth dependent. The perturbing dynamical matrix is supposed to be constant and hermitian. Applying perturbation theory series expmsions for the eigenvalues and eigenvectors of the dynamical matrix are derived. Furthermore these series expansions are used to obtain series expansions for the amplitudes and intensities of the different beams. Two practical examples are discussed. First the influence of weak beams is studied by this method. As a particular result the kinematical expression for the amplitude of the weak beam formed by scattering out of N + 1 strong beams is given. Secondly it is suggested that the method can be applied to study the influence of slightly tilting the crystal around an orientation for which the problem was solved.