In my vision it would seem quite logical that all materials expand when temperature rises. Because the particles get more energy and travel larger distances when moving. But apparently there are some materials that tend to shrink as temperature increases. Why? Which ones?
Water has a very narrow range of temperatures over which it expands when cooling rather than contracting (IIRC +2 to 0 Celsius). This occurs due to the way the highly polar molecules "line up" with each other near the freezing point.
For a more interesting example, consider a number of rubber compounds which shrink as they warm up. In this case it's due to cross-linked molecules which paradoxically "relax" to a smaller configuration as they heat up. I'm not familiar with a good online set of diagrams for this; if I find one I'll post it.
I imagine alot of negative expansion coefficients occour at phase transitions. Probably the temperature increase causes the material to overcome an activation energy and a change in lattice structure occours. In these cases one would not expect these processes to be reversible.