Defining Reference Entropy and Chemical Potential in Different Phases

[M. next]

Supposing that some solid can exist at 2 different phases (had 2 different crystalline structure) at some temperature and pressure. Can we define the same reference entropy or chemical potential for these two states (knowing that we are talking about the same solid)?

 

[M Quack]

There are indeed materials that can have different crystal structures under the same conditions. For example titanium dioxide, TiO2, can be found in the rutile, anatase or brookite crystal structure at room temperature and pressure (Rutile seems to be the equilibrium state, anatase and brookite are metastable). However, the entropies and chemical potentials of the different structures will almost certainly differ by a small percentage.

http://en.wikipedia.org/wiki/Titanium_dioxide

The "reference phase" in this case should clearly be rutile, as it is the equilibrium phase.

 

[M. next]

Thank you for your reply.
So you are saying by a small percentage. Ideally speaking, can I take them the same and neglect this "small" percentage?

And one more thing, why do they differ by a small percentage and not a large one?

 

[M Quack]

This is a bit hand-waving, but if the difference was very large, then the higher (free) energy phase would probably not be meta-stable.

I have no idea how large exactly the differences are, but to first approximation it can probably be neglected in most cases.

A counter-example might be carbon, which can occur as graphite or diamond. Their properties are quite different...

 

[M. next]

Oh to neglect the difference, the higher energy phase must be meta stable?

 

[M Quack]

I guess the definition of meta stable is "has higher energy than the ground state, but has an energy barrier to overcome to get there". Because of the energy barrier the state can "survive" for some time.

If the higher energy state was not meta stable it would be unstable and decay to the ground state.

The idea is that there is only one ground state phase, therefore all others that can exist under the same conditions must be meta stable, i.e. the ground state under different conditions, but that does not spontaneously transform to the ground state when the conditions are changed. Diamond is a good example.

To neglect the differences the two phases must be sufficiently similar. For the different forms of TiO2 that
may be a good approximation. For Graphite/Diamond I am not so sure.

(you may have noticed that I am moving from waving my hands to flailing my arms Other examples are undercooled liquids that remain liquid even below the nominal freezing point. This can be generalized to all first order phase transition that show some hysteresis.

 

[DrDu]

Supposing that some solid can exist at 2 different phases (had 2 different crystalline structure) at some temperature and pressure. Can we define the same reference entropy or chemical potential for these two states (knowing that we are talking about the same solid)?

Of course there is a phase transition line between different crystalline phases where two different phases coexist.
They have the same chemical potential as they are in equilibrium with respect to particle exchange.
An example is the equilibrium between rhombic and monoclinic sulfur.