Phase diagram

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I think this is a result of a compound having different possible lattice structures.
 
Diamond and graphite are the classical example of this; diamond is more stable high temperature and pressure, while graphite is more stable at STP. Of course the activation energy for conversion of diamond to graphite at STP is so high that it would take millions of years to occur.
 
Diamond and graphite are the classical example of this; diamond is more stable high temperature and pressure, while graphite is more stable at STP. Of course the activation energy for conversion of diamond to graphite at STP is so high that it would take millions of years to occur.

Your example is slightly misleading, since it only applies to elements and networked covalent solids like diamond and graphite are really just single molecules.

For compounds, the picture is different. They may become a solid, if the intermolecular forces are sufficiently large enough to allow the individual molecules to settle together in a crystalline structure. Depending upon the method for cooling (e.g., isobaric, adiabatically, et.al.), different lattice structures become more likely - my guess is that entropy and lattice energy work together to determine which configuration is more thermodynamically favorable. Quite a different story than diamond and graphite.

Water is probably the most studied compound on this subject - there are many different thermodynamically stable forms for ice. Here's a relatively recent discovery of another one:

http://arxiv.org/pdf/0906.2489v1
 
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