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Inferring planar disorder in close-packed structures via ε-machine spectral reconstruction theory: examples from
D P Varn1, G S Canright, J P Crutchfield
1Complexity Sciences Center and Physics Department, University of California, Davis, One Shields Avenue, Davis, California 95616, USA. dpv@complexmatter.org
The ε-machine spectral reconstruction theory (εMSR) successfully analyzes X-ray diffraction patterns to reveal stacking structures in close-packed crystals. This method accurately models both ordered and disordered materials, providing insights into crystal defects.
Area of Science:
- Materials Science
- Crystallography
- Data Analysis
Background:
- X-ray diffraction is crucial for analyzing crystal structures.
- Planar-faulted, close-packed structures present challenges in pattern analysis.
- Previous work introduced the ε-machine spectral reconstruction theory (εMSR) for pattern inference.
Purpose of the Study:
- To apply the εMSR algorithm to simulated diffraction patterns from close-packed crystals.
- To evaluate εMSR's effectiveness in reconstructing stacking structures with varying degrees of disorder.
- To define and discuss length parameters for characterizing long-range order in layered materials.
Main Methods:
- Application of the εMSR algorithm to simulated X-ray diffraction data.
- Analysis of reconstructed stacking structures and their statistical properties.
- Definition and calculation of length parameters from the ε-machine model.
Main Results:
- εMSR accurately reproduces stacking structure statistics for memory lengths up to three.
- For longer memory lengths, εMSR generates models capturing key features like multiple faults and crystal structures.
- The algorithm successfully identifies stacking structure even in highly disordered crystals.
Conclusions:
- εMSR is a powerful tool for inferring and modeling stacking structures from diffraction data.
- The method demonstrates robustness across a range of crystal disorder.
- Defined length parameters offer a means to quantify long-range order in layered materials.
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