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Published on: August 25, 2016
X-ray diffraction in perfect t x l crystals. Rocking curves
1Department of Mathematics and Natural Science, Stavanger College, Ullandhaug, 4091 Stavanger, Norway. gunnar.thorkildsen@tn.his.no
Summary
This study presents a formalism for calculating rocking curves in finite crystals, considering factors like refraction and absorption. Results show crystal finiteness significantly impacts rocking curves, especially when dynamical effects are prominent.
Area of Science:
- Solid State Physics
- Crystallography
- X-ray Diffraction
Background:
- Rocking curve analysis is crucial for characterizing crystal properties.
- Existing theories often assume semi-infinite crystals, neglecting finite-size effects.
Purpose of the Study:
- To develop a general formalism for calculating rocking curves in perfect finite crystals.
- To investigate the influence of crystal finiteness on rocking curve asymmetry and width.
Main Methods:
- Utilized the Takagi-Taupin equations as the theoretical basis.
- Incorporated nonsymmetrical scattering, refraction, and anomalous absorption.
- Independently varied crystal thickness (t) and length (l).
Main Results:
- The formalism reproduces standard results for semi-infinite crystals and converges to the kinematical limit for thin crystals.
- Simulations for germanium and silicon demonstrate significant effects of finite crystal dimensions.
- Dynamical effects lead to asymmetric curves with a larger full width at half-maximum than the Darwin width due to combined Laue and Bragg contributions influenced by refraction.
Conclusions:
- Crystal finiteness is a critical factor influencing rocking curve profiles.
- The developed formalism provides a comprehensive approach to analyzing diffraction in finite crystals.
- Refraction plays a key role in the observed asymmetries and broadening in finite crystals.
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