Of course you have to be sure that everything went right with correction for instrumental resolution. Then the question arises, whether you see that behaviour for all your reflection hkl or only for a series of higher order reflections.In the former case, if you have only few reflections, an anisotropy of the line broadening may mimic an S-shaped behaviour of the line widths.

A distinctly S-shaped evoluation has been observed by Rafaja in 2004 (J. Appl. Cryst. 37, 613). I have reported more cases, where at least a non-linear plot should occur, including an example (the example with all the references: Leineweber, Krumeich, 2013; Phil Mag. 93, 4440). The basic origin of such behaviour is sufficiently short range gradients in the crystal/microstructure which leads to hkl-dependent interference phenomena in diffraction.

Of course you have to be sure that everything went right with correction for instrumental resolution. Then the question arises, whether you see that behaviour for all your reflection hkl or only for a series of higher order reflections.In the former case, if you have only few reflections, an anisotropy of the line broadening may mimic an S-shaped behaviour of the line widths.

A distinctly S-shaped evoluation has been observed by Rafaja in 2004 (J. Appl. Cryst. 37, 613). I have reported more cases, where at least a non-linear plot should occur, including an example (the example with all the references: Leineweber, Krumeich, 2013; Phil Mag. 93, 4440). The basic origin of such behaviour is sufficiently short range gradients in the crystal/microstructure which leads to hkl-dependent interference phenomena in diffraction.

Dear Dr Uhlig:

When someone say that have an S or a L curve or a linear curve but with a negative coefficient of angular inclination at a W-H plot, a very interesting paper can be expected. Alternativelly, new advances in processing can be reached.

There is a great number of papers about or involving  W-H plot or its parameters but as a whole this great set does not solve the problem that each researcher have. Despite absent of data here, in a holistic way the question is very interesting, from previous it is possible to attain an another data set that can auxiliate a priori or provides small insight about origem of the collection.  See, in a single W-H plot all (hkl) addressed to all diffraction lines can be plotted simultaneously. But it is interesting that one or more plot with particular information. As an example, microstrain and crystallite size can be derived if one or more crystallographic direction is or are investigated in a individual way.  For this, the inspection of the set of hkl planes allows to generatean  interesting sub-data, in specific whether there is a set  reflections ascribed to paralell  planes. As an example, from original data it is possible to pick up the hkl planes: 100, 200, 400, 600 or another set as: 002, 004, 008 or 240, 480, etc, etc...Well, in this last case a linear plot with two experimental points is obviously a weakness of new data, but it is valid in a proper context. This strategy allows to access, in fact to estimate,  the microstrain in distinct crystallographic direction, being recommended  to make use of an entire set of diffraction lines.  But do not be forgotten that there are another characterization tecniques to support the finds via W-H. Has, an excellent diffractogram and deep know-how in the manipulation of diffractometer is relevant. Be with two or three or four points, some confidence degree about the anysotropy of material is now "visible". From this point, it is possible and necessary to consider the scale of nanopowder. Here, 1 to 10 nm, 10 to 100 nm or 100 to 500 nm show intrinsic features steamming of the process of growthing of nanoparticles. taking in account that pionner crystalline nuclei have 2,5 nm, hypothetically, due the incredible surface energy, this small nanoparticles undergos a coalescence reach the superior interval of size and oncemore, one time more, until the average particle size reached 500 nm, in general a polycrystal. If the process is ideal, a collection of particles is attained which exhibits monodispersed feature.  If not, some nanoparticle has distict crystallite size and microdeformation. Depending on the crystalline symmetry, the previous picture can change and again if there is multiplicity of unitary cells. At least, diffractogram profile via Rietveld method can be applied as further tool. Nowaday, another mixtures can be thinked as same phase but distict symmetry, same symmetry but distict space group 

Thanks a lot for all those very helpful answers.

@ Dr. Leineweber; Is it possible that you send me the papers from you / Coworkers (Leineweber, Krumeich, 2013; Phil Mag. 93, 4440) and Rafaja in 2004 (J. Appl. Cryst. 37, 613) since we dont have acess to this journals from Gießen?

If the materials is cubic you may not find this discrepancy because the type  of the atoms and bonding between them will be the same and the compressed materials will not suffer any deviation from the straight line because the material is isotropic But if your materials is not cubic and have other system the the distribution of the atoms and the different bonding between them will be different may be in  two direction or even three direction depending on the crystal system and space group. So please draw the W-H plot for different orders of ( hkl) separately  i.e 100,200 ,300 ....ect and 111, 222, 333 in case of P lattice for example and then  compare the slope of each curve  with each other, by this method you will be able to understand the cause of this discrepancy. you have to chose the ordering of the reflection which follow its correct space group. By this drawing you will understand the cause of this unexpected shape . 

You may have success to get a "more" linear plot by taking into account the elastic anisotropy of your material according to a proposal by K. Reimann and R. Würschum: J. Appl. Phys. Vol. 81 (1997), p. 7186. For this you need the hkl-dependent elastic moduli. Thereby, in the case of submicrocrystalline electrodeposited Ni we were able to evaluate a size parameter for the coherently scattering regions (one should not call it "grain size"!) and the root mean square of (microscopic) internal stresses (cf. Mat. Sci. Eng. A390 (2005) 42-51, for example). Moreover you should have in mind the problem of determing the shape of the diffraction profiles (including the separation of instrumental broadening), it is often in between Gaussian and Cauchy like and could also depend on hkl. Additionally, a further effect could arise from the application of the uniaxial pressure. It could introduce a change of the initial isotrop distrubution of orientation of the powder particles. Therefore a texture information could be helpful.   

Just a few more infos about my material:

I use mechanical alloyed FeS2 NP as thermoelectric material and in addidion some doping with Co, Mn, Ni and Se

For the peak fitting i used Pawley to get as good as possible fit. At the moment i do some longe range measurments to get some peak from the same order.

The paper from Leineweber et al. was very helpful since a lot of discussion about the "Why can we see that?" was involved.

Thanks again for the contributions and help in that.

Andreas, could you please send me a copy of your article in Phil Mag 2013? Thanks in advance.

Christian, I agree with Andreas that possible artefacts from ALB (anisotropic line broadening) be excluded. In nanomaterials (but not only), ALB might indeed be more frequent than usually assumed.

On the other hand, I'm wondering how you can use the Pawley fit to get a WH plot? In it's original setting, the Pawley fit gives global peak shape parameters while individual FWHMs are needed for the WH plot, or am I missing something here?

Miguel, i´m using the Pawley Fit to get a good integral breadth since each single peak intensity is refined independently and i can extract the data form every peak. As far as i know the beta in WH plot is not the FWHM its the integral breadth. In addition you get the Scherrer konstant from the Pawley Fit which nice especially when you want to compare Scherrer and WH plot.

Pawley fits (like Rietveld or LeBail fits) usually require use of a model for the theta-dependence of peak-width and peak-shape. In the case of anisotropic line broadening, models with explicitly hkl-dependent peak-width and shape are available. Fullprof, I think (I am not a Fullprof user), can provide you the individual peak widths, even corrected for the instrumental resolution. I have seen WH-like plots on the basis of such values provided by Fullprof. However, this mainly reflects the refined parameters of the hkl-dependent line broadening model. WH-like plots should be much preferrably be done on the basis of individually fitted peak widths (corrected for instrumental resolution), which of course requires better data... In my opinion the WH plot can then can serve in selecting or developing  an appropriate hkl-dependent peak-width model for Rietveld, Pawley etc.

Williamson and Hall (1953) proposed a method for Separating crystallite and strain from the integral breadth. The following steps are used:

The profile fitting equation ( Lorenze ,or gausian are used  in order to fit the profile of each peak

2-Decompose the overlapped peaks into its separate peak 

3..Decovolute the experimental broadening β instrement from the observed broadening βobs

4-  in case of Lorentzian Peak shape, Use the following equitation for your (WH) plot.

{βobs- βinst} = λ/{Dv cos θ} +4 εstr {tan θ}

{βobs- βinst} cos θ = λ/{Dv} +4 εstr {sin θ}

Plot { βobs- βinst} cos θ on the y axis and

4 sin θ on the x axis                (Dv is the crystallite size, εstr is the strain 

The intercept will give the crystallite size and the slope will give the strain.

Very important notice : the (FWHM) is not a function of crystallite size and strain in the material, the integral breadth is the correct one.

.

If you have a Uniaxial  pressed  nanoparticles , Then surely  you will get preferred orientation and this will increase the intensities of some  reflections relative to the others, then you will never get the correct WH ,. accordingly you have first  first to correct for this preferred orientation and then do profile fitting for all your diffraction peaks by using the correct profile function  till you get a good R -factor. By this procedure you will obtain at last good WH plot.

Thanks all lot for the help. I found a big problem in my Fitting mostly concerning my peak fitting and the background of my measurments. It looks like the background i use was fitted in a wrong way, which resulted in the downwards curved W-H Plot for some of my Pellets. Others show really nice upwards curving which now can be addressed towards high defect concentrations. Thanks again for the help!

For Scherrer equation, crystallite size was calculated based on the measurement of a(hkl) peak using the following equation:

L =Kλ / Bsize cos θ

where L is crystallite size, K is a dimensionless shape factor (0.9), Bsize is line broadening at half of the maximum intensity (FWHM) in radian, λ is the X-ray wavelength for example for Cu Kα radiation (1.5406 Å) and θ is Bragg angle in degree.

Meanwhile, Williamson–Hall plot was used to estimate the crystallite size and lattice strain of the samples using the following formalism:

Btot = Bstrain + Bsize = 4Cε tanθ + Kλ/ L cosθ

where Cɛ is the lattice strain, Βsize is the particle size broadening, Βstrain is the strain broadening, L is the crystallite size, K is a dimensionless shape factor (0.9), λ is the X-ray wavelength for Cu Kα radiation (1.5406 Å) and θ is Bragg angle in degree.

Then Eq. 2 is multiplied by cosθ to yield:

Btot cosθ = 4Cε sinθ + Kλ/L

Hence, by plotting the graph of Βtot cosθ against 4 sinθ, the lattice strain, Cɛ of the sample can be obtained from the slope (gradient) while the crystallite size can be estimated from the intercept (Kλ/L).