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 material from the broadening of peaks in the diffraction pattern. It provides an average size of the ordered domains 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) in radians
• \( \theta \) — Bragg angle in degrees
• 0.94 — Scherrer constant (shape factor)

Explanation: The equation relates the peak broadening in an XRD pattern to the size of crystallites in the sample, assuming the broadening is solely due to size effects.

3. Importance of Crystallite Size Calculation

Details: Crystallite size is a fundamental material property affecting mechanical strength, chemical reactivity, and other physical properties. Accurate size determination is crucial in materials science and nanotechnology.

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°). For best results, use data from high-quality XRD measurements.

5. Frequently Asked Questions (FAQ)

Q1: What is the 0.94 factor in the equation?
A: This is the Scherrer constant (K) that depends on crystallite shape and size distribution. 0.94 is commonly used for spherical crystals with cubic symmetry.

Q2: What are the limitations of the Scherrer equation?
A: It assumes peak broadening is only due to crystallite size. Other factors like strain, instrument broadening, and defects can affect results.

Q3: How accurate is crystallite size from XRD?
A: Typically ±10-20% for well-prepared samples. For more accurate results, use multiple peaks and advanced analysis methods.

Q4: What's the difference between crystallite and particle size?
A: A particle may consist of multiple crystallites. XRD measures coherently diffracting domains (crystallites), not necessarily whole particles.

Q5: Can I use this for nanocrystalline materials?
A: Yes, the Scherrer equation is particularly useful for nanomaterials (typically <100 nm). For larger crystals, other broadening effects may dominate.