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The Validity of the Column Approximation in Image Contrast Calculations of Crystals Containing Stacking Faults
Author(s) -
Jap B. K.,
Sheinin S. S.
Publication year - 1981
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.2221050115
Subject(s) - stacking , column (typography) , stacking fault , cathode ray , contrast (vision) , boundary value problem , fault (geology) , diffraction , mathematical analysis , electron , mathematics , materials science , optics , physics , computational physics , geometry , quantum mechanics , geology , nuclear magnetic resonance , connection (principal bundle) , seismology
The validity of the column approximation is assessed for image contrast calculations of stacking faults in plate shaped crystals. The basic approach is based on application of the appropriate boundary conditions at the fault to determine the exact wave functions describing the electrons both above and below the fault and does not involve the differential equation approach used in non‐column approximation calculations in the past. In order to assess the validity of the column approximation, a validity assessment parameter, based on the two‐beam theory, is defined. The results obtained show that the validity domain of the column approximation, for a particular stacking fault inclination, decreases with increasing deviation from the Bragg condition, and increases with increasing electron energy. Direct comparison of many‐beam profiles in the noncolumn and column cases show that significant differences in profile shape can be obtained for weak beam diffraction conditions even when the stacking fault inclination is less than 45°.