1. What is the Scherrer Equation?

The Scherrer equation is used in X-ray diffraction (XRD) to estimate the crystallite size of a material from the broadening of a diffraction peak. It relates the size of sub-micrometer particles to the width of their XRD peaks.

2. How Does the Calculator Work?

The calculator uses the Scherrer equation:

Where:

• \( D \) — Crystallite size (nm)
• \( K \) — Shape factor (typically 0.9)
• \( \lambda \) — X-ray wavelength (nm)
• \( \beta \) — Line broadening at FWHM (radians)
• \( \theta \) — Bragg angle (degrees)

Explanation: The equation accounts for peak broadening due to finite crystallite size, with the assumption that strain and instrumental broadening have been accounted for.

3. Importance of Crystallite Size Measurement

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

4. Using the Calculator

Tips: Enter all values with correct units. Typical values: K=0.9, λ=0.15406 nm (Cu Kα radiation). β should be in radians (convert from degrees if needed). θ is the peak position in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical value for K?
A: The shape factor K is typically 0.9 for spherical crystals with cubic symmetry, but can range from 0.62 to 2.08 depending on crystal shape and definition of size.

Q2: How do I convert FWHM from degrees to radians?
A: Multiply degrees by (π/180). For example, 0.5° = 0.5 × (π/180) ≈ 0.0087 radians.

Q3: What are the limitations of the Scherrer equation?
A: It assumes size broadening dominates and neglects strain effects. Only valid for crystallites smaller than ~100-200 nm. Requires proper instrumental broadening correction.

Q4: Which X-ray wavelength should I use?
A: Common lab sources: Cu Kα (0.15406 nm), Co Kα (0.17890 nm), Mo Kα (0.07093 nm). Match to your experimental setup.

Q5: How accurate is crystallite size from XRD?
A: Provides good relative comparison but absolute accuracy depends on proper peak fitting, instrumental corrections, and sample preparation. TEM may be needed for validation.