The Scherrer Formula for X-Ray Particle Size Determination

Формула Шеррера для определения размера частиц методом рентгеновской дифракции
A. L. Patterson
1939-11-15

Scherrer equationX-ray particle size determinationhalf-value breadthintegral breadthtangent plane approximation
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.
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.

Spherical particles used in X-ray particle size determination

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

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1939-11-15
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A. L. Patterson
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