1. What is the Scherrer Equation?

The Scherrer equation is used in X-ray diffraction (XRD) to estimate the size of crystalline particles (granules) in a solid sample. It relates the angular width of diffraction peaks to particle size.

2. How Does the Calculator Work?

The calculator uses the Scherrer equation:

Where:

• \( D \) — Average granule size (nm)
• \( \lambda \) — X-ray wavelength (nm)
• \( \beta \) — Line broadening at FWHM (radians)
• \( \theta \) — Bragg angle (degrees)
• 0.94 — Scherrer constant (shape factor)

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

3. Importance of Granule Size Calculation

Details: Granule size affects material properties like strength, reactivity, and optical characteristics. XRD analysis provides a non-destructive way to measure crystallite size.

4. Using the Calculator

Tips: Enter wavelength in nm, FWHM in radians, and angle in degrees. Typical X-ray wavelengths: Cu Kα = 0.15418 nm, Co Kα = 0.17902 nm.

5. Frequently Asked Questions (FAQ)

Q1: What is the Scherrer constant (0.94)?
A: It's a shape factor that depends on particle shape and how size is defined. 0.94 is common for spherical particles with size defined as diameter.

Q2: What are the limitations of this equation?
A: It doesn't account for strain broadening and is only accurate for particles smaller than about 100-200 nm.

Q3: How to measure FWHM (β)?
A: From XRD data, measure the full width at half maximum of the diffraction peak after subtracting instrumental broadening.

Q4: Why convert angle to radians?
A: The trigonometric functions in programming languages typically use radians, so conversion is necessary for accurate calculation.

Q5: Can this be used for all crystal systems?
A: Yes, but results are most accurate for isotropic materials. Anisotropic materials may require more complex analysis.