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XRD Crystallite (grain) Size Calculator (Scherrer Equation)

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XRD Crystallite (grain) Size Calculator (Scherrer Equation) - InstaNANO. https://instanano.com/all/characterization/xrd/crystallite-size/ (accessed March 27th, 2024).

This Calculator can determine crystallite or grain size by using XRD graph. Peak position and FWHM values are needed

Calculation Tutorial:

STEP1: Open the XRD graph of the material, which is obtained from the instrument.

STEP2: Now zoom on the area for which you want to calculate the crystallite size and note down the angle at which peak is shown and peak Full Width at Half Maximum (FWHM).

STEP3: Now enter the measured Peak Position (i.e. 31.8) and peak FWHM (i.e. 0.5) in desire columns of the calculator. You should get the calculated results of the crystallite size in the “Calculated Result” field.

NOTE: Default value of wavelength of LASER is set is 0.15418 (Cu K-alpha), which is mostly used in the instruments.

Theory Behind Calculations:
X-Rays are having wavelength between 0.01nm to 10nm. Hence X-Rays can penetrate inside the crystal structure of any material very easily; and tells us the properties of material while coming out from that material. Which is why X-Ray spectroscopy is very useful technique for characterization of different types of materials. We can easily calculate the size of particles from Scherrer formula given:

Scherrer Formula:

Dp = (0.94 Χ λ) / (β Χ Cosθ)

Where, Dp = Average Crystallite size, β = Line broadening in radians, θ = Bragg angle, λ = X-Ray wavelength

What is FWHM?
what is fwhm

NOTE: Please don’t worry about the β(in radians), All the calculations are made such that you can enter β (i.e. Full Width at Half Maximum) value directly in degree as shown in “Calculation Tutorial”

6 Question, Ask New
wan.ahweelat says:

Could you kindly give me more examples please and what I should exactly get from the XRD please.thanks in advance

xlfortm1 says:

Why can Scherrer Equation measure only grains smaller than 0.1 micrometers?

ovatan says:

We have two FHWM left and right. Which one should we use

Help Team says:

There is nothing left or right in FWHM, we have added “What is FWHM?” in the calculator tutorial, please check that for better understanding.

Brij Mohan Singh says:

should be take the wavelength K1 alfa wavelength as x-raywavelength

Dheeraj Kumar says:

Dear Brij Mohan, calculator default wavelength (0.15418) is for “Cu K-alpha”, which is the most used X-ray wavelength in the XRD. If your instrument is having a different wavelength then you can enter that also.

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