Try and use FE-SEM with FIB option, you will need to etch the core sheell structure (possibly few layers) and then investigate in Same SEM so they do not oxidise.
Hi, depending on what parameter of the core/shells you want to measure, a straightforward approach would be to use XPS, which will give chemistry and thickness of of the shell.
Article VAMAS Inter-Laboratory Study on Measuring the Thickness and ...
Do elemental mapping in FESEM. First, do the core and then core@shell at very high resolution so that you can able to see a few particles. That will help.
Remember don't forget to dilute your sample, otherwise, you will not be able to get the highly dispersed sample on Stubb.
I think currently single particle ICP-MS is one of the most efficient independent measurement method which able to available to confirm the predicted core/shell nanostructure.
Article Determination of the structure and composition of Au-Ag bime...
XPS is perfect to know the elements of compounds and the chemical binding of each element as well. Narrow scan XPS can specifically be used to measure the intrinsic (core) and extrinsic (shell) domain of your materials.