1. What is the Scherrer Equation?

The Scherrer equation is a formula used in X-ray diffraction (XRD) to calculate the size of crystallites in a solid material from the broadening of peaks in the diffraction pattern. It provides an estimate of the average size of domains in the material that diffract X-rays coherently.

2. How Does the Calculator Work?

The calculator uses the Scherrer equation:

Where:

• \( D \) — Crystallite size (nm)
• \( \lambda \) — X-ray wavelength (nm)
• \( \beta \) — Full width at half maximum (FWHM) of the diffraction peak (radians)
• \( \theta \) — Bragg angle (degrees)
• 0.94 — Scherrer constant (shape factor for spherical crystals)

Explanation: The equation relates the size of sub-micrometre crystallites in a solid to the broadening of peaks in an X-ray diffraction pattern.

3. Importance of Crystallite Size Calculation

Details: Crystallite size is a fundamental parameter in materials science that affects mechanical, electrical, and chemical properties of materials. It's crucial for characterizing nanomaterials and understanding material performance.

4. Using the Calculator

Tips: Enter X-ray wavelength in nm, FWHM in radians, and Bragg angle in degrees (0-90). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the Scherrer constant (0.94)?
A: The value 0.94 is a shape factor for spherical crystals with cubic symmetry. It may vary (typically 0.89-1.0) depending on crystal shape and definition of size.

Q2: What are the limitations of the Scherrer equation?
A: It doesn't account for strain broadening, instrumental broadening, or size distributions. It's most accurate for sizes below 100-200 nm.

Q3: How to measure FWHM properly?
A: FWHM should be measured after subtracting instrumental broadening, typically using a standard sample to determine instrumental contribution.

Q4: What X-ray wavelengths are commonly used?
A: Cu Kα (0.15418 nm) and Mo Kα (0.07093 nm) are common laboratory sources. Synchrotron radiation can provide various wavelengths.

Q5: How to convert FWHM from degrees to radians?
A: Multiply degrees by π/180. Some instruments report FWHM in 2θ degrees, which needs conversion to θ before use in the equation.