najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2018-9-3-364-369najo-798Research ArticlePHYSICSФИЗИКАScherrer formula: estimation of error in determining small nanoparticle sizeVorokhA. S.

91 Pervomaiskaya st., Ekaterinburg

vorokh@ihim.uran.ruInstitute of Solid State Chemistry of the Ural Branch of the Russian Academy of SciencesRussian Federation20181408202593364369Copyright © Vorokh A.S., 20252025Vorokh A.S.Vorokh A.S.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/798

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 Khkl 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.

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The authors declare that there are no conflicts of interest present.