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To my understanding it is possible to extract information about the valence/oxidation state of an ion in a material by using X-ray photoelectron spectroscopy (XPS) or X-ray absorption near edge spectroscopy (XANES).

However it's only possible to do element identification (without any knowledge about the oxidation state) with X-ray fluorescence (XRF) or energy-dispersive X-ray spectroscopy (EDX).

My question is: What's the difference between these two sets of techniques when it comes down to determining the oxidation state of ions in the specimen under consideration?

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In principle, EDX can also measure the oxidation state of a compound, but the difference between XPS and EDX comes down to the energy $\textit{resolution}$ of the detectors in each case. EDX detects X-rays from higher level shell electrons falling into core electron shells after an electron beam has knocked out the core electron. XPS measure the kinetic energy of a core electron that has been knocked out by and X-ray

The energy of a core electron is affected by the oxidation state and can vary by a couple of eV, which goes back to my initial statement that EDX and XPS are measuring the same energy.

The difference is that EDX detectors have resolutions well above 2 eV, which is a consequence of the technological limits of measuring X-ray energies, whereas measuring electron energies is as simple as passing them through a magnetic prism which (analogous to a light prism) separates electrons smoothly based on their energy, attaining sub eV resolution.

This site has a good explanation of how the resolution of EDX detectors is calculated.

http://www.ammrf.org.au/myscope/analysis/eds/spectralresolution/

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