CrystallographyLab Level
Scherrer Calculator
Estimate crystallite (grain) size from XRD peak broadening. Corrects FWHM for instrumental broadening.
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Å
E.g. 1.5406 for Cu K-alpha
degrees
Position of peak center
Full Width at Half Maximum
Dimensionless shape parameter, usually 0.9
Calculated Grain Size
Estimated average crystal diameter
Enter valid inputs to calculate size.
Formula: Scherrer Equation
D = K · λ / (β · cos(θ))
Where:
D=Average crystallite grain size (nm or Å)
K=Shape factor (dimensionless) (0.9)
λ=X-ray wavelength (Å)
β=Corrected FWHM in radians (rad)
θ=Bragg angle (half of peak position 2θ) (rad)
* To use this formula correctly, the FWHM input (which is in degrees by default) is automatically converted to radians. The peak position 2θ is divided by 2 to yield θ before trigonometry functions.
Scientific Assumptions & Methodology
- Broadening is assumed to be solely due to crystallite size, neglecting lattice strain effects.
- Peak shape is assumed to be approximately Gaussian or Lorentzian.
- The shape factor K is typically 0.9 for spherical crystallites.
Limitations & Educational Warnings
- The Scherrer equation is an estimate, valid for crystallite sizes under 100 nm (1000 Å).
- If instrumental broadening matches or exceeds observed broadening, the corrected size is undefined.