1. What is the Scherrer Equation?

The Scherrer equation is used in X-ray diffraction to estimate the size of crystallites in a solid material from the broadening of peaks in the diffraction pattern. It provides an average crystallite size in the direction perpendicular to the reflecting planes.

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 diffraction peak (radians)
• \( \theta \) — Bragg angle (degrees)
• 0.94 — Scherrer constant (shape factor)

Explanation: The equation relates the peak broadening in an XRD pattern to the size of the crystallites, with smaller crystallites producing broader peaks.

3. Importance of Crystallite Size Calculation

Details: Crystallite size is a fundamental material property affecting mechanical strength, chemical reactivity, and other physical properties. It's crucial in nanomaterials research, quality control, and materials characterization.

4. Using the Calculator

Tips: Enter wavelength in nm, FWHM in radians, and angle in degrees. Ensure all values are positive (wavelength > 0, FWHM > 0, angle between 0-90°).

5. Frequently Asked Questions (FAQ)

Q1: What is the Scherrer constant (0.94)?
A: The value 0.94 is a shape factor assuming spherical crystallites. It may vary (0.89-1.0) depending on crystallite shape and definition of size.

Q2: What are typical crystallite sizes?
A: Typically ranges from 1-100 nm. Below 10 nm is considered nanocrystalline, while larger sizes are bulk materials.

Q3: What are limitations of the Scherrer equation?
A: It doesn't account for strain broadening, instrumental effects, or anisotropic crystallite shapes. More sophisticated methods like Williamson-Hall analysis may be needed.

Q4: How to convert FWHM from degrees to radians?
A: Multiply degrees by π/180. Many XRD software packages can output FWHM directly in radians.

Q5: What X-ray wavelengths are commonly used?
A: Cu Kα radiation (λ = 0.15406 nm) is most common in lab XRD systems. Other targets include Mo (0.07093 nm) and Co (0.17890 nm).