X-ray crystallography; intensity peaks vary with voltage

[ngc2024]

Homework Statement

I have done a simple lab experiment to find the lattice constant for NaCl. Using a diffractometer, radioactive counts were measured as a function of crystal orientation angle for electron voltages of 20 and 30 kV. The average lattice constant found wasclose to the accepted value, but closer for 20kV.

The issue is that the graphs for the two voltage levels are very similar, but the characteristic peaks (Kα and Kβ) consistently occur at slightly smaller (about 0.5 - 1 degrees) for 20 kV than for 30kV. My understanding is that the peaks should theoretically be in the same position, and I am not able to suggest any likely reason for this apparent systematic error.

Homework Equations

Bragg's law
nλ = 2d sin Θ

The Attempt at a Solution

I have been trying to figure out if this is a known phenomena or just due to some experimental flaw such as crystal impurities. Several sources say the peaks should be in the same position (e.g. http://pd.chem.ucl.ac.uk/pdnn/inst1/xrays.htm), but I have also found claims for the opposite (e.g page 6 in https://books.google.no/books?id=i_...ce=gbs_ge_summary_r&cad=0#v=onepage&q&f=false) .

Either way, I don't understand the underlying mechanism, and help would be greatly appreciated!

 

[mfb]

but I have also found claims for the opposite (e.g page 6 in https://books.google.no/books?id=i_...ce=gbs_ge_summary_r&cad=0#v=onepage&q&f=false) .

The angle discussed there is the x-rax emission relative to the incoming electron beam, it has nothing to do with the refraction angle you measured.

I would expect some mechanical issue - the crystal tilted a bit, or some other parts of the setup moved a bit relative to each other. For an ideal setup the peak should be nearly* exactly at the same angle.

radioactive counts

There is no radioactivity involved.

* a different background spectrum has a small influence on the precise peak position (unless you determine it with a fit to background and peak), but for narrow and large peaks this effect is negligible.

 

[ngc2024]

Okay, I see. Thanks!