Dear Neha,

and what is about the error (or much better uncertainty) of Scherrer's constant K that involves in the calculations and even strain? It is much larger than your calculated low percentage value.

http://prism.mit.edu/xray/oldsite/CrystalSizeAnalysis.pdf

https://www.researchgate.net/post/How_to_calculate_the_error_in_crystallite_size_determination_from_Scherrer_equation

Crystallite size calculation via XRD peak width(s) is a very rough size estimation, which depends on the model being behind and the real shape as well as shape- and size distribution. I would not assign any error to that estimation. Every one from the XRD community dealing with those numbers know that they are very, very rough numbers giving just the order of magnitude or something like that.

So please 'hands off' presenting errors.

Final remark: an error of 1,12% of 48nm leads to a value of about 0,54nm.

Dear Neha,

and what is about the error (or much better uncertainty) of Scherrer's constant K that involves in the calculations and even strain? It is much larger than your calculated low percentage value.

http://prism.mit.edu/xray/oldsite/CrystalSizeAnalysis.pdf

https://www.researchgate.net/post/How_to_calculate_the_error_in_crystallite_size_determination_from_Scherrer_equation

Crystallite size calculation via XRD peak width(s) is a very rough size estimation, which depends on the model being behind and the real shape as well as shape- and size distribution. I would not assign any error to that estimation. Every one from the XRD community dealing with those numbers know that they are very, very rough numbers giving just the order of magnitude or something like that.

So please 'hands off' presenting errors.

Final remark: an error of 1,12% of 48nm leads to a value of about 0,54nm.

As Gerhard Martens already explained, the grain size calculations from XRD are just estimations. I also wouldn't do any error calculations here.

If you nevertheless want to have an estimate for the error (or better the statistical uncertainty), I would recommend using a more advanced method than the Scherrer equation. With Williamson-Hall or Warren-Averbach, you can already get an error from the quality of the (linear) fits. Even more sophisticated methods also extract errors from the quality of fitting. But always be aware that the assumptions of the models may introduce (systematic) errors that are not necessarily included in these estimated errors.

Just as a side note: the "Debey Scherrer equation" doesn't exist, it's just the "Scherrer equation" as was already discussed in a nice paper by Holzwarth: https://www.nature.com/articles/nnano.2011.145

Thank you Gerhard Sir,

According to you we just have to write the answer what we get from the calculation of Scherrer's equation.

But from someone I got suggestion to add error in the calculated crystallite size value and that error is 5%. That person told me to just multiply the calculated crystallite size value with 0.05.

I could not understand why 5%? Is it true? If yes then why 5%?

Dear Neha,

I do not understand the 5% either.

Please have a look at the range of Scherrer's constant K ranging from 0,8 to about 1,4 from the following link (size and strain broadening section):

https://en.wikipedia.org/wiki/Powder_diffraction

Taking the mean of K=1,1 we have K values of 1,1+-0,3, i.e +-~30%. This 30% error is a number which we all can live with (my personal opinion).

Remark: in the above PPT on 'Crystallite Size Analysis' from Scott A Speakman, the K-value range is given from 0,62 < K < 2,08. So you see that you are also allowed to assign much larger errors than 'only' the 30% just mentioned.

Without any knowledge on crystallite shape and without any calibration with respect to known size and similar shape you end up with such large error values.