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 meand its esured 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 extracted. Extensions recover a si of the Scherrer analysis can, in favorable cases and with additional assumptions, yield a crystallite-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 [23]. Different routes to the same quantity give systematically different answers, as comparisons on hydroxyapatite show [34], and the same caution applies when the phase sits in a deformed matrix [45]. WThether the resulting value should be reais best regarded as a physicaln apparent domain dimension or as an instrumental index of peak width dsize whose physical interpretation depends on how much of the profile has been modelled; current surveys place these classicalled and on the corrections applied; it should not be equated with a unique physical dimension unless those effects are adequately treatments alongside machine-learning analysis of diffractioned. 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 instrumental corrections data [56].
- scherrer equation
- x-ray line broadening
- coherent diffraction domain
- microstrain
- peak profile fitting
- powder diffraction
- domain size distribution
References
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- Ferguson, I.F. Crystallite size, strain and shape determinations on thoria from X-ray line broadening studies. PhiGesing, T. M.; Robben, L. Determination of the average crystallite size and the crystallite size distribution: the envelope function approach EnvACS. Journal osophical Magazine 1965, 12, 1115-1122. [CrossRef]f Applied Crystallography 2024, 57, 1466-1476. [CrossRef]
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