Composition maps may be obtained by EDS, AES and XPS techniques. Please indicate the right technique(s) for each of the following types of samples: thin film of oxides, polycrystalline metals, and nanometer-thick coatings of metal on a polymer.
TOF-SIMS can give you both a surface elemental composition map and a depth composition map. The technique uses a focused primary ion beam to remove chemical species from the surface of a sample. The ionizing interaction of the primary beam with the sample produces secondary ions that are removed from the sample surface. The secondary ion beam is analyzed by a mass spectrometer by measuring the time it takes the secondary ions to leave the sample surface and reach the detector. Therefore, ToF-SIMS is an effective technique for determining the elemental and molecular composition of a sample via the acquisition of mass spectra. Furthermore, the distribution of chemical species can be investigated from groups of spectra obtained by rastering the beam across the sample surface or by forming a depth profile as the beam etches into the sample. The technique would be applicable to your three samples particularly if they are flat, thin films.
BY SEM with EDS is possible to analize thin film of oxides,polycrystalline metals, and nanometer-thick coatings of metal on a polymer but this depend of elemental composition, thickness and if you can reduce the voltage in the SEM.
XPS can be used if the thickness is some nanometers.
You ask the technician of each system to the specific conditions.
EDS, XPS and AES are non-destructive techniques however SIMS is a destructive one as cited by Richard. There are several other surface sensitive techniques also.
XPS and AES are largely used for surface analysis (analyse from a few nm to several 10th of nm) depending on the energy of electrons (escape depth) however EDS mainly probes some µm.
The choise of techniques depends on what you want and what are the constraints that you have.