The basic broadening effect produced by powder diffractometers was mathematically described by Caglioti et al., whose simple equation identifies a theta dependence on the broadening. Caglioti expression for instrumental broadening was specifically derived for neutron diffractometers.  Your choice of peak profile will dictate which of the described broadening factors can be included in the calculation. Gaussian and Lorenzian by default are almost using the same parameters for Instrumental broadening U, V, W. Once the instrumental broadening have well known origins, is more usual describe them with simple functions like Gaussian and Lorenzian. For more parameters and their effect on the description, search for Pearson VII and Tomandl Pseudo-Voight that will allow the extra use of NA, NB and NC parameter. However U,V and W are usually described as Instrumental broadening, and NA, NB and Nc are described as Profile parameters. In specific literature you may find more detailed discussion on those functions. For usual instrumental profile evaluation Gaussian peak function is the usual choice, once the origins of instrumental parameters are well known.

Voigt is a convolution of Gauss and Lorentz. The analytical expression must be approximated numerically in peak fitting. We cannot directly extract a physical meaning for a single half width for a Voigt function. Rather, in many spectroscopy applications, we understand the half width of the Lorentz contribution to be the intrinsic line width and that for the Gauss to be broadening (thermal, collision, instrument factors). Unfortunately, we also can only approximate the two separate contributions in the Voigt because it is an approximation and/or the exact separation requires a mathematical but numerical deconvolution operation.

I am otherwise curious that you post a Lorentz for an instrument term. I believe the transmission function of any instrument is always modeled as Gaussian broadening (convolution) of the intrinsic sample response function.

The basic broadening effect produced by powder diffractometers was mathematically described by Caglioti et al., whose simple equation identifies a theta dependence on the broadening. Caglioti expression for instrumental broadening was specifically derived for neutron diffractometers.  Your choice of peak profile will dictate which of the described broadening factors can be included in the calculation. Gaussian and Lorenzian by default are almost using the same parameters for Instrumental broadening U, V, W. Once the instrumental broadening have well known origins, is more usual describe them with simple functions like Gaussian and Lorenzian. For more parameters and their effect on the description, search for Pearson VII and Tomandl Pseudo-Voight that will allow the extra use of NA, NB and NC parameter. However U,V and W are usually described as Instrumental broadening, and NA, NB and Nc are described as Profile parameters. In specific literature you may find more detailed discussion on those functions. For usual instrumental profile evaluation Gaussian peak function is the usual choice, once the origins of instrumental parameters are well known.

Good fundamental question! I'm keenly interested.

In my opinion, once you have the true instrumental profile either by numerical simulation or experimentally using a "true" standard specimen, the need for assuming any arbitrary shape would be obviated :-)

Here is an example using GaAs (004) reflection and comparing it to the Bruker LEPTOS generated "strain free state" Bragg profile. β in Radians (integrated breadth of the Bragg profile) and not FWHM ought to be used for all your computations anyway.

Some helpful information in the link attached for the conventionalists still using linear diffractograms a century after the Braggs' Nobel Prize! Evolve :-)

"Source of Peak Broadening" Courtesy School of Crystallography, Birkbeck College, University of London

BTW once any type of beam conditioner is introduced in the diffractometer, which is quintessential for resolution, the shape is highly instrument specific. The shape of the Bragg profile has a whole lot of other Nano structural information such as defect types as well.

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

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.researchgate.net/post/Is_it_possible_to_determine_the_type_morphology_of_defects_in_single_crystals_by_the_shape_of_the_Bragg_XRD_Rocking_Curve_Profile

 I fully agree with you points. The normal way to measure sample broadening contribution is to first determine and model the diffractometer's broadening instrument profile. To do so, is necessary to use a "near-perfect sample", I don't like this expression, what would be a near-perfect sample anyway... and model the diffractometer+near-perfect-sample line profile. At this point, we need to consider that even a simple mistake in sample positioning, which is not a diffractometer neither one intrinsic sample problem will disturb the profile. The so called instrument broadening is in fact a more broad correction, the positioning of the sample could be (not necessary is) a recurrent equipment/sample holder problem. In fact what is done is to model the total answer of the diffractometer (equipment+tube age+sample positioning+ any sort of no conformity) based on a well stoichiometric and size described sample, like LaB6, BaF2, NIST Silicon powder. Based on the fitted total profile, knowing the sample it self as a standard we evaluate the total equipment broadening. So, repeating the measurement with the desired sample we suppose to determine the total broadening of a working sample. Based on that, the peak profile shape will be straight related to a specific instrument and/or sample preparation procedure previous to your analysis. Now, we could go on the fundamental parameter calibration discussion, and once again the sample preparation and/or positioning would come to the attention changing all answer for the whole system.

As Dr Ravi attached link: http://pd.chem.ucl.ac.uk/pdnn/peaks/broad.htm, the peak broadening not only Gaussian and Lorentzian function (convoluted in a simple way)  but there's also other complicated terms from the way beam monochromatized, goniometer, detector, and nature of the specimen.

In my opinion the best method to get the instrument contribution is by Fundamental Parameters Approach (FPA) - "Instrumental and sample aberrations are calculated from first principles, and convoluted with the emission profile to form the final line profile. This methodology eliminates the need for a standard." J. Appl. Cryst. (1992). 25, 109-121 "A Fundamental Parameters Approach to X-ray Line-Profile Fitting".