Relative weighting of patterns neutron/synchrotron co-refinement

josh

Hello all,

Is there a best practice for how to treat weighting in a co-refinement? I have synchrotron and cw neutron patterns (both .xye) that refine together nicely. However, due to the extremely high resolution of the synchrotron data, the synchrotron fit is "worse" (gof ~ 2) than the neutron fit (gof ~ 1).

Should I keep the default weighting (presumably 1 / SigmaYobs^2 for .xye data)? Or should I be specifying weighting functions each time? I notice that in John Evans's input files for joint refinement using distortion modes, weightings are often provided explicitly.

Thank you in advance for the input!

rowlesmr

Hi Josh

I don't think there is a consensus anywhere.

I had a discussion with Bill David several years ago, and he suggested scaling each data set so that it contributes equally to the minimisation function.

I did a proof of concept, and started writing up a little paper, but got a new job, and it didn't go anywhere.

Matthew

johnsoevans

Josh,

I'm not sure which of my files you're looking at but I guess that I did exactly what Matthew suggested. i.e. the weighting is such that the neutron and X-ray data sets contribute equally to Rwp. If you choose to do this it's something you should report in any eventual publication.

John

josh

Thank you Matthew and John, this approach seems to be working. Specifically, for the synchrotron pattern I am now specifying:

weighting = 0.2 / SigmaYobs^2;

Where the 0.2 was chosen by trying various values until the goodenss of fit (r_wp/r_exp) for the synchrotron matched the gof of the neutron. For anyone else trying to do this, note that because of the definitions of r_wp and r_exp, the r_wp of the synchrotron pattern shouldn't change much as a function this global weight, but the r_exp changes a lot. The chi (squared) can therefore be manipulated to be equal to any arbitrary value based on this weighting scheme.

In addition to these posts, I found this link helpful:
https://wiki-ext.aps.anl.gov/ug11bm/index.php/Combined_X-Ray_and_Neutron_Refinements

According to that link, the weighting the synchrotron pattern "increases uncertainties slightly, but decreases possible influence of systematic error."

-Josh

hanna

Hi everyone,

I'm currently trying a combined refinement and ran into the problem of weighting and thought I'd get some advice from more experienced people. I read the link Josh posted, but still not entirely sure how to go about it for my data.

I have a neutron TOF xye dataset and a synchrotron xy file. It's high-pressure data, so the data aren't amazing, particularly not the neutron. Using the default weighting, the fit appears totally dominated by the X-ray data: the global Rwp is basically identical to the X-ray Rwp. I assume is due to the lack of uncertainties for the X-ray data and the much higher intensity.

I was considering weighting the X-ray data manually until the global Rwp is the average of the X-ray and neutron Rwps, which is what I intuitively had expected to find. Would that make sense? Is there anything special to consider when using one xye and one xy data set?

Thanks in advance for your advice.
Hanna

johnsoevans

TOPAS will be applying 1/SigmaYobs^2 weighting on both data sets by default. For the .xye data SigmaYobs will come from the xye file. For the .xy, the default is to assume Poisson statistics (sigYobs=Yobs^0.5). The weighting is then 1/Yobs.

If you search topas.inc for "weighting" you'll see the type of equation used. The only subtlety is that by default a weighting of 1 is applied if SigYobs < 1. This is to stop very small values of SigYobs leading to very high weightings. On some tof instruments, for example, data reduction problems can lead to tiny esd's at the extremes of tof, which prevent sensible refinement.

You can apply whatever weighting you think appropriate for your data. One option, as you say, is to give the two data sets approximately equal impact on Rwp. For PDF fitting it's common to use weighting = 1; to apply equal weights to all points.