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Powder diffraction

Nature Reviews Methods Primers volume 1, Article number: 77 (2021) Cite this article

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An Author Correction to this article was published on 25 November 2021

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Abstract

Powder diffraction is a non-destructive technique, which is experimentally simple in principle. Because the physics behind diffraction is well understood, an exceptionally large amount of information can be obtained from a single measurement. The positions and relative intensities of the peaks yield a fingerprint that can be used for qualitative phase analysis. Quantitative phase analysis can be obtained by detailed analysis of the intensities. Unit cells can be derived from the peak positions. Crystal structures can be solved using powder diffraction data and refined by the Rietveld method. The peak profiles contain information about crystallite size, strain and nanostructure. Non-idealities in the intensities give information on texture. Abandoning the crystallographic model provides information about local structure, by pair distribution function analysis. For powder diffraction, everything is a sample; the technique is commonly applied to characterize minerals, ceramics, metals and alloys, catalysts, polymers, pharmaceuticals, organic compounds, environmental and forensic samples, among others. The major features of contemporary laboratory powder diffractometers are described. Methods for obtaining suitable powder specimens are summarized. Major applications of qualitative and quantitative phase analysis, structure solution, size/strain/nanostructure analysis using peak profiles, texture analysis and pair distribution function analysis are introduced.

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Fig. 1: Diffraction principles.
Fig. 2: Schematic of the information content of a powder pattern.
Fig. 3: Diffractometer geometries.
Fig. 4: Specimen preparation.
Fig. 5: 2D powder diffraction patterns.
Fig. 6: Red flagstone and Nature’s Bounty B-Complex phase analysis.
Fig. 7: Relationship between electron density and diffraction pattern.
Fig. 8: Total scattering analysis.
Fig. 9: Representative case studies of application of powder X-ray diffraction in characterization of pharmaceutical materials, with indomethacin as the model drug.
Fig. 10: International Union of Crystallography Commission on Powder Diffraction Reynolds Cup round robin example results.

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Acknowledgements

S.J.L.B.’s research is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences (DOE-BES) under contract no. DE-SC0012704.

Author information

Authors and Affiliations

  1. Department of Physics, North Central College, Naperville, IL, USA

    James A. Kaduk

  2. Department of Chemistry, Illinois Institute of Technology, Chicago, IL, USA

    James A. Kaduk

  3. Deprtment of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA

    Simon J. L. Billinge

  4. Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, USA

    Simon J. L. Billinge

  5. Max Planck Institute for Solid State Research, Stuttgart, Germany

    Robert E. Dinnebier

  6. Bruker AXS Inc., Madison, WI, USA

    Nathan Henderson

  7. CSIRO Mineral Resources, Clayton South, Victoria, Australia

    Ian Madsen

  8. Laboratory of Crystallography, University of Geneva, Geneva, Switzerland

    Radovan Černý

  9. Department of Civil, Environmental, and Mechanical Engineering, University of Trento, Trento, Italy

    Matteo Leoni

  10. Saudi Aramco R&D Center, Dhahran, Saudi Arabia

    Matteo Leoni

  11. Department of Industrial Engineering, University of Trento, Trento, Italy

    Luca Lutterotti

  12. Department of Pharmaceutical Sciences & Research, University of Minnesota, Minneapolis, MN, USA

    Seema Thakral

  13. Université de Caen Normandie, CRISMAT-ENSICAEN, IUT Caen, Caen, France

    Daniel Chateigner

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Contributions

Introduction (S.J.L.B. and R.E.D.); Experimentation (N.H.); Results (I.M., J.A.K., R.Č., M.L., L.L. and D.C.); Applications (S.J.L.B., S.T. and J.A.K.); Reproducibility and data deposition (J.A.K. and N.H.); Limitations and optimizations (J.A.K.); Outlook (J.A.K.); Overview of the Primer (J.A.K.).

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Correspondence to James A. Kaduk.

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Nature Reviews Methods Primers thanks C. Malliakas and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Related links

Advanced Photon Source: https://11bm.xray.aps.anl.gov/absorb/absorb.php

Cambridge Crystallographic Data Centre: www.ccdc.cam.ac.uk

checkCIF: https://checkcif.iucr.org

CIF deposition and validation service: https://ccdc.cam.ac.uk/deposit

Combined Analysis: http://www.ecole.ensicaen.fr/~chateign/formation/

Crystallographica Search-Match: https://crystallographica-search-match.software.informer.com/3.1/

Inorganic Crystal Structure Database (ICSD): https://icsd.products.fiz-karlsruhe.de

International Centre for Diffraction Data: https://icdd.com

JADE Pro: https://www.jadeworld.com/jade-platform/developer-centre/download-jade

Match!: https://www.crystalimpact.com/match/

Pauling File: https://paulingfile.com

Pearson’s Crystal Data: https://crystalimpact.com/pcd

Powder Diffraction File: https://icdd.com/pdfsearch/

Reynolds Cup: https://www.clays.org/reynolds/

Siroquant: https://www.siroquant.com/

Glossary

Unit cell

The unit cell is the parallelepiped built on the vectors, a, b and c, of a crystallographic basis of the direct lattice. Its volume is given by the scalar triple product, V = (a, b, c), and corresponds to the square root of the determinant of the metric tensor.

Short-range atomic order

The regular and predictable arrangement of atoms over a short distance, usually with one or two atom spacings. However, this regularity does not persist over a long distance, and is aperiodic. Examples of materials with short-range order include amorphous materials such as wax, glass and liquids

Pair distribution function

A representation of the probability of finding two atoms in a material separated by some distance r. It is often present with respect to the probabilities in a random distribution of atoms, so some probabilities are positive and others are negative.

Long-range order

The property of crystal structures in which atoms are arranged with translational periodicity over extents of at least three unit cells. This is the property that gives rise to Bragg peaks.

Diffraction angle

The angle between the incident and diffracted X-ray beams

Goniometer

An instrument for the accurate and precise measurement of angles. A goniometer is the heart of a powder diffractometer, capable of measuring angles to 0.001–0.0001°.

Collimators

Devices that narrow and/or shape a beam of X-rays. In a powder diffractometer, they can take the form of a slit, tube or set of parallel plates.

Fluorescent X-rays

Secondary X-rays emitted when an atom is bombarded by high-energy X-rays that knock an electron from a core orbital. The fluorescent X-rays are emitted when an electron in a higher-energy orbital fills the hole.

Preferred orientation

Preferred orientation arises when there is a stronger tendency for the crystallites in a powder or a texture to be oriented more in one way, or one set of ways, than all others.

Rietveld refinement

A method of analysing powder diffraction data in which the crystal structure is refined by fitting the entire profile of the diffraction pattern to a calculated profile using a least-squares approach. There is no intermediate step of extracting structure factors, and so patterns containing many overlapping Bragg peaks can be analysed.

Chebyshev background function

A background function using Chebyshev polynomials Tn(x), often shifted Chebyshev polynomials of the first kind. The polynomials are defined by recursion relations: T0(x) = 1, T1(x) = x, T2(x) = 2x2 – 1, and Tn + 1(x) = 2xTn(x) – Tn - 1(x). The value of x is often not 2θ but some value within the range of the diffraction pattern, such as {[2(2θ – 2θmin)] / (2θmax – 2θmin)} – 1.

Hanawalt search

A search/match phase identification method that uses the three strongest, most intense peaks for the search phase and the eight strongest peaks for the match phase.

Multiple pattern technique

The process of measuring multiple powder patterns from a specimen as a function of a variable such as temperature or degree of orientation, with the objective of obtaining a more accurate set of observed structure factor amplitudes Fhkl than could be obtained from a single pattern.

Anisotropic broadening

Broadening of diffraction peaks, which varies as a function of the direction in the crystal lattice corresponding to the peaks.

Polymorphs

Two or more different crystal structures of a single chemical substance. In the pharmaceutical world, the term is often incorrectly extended to include hydrates and solvates, which should instead be called pseudopolymorphs.

Co-crystals

Solids that are crystalline single-phase materials composed of two or more different molecular or ionic compounds, generally in a stoichiometric ratio, which are neither solvates nor simple salts.

Density functional theory

An approach to quantum mechanical calculations, especially in the solid state, in which the properties of many-electron systems are described by functionals, which are functions of another function. In density functional theory methods, the functions model the electron density.

Electron crystallography

Crystallography carried out using electrons rather than X-rays or neutrons as the probe. Generally performed in a transmission electron microscope.

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Kaduk, J.A., Billinge, S.J.L., Dinnebier, R.E. et al. Powder diffraction. Nat Rev Methods Primers 1, 77 (2021). https://doi.org/10.1038/s43586-021-00074-7

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