# When using the Debye-Scherrer equation for calculating particle size (D=Kλ/(β cos θ) does one have to halve the FWHM(β)? Must all angles be in Radians?

The Debye-Scherrer method is used to obtain X-ray diffraction measurements in powders.This method is applicable to crystallites ranging from 1.0 to 0.01 μm in diameter, but the grains must have good crystallinity.

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Matteo Leoni· Università degli Studi di TrentoMy suggestion is always: if you want to drive a car on a public road, first learn to drive.

So please, before using ANY tool, first open a book or browse through the Internet to find out what is all about and to find out the relevant literature IN the field (too many people look for literature on Scherrer equation in papers that have nothing to do with X-ray diffraction). You can find the derivation of Scherrer equation in any X-ray (powder) diffraction book and if you look at that derivation, you find the answer to your question as well (any student know that angles, especially in trig formulas are in radians). Plus β and FWHM are two different things (the integral breadth versus the full width at half maximum) that may or may not be the same ofr a given peak.

This said, Scherrer equation give you a number related to the distribution of length of columns composing your specimen. It CAN be related, under quite strict hypotheses, to the mean domain size. In general, knowing the domain shape (that you can hardly guess from Scherrer formula), the value you obtain is a ratio between high order moments (4th over 3rd) of the size distribution. For some discussion:

https://www.researchgate.net/publication/200045699_Line_broadening_analysis_using_integral_breadth_methods_a_critical_review

(Scherrer formula is the size part of the Williamson-Hall method).

So forget about "particle size". And forget about being able to characterize anything above 100 nm using Scherrer equation (the equation does not include instrumental and strain broadening effects always present in a pattern). Moreover, talking about "crystallinity" is also not appropriate as you characterize the crystalline part of your material only.

If you are still convinced that Scherrer formula is of any quantitative use in 2013 (it is good for qualitative comparison), then:

* D and λ have the same unit of measurement (e.g. nm as per SI)

* FWHM is the full width at half maximum of the peak (not half of it) in rad. As you have it in deg from the machine, just multiply by pi/180

* theta is half of Bragg angle in rad

If you want to work quantitatively then first open a good book on diffraction and then have a look at more modern analysis techniques (e.g. Whole Powder Pattern Modelling, https://www.researchgate.net/publication/11527348_Whole_powder_pattern_modelling) that can give quantitative information compatible with the microstructure of the material.

Matteo Leoni· Università degli Studi di TrentoSitarama, I think most people do not care about the instrument correction simply because they found that someone else was using Scherrer formula that way and they decided to do the same. I cannot count the number of wrong citations to Scherrer (1918) and I am pretty sure most people out there never saw or read it (they just keep citing something they found in other publications). Believe or not, in that article there is no mention on how to derive the formula!