XPS (highly surface-sensitive) and FT-IR are generally the best techniques for probing core-shell structures. You get some indirect signatures from UV-Vis-NIR absorption and XRD FWHM also. EDX can give you a rough composition of your material. So, comparing in reference to the composition of pure material, you can drop some conclusion about the presence of coating agent. However, I think it is difficult to confirm formation of core-shell nanostructures from EDX conclusively, and it is not recommended in general.

EDX technique can only confirm the error in making core-shell. The minimum amount of core element presence might have the possibility of nanocomposite instead of core-shell formation. If you are not getting the presence of any error (core element) in EDX and in XRD, it is sure for your core-shell formation. But to prove it you have to go for further characterization.

Core shell structure can be confirmed by stereo microscope technique

Depth profiling XPS or XPS with tunable synchrotron radiation can be useful tool for confirming the core-shell structure. Following article can be helpful in this regard-

J. Am. Chem. Soc. 2009, 131, 41, 14644–14645

If your have rather large (like 100 nm) particles, which consist not just of light elements, you may see increased quantity of element from shell on the edge of particle, and more of element of core in its middle.

SEM based EDX technique can only be helpful to confirm core shell structure if you would be able to find an opening at the shell. One has to perform EDX mapping to ensure the core shell structure from the shell opening area. However, XPS depth profiling would be the best technique (except TEM) to confirm core shell structure while the shell thickness is under 10s of nanometers.

Himadri Raha , EDS is technique affiliated not just with SEM but with TEM as well.

Vladimir Dusevich I know that.