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From statistical mechanics, one could calculate phase transition of gas and liquid from Van der Waals's equation. The characterization was from $p(v)\sim v$ diagram, i.e. the compressability.

However, how to characterize the transition from liquid to solid? i.e. from usual experience the compressability of liquid and solid differ, but didn't seem to be of a very dramatic way like that from gas to liquid.

How to characterize phase transition from liquid to solid?

Especially, could you point a way of how to calculate the $0 ^\circ C$ for which water will turn to ice?

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  • $\begingroup$ Evaporation and condensation are dramatic? $\endgroup$ May 9 '20 at 0:53
  • $\begingroup$ @probably_someone It could be(with constant shocking/disturbance to avoid the super cool liquid etc.). Basically keep the phenomenon explainable by statistical distribution. $\endgroup$ May 9 '20 at 1:08
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    $\begingroup$ Probably a T-S diagram will be more dramatic? $\endgroup$
    – plasmachu
    May 9 '20 at 2:23
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The symmetry that is breaking in the liquid-solid transition is translational symmetry. In solid state there is a concept of bond length that is absent in liquids. In other words, if you track two atoms in a liquid and wait long enough, the distance between them changes. However, if you do the same in a solid, their position will remain static basically forever.

So the order parameter for liquid-solid transition would involve defining an atomic correction function: $$G(x,x’;t-t’)$$

For liquids, this function goes to zero as time goes to infinity. But not for solids. This experimentally can be calculated from the X-ray diffraction spectra.

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