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Theory of Small‐Angle X‐Ray Scattering Caused by Incompatibilities in Elastic Anisotropic Media and the Application to Dislocations in H.C.P. Crystals
Author(s) -
Michelitsch Th.
Publication year - 1997
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 - 10.1002/1521-3951(199709)203:1<3::aid-pssb3>3.0.co;2-q
Subject(s) - small angle x ray scattering , isotropy , fourier transform , scattering , ansatz , anisotropy , dislocation , tensor (intrinsic definition) , stress field , symmetry (geometry) , materials science , condensed matter physics , optics , physics , geometry , quantum mechanics , mathematics , finite element method , thermodynamics
So, far, the Small‐Angle X‐Ray Scattering (SAXS) amplitude caused by internal stress sources which are described by an incompatibility field was calculated for isotropic and cubic crystal symmetry by Kröner and Seeger. In this work this problem has been solved for arbitrary crystal symmetry within the framework of the linear anisotropic elasticity theory. Using the unique decomposition of the elastic strain tensor into the deformational and incompatible parts as an ansatz, the SAXS amplitude has been obtained by Fourier transformation of the basic equations of the internal stress theory. The integration problem can be reduced to the Fourier transformation of the incompatibility tensor only. A calculation of the volume dilatation field can be avoided in this way. The calculated SAXS amplitude is applied to dislocation loops in h.c.p. crystals. It is shown which information about these dislocation loops is available by measuring SAXS intensity contours.