The instrument is quite ok. It is a Bruker Phaser D2 and there is no strange behavior when I measure in powder form. I measured this muscovite sheet and others too just to have an internal standard reference. The behavior seems to be related also to the thickness of the sheet I use. The thicker the sheet is the more intense this zoomed behavior.
P.S. " what was the aim of your measurement " is curiosity a good goal?
What you see here is the contribution of the device to your peak shape. The step you see left of each peak is the K-edge of your filter. The distance between the step increases with increasing 2theta value. The smaller peaks are the Kß wavelength and the strange "foot" of your peaks is what is called "tubetail", which basically is a result of a defocused electron ray on the target material (copper in your case) in your X-ray tube! The very high diffraction efficiency of your muscovite plate unveils these characteristics. If you look carefully, you can find them in your "normal" powder diffraction diagrams as well!
That is spot on regarding the tail. A hint is always what one needs to find the needle in a huge hay pile of literature on the topic. This picture (4.11) in "Principles and Applications of Powder Diffraction" seems to explain the first steps at the basis of the peaks.
There is still another contribution to the peaks heavily skewed to the right. Any hint for that one?
You mean the asymmetry? This is most probably due to the density distribution of X-rays on your sample. This in turn depends on the source, the slits etc. (i.e. the optical path). It is supposed to be worse at low angles and better at higher angles. Software like BGMN (I use the GUI Profex) is capable of simulating the peakshape and considering it during the quantification (Rietveld). I attach two pictures of our device function at lower and higher angle...
Thanks for that bit. I have to digest whether we meant the same thing. The behaviour I was referring to seems to be more obvious for the 001, 003, and 005 (odd) basal peaks, while for the even peaks the drop is steeper. The behaviour does seem to be less obvious at higher angles.