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This article is cited in 82 scientific papers (total in 82 papers)
PHYSICS
Scherrer formula: estimation of error in determining small nanoparticle size
A. S. Vorokh Institute of Solid State Chemistry of the Ural Branch of the Russian Academy of Sciences,
91 Pervomaiskaya st., Ekaterinburg, Russia
Abstract:
The lower limit of the applicability of the Scherrer formula has been established by calculating the diffraction patterns from model nanoparticles
by the Debye formula. Particle size was calculated using the Scherrer formula for different $hkl$-peaks. The obtained data of particle sizes were
compared with “real” sizes of model particles in the same $hkl$-directions. The form-factor $K_{hkl}$ was analyzed as main correction of Scherrer
formula. It was shown that the Scherrer formula error increases nonlinearly at particle sizes less than 4 nm. For any $hkl$ direction, the absolute
error of average particle size determination using formula does not exceed 0.3 nm. Analysis shows that average particle size can be determined
by Scherrer formula from single diffraction peak of experimental pattern for center-symmetrical particles.
Keywords:
Scherrer formula, nanoparticle size, Scherrer limit, Debye equation.
Received: 30.11.2017 Revised: 03.04.2018
Citation:
A. S. Vorokh, “Scherrer formula: estimation of error in determining small nanoparticle size”, Nanosystems: Physics, Chemistry, Mathematics, 9:3 (2018), 364–369
Linking options:
https://www.mathnet.ru/eng/nano319 https://www.mathnet.ru/eng/nano/v9/i3/p364
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