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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