The Scherrer Formula for X-Ray Particle Size Determination
Формула Шеррера для определения размера частиц методом рентгеновской дифракции
1939-11-15
SCID: 54.1/gr6r2t4s
Discuss with AI
Scherrer equationX-ray particle size determinationhalf-value breadthintegral breadthtangent plane approximation
Figures from the paper
Abstract (AI)
An exact derivation of the Scherrer equation is given for particles of spherical shape, values of the constant for half-value breadth and for integral breadth being obtained. Various approximation methods which have been used are compared with the exact calculation. The tangent plane approximation of v. Laue is shown to be quite satisfactory, but some doubt is cast on the use of approximation functions. It is suggested that the calculation for the ellipsoidal particle based on the tangent plane approximation will provide a satisfactory basis for future work.
Key Findings
1
A tangent plane–based calculation for ellipsoidal particles is suggested as a satisfactory basis for future work.
2
Common approximation methods are compared against the exact spherical calculation.
3
The Scherrer equation is derived exactly for spherical particles.
4
The tangent plane approximation of v. Laue is found to be quite satisfactory.
5
Use of approximation functions is questioned due to identified doubts.
6
Values of the Scherrer constant are obtained for both half-value breadth and integral breadth.
Research Object
Spherical particles used in X-ray particle size determination
Research Subject
Derivation and evaluation of the Scherrer equation/constants (for half-value breadth and integral breadth), comparison of approximation methods (including Laue's tangent plane) and implications for ellipsoidal-particle calculations
Publication Details
Publication Date
1939-11-15
Journal
Publisher
ISSN
Access Type
Author Information
Download PDF
Subscribe to digest