[Physics] Is the thickness of a sample related to the intensity of x-ray diffraction

condensed-matterdiffractionsolid-state-physicsx-ray-crystallographyx-rays

I understand that in general if we're adding more planes of atoms (increasing thickness of sample) then the intensity would increase because we have more constructive interference. But isn't there a breaking point for this? Shouldn't there be a finite thickness past which the intensity decreases?

Best Answer

Yes, there is such a point. The precise formula varies as a function of the scattering geometry, but if we consider a special case:

  1. normal incidence on a flat sample and
  2. small scattering/diffraction angle

it is quite simple: the scattered intensity is proportional with the sample thickness $d$ but it gets attenuated as $\exp(-\mu d)$ (the Beer-Lambert law with $\mu$ the absorbance).

The strongest signal is thus obtained at the maximum of $I_S \sim d \exp(-\mu d)$, which occurs at $d = 1/\mu$, i.e. a transmission of $1/\text{e}$. Beyond this value, the attenuation (an exponential effect) dominates the increase of scattering volume (a linear effect).

Related Question