usually, in most of the xrd analysis intensity peaks fall at a higher angle.
Hello, as the angle of diffraction increases, the X-rays are diffracted by atoms that are deeper within the crystal and this can result in some of the X-rays being absorbed by the sample, resulting in a decrease in the intensity of the diffraction peaks.
The intensity of the peaks is proportional to the square of the structure factor, which depends on the difference between the scattered and the incident wave momentum, position, and the perturbation potential caused by the X-Ray. The difference between the scattered and the incident waves must be equal to a reciprocal lattice vector, known as the "Laue condition" and equivalent to the "Bragg condition". Therefore, it is proportional to the sin of the angle (d = lambda / 2sin theta), as theta increases the d will decrease, leading to less spaced planes which will decrease the perturbation resulting in lower structure factors, and as a consequence, the amplitude of the peaks will be lower.
You can interpret this from a qualitative or a quantitative perspective.
Best wishes.
Dear Chandra Kharvi ,
in addition to the x-ray absorption issue mentioned by Ayoub El Bendali there is the angular dependence of the atomic formfactor (also known as the atomic scattering factor or the coherent scattering factor).
Please see for example the first Fig. in :
https://en.wikipedia.org/wiki/Atomic_form_factor
See for example also:
https://www.xtal.iqfr.csic.es/Cristalografia/parte_05_7-en.html
Best regards
G.M.
Dear Chandra Kharvi,
The peaks decresaes in intesity at higher angle on account of the form factor. The dimensions of the atomic diameter and of the X-ray wavelength are similar (X-ray are scattered by electrons --> elastic scattering).
Imagine two parallel X-rays scattered at two different positions of a same electronic cloud (that we assume a sphere). if the scattering is 0, the two X-rays will emerge from the atomic cloud without changing their original direction, the path difference will be 0 and hence no destructive interference will be present.
Now consider a scattering angle different from 0. the scattering angle will produce a slight difference between their path that increases with the increase of the angle. This will produce a progressive destructive interference in the scattered intnsity and hence you see a decrease of the peaks intensities at higher angles.
In neutron diffraction this does not occur because the scatterer points are the atomic nuclei, whose size is several order of magnitude lower that that of the radiation wavelength. In neutron diffraction you will see high intensity (nuclear) peaks at high angle. Nontheless, with neutron you also have scattering by unpaired electrons forming a magnetic structure, that is magnetic peaks. In this latter case you have a similar situation than X-ray, since that your scattering centre is now in the electron cloud. At the end in neutron diffraction pattern you will have magnetic peaks whose intensity rapidly decreases with scattering angle and nuclear peaks whose intensity is not depenedent on the angle.
Best Regards
The general equation for diffraction intensity is given in the image, without talking about all other factors, we can see that on increasing the angle, let's say
180 ̊ >2𝜃>0 ̊ or 90 ̊>𝜃>0 ̊, the function in the bracket decreases at high angle values approx 1/200th times than initial small angle values. To know the physical interpretation of this formula you can see this youtube video by IIT Delhi Professor.
https://www.youtube.com/watch?v=Z5aCuGxUPpI&t=2192s
To get a sustainable solution to your problem, please refer to the preprint article given at link DOI: 10.13140/RG.2.2.27720.65287/3 or at link https://www.researchgate.net/publication/352830671.
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