Is it possible to reassemble a perfectly cleaved crystalline solid?

For example, see cold or contact welding of ultraclean, similar metallic surfaces under ultrahigh vacuum conditions.

After a few such experiences with what I thought were cleverly designed friction fittings for some electron beam optics, I soon learned to either use different metals, or sprinkle a bit of dry molybdenum disulfide on the joints to dirty them up!

Of course, as the article makes clear, these are nano or micro crystals. You could probably get an article in Science if you could do it with silicon. Or maybe a patent. Entropy is against you, and gets worse as size goes up. You can actually calculate this. Expect to test for all of the many dislocation types known to crystallographers.

One word answer: Yes! To add a little to Peter Diehr's reference to cold welding, here is a physically insightful argument that the answer to your question is yes due to Richard Feynman. He asks the rhetorical question: suppose we re-align the two halves so that all the atoms on either side of the cleave are in the same positions as they would be in the periodic lattice of a single connected piece of the same metal. Where then is the information that tells which former half of the rejoined piece each atom formerly belonged to? Or, more "teleologically": how does each atom know which half it formerly belonged to? Feynman deduces that there can be no difference between the re-aligned two halves and the single connected metal block.

Of course, this argument tacitly assumes that the states of all the delocalized electrons have reached the steady state that they would have in the single, rejoined piece of metal - witness that the steady states for the rejoined and re-aligned systems are indeed identical - and that there is no energy or other barrier to the electrons' reaching this steady state. If there were, then there would be an encoding of where the barrier lay.

But, assuming there is nothing stopping progress to the steady state for the electrons, the argument holds good. So it's not a perfect argument, but it is a simple, compelling one.