Analyze XRD peak width using Scherrer-based engineering calculations. Average multiple peaks with instrumental broadening correction. Get clear charts, exports, and reliable nanostructure estimates fast.
Enter experimental XRD values. The calculator corrects instrumental broadening and estimates crystallite size using the Scherrer approach.
The calculator uses the Scherrer equation for apparent crystallite size estimation:
D = (K × λ) / (β × cosθ)
Instrument correction is applied before size calculation:
β = √(βm² − βi²)
Here, βm is measured FWHM and βi is instrumental FWHM. The calculator also reports d-spacing using Bragg geometry, a simple microstrain estimate, and a derived dislocation density indicator.
Example values below use Cu Kα radiation, K = 0.90, and instrumental FWHM = 0.10°.
| Peak | 2θ (°) | Measured FWHM (°) | Corrected FWHM (°) | Crystallite Size (nm) | Microstrain (%) |
|---|---|---|---|---|---|
| Peak 1 | 28.50 | 0.32 | 0.3040 | 26.9645 | 0.5222 |
| Peak 2 | 47.40 | 0.41 | 0.3976 | 21.8199 | 0.3952 |
| Peak 3 | 56.30 | 0.45 | 0.4387 | 20.5358 | 0.3578 |
| Peak 4 | 69.20 | 0.52 | 0.5103 | 18.9131 | 0.3228 |
| Peak 5 | 76.50 | 0.59 | 0.5815 | 17.3975 | 0.3218 |
It estimates apparent crystallite size from XRD peak broadening using the Scherrer relation. It also reports corrected broadening, d-spacing, microstrain indication, and an average across valid peaks.
Measured peak width includes both sample broadening and instrument broadening. If you do not subtract the instrumental portion, crystallite size will usually be underestimated.
Use the wavelength of the X-ray source used during measurement. Cu Kα is common at 1.5406 Å, but cobalt, chromium, molybdenum, or custom wavelengths may apply.
A value near 0.90 is widely used for quick engineering estimates. However, K can vary with crystallite shape, peak definition, and analysis assumptions.
Yes. Using several clean peaks often improves interpretation. This calculator computes each peak separately, then summarizes the average, median, spread, and related indicators.
A warning appears when measured broadening is less than or equal to instrumental broadening. In that case, corrected broadening becomes zero or imaginary, so size cannot be calculated reliably.
No. Scherrer sizing is a practical first estimate. For stronger separation of size and strain effects, methods like Williamson–Hall, Rietveld refinement, or TEM validation are often preferred.
Input wavelength is in angstroms, peak angles are in degrees, corrected broadening is internally converted to radians, and crystallite size is reported in nanometers.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.