The reference for the WSODF model in MAUD is: Popa, N. C. & Balzar, D. (2001). J. Appl. Cryst. 34, 187-195.

But! They published the addendum in 2014 indicating that some of the tensor coefficients they computed back in 2001 and that currently (at least up to MAUD beta 2.55, and maybe after it, I have not checked) are hard-coded into MAUD are wrong. Thus it is better not to use this model just yet, if you are looking for a physical meaning.

Are you sure that the anisotropic peak broadening is not happening due to stress anisotropy? As I understand, you have synchrotron data from 2D detector, why should you integrate them all into 1 pattern?

Have you seen the paper  Wenk, H.-R. et al. (2014) Powder Diffraction 29, 220-232. doi:10.1017/S0885715614000360. ? The supplementary to this paper describes the step-by-step analysis of synchrotron diamond cell experiment.

 Thank you for the link and the note about the model, I had missed that.

I am familiar with the great paper by Wenk et al. We work in axial mode in the diamond cell though, not radial as in the paper. This changes the angles a bit, in a way that still confuses me on occasion. I will return to their DAC model in a second.

After your question about stress anisotropy, I went and loaded the data in 2D instead of the collapsed version (generated during the beamtime and what I was using for the initial analysis that led me here). I should mention that the data I first posted was measured using Si-oil as the pressure medium. It looked like there was some anisotropy (wiggly lines in the cake plot), so for comparison I also loaded data we have on the same compound, but with He as the pressure medium. I expected there to be less anisotropy here, but that turned out not to be the case!

I have attached a 2D version of the refinement and data set I first posted (CeN_Si-oil.par + CeN_Si.esg) as well as one for the He experiment (CeN_He.par + CeN_He.esg). In the He experiment, there is huge anisotropy on the {111} ring, but almost nothing on the {200}. For some reason, the Si-oil experiment is less so.

Now, returning to the DAC model in MAUD, I have been unable to find any combination of parameters that can reproduce the observed pattern. No matter what I do, I still get larger “wiggles” on {200} than in the data.

I hope someone can give me some clues on how to proceed.

According to your reported findings related to the (a,b, c)  values before and after the test , Poisson's' ratio is about  0.436  which is very close to  0.5, which is the  limit corresponds to incompressible solids, where  the volume change should be nil.  That is what you have being observing.  

My guess is: The relative shift between 111  and 200  can be only interpreted by the indication of  extrinsic stacking fault formation during severe  deformation.  That doesn't breakdown the cubic symmetry which is  fcc  in the present case.  Best Regards

I work with x-ray optics and could not help you with this problem. But I am trying to macrostrain (traction) perfect single silicon crystals by pulling and measuring in situ with double crystal X-ray diffraction the variation of lattice parameter. I have strong doubts on how to do it and maybe you could help me with that. If so, please, send me your email address. My address is [email protected]. Thank you in advance.

Just for the people who are following this question, I figured I would return with an update on a solution. As was alluded to by Mr. Vasin above, there is a model in MAUD called "Radial Diffraction in the DAC". It took me a bit of digging to understand what the model actually covers, but the relevant paper is the one by Singh et al: http://scitation.aip.org/content/aip/journal/jap/83/12/10.1063/1.367872 

I'm still having significant trouble figuring out exactly how the angles that one refines are defined, but as I understand it, the first angle (alpha) is the angle between the primary stress direction and the Z axis (wherever that might be located in real space), while the beta angle is then a further rotation about Z (again, I wouldn't be able to tell you which direction is positive in real space). I suspect I just need to sit down and think really hard about it for a while, using the guides by Sébastien Merkel found here: http://merkel.zoneo.net/RDX/index.php?n=Maud.DefineTheCompressionDirection )

Either way, you then refine a Q-value for each peak in your pattern which will both produce peak shifts and (depending on your alpha and beta values) more or less "wiggles" in the 2D pattern. One could be in a situation where the strain is distributed in such a fashion that you do not see the sine-wave wiggles in the sliced integration, or as is the case in my data the angles could be such that you do indeed see the oscillations.

The procedure I've found to work for doing the actual modelling is to guess at an initial Q-value (about 0.003, recommended by Sébastien Merkel here: http://merkel.zoneo.net/RDX/index.php?n=Maud.Stress ) and then manually tweaking the angles until you have a fair agreement between the observed and calculated oscillations. Once you get this, you can enable them as parameters in the refinement.

Finally, to answer my own original question: "What are the changes in true unit cell volume when applying a macrostrain model?" The volume will decrease when the model above is implemented (this is also remarked upon in the paper by Singh et al.) so it is an important effect to account for if you plan on fitting equations of state to your data!

Hello!

As far as I know, Dr. Sébastien Merkel is the one who implemented the "Radial Diffraction in the DAC" model into MAUD, so probably you could ask him is it possible to apply it for the axial setup (there may be some limitations in the code). Anyway, as I recall the papers of Singh et al., they have considered some mixture of Voigt and Reuss models for the isotropic material. From looking in your data it seems that there are too few grains in it to consider the material isotropic (at the very least, and also to say that it is Voigt, Reuss, or some average), so once again the physics behind the model will be a bit lost. And you should probably enable the "Arbitrary texture" model to describe preferred orientations; this will to some degree take care of intensity variations due to 'graininess'.

Also in this model (see the Appendix to Wenk et al. Powder diffraction 2014 paper) “Beta” is the angle between the sample Z axis and the maximum stress direction. “Alpha” is a rotation around Z. Stress models in MAUD always consider Z axis normal to the pole figure projection, so for your .par files this means that Z || incoming beam.

And as Dr. Tarik Ömer Oğurtani noted earlier, the difference between 111 and 002 peaks positions is most likely due to some planar defects (if you are 100% sure in your instrument!).