What should be the detector angle for High- energy X-ray (80keV) in an Energy Dispersive X-ray Diffraction technique? Can any body suggest me the exact calculation to set our Energy dispersive detector to record the diffraction pattern in an energy dispersive X-ray diffraction using 80 keV X-ray to observe the diffraction pattern of quantum dots and rods etc. Usually researchers are set their detector at around 10 deg. or less angle . Why it is so?
Well, I assume you want to measure your diffraction pattern in transmission geometry - using high energy X-rays, the penetration is very stron, so the reflection geometry is not that favourable in general. So, by using Braggs law and substituting the X-ray energy for the wavelength, you may easily calculate that
h*c / d * E = sin theta, i.e. theta = arc sin (h*c / d * E), where d is the lattice spacing of your sample. Thus, depending on d and the considered energy range (you meant that you want to perform energy-dispersive diffraction), you will directly get the desired angle!
Hope this helps, Dirk
Thanks Dirk!
This is for sample of known 'd' value. For sample of unknown "d" value, what we expect form the new materials ( quantum dot, rod etc), create the problem to set the proper low angle. Usually, the 'd' value of above materials are different from its bulk material. Again, for very low crystallite size like glass or liquids (
I will assume that the incident beam is not simply 80keV but a band of energies close to 80keV (otherwise you would not be doing an energy dispersive diffraction measurement!). The reason the detector is at a low angle is because atomic scattering factors drop as a function of angle. This means that to maximize the intensity of scattered radiation, you want to keep the angle as low as possible consistent with Bragg's law, the targeted d-spacing and the energy bandwidth.
Along with previous answers, a simple expression to use is
E d sin(theta) = 6.2 kev.Ang
Its easier with an example, E is obviously near 80 keV (as you requested). Let's
assume that you have a scattering peak (or d-spacing (if crystalline) of say 4 Ang.
then 80 x 4.0 x sin(theta) = 6.2
this gives theta = 1.1 degrees
But the peak by conventional definition is at 2xtheta = 2.2 degrees.
For such a small angle the peak will inevitably suffer from some geometrical broadening (known as the cot(theta) effect) but try and it may be good enough.
If you insist on larger angles, then E would have to be smaller but then you will
suffer from sample absorption of the X-ray single. Which do you want least:
absorption or broadening? I usually suffer the broadening because then at least you have something you can see even if its broader than you wish.
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