Scherrer equation

The Scherrer equation provides the ability to determine the crystal size in the experimental X-ray diffraction. It goes back to the Swiss physicist Paul Scherrer.

In general, can the diffraction pattern of the X-ray diffraction described by the Bragg equation. However, a prerequisite to the Bragg equation is that the investigated crystals have a certain thickness and thus a sufficient number of parallel lattice planes with interplanar spacing d hkl are present. In the powder method ( Debye Scherrer method ) The crystals thus typically have a particle size of at least 0.1 microns. In the crystal structure analysis of single crystals, the crystals usually 50-500 microns in size.

When the crystals are very small, which has a broadening of the X-ray reflections result. The spacers is given by the Scherrer's equation:

Δ ( 2θ ) is the full width at half maximum of the reflection is measured in radians, K is the Scherrer's shape factor having a value of about 1, λ is the wavelength of X-rays, θ is the diffraction angle (sometimes called 2θ / 2 hereinafter) and L is the extension of the crystal perpendicular to the planes of the reflex.

When the crystal size is known, the broadening of the reflection can be calculated and vice versa from the reflection broadening the size of the crystals. The Scherrer equation is valid at a crystal size of less than 100-200 nm