Combined X-Ray and Neutron Refinements

Because of the distinct elemental sensitivity of x-ray and neutron probes in powder diffraction, many systems benefit enormously from a complementary study exploiting both. The combined analysis of these two datasets often can reveal subtle structural details and understanding far beyond that possible with a single measurement.

News: Approved ORNL Spallation Neutron Source (SNS) users of the POWGEN neutron powder diffraction (NPD) beamline may now obtain streamlined access to high-resolution synchrotron diffraction (SXPD) data on the same samples at beamline 11-BM of the Advanced Photon Source. (read more)

Experiment Hints

• Sample Powder: Ideally, you will make both measuremtns on the *same* sample powder. It is not always safe to assume that different samples (made on a different day, different furnace, etc) will give the same diffraction pattern.

• Temperature It is difficult to make both the x-ray and neutron measurements at exactly the same temperature. For example, one could be at 25 C, and the other at 298 K; close but not exactly the same. Is this important? The answer may depend on the sample.

Weighting datasets

In principle, one should not need to weight or scale any of the datasets. If the exact same sample is measured at precisely the same temperature on calibrated instruments, then a single structural model for your refinement should fit both datasets perfectly. To state this in a different way; based on statistical arguments alone, weighting factors should be 1. When this is done, the resulting model is fit against all data weighted by its experimental uncertainty.

In practice, your combined refinement may not always be so simple. The datasets from distinct probes will likely be sensitive to different aspects of the structure, and may have different systematic errors. Changing the weighting of these respective datasets can bias the final refinement (which might be a good or bad thing!).

Here is a good test.

Acknowledgements

thanks to Ashfia Huq, Robert Von Dreele, and Brian Toby for their insight on this topic

Assuimg

  The justification for weighting dataset other than unity comes from arguments about systematic errors, which is outside of statistics. If we assume that the x-ray and neutron data each have different systematic errors, then by giving them approximately the same leverage on the fit parameters, we allow the systematic errors to have the best chance of canceling out. 

Ashfia, Actually this is a real hard question. Perhaps a useful 1st guide is to make sum(w*d**2)/Ndata the same for all data sets. That way each data point has the same impact on the least squares. But then again you want the chi**2 > 1. (say 2-4?). And all this only for the final refinement with all the systematic stuff taken care of by the model. Order of magnitude on these things is probably OK so it isn't a real hard thing to manage in the end.

Here is what Bob said and I think using same order of magnitude for sum(w*d**2)/Ndata makes more sense than using just sum(w*d**2) as I originally thought.