Manual Plot of FWHM from XRD Data

How to Plot FWHM Manually from X-Ray Diffractogram Data

Rizky Arief Shobirin

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[1] Department of Chemistry, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Indonesia 65100

[2] Research Center of Civilization, University of Brawijaya, Indonesia 65100

*email : rizky_ariefs@yahoo.com, rashobirin@gmail.com

This is just a short manual instruction for determine the FWHM (full width at half maximum) in x-ray diffractogram data. It will important if your instrument do not determine the FWHM accurately, but you need the data for determination of crystallite size-strain.

So, please check.

Run gnuplot (in windows : first you must download and install it).

Copy your diffractogram data in same location where gnuplot installed in your computer.

Type the command for running your diffractometer data in gnuplot. And the result you will find the diffractogram, which showed below.

Then, magnify your diffractogram’s peaks as your estimation, then plot your peak’s coordinate, where 2θ as x axis, and I as y axis.

From the peak’s coordinate, you have create an additional equation to know your half maximum peak by type “y=[intensity you have observed]/2” in gnuplot. Iy axis.

For the next step, plot again the diffractogram data and the additional equation, so you will find the relation of the equations and you will able to plot the two coordinates of 2θ in same half peaks, which is shown below.

So, from the difference of 2θ in same intensity, we could calculate the FWHM in degrees.

And the next step is transformation from degree of divided-FWHM to radians, and finally you will able to calculate the crystallite size by scherrer equations or with williamson-hall method.