Formula Used
The Debye–Scherrer equation estimates crystallite size from peak broadening:
D = (K × λ) / (β × cosθ)
- D is the crystallite size.
- K is the shape factor (commonly 0.9).
- λ is the X-ray wavelength.
- β is the corrected FWHM (radians).
- θ is the Bragg angle, θ = (2θ)/2.
Optional correction used here: β = sqrt(βobs² − βinst²) when βobs > βinst.
How to Use This Calculator
- Select a wavelength preset or enter a custom value.
- Set units for FWHM and the 2θ angle inputs.
- Enter at least one peak’s 2θ and observed FWHM.
- If available, enter instrumental FWHM for correction.
- Press Calculate Size to view results above.
- Use the download buttons to export your report.
Example Data Table
| Peak | 2θ (deg) | Observed FWHM (deg) | Instrument FWHM (deg) | Typical note |
|---|---|---|---|---|
| 1 | 44.67 | 0.28 | 0.10 | Moderate peak broadening |
| 2 | 64.99 | 0.32 | 0.10 | Second reflection for averaging |
| 3 | 82.33 | 0.40 | 0.10 | Higher angle often improves sensitivity |
Values are illustrative. Use your measured FWHM from peak fitting.