Quantum mechanics

Ellipsoid

Nuclear physics

Basis (linear algebra)

Tangent

Plane (geometry)

Particle size

Computer science

Scherrer equation

Physical chemistry

Physics

Tangent space

Mathematics

Optics

Astronomy

Work (physics)

Mathematical analysis

Geometry

Chemistry

Programming language

X-ray

Diffraction

Constant (computer programming)

Physical Review

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.

The Scherrer Formula for X-Ray Particle Size Determination