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Modelling of diffraction from fibre texture gradients in thin polycrystalline films
Author(s) -
Birkholz M.
Publication year - 2007
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889807027240
Subject(s) - texture (cosmology) , crystallite , tilt (camera) , materials science , intensity (physics) , diffraction , optics , reflection (computer programming) , pole figure , orientation (vector space) , distribution function , symmetry (geometry) , crystallography , condensed matter physics , geometry , physics , mathematics , chemistry , image (mathematics) , quantum mechanics , artificial intelligence , computer science , metallurgy , programming language
Crystallographic textures in thin polycrystalline films typically exhibit a rotational symmetry, i.e. they occur as a fibre texture with the texture pole being orientated in the direction of the substrate normal. As a further characteristic of thin‐film textures, it was often observed that the degree of preferred orientation increases with increasing thickness. It is shown in this work how a fibre texture gradient may be modelled in kinematical X‐ray diffraction and which effects it has on the intensity mapping of the I HKL reflection, when the HKL pole is the fibre axis. A general expression for I HKL is derived for a depth‐dependent fibre texture that is based on the finite Laplace transform of the texture distribution. The concept is outlined for the cos n ψ function to model the tilt‐angle dependence of intensity, with the parameter n denoting the degree of texture. It is found that the measured intensity distribution sensitively depends on the ratio of texture gradient over X‐ray attenuation coefficient. For particular cases, it is found that the maximum intensity may occur for non‐zero tilt angles and thus arise at a different tilt angle from the pole of the fibre texture.