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Crystallite Size: History
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Contributor: Jack Zhong

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 extracted. Extensions 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 [3]. Different routes to the same quantity give systematically different answers, as comparisons on hydroxyapatite show [4], and the same caution applies when the phase sits in a deformed matrix [5]. The resulting value is best regarded as an apparent domain size whose physical interpretation 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 adequately 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 instrumental corrections [6].

  • scherrer equation
  • x-ray line broadening
  • coherent diffraction domain
  • microstrain
  • peak profile fitting
  • powder diffraction
  • domain size distribution

References

  1. Bienenstock, A.; Determination of Crystallite Size Distributions from X-Ray Line Broadening. Journal of Applied Physics 1961, 32, 187-189, 10.1063/1.1735975.
  2. Gesing, T. M.; Robben, L.; Determination of the average crystallite size and the crystallite size distribution: the envelope function approach EnvACS. Journal of Applied Crystallography 2024, 57, 1466-1476, 10.1107/S1600576724007362.
  3. Ferguson, I.F.; Crystallite size, strain and shape determinations on thoria from X-ray line broadening studies. Philosophical Magazine 1965, 12, 1115-1122, 10.1080/14786436508228664.
  4. Rabiei, M.; Palevicius, A.; Monshi, A.; Nasiri, S.; Vilkauskas, A.; Janusas, G.; Comparing Methods for Calculating Nano Crystal Size of Natural Hydroxyapatite Using X-Ray Diffraction. Nanomaterials 2020, 10, 1627, 10.3390/nano10091627.
  5. Feijoo, I.; Cabeza, M.; Merino, P.; Pena, G.; Pérez, M.; Cruz, S.; Rey, P.; Estimation of crystallite size and lattice strain in nano-sized TiC particle-reinforced 6005A aluminium alloy from X-ray diffraction line broadening. Powder Technology 2019, 343, 19-28, 10.1016/j.powtec.2018.11.010.
  6. Surdu, V.A.; Győrgy, R.; X-ray Diffraction Data Analysis by Machine Learning Methods—A Review. Applied Sciences 2023, 13, 9992, 10.3390/app13179992.
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