Scherrer Equation

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[edit] Introduction

The Scherrer Equation is used frequently in X-Ray analysis, particularly powder diffraction, of materials. It relates the peak breadth of a specific phase of a material to the mean crystallite size of that material. It is the quantitative equivalent of saying that the larger a material's crystallites are, the sharper its XRD peaks will be.

The equation takes the form: \beta_{hkl}=\frac{K \lambda}{L_{hkl}\cos \theta_{hkl}}

Where:

β is the breadth of the peak of a specific phase (hkl)

K is a constant that varies with the method of taking the breadth (0.89<K<1)

λ is the wavelength of incident x-rays

θ is the center angle of the peak

L is the crystallite length


"The Scherrer Formula for X-Ray Particle Size Determination" (Nov 1939). Phys. Rev. 56: 978-982. American Physical Society. doi:10.1103/PhysRev.56.978.