1. What is the Scherrer Equation?

The Scherrer equation is used in X-ray diffraction (XRD) to estimate the size of crystallites in a solid sample. It relates the size of sub-micrometer particles to the broadening of peaks in the diffraction pattern.

2. How Does the Calculator Work?

The calculator uses the Scherrer equation:

Where:

• \( D \) — Mean crystallite size (nm)
• \( K \) — Shape factor (typically 0.9)
• \( \lambda \) — X-ray wavelength (nm)
• \( \beta \) — Line broadening at FWHM (radians)
• \( \theta \) — Bragg angle (degrees)

Explanation: The equation shows that smaller crystallites produce broader diffraction peaks, while larger crystallites produce sharper peaks.

3. Importance of Grain Size Calculation

Details: Grain size affects material properties like strength, ductility, and electrical conductivity. XRD provides a non-destructive way to measure crystallite size in polycrystalline materials.

4. Using the Calculator

Tips: Enter all values with correct units. Common X-ray wavelengths: Cu Kα = 0.15406 nm, Co Kα = 0.17902 nm. Remember to convert FWHM from degrees to radians if necessary.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical value for K?
A: The shape factor K is typically 0.9 for spherical crystals with cubic symmetry, but can range from 0.62 to 2.08 depending on crystal shape.

Q2: How accurate is the Scherrer equation?
A: It provides an estimate of crystallite size but doesn't account for strain broadening. For more accurate results, use Williamson-Hall analysis.

Q3: What are the limitations of this method?
A: It only measures coherently diffracting domains, not particle size. Results are less accurate for sizes >100-200 nm.

Q4: How to measure FWHM (β)?
A: Measure from XRD pattern after subtracting instrumental broadening, typically using peak fitting software.

Q5: Can this be used for all materials?
A: It works best for crystalline materials with small crystallites (<100 nm) and minimal strain broadening.