Hey guys, how's it going? So in this tutorial, I'm going to show you guys how to calculate FWHM for the various peaks in your X-RD pattern. Now the FWHM is given by a formula something like this. This is called the ShrR formula. So here beta is your full width at half maximum and it is very proportional to 2 theta or dependent on that. Then it is equal to K lambda by L cos theta where L is the crystallite size. Therefore the peak width is needed to calculate the crystallite size for your sample. And that is what I'm going to show you how to do that. And the factor K here is, you know, it can take several values depending on the type or the shape and size of your sample. So it can either take 0.89.94 and many people just take it to be 1. It doesn't really matter that much. Then lambda is the wavelength of your X-ray. And cos theta here, theta would be the angle or the position of the peak and beta. That is a full width at half maximum or the FWHM should be in gradients. So many people make the mistake. When I used to do that or did that one time at least, that I took beta in, you know, degrees. So you have to take that in gradients. And another way to calculate the crystallite size could be to use the integral breadth instead of FWHM. And that can also be done pretty easily. But I will show that in some other video and this video will be dedicated to only, you know, learning how to calculate the FWHM. So how to calculate the FWHM would be to use some kind of software that performs a Gaussian fit for my X-ray beta. And in my case, I will be using origin. And so you should, you know, if you don't have origin, then you should get origin. Or maybe it was some of the tutorial because this one is based on origin. So another thing to know is that I'm not sure about that. But I don't think that origin version less than 8 or 8.5 can do this. I have got origin 9, but, you know, just make sure that you get some latest origin to do this because I'm not sure if versions before 8.5 could do this. I mean, they do have, you know, wizard that performs a fit, but I'm not really sure how well that, you know, is. Okay, so enough with the chit chat. And now let's begin to calculate the FWHM for my exciting pattern. So I have my, you know, ex-hardy data in this notepad file or TXT file. So let me just copy all that. And, you know, okay, so let's copy all the data. And now we will plot it. Oh, oops. I'm going to have to repeat that again. Okay, so just copy all the data down till the very end. Press Ctrl C and paste it in the ex-old. Okay, so now I have the data. Okay, so just what I did was I pressed Ctrl and selected the two columns and right-click on them, then went to plot and went to line, then line. So that will plot your ex-hardy pattern. Okay, so here is the ex-hardy pattern. As you can see, I have already made TNT that shows two TNT here and the XCD here. And you can just label whatever you want here. Okay, so let's say I want to get the FWHM for this particular peak. Right? This is the highest intensity peak. And it should be noted that to get, you know, the pristly side it is advised to get the width of the most intense peaks of your ex-hardy pattern. So just press here to scale in to this peak. Okay, and make sure you have some of the background radiation on the both sides. And then go to analysis, then two peaks and baselines, then multiple peakfict and open the dialog. Okay, so in this dialog, what you need to do is you need to select a peak function and I'll be using Gaussian function. Okay, I will prompt you to double-click to pick the peaks. In my case, it's just one. So I'll just go ahead and here I'll double-click it and then open N-lift. That is, that stands for non-linear fit. Okay, so here it is showing you various parameters like base, center amplitude, FWHM, etc. Now what you need to do is you need to click here that is fit until converged and voila your Gaussian fit is ready and you can get the parameters from here. So that is the FWHM for this particular fit is 0.49842. Okay, then and you know this, you know, dialog box also shows you the kind of function that you are using to fit your data. And you can use many of the functions by, you know, just into settings and bringing up some of the functions, you know, filling your data. So any who what we needed was after BWHM using the Gaussian fit and we got it. So just go ahead and press done and it will generate a good, you know, nice table for you. So this is some statistical data like the R2 values, etc. And a lot of data is here and you can just, you know, check the fitted points also here. Then I don't need that. All I need is, you know, the plot right here. So I've got that. So here I have my, you know, equation of the Gaussian fit, the R reduced sky square value, the adjuster square, etc. and all the parameters for the fit. Okay, so that's how you calculate the Gaussian fit for a particular peak. And in case you wanted to do a lot of peak set ones, then what you could have done was, you know, just, okay, so to illustrate that, let me just create another graph. So I'll just go to this book back sheet one. And let me just create another graph to show you how to, you know, get the Gaussian fit for a number of peaks at once. So what you need to do is basically just go ahead and select multiple peaks and then go to analysis multiple peak fit. That is what we use last time. Okay, so Gaussian, okay, select the peaks by double clicking on those open and left non-linear fit. Okay, and then just fit them until they converge. Okay, now as you can see the iterations keep on going and going and they will probably go until 100. I'll just go ahead and start with right now. So what you can see is that even after so many iterations, it just couldn't provide a fit for this third peak. So maybe we should, you know, select the peaks a little differently. So maybe we can get, you know, these two peaks at once, but not the third peak along with them. So that is a common problem. So it is usually advised to, you know, only take the most intense peaks for your, you know, for the analysis of crystallite size. And as you could see that that peak, the third peak was pretty much, you know, relatively really small compared to these two. So they were some problem with that. And here what I've done is I just press this and I got, you know, the Gaussian fit for the two peaks at once. And we can see that it's pretty good actually the blue curve if you see. It is pretty much the same or is approximating the original data pretty good. So the two FWHM for the two peaks are, you know, 0.199 and 0.21. Okay, so well that's it. That's how you perform a Gaussian fit for your peaks and your excited data and get the FWHM and does calculate the crystallite size using the formula that I just mentioned. Okay, well hope you enjoyed this video and learned something from it. And if you did, don't forget to hit the like button and subscribe to my channel for more videos like this. And thanks for watching and have a great day. .