Scherrer formula: estimation of error in determining small nanoparticle size

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.