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X-Ray Powder Diffraction

  1. Abraham Clearfield,
  2. Nattamai Bhuvanesh

Published Online: 15 DEC 2011

DOI: 10.1002/9781119951438.eibc0307

Encyclopedia of Inorganic and Bioinorganic Chemistry

Encyclopedia of Inorganic and Bioinorganic Chemistry

How to Cite

Clearfield, A. and Bhuvanesh, N. 2011. X-Ray Powder Diffraction. Encyclopedia of Inorganic and Bioinorganic Chemistry. .

Author Information

  1. Texas A&M University, College Station, TX, USA

Publication History

  1. Published Online: 15 DEC 2011

Abstract

Crystalline solids may be described as containing a unit of matter that when repeated in three-dimensional space reproduces the crystal. Because of the periodic nature of crystals and the fact that the distances between the atoms, that is, bond distances, are of the same order of magnitude as X-ray wavelengths, the crystals act as diffraction gratings toward X-ray beams. Diffraction from a small single crystal produces a three-dimensional array of spots whose geometry can be related to the geometry of the unit cell and the three noncoplanar vectors that describe the periodic arrangement of the unit cells. Knowledge of the intensities of the diffracted radiation allows the determination of the atoms within the unit cell.

Many compounds occur as polycrystalline solids or powders. Most solids in nature are present as mixtures of two or more crystalline phases. Such materials still diffract X-rays but the three-dimensional array of spots is condensed into a one-dimensional array of diffraction lines or near Gaussian peaks. Because of this low dimensionality much less data are obtained; however, a great deal of information may still be derived from the powder pattern referred to as X-ray powder diffraction (XRPD) for XRPD pattern. In its simplest form the XRPD may be used as a fingerprint to identify a particular phase or mixture of phases. The amount of each phase may be determined quantitatively.

As the crystallite size decreases, the X-ray peaks broaden, so it is possible to obtain a measure of the crystallite size. Lattice strain also contributes to peak broadening, requiring that the two effects be separated for accuracy in interpretation of the data. The advent of high speed computers and highly engineered diffractometers allows for rapid accurate analysis of powder mixtures or the study of solid solutions, defects and other complexities of crystalline material. It is, in many cases, possible to determine the crystal structure of compounds from their X-ray powder data and this aspect of powder diffractometry is included here. Diffraction does not occur from amorphous solids, but X-rays are scattered and much information on particle size and short range order can be obtained from small angle X-ray and neutron scattering studies. Furthermore, EXAFS and Atomic Pair Distribution functions provide a means of probing the structures of amorphous and semicrystalline materials.

Keywords:

  • X-ray diffraction (XRD);
  • powder diffraction pattern;
  • unit cell;
  • Bravais lattice;
  • unit cell indexing procedures;
  • interstitial solid solution;
  • substitutional solid solution;
  • preferred orientation (PO);
  • lattice strain;
  • crystallite size;
  • thermodiffraction;
  • reciprocal space;
  • real space methods;
  • thermal expansion coefficients;
  • x-ray reflections;
  • Bragg angle;
  • profile fitting