FWHM & Crystallite Size from XRD using Origin | 2 methods | Scherrer equation

FWHM & Crystallite Size from XRD using Origin | 2 methods | Scherrer equation


I will show how to determine the “Full width
at half maxima” by 2 different ways. The method which most of the researchers use. And then, the method which I use and I think
better. After very briefly talking about the Scherrer
equation, I will show how you can calculate crystallite
size easily. One manually writing the formula. Or, alternatively using my templates as an
automatic calculator. After plotting the data, go to analysis. Choose “Peaks and Baselines”, and then select
“Multiple Peak Fit”. Open Dialog… If you are using an older version of Origin,
you may need to enter the number of peaks. If you are new to “Multiple Peak Fit”,
I suggest you to watch my previous video on “Multiple Peak Fit”. Link is given in the description. .
Here, you have to choose the peak type. In most of the cases for XRD, Gaussian or
Lorentzian work better. I will compare both. First, I will use the Gaussian. Double click on the peaks to select them. When you are done selecting, “Open non-linear
fit”. Here, you can find tonnes of information regarding
the fit. I have to use “Fit until converge” option. Now the fit has converged at 18 iterations. It may go more than even 100 if there are
several types of peaks and noisy background. Click OK as it is completed. Let’s have close look,
How well it is fitted. At lower, around the background,
the peaks are not fitted well. However, you can still use it,
as we are concerned about the full width at half maxima. Let’s check it with Lorentzian shape. Resizing for better visibility. Adjusting the scale though it is not very
important. Now I have to choose Lorentz here. This is better than the previous fit. Up to now, I have shown how it is done most
of the researchers. But, I suggest you to use the following method. Instead of using multiple peak fit, use quick
fit. Go to Gadgets. Then Quick fit. Choose “Peak – Lorentz” as we know Lorentz
fits better. Now, you have to just magnify the peaks one
by one. First, do for the first peak. Looks good. If necessary,
You can adjust the highlighted region by dragging the sides. Find the fitted parameters from here. Keep only values, separated by single space. Select all. Copy them. Cancel the change, as we have copied already. Make a new sheet. Write the parameters and units. Paste the copied values. Repeat the steps for other high-intensity
peaks. W represents the Full width at half maxima. We have extracted values from 5 peaks. For calculation of crystallite size,
3 to 5 peaks will be okay. In the next half, I will these values to calculate
crystallite size. Before, doing that let’s know the important
basics. This is the Scherrer equation. L is crystallite size which we want to calculate. All angles are in radian. K is constant. In most of the cases for spherical crystallites,
you can use 0.94 or close to 1. So, the formula you have to insert in Origin
or Excell is this. Let’s do it. The first column is for K.
Second is Lambda in Angstrom. Peak position, 2 theta.In degree. Half-width at full maxima. in degree. Last column for calculated crystallite size. in nanometer. I am using K as 0.94. The wavelength of X-ray as 1.54178 angstroms. These are constant for all peaks. Copy and paste calculated values. Now carefully enter the formula. First column, K.
Multiplication. Second column, Lambda. Division. Radians of FWHM. Division. Cos of peak position. In radians. As it is 2 theta, divide by 2. For Angstrom to nanometer divide by 10. Close the brackets. Press ok. You got the crystallite size. Seems preferential growth of crystallite. Or could be a technical problem. If you see such difference, ignore the low-intensity
peaks. Now alternatively,
You can download these templates from the link given below. In both these Excel or Origin, I have inserted
the formula. You just have to paste the values from
the full width at half maxima calculation.

7 thoughts on “FWHM & Crystallite Size from XRD using Origin | 2 methods | Scherrer equation

  • April 30, 2019 at 3:48 am
    Permalink

    Hi. I tried analyze my XRD data. After picking up the peak, and try to "Fit till Converge", The last message says "Fit did not converge".. So, what should I do?

    Reply
  • August 27, 2019 at 7:38 am
    Permalink

    You are the champ.

    Reply
  • October 9, 2019 at 1:26 pm
    Permalink

    Foi de grande ajuda este tutorial! Muito obrigado por compartilhar seu conhecimento. Thanks to share your knowledge!

    Reply
  • October 30, 2019 at 6:01 am
    Permalink

    Instrumental brodening needs to be subtracted.

    Reply
  • November 21, 2019 at 1:27 pm
    Permalink

    Thank you so much for your video. It helped me a lot! 😊

    Reply
  • December 19, 2019 at 10:14 am
    Permalink

    FWHM should be multiply with cos theta, right?

    Isn't it should be:
    (Col("K")*Col("λ"))/radians(Col("FWHM"))*cos(radians(Col("Peak Position 2theta"))/2)/10

    instead of:
    (Col("K")*Col("λ"))/radians(Col("FWHM"))/cos(radians(Col("Peak Position 2theta"))/2)/10

    Please correct me if I'm wrong. TQ

    Reply
  • December 25, 2019 at 8:29 am
    Permalink

    Thanks a lot it is working sir…..

    Reply

Leave a Reply

Your email address will not be published. Required fields are marked *