I estimated the average crystallite size of BiSn binary alloy using scherrers formula and since anisotropic microstrain is observed, I did Williamson hall analysis by fitting with a gaussian, lorentzian and pseudo voigt profile. The values differ much and are : ~42 nm ( Scherrer formula ) ; ~ 51 nm ( Gaussian ) ; 68 nm ( Lorentzian ) and ~ 99 nm when fitted with a pseudo voigt function. Could someone guide.
Intriguing that you see such a difference between the Voigt and other results. From my experience of analysing peak functions in other applications, Gaussian and Lorentzian typically found the correct peak centre, within appreciable errors, but a Voigt yielded a better fit to the shape of the peak than the others, and hence had a lower residual.
Have you attempted to assess the quality of each of the fits?
You use different formulae, with different assumptions, and different routes and get different results. Why does this surprise you?
Thank you Alexander, thank you Alan for ur time and response. I followed all the procedures and was not expecting agreements. I was wondering about the big difference. Have you come across such big discrepancies? Have I erred somewhere?
@A S Pillai Thank you for your response. I think you'll find that in crystallite and particle size science that these would not be considered not 'big discrepancies'. Plus the term 'discrepancy' implies culpability or a fault of a technique, operator, or interpretation - I'd prefer the term 'differences'. Different, yes, but not an order of magnitude different. There are many reasons for broadening (size, strain etc) of an x-ray diffraction peak and separating these factors out is close to impossible. You're also 'imaging' a heterogeneous structure and thus every sample is different - all samples are wrong: some more than others. You also have the situation that you may have incomplete alloying in some parts of the structure (I had this exact problem with PdAg alloys in the 1970's during my Ph.D) . Further, all these interpretations produce only a single number when the killer word in crystallite or particle size distribution is the last one - 'distribution'. The math is different - there are different means - take a look at the attached. My last point is that some form of imaging - electron microscopy - is vital in understanding the variability of your materials. Enjoy and understand the differences - they actually provide more insight to your material.
Did you calculate these values automatically by using software or calculate yourself? Generally software’s calculate different values in same manner so, I suggest calculating by their formula or calculating more times and finally calculating their average.
@Hadi Averaging averages is a very dangerous concept. Read a few statistics texts to find out why. 'Averaging' an apple with a pear does not produce a papple - they're different fruit....
@ Alan according to calculating by software for same XRD pattern and same method, results are different but in near values. What is your idea about it? Averaging is wrong way? What I mean is that averaging of Apple separately and Pear separately. For example, Is it possible to averaging different results of Lorentizan values which calculated by software for the same XRD Pattern?
@ Hadi My understanding of the question is that the stated methods (Scherrer, Gaussian, Lorentzian and pseudo-Voigt) are different routes with differing assumptions. One should only average results that are stable and come via the same route with the same assumptions. Now if you're simply having 5 estimates by the Scherrer formula on the same diffraction peak (on the same film or diffractometer chart), I would agree with you. The differences here relate to the instrumental variation (which is always the smallest variable in the error budget) in estimating the peak width. However, if you took 5 measurements on the same peak analysis from 5 separate samples then the average here represents the heterogeneity of the material. If the sample is changing during the consecutive measurements (damage by x-rays for example), then averaging here simply is as meaningless as averaging the particle size distribution from dissolving sodium chloride in water (this is a kinetic study). Stability is key before averages are taken and an understanding of what is being averaged is vital. Once the average is taken it may be impossible to go back (e.g. the integration of a light signal).
- Badges
- Science topic