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X-ray Crystallography02:18

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The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
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X-ray diffraction or XRD is an analytical tool that utilizes X-rays to study ordered structures such as crystalline organic and inorganic samples, polycrystalline materials, proteins, carbohydrates, and drugs.
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Use of Bayesian Inference in Crystallographic Structure Refinement via Full Diffraction Profile Analysis.

Chris M Fancher1, Zhen Han2, Igor Levin3

  • 1Department of Materials Science and Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA.

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|August 24, 2016
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Summary

This study introduces a Bayesian inference method for refining crystallographic structures, offering improved uncertainty quantification compared to traditional Rietveld refinement.

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Area of Science:

  • Crystallography
  • Statistical Modeling
  • Materials Science

Background:

  • Crystallographic structure refinement is crucial for materials characterization.
  • Accurate uncertainty estimation in structural parameters is often challenging.
  • Existing methods like Rietveld refinement may not fully capture error structures.

Purpose of the Study:

  • To present a novel Bayesian inference method for crystallographic structure refinement.
  • To improve the quantification of uncertainty in model parameters.
  • To compare the performance of the Bayesian method against Rietveld refinement.

Main Methods:

  • Stochastic sampling of model parameters using Markov chain Monte Carlo (MCMC).
  • Construction of posterior probability distributions for all model parameters.
  • Modeling of heteroskedasticity and correlation in the error structure.
  • Application to a silicon standard reference material from NIST.

Main Results:

  • Bayesian inference provides estimates and uncertainties for model parameters.
  • The method successfully quantifies uncertainty by modeling error structures.
  • Demonstrated improved estimation of true model uncertainties compared to Rietveld refinement.

Conclusions:

  • Bayesian inference offers a robust approach for crystallographic structure refinement.
  • The proposed method enhances the reliability of uncertainty estimates.
  • This technique provides a more accurate assessment of structural model uncertainties.