Energy Conservation And X-ray Diffraction

[darkfield]

I have a question regarding X-ray diffraction and energy conservation.

If one considers elastic scattering from a rod-like structure, the observed diffraction pattern will change as the sample is illuminated from different directions. For some directions the pattern will be point-like, and for other angles like a circle, all according to the Ewald sphere.

Now, my question is, will the energy scattered to a specific radius |q| in the reciprocal space be constant, assuming that the scattering volume is constant? I.e. will the same amount of energy be scattered to the points as for the whole ring? Or will more of the beam just continue in the forward direction in some cases, just to make sure the overall energy is conserved?

 

[Darwin123]

I have a question regarding X-ray diffraction and energy conservation.

If one considers elastic scattering from a rod-like structure, the observed diffraction pattern will change as the sample is illuminated from different directions. For some directions the pattern will be point-like, and for other angles like a circle, all according to the Ewald sphere.

Now, my question is, will the energy scattered to a specific radius |q| in the reciprocal space be constant, assuming that the scattering volume is constant? I.e. will the same amount of energy be scattered to the points as for the whole ring? Or will more of the beam just continue in the forward direction in some cases, just to make sure the overall energy is conserved?

The crystal casts a shadow which makes up for both scattered and absorbed xrays. The shadow of the crystal can only be observed at very small scattering angles. In an experimental setup in xray diffraction, the xray detectors are always located outside the shadow of the crystal.

Some xray diffraction calculations do include an exponential decay in the xray beam, often referred to as Beer's Law extinction. Beer's Law extinction always includes the loss of energy due to the shadow of the individual atoms. If the sample is thin enough, one can ignore the exponential decay of the xray beam in the sample.

Something usually ignored in the introduction to xray scattering is the extinction term. The extinction term describes how the "shadow" contributes to the balance of energy.

If the detectors are outside the shadow of the crystal, then the "shadow" can't affect the xray pattern itself. It can effect the intensity of the diffraction lines, but the relative intensities are not affect by extinction. Furthermore, the relative intensities are not effected by "Beer's Law" extinction. Therefore, one can interpret the pattern of xray lines accurately as long as the detectors are outside the "shadow" of the crystal.

Scientists who are interested only in the atomic structure of the crystal consider the extinction terms as "noise". They do xray diffraction experiments in which the xray detectors are located entirely outside the shadow of the crystal.

Sometimes, one wants to know how much of the incident xray radiation was absorbed. Sometimes, one wants to measure the Beer's Law extinction coefficient. Then one tries to place the detectors entirely within the shadow of the crystal. However, this is not considered a diffraction experiment. This is referred to as a transmittance measurement. In a transmittance measurement, the pattern of the xray diffraction is "noise".

The extinction coefficient contains a lot of detail on the electronic structure of the crystal. Therefore, scientists sometimes want to measure only the Beer's Law coefficient without interference. Therefore, the may add an extra device after the crystal to scramble the xray diffraction pattern. However, this is not a diffraction experiment.