"Many researcher use FWHM because it's easier", correct! Also expedient :-)

However, the way the data is acquired and stored, the converse is true. The determination of half height requires the correct estimation of "background signal" or "base-line" as well as the correct "peak value".

Here are some suggestions that may be executed using Excel with little trouble:

• Integrated Intensity = Sum of all (intensity value minus the "base-line" minimum value), shoulder to shoulder for the Bragg peak.
• Integrated Breadth = Integrated Intensity/(Peak Value minus "base-line" minimum value)

There is no need to assume the Bragg profile shape for such computations. In case of FWHM use, one needs to assume the Bragg profile shape to compute "integrated breadth". "Integrated Breadth" values computed numerically from the XRD relative intensity data as described above would have less influence due to the statistical "chatter" seen on all XRD profiles due to the "scintillation counting" process.

BTW the relationship between FWHM and "integrated breadth" in the case of a "Gaussian" Bragg profile shape is:

Integral Breadth, β, is related to the FWHM peak width, H, by

                          β = 0.5.H.(π / loge2)1/2

P.S.: In the good old days, one would have to cut out the Bragg profile from a paper plot and weigh it to estimate the "integrated intensity" :-) Capiche? The resolution in the Bragg profile shown below is 0.00004o per video frame (0.0005 DPS), 1x1 mm integrating window @165mm SDD.

http://pd.chem.ucl.ac.uk/pdnn/peaks/gauss.htm

It's better to consider FWHM.

Dear Vibhor Atreya,

The FWHM is a better measure of XRD peak width

"but I get better fits using integral breadth". How did you compute "integrated breadth"?

In general, most mathematical relationships involving "defect density" utilize "integrated breadth". So even when using HWHM or FWHM, it is common practice to convert to "integrated breadth" ("beta",  β in Radians), by assuming the shape of the profile. These shapes assumed include Gaussian, Lorentzian, Pseudo-Voigt, Pearson VII etc. Practically, the Bragg profile is never any of these shapes. Close but no cigar! The correct "instrument profile" needs to be either computed numerically for the "strain free" state or obtained experimentally using some sort of a "standard".

Defects seem to disproportionately affect the shoulder and tail areas of the Bragg profile well below the "half intensity" point. Therefore, such defects may be undetectable using the HWHM or FWHM. See the example of a LiF2 crystal noted below. A comparison between FWHM Map and "integrated breadth squared" map clearly shows the difference in image contrast favoring better spatial resolution as well as dynamic range using β2. Bragg angle for LiF2 (113)- is 78.7301o 2ϴ with 0.48 Arc Sec increment per video frame rocking (ordinate axis of Bragg profile). The last image is a typical rocking curve profile obtained by integrating the 25mm diameter 2D detector FoV (field of view) as is done conventionally using the 0D point or scintillation counter/detector.

This was an example for a large mono crystal. In your case, with a powder sample, the concept is similar. I would think that the use of "integrated breadth" would be more apropos than the FWHM or HWHM. By default it ought to be "integrated intensity" and "integrated breadth" just by the nature of data acquisition used in your case.

You may download original images to magnify.

https://www.flickr.com/photos/85210325@N04/34003566875/

https://www.flickr.com/photos/85210325@N04/31825436001/

https://www.flickr.com/photos/85210325@N04/31958849332/in/photostream/

I strongly concur Dr.Ravi Ananth. I think also that the using of "integrated breadth" gives more accurate results than the FWHM or HWHM. Many researcher use FWHM besause it's easier than "integrated breadth".

Good Luck

"Many researcher use FWHM because it's easier", correct! Also expedient :-)

However, the way the data is acquired and stored, the converse is true. The determination of half height requires the correct estimation of "background signal" or "base-line" as well as the correct "peak value".

Here are some suggestions that may be executed using Excel with little trouble:

• Integrated Intensity = Sum of all (intensity value minus the "base-line" minimum value), shoulder to shoulder for the Bragg peak.
• Integrated Breadth = Integrated Intensity/(Peak Value minus "base-line" minimum value)

There is no need to assume the Bragg profile shape for such computations. In case of FWHM use, one needs to assume the Bragg profile shape to compute "integrated breadth". "Integrated Breadth" values computed numerically from the XRD relative intensity data as described above would have less influence due to the statistical "chatter" seen on all XRD profiles due to the "scintillation counting" process.

BTW the relationship between FWHM and "integrated breadth" in the case of a "Gaussian" Bragg profile shape is:

Integral Breadth, β, is related to the FWHM peak width, H, by

                          β = 0.5.H.(π / loge2)1/2

P.S.: In the good old days, one would have to cut out the Bragg profile from a paper plot and weigh it to estimate the "integrated intensity" :-) Capiche? The resolution in the Bragg profile shown below is 0.00004o per video frame (0.0005 DPS), 1x1 mm integrating window @165mm SDD.

http://pd.chem.ucl.ac.uk/pdnn/peaks/gauss.htm

Thank you Ravi Ananth. Indeed I did not assume any profile shape while computing the integral breadth, I get better results in the sense that since I am trying to make a fit using peak widths (a williamson hall plot), I get less scatter when I use integral breadths. Although in my case I will have to use FWHM only, it gives some other advantages (besides the easiness part! ;-)

It was a good discussion. Thank you for your input. 

"I will have to use FWHM only, it gives some other advantages", like what Vibhor?

I'd like to know as well :-)

That still doesn't obviate the need to convert the FWHM to "integrated breadth" in order to use in any of the conventional XRD analyses including the Scherrer Equation or the W-H Analysis, does it?

I have split peaks in my sample XRD which are very close and difficult to resolve. Therefore, I had to use peak profile fitting in order to deconvolute them. Once there is a need to do profile fitting, then it does not matter if I take FWHM or IB. Yes, in my other samples there was no splitting and I got very good fit using IB without any profile fitting. According to the original paper by Williamson and Hall, they mention FWHM and IB both should do the job, although I see mostly research papers use FWHM. It was just that I got good fits using IB, and that may be because just by measuring the area and the peak we avoid even the little error that might creep in when doing the profile fits.

Post your "peak splitting" XRD data for better feedback.

• What is the powder size? Beam conditioning (as Mark points out next)?
• Have you considered using a simple "dental film" at the "peak splitting" Bragg angle in front of your point counter to better understand the 2D XRD signal?
• "It was just that I got good fits using IB", that in itself should be experimental evidence of the efficacy of IB versus FWHM, right?  :-) Why don't you plot them and show?

Note: In fact it is a lot easier to compute IB directly from XRD data (unprocessed), using Excel or other tools including Origin, than estimating FWHM consistently using manual methods or approximate curve fitting.  The contributions from the shoulder and tail regions below the "half height" will be lost if one considers only the FWHM. These shoulder and tail areas are critical for quantifying the micro lattice strain state in each subject sampling VOXEL on the sample surface. BTW I am also a recovering FWHM user :-)

FWHM or IB? What is your verdict? https://www.flickr.com/photos/85210325@N04/31988536281/in/photostream/

https://www.researchgate.net/post/What_is_the_likely_Nanostructural_origin_for_observations_of_the_LiF_113-XRD_reflection_rocking_curve_integrated_breadth_squared_b2_map

https://www.flickr.com/photos/85210325@N04/31988536281/in/photostream/

Dear Vibhor,

May I ask you

(1) What material are you studying? At least symmetry?

(2) How do you account for instrumental broadening?

(3) Do you  use primary monochromator or the Rachinger procedure  for stripping out K_alpha2 contributions?

As for the discussion, I largely agree with Ravi'.

However, if using Rachinger procedure, there are problems (e.g., materials with small broadening) when calculation of integral breadth is uncertain because of the artificial oscillations.

In any case the Willamson-Hall method is just a rough model to describe line broadening effects. A good review is attached

I have similar querry . I am unable to decide .FWHM or Integral beadth?