If you want the vertical gradient you have a couple of choices - you can use a technique like SIMS to ablate the coating layer by layer, get the elemental composition as you work your way down. We’ve used that with polymers to see if components are evenly distributed or if some components are concentrated at the surface.
You can also fracture the substrate and coating, then use SEM-EDX type technique to determine the elemental gradient. SEM will also show structural gradient.
If if you want the horizontal gradient, SEM-EDX works as wall.
I agree with James E Hanson . And I am explaining more one partially mentioned option. It is SEM mapping with using back scattered electrons, which are more sensitive to atomic number. This you need to mapping in fractured sample in the fractured plane perpendicular to surface.