Enter the X-ray wavelength, full width at half maximum, and Bragg angle into the calculator to determine the crystal size using the Scherrer formula.
Scherrer Formula
The Scherrer formula is used to estimate the size of crystallites in a material from the broadening of a peak in a diffraction pattern. The formula is given by:
D = (K * λ) / (β * cos(θ))
Variables:
- D is the crystal size (Ångströms)
- K is the shape factor (approximately 0.9)
- λ is the X-ray wavelength (Ångströms)
- β is the full width at half maximum (FWHM) in radians
- θ is the Bragg angle in degrees
To calculate the crystal size, multiply the shape factor by the X-ray wavelength, and divide by the product of the full width at half maximum and the cosine of the Bragg angle.
What is the Scherrer Formula?
The Scherrer formula is a widely used equation in X-ray diffraction studies to estimate the size of crystallites in a material. The formula relates the size of the crystallites to the broadening of the X-ray diffraction peak, which occurs due to the finite size of the crystallites and the presence of lattice strain. The Scherrer formula is particularly useful for materials with nanoscale crystallites.
How to Calculate Crystal Size using the Scherrer Formula?
The following steps outline how to calculate the crystal size using the Scherrer Formula.
- First, determine the X-ray wavelength (λ) in Ångströms.
- Next, determine the full width at half maximum (β) in radians.
- Next, determine the Bragg angle (θ) in degrees.
- Use the Scherrer formula: D = (K * λ) / (β * cos(θ)), where K is approximately 0.9.
- Finally, calculate the crystal size (D) in Ångströms.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
X-ray wavelength (λ) = 1.5406 Ångströms
Full width at half maximum (β) = 0.000290888 radians
Bragg angle (θ) = 22.5 degrees
