Generally, the Scherrer formula is used to determine the crystallite size or grain size. In this formula why the constant term K is taken as 0.9 or 0.94?
you can take any number you like, as with the result of Scherrer formula you can just play bingo.
f you just want to know the mathematics behind this, the number comes out easily if you approximate the diffraction profile for a single ideal sphere with a Gaussian.
I seriously doubt you are analyzing the diffraction pattern for a single non atomistic sphere and I also doubt your peak profiles are Gaussian...
Most scientists still in 2012 use this formula to model the broadening of the diffraction peaks without knowing what is the meaning of the result and without reading the journals where it is clear that Scherrer formula is dead for proper domain size analysis. This is why the value f the constant makes zero or no difference!
you can take any number you like, as with the result of Scherrer formula you can just play bingo.
f you just want to know the mathematics behind this, the number comes out easily if you approximate the diffraction profile for a single ideal sphere with a Gaussian.
I seriously doubt you are analyzing the diffraction pattern for a single non atomistic sphere and I also doubt your peak profiles are Gaussian...
Most scientists still in 2012 use this formula to model the broadening of the diffraction peaks without knowing what is the meaning of the result and without reading the journals where it is clear that Scherrer formula is dead for proper domain size analysis. This is why the value f the constant makes zero or no difference!
Hi, K is based on the geometry of the crystal and 0.94 is when it is spherical (and cubic symmetry).............. people use values between 0.87 and 1.1, choice is yours!
Hi, to continue with Matteo's comment, you can try a so called Williamson-Hall analysis to get a more accurate and scientific approach to the question of line broadening.
K depends on the many factors like on the shape of the particles, hkl indexes of the reflector planes, on the particular definition used fo define the beam width as well as the definition used assigned to the particle size. In the case of spherical particles (mostly used), the adopted value of the constant is 0.9, but K may be attributed in the range between 0,7 and 1,7. So, make the best choice for your case!
to continue the comment of Jules, the WIlliamson-Hall approach is as inaccurate as the Scherrer formula (as it is based on it...). The real truth is that people should READ the literature (the one in the field, not the application in another field done by someone totally inexpert) and check the latest advancements. In 2012, presenting quantitative values using the Williamson-Hall or the Scherrer formulae or saying you determine the "grain size" is TOTAL NONSENSE
Dear Navajyoti, quantitative values calculated using any form or modification of Scherrer is inaccurate at best. Prof. Leoni is an expert in this field and I suggest you follow some of his publications, earlier from 2001 - 2004 and few from 2010 - 2011 (there are so many!) + a thesis by Kenneth Roy Beyerlein (available in web, Georgia Tech) where you will find excellent information regarding limitations of Scherrer formula, more accurate way to do it and related literature. I am sure Prof. Leoni would be able to better direct you regarding this; unlike many of us, Prof. Leoni is being modest to draw attention to his own publication (!!). There is also "Powder diffraction : theory and practice" / editors, Robert E. Dinnebier and Simon Billinge that will be handy.
As a side note, this is the best part of RG, that you get feedback from the experts in the field.
Here is a link: http://mysite.du.edu/~balzar/breadth.htm
A program based on Double Voigt type treatment of Scherrer formula-- I am not an expert to call this inadequate, but (be warned about the validity) I will probably not use it without secondary verification on the size analysis (my personal opinion).
Hope this helps--
Palash
Lets cross ref this post with this one: https://www.researchgate.net/post/X-ray_diffraction
In the beginning of this topic, Navajyoti Choudgury asked WHY the constant K is taken as 0.94 in the Scherrer formula and he didn't ask about the best approach he should use. For my opinion, questions and answers here are made in order to build the intellectual capacity of students and/or researchers logged here in RG, even if these people made wrong comments in any other topic. In this case, people with further knowledge should remark the others to help them. Savvy people should never criticize comments made earlier.
By ending my comment, i aggred with Palash when suggested read some Prof Leoni papers who is expert in this field or try other program which best suits to your case.
All the best!
Can't agree more André -- I lost the focus there a bit. Thanks for the reminder! :)-
Oh dear.. no offence intended, but this wins the prize for the most absurd answer!
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