If you have data with low counting statistic, the option 1 will multiply both the intensity value of your peaks but also that one of the noise. Option 2 also has no physical sense as Dirk said. The best solution i think, is to collect again your data, if possible and use a better counting statistic.

You need not to do this rietveld refinement will not give good results by doing this. It is better do refine with the original data.

What should be the purpose of such a treatment? The only reason I may imagine is that your fitting algorythm is unstable ... But both of the suggested methods do not make any physical sense, and I would avoid both of them!

If you have data with low counting statistic, the option 1 will multiply both the intensity value of your peaks but also that one of the noise. Option 2 also has no physical sense as Dirk said. The best solution i think, is to collect again your data, if possible and use a better counting statistic.

I fully agree with Carlotta - repeat your experiment as often as you can to improve counting statistics.

Thanks for the valuable feedback. One more query: superlattice peaks have low counts in general. How to improve its contrast w.r.t. background counts?

I think that it depends on the systems you’re studying. I will report my experience just to make an example. I often analyze iron and nickel compounds. As it is well known, if you’re using a Cu X-ray tube the principal line of copper radiation falls just within the absroptive band of iron (we have a Bruker D8 advance with a Linx eye detector). This cause a rise in background and can be annoying.

A few month ago, I read about an escamotage to improve the ratio peaks/bkg by setting different values (wrt to the default settings) for the the Discr. Window width and the Discr. Lower level of the detector just to partially eliminate fluorescence contributions. If you have a LinxEye I can tell you how to set the detector for this purpose.

In fact using a secondary monochromator helps as well to discriminate e.g. flurescence radiation of different elements within the samples. However I think this is not the essential point, because in fact superlattice peaks might be quite weak because of the small number of layers that contribute to the superlattice-signals. I am afraid that there is no simple way to improve data quality: More photon flux would help - use a synchrotron beam or a rotating anode with a broad-band (i.e. multilayer) monochromator (the superlattice peaks are usually not that narrow, so you do not need resolution, but flux helps). A collimating mirror in the incident beam would also help to increase the flux on the sample. A second monochromator the diffracted beam to reduce the influence of fluorescence radiation would also help. But all of these experiments are quite far away from being standard at most diffractometers, unfortunately :-(.

Allow me to add that manipulating data before a Rietveld refinement is in most cases, at least, wrong. You will end up with data where the standard uncertainty of each intensity (used to calculate Rwp) will be different than the sqrt of the intensity therefore, unless calculated and given explicitly with your intensities, will be handled wrong by all refinement programs and will lead you to a statistically inaccurate solution.

If you multiply your data by a constant (e.g 100), your standard uncertainty (s.u.) in each intensity must be multiplied by the same number (100) to maintain the relative precision of each intensity value. But if you don't include your s.u. explicitly in your data file and tell the Rietveld refinement program to use the special s.u. then your program will assume the s.u. is the square root of the intensities, so the uncertaintainty calculated by sqrt(I) will be estimated to be sqrt(100*I)=10sqrt(I) only 10 times larger than the original s.u. or 10 times lower than the real s.u. and your refinement will probably show a HUGE Rwp value (considering that s.u.s are dividing the Iobs-Icalc terms in Rwp) and you will get no better result than the original one.

If you add a constant number to your intensities (e.g. 100) you will have the opposite effect, your Rwp will be smaller because the new s.u. of your data will be estimated to be larger than the real s.u. (the new s.u. of each intensity will change by a different number depending on the intensity value) because the sqrt of the new intensity (used for calculated Rwp) will be larger than the real one while Iobs-Icalc will remain the same because the new data, shifted by 100 counts will have the same fit as the undmodified data except for an increased background signal (100 counts higher). This will leave your peak intensities unchanged, therefore the same intensities coming from diffraction, or the same data as the original one (without adding 100) leading to the same refinement result. The reduced Rwp will not imply a better result but just an apparent better fit of the intensities (mainly in the background) but the fit will still have the same absolute differences, therefore your model will be exactly the same quality and you'll se a fake smaller Rwp for the same result.

In summary, you'll never get better results by treating your data than the information that is contained in your data, that is, you'll never get better quality intensities by mathematical manipulation without faking something.

If you need to improve your peak/background ratio for small peaks you have to check what is the origin of the background below that peak.

- If the background comes from the sample in the same path and wavelength as your peak intensity (e.g. amorphous content of your sample) then you have no way of chaging the relative peak/background ratio, but if you count longer the relative uncertainty in the intensities will be smaller and your small peaks will be more accurately determined and possibly well accounted for in your Rietveld refinement.

- If the background comes from other sources or in a different wavelength then you can improve the peak/background ratio by removing the source of background.

-- If your background is fluorescence from Fe in your sample you will need to modify your detector system either to remove the fluorescent component by using a diffracted beam monochromator (as suggested by Dirk) or modify the solid state detector's sensitivity to be blind to the fluorescent wavelength (as suggested by Carlotta).

-- If your background comes from scattering at low 2theta angles (or some other scattering sources) you may reduce it by reducing the size of your incident and scattering slits thus reducing the path for undesired X-rays to reach your detector. This is critically important in Bragg-Brentano (reflection) geometry where the incident beam may spill out of your sample at low angles due to the relatively large intersection area between the beam and your sample at low angles. This spilled radiation will be scattered by the sample holder edges and air between your sample and the detector making a large background in a classicaly shaped decaying background. This may also reduce your small peak intensity but the peak/background ratio will improve significantly.

I hope this helps.

Don't do that on any XRD data... As explained before me, it's not simply multiply or adding it...