Scherrer after sixty years: a survey and some new results in the determination of crystallite size
01 Apr 1978-Journal of Applied Crystallography (International Union of Crystallography)-Vol. 11, Iss: 2, pp 102-113
TL;DR: In this article, the Scherrer constants of simple regular shapes have been determined for all low-angle reflections (h2 + k2 + l2 ≤ 100) for four measures of breadth.
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.
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TL;DR: Efficient organic-inorganic perovskite light-emitting diodes were made with nanograin crystals that lack metallic lead, which helped to confine excitons and avoid their quenching.
Abstract: Organic-inorganic hybrid perovskites are emerging low-cost emitters with very high color purity, but their low luminescent efficiency is a critical drawback. We boosted the current efficiency (CE) of perovskite light-emitting diodes with a simple bilayer structure to 42.9 candela per ampere, similar to the CE of phosphorescent organic light-emitting diodes, with two modifications: We prevented the formation of metallic lead (Pb) atoms that cause strong exciton quenching through a small increase in methylammonium bromide (MABr) molar proportion, and we spatially confined the exciton in uniform MAPbBr3 nanograins (average diameter = 99.7 nanometers) formed by a nanocrystal pinning process and concomitant reduction of exciton diffusion length to 67 nanometers. These changes caused substantial increases in steady-state photoluminescence intensity and efficiency of MAPbBr3 nanograin layers.
2,295 citations
TL;DR: Paul Scherrer and Peter Debye developed powder X-ray diffraction together, but it was Scherrer who figured out how to determine the size of crystallites from the broadening of diffraction peaks.
Abstract: Paul Scherrer and Peter Debye developed powder X-ray diffraction together, but it was Scherrer who figured out how to determine the size of crystallites from the broadening of diffraction peaks.
1,970 citations
TL;DR: In this article, the intrinsic catalytic activity and durability of carbon supported Ru, Ir, and Pt nanoparticles and corresponding bulk materials for the electrocatalytic oxygen evolution reaction (OER) were examined by surface-sensitive cyclic voltammetry.
Abstract: A comparative investigation was performed to examine the intrinsic catalytic activity and durability of carbon supported Ru, Ir, and Pt nanoparticles and corresponding bulk materials for the electrocatalytic oxygen evolution reaction (OER). The electrochemical surface characteristics of nanoparticles and bulk materials were studied by surface-sensitive cyclic voltammetry. Although basically similar voltammetric features were observed for nanoparticles and bulk materials of each metal, some differences were uncovered highlighting the changes in oxidation chemistry. On the basis of the electrochemical results, we demonstrated that Ru nanoparticles show lower passivation potentials compared to bulk Ru material. Ir nanoparticles completely lost their voltammetric metallic features during the voltage cycling, in contrast to the corresponding bulk material. Finally, Pt nanoparticles show an increased oxophilic nature compared to bulk Pt. With regard to the OER performance, the most pronounced effects of nanosca...
1,885 citations
TL;DR: In this article, a modified Scherrer equation (MSE) method was proposed to calculate the nano-scale size of bovine bone using XRD radiation of wavelength λ (nm) from measuring full width at half maximum of peaks (β) in radian located at any 2π in the pattern.
Abstract: Scherrer Equation, L=Kλ/β.cosθ, was developed in 1918, to calculate the nano crystallite size (L) by XRD radiation of wavelength λ (nm) from measuring full width at half maximum of peaks (β) in radian located at any 2θ in the pattern. Shape factor of K can be 0.62 - 2.08 and is usually taken as about 0.89. But, if all of the peaks of a pattern are going to give a similar value of L, then β.cosθ must be identical. This means that for a typical 5nm crystallite size and λ Cukα1 = 0.15405 nm the peak at 2θ = 170° must be more than ten times wide with respect to the peak at 2θ = 10°, which is never observed. The purpose of modified Scherrer equation given in this paper is to provide a new approach to the kind of using Scherrer equation, so that a least squares technique can be applied to minimize the sources of errors. Modified Scherrer equation plots lnβ against ln(1/cosθ) and obtains the intercept of a least squares line regression, ln=Kλ/L, from which a single value of L is obtained through all of the available peaks. This novel technique is used for a natural Hydroxyapatite (HA) of bovine bone fired at 600°C, 700°C, 900°C and 1100°C from which nano crystallite sizes of 22.8, 35.5, 37.3 and 38.1 nm were respectively obtained and 900°C was selected for biomaterials purposes. These results show that modified Scherrer equation method is promising in nano materials applications and can distinguish between 37.3 and 38.1 nm by using the data from all of the available peaks.
1,418 citations
Cites background from "Scherrer after sixty years: a surve..."
...For an excellent discussion of K, a good reference is the paper “Scherrer after sixty years” in 1978 [2]....
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TL;DR: This study investigates colloidally prepared, highly monodisperse CoPt3 nanoparticles by transmission electron microscopy, small-angleX-ray scattering (SAXS), and powder X-ray diffraction (XRD), and examines to which extent agreement is obtained by the different techniques when applied to small nanocrystals in the size range below 10 nm.
Abstract: One of the most fundamental tasks in nanoscience is the accurate determination of particle sizes. Various methods have been developed to elucidate the mean particle diameter and the standard deviation for an ensemble of nanocrystals. However, good agreement between the results from different methods is not always encountered in the literature. In this study, we investigate colloidally prepared, highly monodisperse CoPt3 nanoparticles by transmission electron microscopy (TEM), small-angle X-ray scattering (SAXS), and powder X-ray diffraction (XRD). The results are compared in order to examine to which extent agreement is obtained by the different techniques when applied to small nanocrystals in the size range below 10 nm. In particular, the applicability of the simple Scherrer formula for size determination from the broadening of XRD reflections is checked. When the different techniques are correctly applied, the results from all methods are in good agreement.
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46,339 citations
Book•
01 Jan 1954
6,295 citations
TL;DR: The first results of the X-ray method dealt with the stereochemistry of the solid state, which always had been nearly impossible to attack with previous methods as discussed by the authors, and this side of the development is by no means neglected in the first volume of the work before us; the title seems adequate because of the preponderant role the crystalline state has played in the great majority of investigations.
Abstract: THE goal of chemistry is the determination of the atomic arrangement in space, which will be able to account for all the properties of matter under consideration. The greatest achievements in this direction have been obtained by the application of purely chemical methods, essentially because of the wonderful artistic skill of generations of chemists. Since von Laue's discovery of the diffraction of X-rays, and Sir William and W. L. Bragg's first X-ray analysis of the crystalline state, however, the way has been opened to a much more intimate knowledge of the atomic pattern. It is characteristic that the first results of the X-ray method dealt with the stereochemistry of the solid state, which always had been nearly impossible to attack with previous methods. The X-ray method afterwards proved to be no less important for the structural analysis of liquids and of single molecules in the gaseous state, and this side of the development is by no means neglected in the first volume of the work before us; the title seems adequate because of the preponderant role the crystalline state has played in the great majority of investigations. The Crystalline State. Edited by Sir William Bragg Dr. W. L. Bragg. Vol. 1: A General Survey. By W. L. Bragg. Pp. xiv + 352 + 32 plates. (London: G. Bell and Sons, Ltd., 1933.) 26s. net.
91 citations
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01 Jan 2000
TL;DR: Wilson as discussed by the authors showed that crystal-structure determination is closer to chemistry than to physics, and that the results are certainly of chemical interest, but the methods are essentially physical. But this subject is not dealt with at all in this book.
Abstract: THIS work fully maintains the standard that is now expected from this well-known series. The author has set himself well-defined limits, has stated these clearly in the preface, and has treated the subject-matter within these limits in a workmanlike fashion. It is unfortunate, therefore, that the main title of the book is deceptive, and that it has to be qualified by a sub-title ; a book on X-ray optics should have image formation as its main content ; but this subject is not dealt with at all in this book. The author justifies this omission on the grounds that crystal-structure determination is closer to chemistry than to physics. The reviewer does not agree with this ; the results are certainly of chemical interest, but the methods are essentially physical.X-Ray Optics The Diffraction of X-Rays by Finite and Imperfect Crystals. By A. J. C. Wilson . (Methuen's Monographs on Physical Subjects.) Pp. vii + 127. (London : Methuen and Co., Ltd., 1949.) 6s. net.
89 citations