**XRD size calculation based on Scherrer equation**

###### Peak Position (2 Theta)

Peak Width/FWHM (2Theta)

X-Ray Wavelength

## Results

nm

**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

**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”

## 15 Comments. Leave new

Step one: Prepare a suitable sample, one with an appropriate size range and prepared to avoid preferred orientation.

It is very good web.

This does not take into consideration instrumental widths right?

How to do correction in fwhm values. While calculating fwhm for clays

Thank you very much. It is useful.

it’s good idea to help researchers

THANK YOU..BUT K=0.94 IS FOR COPPER RADIATION

I THINK YOU HAVE TO ADD OTHER CONSTANT LIKE K=0.89 FOR COBALT RADIATION..

YOURS

K depends on the crystal shape factor, K~0.9 for spherical crystallites.

why The crystallite size of Ca-substituted in YBCO at Ba site samples was decreased for high concentration and increased for low concentration

Very good, but shape faktor for different crystals is vary.

That has got a necessity for new section which can insert shape factor.

Thank you so much it is a easier way to calculate particle size of nano materials.

I agree with your details , fantastic post.

what if we have multiple peaks as in the case of silver nanoparticles? which peak should we select?

Thanks for this helpful site to find crystal size.

Very useful