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Bayesian Approaches to Uncertainty Quantification and Structure Refinement from X-Ray Diffraction

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Materials Discovery and Design

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 280))

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Abstract

This chapter introduces classical frequentist and Bayesian inference applied to analyzing diffraction profiles, and the methods are compared and contrasted. The methods are applied to both the modelling of single diffraction profiles and the full profile refinement of crystallographic structures. In the Bayesian method, Markov chain Monte Carlo algorithms are used to sample the distribution of model parameters, allowing for the construction of posterior probability distributions, which provide both parameter estimates and quantifiable uncertainties. We present the application of this method to single peak fitting in lead zirconate titanate, and the crystal structure refinement of a National Institute of Standards and Technology silicon standard reference material.

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Acknowledgements

The authors acknowledge the support from the National Science Foundation under awards DMR-1409399 and DGE-1633587.

Author information

Authors and Affiliations

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

    Alisa R. Paterson & Jacob L. Jones

  2. Department of Statistics, North Carolina State University, Raleigh, NC, 27695, USA

    Brian J. Reich & Alyson G. Wilson

  3. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    Ralph C. Smith

Authors
  1. Alisa R. Paterson
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  2. Brian J. Reich
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  3. Ralph C. Smith
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  4. Alyson G. Wilson
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  5. Jacob L. Jones
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Corresponding author

Correspondence to Jacob L. Jones .

Editor information

Editors and Affiliations

  1. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA

    Turab Lookman

  2. Los Alamos National Laboratory, Los Alamos, NM, USA

    Stephan Eidenbenz

  3. Brookhaven National Laboratory, Brookhaven, NY, USA

    Frank Alexander

  4. Los Alamos National Laboratory, Los Alamos, NM, USA

    Cris Barnes

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Paterson, A.R., Reich, B.J., Smith, R.C., Wilson, A.G., Jones, J.L. (2018). Bayesian Approaches to Uncertainty Quantification and Structure Refinement from X-Ray Diffraction. In: Lookman, T., Eidenbenz, S., Alexander, F., Barnes, C. (eds) Materials Discovery and Design. Springer Series in Materials Science, vol 280. Springer, Cham. https://doi.org/10.1007/978-3-319-99465-9_4

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