How exactly does diffusion of two polished metals in solid state work? I've just learned that if you keep two polished metals pressed hard to each other surface to surface for a prolonged period of time substantial diffusion will occur. I understand how diffusion works in liquids and gases, because molecules are able to jump to a set of totally different neighbors. Let's say both metals are FCC, how would it work? What will the resulting lattice be?  
 A: In short: The perfect solid where every atom remains at its lattice site and only vibrates about it a little is a lie. Atoms in crystals can and do hop about, so that diffusion between polished metal surfaces is not surprising.

I will try to expand on the above and add some additional information and discuss factors that can influence the diffusion rate in solids.
That a crystalline solid has a perfect lattice is a lie as well, there are always some defects. Defects can be classified based on their dimensionality


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*Point defects are sites where an atom is missing or a impurity atom is placed, or where an atom is between the usual lattice sites.

*line defects are defects where something is wrong with the lattice along some linear extent, the typical example are screw dislocations and edge dislocations (where a layer of the crystal structure simply ends along some line)

*planar defects, such as surfaces, grain boundaries, or stacking faults (this can happen in fcc and hcp lattices, whose only difference is whether the stacking pattern is ABCABC... or ABAB..., it can happen that one layer is skipped or a wrong one inserted, so that the real structure is, for example ...ABABCABAB...
And those defects are not static, but also affected by thermal fluctuation.
Point defects are created all the time by thermal fluctuations (the atoms are vibrating stochastically and from time to time, the energy of some atom is high enough for the atom to hop from its place to an interstitial site – the result is called a Frenkel defect – those are especially common in ionic solids where on of the ions is much smaller than the other). The end points of line defects are also moving due to such thermal effects, in fact the can be quite mobile depending on the material and the temperature. The same holds for some of the planar defects, especially along grain boundaries it is much easier for an atom to move around, since they are not bound as tightly as in the ideally stacked crystal. Therefore, diffusion in metals is typically much faster along grain boundaries.
