Volume vs pressure in solids

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fluidistic
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I wonder what happens when one compresses a solid, let's say iron. In thermodynamics state functions are all smooth and differentiable, in other words V(P,T) would have no discontinuity.
Let's assume that we have an iron phase alpha at room temperature and pressure. We compress the rod up to many giga bars. At one moment, I guess, there will be a phase transition. There will be iron gamma (or any other phase) in very few percentage compared to iron alpha. We further increase the pressure, there will be more and more iron gamma until eventually we reach an iron alpha-free iron, i.e. it transformed into iron gamma entirely. And if we increase more and more the pressure it will again suffer a "smooth" phase transition. Is this correct?
I wonder what happens with the volume at any pressure. If there some discontinuity when there are phase transitions?
If I have a phase fcc at start and I increase the pressure, can I obtain a bcc phase after? I would like to have a description at the molecular level, if possible. For example if I have an fcc phase at start, I compress and the only effect would be to reduce the interatomic distance, until there's a change of phase to bcc. Some parts of the original crystal would change from fcc to bcc and the bcc unit cell will have a much lesser length than the fcc one. I am not sure this is possible/correct, I wonder what really happens.
Only curiosity, not an assignment question.
Thank you guys!
 

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DrDu
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Yes, it is typical that state functions are discontious or have discontinous derivatives at phase transition.
The situation that you have a mixture of two phases (gamma and alpha iron) is also typical. You may want to have a look at the discussion of the van der Waals gas in any intro thermodynamics book, namely the so called Maxwell construction.
 
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fluidistic
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Yes, it is typical that state functions are discontious or have discontinous derivatives at phase transition.
The situation that you have a mixture of two phases (gamma and alpha iron) is also typical. You may want to have a look at the discussion of the van der Waals gas in any intro thermodynamics book, namely the so called Maxwell construction.
Ah I see... yeah I remember what happened in the Van der Waals gas, I didn't realize it could apply to solids too.
 

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