Scherrer after sixty years: A survey and some new results in the determination of crystallite size

Abstract

Existing knowledge about Scherrer constants is reviewed and a summary is given of the interpretation of the broadening arising from small crystallites. Early work involving the half‐width as a measure of breadth has been completed and Scherrer constants of simple regular shapes have been determined for all low‐angle reflections (h2 + k2 + l2≤ 100) for four measures of breadth. The systematic variation of Scherrer constant with hkl is discussed and a convenient representation in the form of contour maps is applied to simple shapes. The relation between the `apparent' crystallite size, as determined by X‐ray methods, and the `true' size is considered for crystallites having the same shape. If they are of the same size, then the normal Scherrer constant applies, but if there is a distribution of sizes, a modified Scherrer constant must be used.

Effect of Urea Excess on the Properties of the MgAl2O4 Obtained by Microwave-Assisted Combustion

“…It is also interesting to emphasize that, according to the materials obtained and the methodology employed in this paper, an increase in crystallite size also resulted in an increase in specific surface area. In this case, it was confirmed that, in fact, "crystallite size" is not a synonymous for "particle size", as it is emphasized by other authors 45,48 , once that the individual particles may contain several crystallites 41 . In addition, it is well known that the specific surface area and particle size values have an inverse relation to each other, which can be represented by Eq.…”

“…The average crystallite size of the solids was estimated from the X-ray patterns, using the Scherrer equation and applying the integral width method, defined as the total area under the maximum diffraction peak divided by the peak intensity 45 . The diffraction peak that was considered in the calculations was the one corresponding to the plane (311), which occurs at 2θ = 36.8.…”

Synthesis of hexagonal close-packed gold nanostructures

“…In addition, the reflections from the (110) h square basal planes of AuSSs are barely observable because of the ultrathin nature of the AuSSs. The 2.4-nm dimension, normal to the (110) h plane, results in a weak and broad reflection peak based on Sherrer's theory 19 , whereas the fcc Au nanoparticles, which are 10-25 nm in diameter, produce strong reflections. For comparison, a concentrated solution (similar to a paste) of AuSSs was deposited on a glass slide, so that the AuSSs did not show the preferred orientation.…”

One-Pot Synthesis of Biocompatible Silver Nanoparticle Composites from Cellulose and Keratin: Characterization and Antimicrobial Activity

“…at half-maximum (fwhm; β value in the equation) of their corresponding XRD peaks: 47,48 where τ is the size of the NP, λ is the X-ray wavelength, and k is a constant. 31,32 The size of the metallic AgNP in the [CEL+KER+Ag 0 ] composite was found to be 9 ± 1 nm, while the AgClNP in the [CEL+KER+Ag + ] composite has a size of 27 ± 2 nm.…”