energy-dispersive X-ray spectroscopy

Energy-dispersive X-ray spectroscopy, EDS, is the attachment that turns an electron microscope from a camera into a chemist: while the SEM or TEM beam is imaging a spot, EDS reads the X-rays that spot gives off and tells you WHICH elements are there and roughly how much. It answers 'what is this made of?' for the exact feature you are looking at — a particle, an inclusion, a corrosion product.

When the high-energy electron beam knocks an inner-shell electron out of an atom, an outer electron drops in to fill the hole and releases the energy difference as an X-ray. Crucially, that energy is a fingerprint of the element — iron always emits at about 6.4 keV, aluminium at about 1.5 keV — because each element's electron shells sit at unique energies. The EDS detector sorts the incoming X-rays by energy into a spectrum of peaks; the peak positions name the elements and the peak sizes estimate the amounts.

EDS is the routine way to identify an unknown inclusion, map how an element is spread across a surface, or check that a coating has the right composition. Honest limits: it is poor at light elements (hydrogen and helium give no useful signal, and carbon, nitrogen, oxygen are unreliable), it averages over a micrometre-sized pear-shaped volume rather than a true point, and its 'amounts' are semi-quantitative unless you calibrate against standards. It tells you which elements, not how they are chemically bonded.