Tuesday, 10 January 2017

XRD Crystallite Size Calculator (Scherrer Equation)

XRD Crystallite Size Calculator (Scherrer Equation)

Calculation Tutorial:

STEP1: Open the XRD graph of the material, which is obtained from the instrument. 2 Theta I n t e n s i t y 20 25 30 35 40 45 0 1000 2000 3000 4000 5000 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). Raw HTML 2 Theta I n t e n s i t y 20 25 30 35 40 45 0 1000 2000 3000 4000 5000 31.8 0.5 (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"