Indeed, electrons undergo diffraction at a crystalline target. Therefore an electron beam hits a suitable crystal lattice, one can see on a screen an interference pattern typical for waves. The beam here is comprised of a lot of electrons in same way as electromagnetic waves are thought consisting of photons. A question arises what if we consecutively shot out electrons one by one, keeping time intervals between them much longer than time needed for interaction with the target. Such an experiment was carried out by Fabrikant and associates in 1949. After interaction with the target each electron changed its direction and hit the screen seemingly at random position. As many electrons reached the target, their traces on the screen gradually amalgamated into the interference picture. Putting that differently, a single electron behaves like a particle whose trajectory can be only predicted statistically, in terms of probability. Mathematically, an electron couldn’t be represented as a wave packet, i.e. a sum of waves, since such a wave packet would be spreading in space, infinitely increasing its length with time. Practically, if an electron was a combination of waves then each electron in the experiment would produce an interference pattern — yet not that bright — what waves normally do.
Those small yet wise 🙂