When studying EXAFS and XPS, I often see that "X-rays bounce electrons from atoms".
Where will the electrons that are blown off the atoms by X-rays eventually go?
In the case of EXAFS, I think that "electrons are blown off from the atom, but they remain in the substance, and the electrons eventually return to the original atom." Is this the correct answer?
In the case of XPS, how should it be interpreted?
Regarding the EXAFS effect: if we stay within the framework of a corpuscular model in which the electrons have actual tracks, your explanation is correct. In reality it is of course an outgoing/incoming interference effect in the framework of a many-particle wavefunction in which individual electron paths don't exist.
After all, EXAFS is just a fine structure atop a much larger absorption edge-determined band. Most of the electrons just go somewhere into the solid and their energy gets dissipated wherever.
Regarding XPS: well, you detect these electrons since they go out of the crystal to the gas phase. If the sample is properly grounded, the states will get refilled from the bulk in time. Otherwise you will observe charging, usually manifested in increasing binding energies.
This is an important question, because it is based on the fundamental interpretation of photoionization.
The interpretation of "the electrons eventually return to the original atom" is originated from the multiple scattering theory used for band structure calculation (MS, KKR, or Green's function method), where spherical electron waves form standing waves in the solid.
An illustrative figure is added here taken from a surface science book chapter of mine:
https://www.researchgate.net/publication/348443095
In order to understand the unification of corpuscular and wave pictures, you need to understand the relation of group velocity and phase velocity of an electron:
https://www.researchgate.net/publication/348443339
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