# Talk:Refraction distortion

## Grazing-Incidence Peak Position Analysis: Refraction Correction

TO BE COMPLETED: ROUGH NOTES BELOW

1. Some scattering patterns are centered around the direct beam, and some are centered around the reflected beam. This is explained quite nicely in the reference you mentioned in your writeup (Macromolecules 2005, 38, 4311). For peaks centered around the direct beam, you can just use the regular q-values (as output by view.gtk or whatever). However for the peaks centered around the reflected beam, you have to compensate for this shift in q-space. This is why peaks sometimes look doubled along qz or don't fall into naive patterns.

In order to know whether a given peak is a 'direct' or 'reflection' peak, you can look at how the peak changes as a function of incident angle. Reflection peaks will shift upwards along qz as you increase the incident angle (and will correspondingly decrease in intensity). If you go to very large incident angle, you should only see direct peaks.

Another way to determine whether peaks are direct or reflection is to index all the peaks in your pattern to the expected unit cell (see next point).

2. In GISAXS, peak positions along qz are distorted by the refraction of the beam (and scattering) at the film-air and film-substrate interfaces. This can get quite complicated, but reasonable equations have been published that account for these effects. Using these equations, you can shift the apparent q-position to the 'true' q-position (in reciprocal-space) and only then is the conversion to real-space distance valid.

Papers that discuss refraction correction: Busch, Rauscher, Smilgies, Posselt, Papdakis J. Appl. Cryst. 2006, 39, 433 doi: 10.1107/S0021889806012337 Macromolecules 2005, 38, 4311 doi: 10.1021/ma047562d Sinha et al. Phys. Rev. B 1988, 38, 4, p.2297.

Others that might help: Lazzari et al. Phys. Rev. B 2007, 76, 125411. IsGISAXS manual http://ln-www.insp.upmc.fr/axe4/Oxydes/IsGISAXS/figures/doc/manual.html Toney and Brennan, Phys. Rev. B 1989, 39, 7963. Breiby et al. J. Appl. Cryst. (2008). 41, 262–271. doi: doi:10.1107/S0021889808001064

Peaks far from the horizon undergo less refraction distortion, and so the correction might not be so large. But in some cases it can be substantial.