Scherrer Equation unit dilemma

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In summary, the Scherrer equation used in powder diffraction is L = (0.9λ)/(βcosθ), where λ is the radiation wavelength in angstroms, β is the FWHM in radians, θ is the Braggs angle in degrees, and L is the particle size in angstroms. The units for β and θ should be in radians, as confirmed in an old discussion thread and by the lecturer's notes.
  • #1
NaN089
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Hi,

I am a bit confused about the units of

L = (0.9λ)/(βcosθ)

the Scherrer equation used in powder diffraction. My idea is

λ= radiation wavelength with unit (angstrom)
β= FWHM with unit (radians)
θ= braggs angle with unit (degrees)
L= particle size with unit (angstrom)

Am I right in saying so?

Thanks
 
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  • #3
Thank you for your help. The notes that my lecturer gave had the info that I provided here. I was a bit confused and had to check with someone else. Now I know it was a printing mistake. They need to be in radians.

Thanks
 

1. What is the Scherrer Equation unit dilemma?

The Scherrer Equation unit dilemma refers to the discrepancy between the units used in the Scherrer Equation, which is a formula used to calculate the particle size of crystalline materials. The equation can be written in either length or angle units, leading to confusion and potential errors in the calculated results.

2. How does the Scherrer Equation calculate particle size?

The Scherrer Equation uses the full width at half maximum (FWHM) of the diffraction peak from a crystalline material to determine its particle size. This value is then plugged into the equation, which takes into account the wavelength of the X-rays used, the diffraction angle, and a dimensionless shape factor to calculate the particle size.

3. What are the two versions of the Scherrer Equation?

The two versions of the Scherrer Equation are the length-based version and the angle-based version. The length-based version uses the FWHM in length units (such as nanometers or micrometers), while the angle-based version uses the FWHM in angular units (such as degrees or radians).

4. Which version of the Scherrer Equation should I use?

The version of the Scherrer Equation to use depends on the units of your diffraction data. If your data is in length units, you should use the length-based version. If your data is in angular units, you should use the angle-based version. It is important to be consistent with your units to avoid errors in the calculated particle size.

5. Can the Scherrer Equation be adjusted for different materials?

Yes, the Scherrer Equation can be adjusted for different materials by using a different shape factor. The shape factor takes into account the crystal structure and shape of the material being analyzed. Different materials will have different shape factors, so it is important to use the appropriate value for accurate results.

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