Scherrer equation

The Scherrer equation estimates the average size of coherently diffracting crystallites from X-ray diffraction peak broadening, after correcting for instrumental broadening and choosing a shape factor.

X-ray diffraction: A technique that uses X-ray scattering to determine structural information about crystalline materials. The equation extracts crystallite-size information from broadened diffraction peaks.
Crystallite: A small crystalline region with an ordered lattice, which may form part of a larger particle or aggregate. A crystallite's coherent size is the physical quantity the equation seeks to estimate.
Paul Scherrer: A Swiss physicist who developed an early relation between X-ray diffraction line broadening and crystallite size. The equation bears his name and grew from his diffraction research.
Powder diffraction: Diffraction measurement from a sample containing many crystallites in varied orientations. Powder patterns commonly provide the peaks used for Scherrer estimates.
Warren–Averbach method: A Fourier analysis of diffraction line profiles used to separate crystallite size and lattice-distortion effects. It separates broadening contributions more fully than the Scherrer approximation.
Bragg's law: The condition relating X-ray wavelength, crystal-plane spacing, and diffraction angle for constructive interference. It identifies the diffraction angles whose peak widths enter the estimate.
X-ray line broadening: The widening of diffraction peaks caused by sample properties and measurement conditions. The Scherrer method interprets one source of this broader phenomenon.
Peter Debye: A Dutch-American physicist whose work included foundational theories of X-ray scattering and diffraction by matter. His diffraction theory helped establish the physical setting for interpreting broadened lines.
Nanocrystalline material: A material composed of crystalline grains or domains with nanoscale dimensions. Small domains produce broadened peaks that can be assessed with the equation.
Whole powder pattern modelling: A diffraction-analysis approach that models an entire powder pattern using structural and microstructural descriptions. It can represent size distributions and shape effects beyond a single-width estimate.

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