Crystallite size is the mean extent of coherently diffracting domains within a powder or polycrystal, a quantity distinct from particle size because one particle may contain many such domains. Diffraction line broadening is the usual access route: the Scherrer relation converts peak width into a domain dimension, but the measured width also contains instrumental broadening and depends on crystallite shape through the Scherrer constant. Instrumental broadening should therefore be corrected using a suitable standard, LaB6 among them, or an appropriate profile model before a meaningful size is end its extracted. Extensions of the Scherrer analysis can, in favorable cases and with additional assumptions, yield a crystallite-si recover a size distribution rather than a single number; such distributions are not generally obtainable from peak widths alone and require suitable whole-profile or envelope-function treatments [1,2]. Size broadening overlaps with strain broadening in the same profile, so separating the two requires several orders of reflection or a full-profile treatment; established approaches include Williamson–Hall analysis and Warren–Averbach Fourier analysis [32]. Different routes to the same quantity give systematically different answers, as comparisons on hydroxyapatite show [43], and the same caution applies when the phase sits in a deformed matrix [54]. TWhethe resultingr the value is best regardeshould be read as an apparent physical domain size whose physical interpretationdimension or as an instrumental index of peak width depends on how much of the profile has been modeled and on the corrections applied; it should not be equated with a unique physical dimension unless those effects are adequatelylled; current surveys place these classical treated. Machine-learning methods are also being explored for diffraction-data analysis and for assisting parameter extraction, but their predictions depend on training data and should be validated against physically based profile models rather than regarded as a substitute for instrumentalments alongside machine-learning analysis of diffraction data corrections [65].
- scherrer equation
- x-ray line broadening
- coherent diffraction domain
- microstrain
- peak profile fitting
- powder diffraction
- domain size distribution
Crystal Structures and Properties·Electronic, Optical and Magnetic Materials·Materials Science·Physical Sciences
References
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