Xrd Particle Size Calculator

Scherrer Equation:

\[ D = \frac{K \lambda}{\beta \cos \theta} \]

Shape Factor (K):

unitless

Wavelength (λ):

FWHM (β):

radians

Angle (θ):

degrees

Particle Size (D):

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1. What is the Scherrer Equation?

The Scherrer equation is used in X-ray diffraction (XRD) to estimate the size of crystalline particles in the nanometer range. It relates the angular width of diffraction peaks to particle size, assuming the broadening is due to size effects rather than other factors like strain.

2. How Does the Calculator Work?

The calculator uses the Scherrer equation:

\[ D = \frac{K \lambda}{\beta \cos \theta} \]

Where:

\( D \) — Particle size (nm)
\( K \) — Shape factor (typically 0.9 for spherical particles)
\( \lambda \) — X-ray wavelength (typically 0.15406 nm for Cu Kα radiation)
\( \beta \) — Full width at half maximum (FWHM) of diffraction peak in radians
\( \theta \) — Bragg angle in degrees

Explanation: The equation shows that smaller particles produce broader diffraction peaks, while larger particles produce sharper peaks.

3. Importance of Particle Size Calculation

Details: Particle size affects material properties like strength, reactivity, and optical characteristics. XRD particle size analysis is crucial in materials science, nanotechnology, and pharmaceutical development.

4. Using the Calculator

Tips: Enter the shape factor (typically 0.9), X-ray wavelength (0.15406 nm for Cu Kα), FWHM in radians, and Bragg angle in degrees. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical value for K?
A: The shape factor K is typically 0.9 for spherical particles, but can range from 0.62 to 2.08 depending on particle 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) ≈ 0.00873 radians.

Q3: What are the limitations of the Scherrer equation?
A: It assumes size broadening dominates over other effects (strain, instrument broadening) and is most accurate for particles <100 nm.

Q4: Can I use this for non-crystalline materials?
A: No, the Scherrer equation only applies to crystalline materials that produce sharp diffraction peaks.

Q5: What X-ray wavelength should I use?
A: Common lab sources: Cu Kα = 0.15406 nm, Mo Kα = 0.07093 nm, Co Kα = 0.17890 nm.