Hi Dave

Never really went into this before. After you asked the question I did a quick search to satisfy my curiosity. I came to the conclusion that the PHD types are still trying to figure it out, so the best they can provide are theories that are based on stuff us regular people can't understand. I suspect that as soon as someone will actually understand this, the explanation will be much simpler.

From a conceptual point of view, I guess it is not so difficult, but will probably not really answer your question, but I will go through the exercise in any case.

The change of a substance's volume really just equates to a change in the substance's density. The density of a crystalline substance is related to the atomic weight, its structural "packing" (crystal structure in our case) and attraction of the atoms that make up the structure. Given that the material we are looking at is constant (Invar) the atomic weight can not change, so this part falls away. The remaining factors are the crystal structure and attraction between atoms. Most metals will expand when heated. The common explanation being that the atoms vibrate more, so on average are further appart. This is true for a solid material when you are considering two atoms, but when you consider a large number of atoms vibrating, then on average there will be little difference in the average distance of the atomic spacing. The real reason is that the bonds holding the atoms become weaker with increasing temperature, resulting in a larger spacing. As long as nothing happens with the "packing density" of the crystal structure, the metal will expand.

There are many substances (mostly materials composed of more than one type of atom - In other words molecules or "alloys") that display different behaviour over relatively small temperature changes, that appear anomolous to us, because they may actually contract when the temperature increases. Mostly these are explained by minor changes in the "packing" of the atoms relative to each other. Not a big enough change to be considdered a phase change, but enough to counteract the expansion due to the reduction in atomic bonding attraction, and result in a contraction of the material over this temperature range while the temperature is increasing. To imagine this in your mind's eye, imagine that as the temperature increases, some of the atoms in the Invar crystal structure moves away from each other, but that this allows some of the other atoms to move closer together, because this would be a lower energy result for the material as a whole at that slightly higher temperature. The nett result being a contraction of the unit crystal size, rather than a change to the crystal structure as such, which can be seen as a volume contraction, or increase in density without a phase change.

Exactly what drives such behaviour in the case of Invar is what the clever people are trying to figure out. (And maybe have, only I have not seen anything that says this is definately how it works! Only a mish-mash of theories.)

I suspect this is not the definitave answer you were looking for, but may satisfy your curiosity for now. (Good enough for me, for now!)

Regards
Niekie