Materials Science

Calculating Crystallite Size from XRD Data (Scherrer Equation)

ENGPublished August 2026 · 7 min read

X-Ray Diffraction (XRD) peak broadening contains key structural information about nanomaterials. The Scherrer Equation relates the Full Width at Half Maximum (FWHM) of a diffraction peak to the average crystallite domain size:

$$\tau = \frac{K \cdot \lambda}{\beta \cdot \cos\theta}$$
  • D: Mean crystallite size (nm).
  • K: Shape factor (typically 0.9 for spherical crystallites).
  • λ: X-ray wavelength (e.g., 0.15406 nm for Cu K-alpha).
  • β: FWHM in radians (corrected for instrumental broadening).
  • θ: Bragg angle (half of 2θ).

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