Suppose we have an X-ray tube R which emits X-rays of intensity $I_s(\lambda)$, obeying the Kramers' law. The X-rays then come to the cubic crystal K under the angle $\vartheta$, where diffraction occurs. The first Bragg peak will be at the angle $2\vartheta$, that's where we place our detector GM. The detector measures intensity $I_r(\vartheta)$. scheme .

Now, according to the Bragg condition, the detected intensity will be proportional to the intensity of the source: $$ I_r(\vartheta) \propto I_s(\lambda = 2d \sin \vartheta). $$

But the measured intensity must also decrease with larger $\vartheta$: when a ray comes almost parallel to the crystal, most of it will reflect, but when it comes almost perpendicular, most will get absorbed. I imagine this works similarly to the Fresnel equations in optics, but I wasn't able to find any source that would discuss something like that for the diffraction on a crystal.

So my question is, if $$ I_r(\vartheta) = R(\vartheta) \; I_s(\lambda = 2d \sin \vartheta), $$ then what is the equation for $R$?

EDIT: I found that intensity should be proportional to the absolute value of the structure factor squared: $$ I \propto |F_{hkl}|^2$$ Where do find its value for a specific crystal (eg. LiF) and what do the indices $h, k, l$ mean? How do I calculate the intensity for a specific angle?


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