1. What is the Scherrer Equation?

The Scherrer equation is used in X-ray diffraction (XRD) to estimate the size of crystalline particles from the broadening of diffraction peaks. It relates the particle size to the peak width at half maximum (FWHM), X-ray wavelength, and diffraction angle.

2. How Does the Calculator Work?

The calculator uses the Scherrer equation:

Where:

• \( D \) — Particle size (nm)
• \( \lambda \) — X-ray wavelength (nm)
• \( \beta \) — Full width at half maximum (FWHM) in radians
• \( \theta \) — Bragg angle in degrees
• 0.94 — Scherrer constant (shape factor)

Explanation: The equation accounts for the broadening of diffraction peaks due to finite crystallite size, with smaller particles producing broader peaks.

3. Importance of Particle Size Calculation

Details: Particle size determination is crucial in materials science for understanding material properties, catalytic activity, and performance in various applications.

4. Using the Calculator

Tips: Enter wavelength in nm, FWHM in radians, and angle in degrees. All values must be positive (angle between 0-90°).

5. Frequently Asked Questions (FAQ)

Q1: What is the Scherrer constant (0.94)?
A: It's a shape factor that depends on crystallite shape and how width is measured. 0.94 is common for spherical crystals with FWHM.

Q2: What are typical wavelength values?
A: Common X-ray sources: Cu Kα (0.154 nm), Co Kα (0.179 nm), Mo Kα (0.071 nm).

Q3: What are limitations of the Scherrer equation?
A: It doesn't account for strain broadening and is accurate only for sizes below ~100-200 nm.

Q4: How to convert FWHM from degrees to radians?
A: Multiply degrees by (π/180). Some XRD software provides values directly in radians.

Q5: Can this be used for all crystal systems?
A: Yes, but results are most accurate for isotropic materials and when using the most intense peak.