# Phase transitions between solid and liquid. Critical point CP

1. Jul 29, 2011

### Petar Mali

Look at a simple single - component system. And PT diagram for this system. Suppose that supstance we looking at has three phases solid, liquid and gas. In that case we have critical point between liquid and gas phase, but not between solid and liquid phase. Why? Why solid - liquid coexistence curve doesn't end in critical point?

This is because solid has crystalline symmetry. In other hand liquid is homogeneous and isotropic. So liquid has much greater degree of symmetry than solid.

What do you think about paper which I attach in the post. This is simulation, not experiment. I think that this is interesting to discuss!

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2. Jul 29, 2011

### genneth

You had it correct. If two phases have different (broken) symmetries then there cannot be a continuous phase transition between them, and so no critical points. The paper that you attached was considering something which is not quite a straightforward liquid, in that it had ordering (and went through several intermediate phase transitions, all of which would have to not have critical points, before ending up in a phase which had the same symmetries as the final solid phase).

3. Jul 24, 2012

### physquirrel

The question is not that simple. The lack of the critical point is due to the finite spatial size of the particles, I think. At high temperatures the liquid-solid coexistence line becomes horizontal in the pT diagram, so the temperature turns to be only a scale, because the kinetic energy wins over the attractive part of the pair potential. So any system should converge to the appropriate hard-sphere system at high temperatures, where the solid-liquid transition is of geometrical root. Once you have a horizontal line in the pT diagram, it cannot end up with a critical point... We know model potentials and also continuum theories in which there IS a critical point between the 'solid' and the 'liquid' (so ordered and disordered phases), and my opinion is that the usual 'symmetry' arguing is basically wrong. The whole question is up to the pair potential. For the Z2 potential, there is a critical point, as well as in the Phase-Field Crystal (or Swift-Hohenberg), but nature does not seem to behave like a Z2...

Last edited: Jul 24, 2012