I am trying to distinguish magnetite, hematite, and goethite in our filters, is there any way to do it? Could the X-ray absorption spectroscopy do the job?
please get familar with x-ray near edge structure (XANES) or near x-ray absorption fine strucure (NEAFS) which are similar names for the finestructure around the x-ray absorption edge.
The oxidation state causes a shift of the x-ray absorption edge energy, here in your case that of Fe.
See for example Fig. 3 of Article Removal of Pertechnetate From Simulated Nuclear Waste Stream...
But I must admit, that the differences in the K-edge positions for your three materials are quite small. So it will be a challenge to really differentiate between these positions.
For other materials such as FeO and Fe2O3 the situation is quite relaxed; see for example Fig. 5 in Article An X-ray Absorption Near-Edge Structure (XANES) Study on the...
See also the differences of the positions of the pre-edge structures of your materials in Fig. 7 of
Article Effects of crystallite size on the structure and magnetism o...