Is there any substance with segments of its phase change diagram lines going in a negative direction?

To explain:

Generally, as phase change diagrams go, with heat increasing, and pressure constant, substances tend to evaporate, sublimate or melt; cooling produces the opposite, fusion (freezing), deposit or condensation into liquid from vapor.

But the diagrams are rarely straightforward - water, for example, has a multitude of forms of ice, where not all forms are obtainable through transitions "from any direction". There are many obscure factors that define when each transition can occur.

Is there any substance, that - without transforming into another substance (say, polymerization) - possesses an area of the phase change diagram (possibly way off "room conditions") where the transition goes in the opposite direction - heating leads to a - not necessarily more dense - but 'more solid' state? Something like thermally hardened glue, but without a chemical transition?

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    $\begingroup$ Ice at $0$ºC melts when compressed ... $\endgroup$ Commented Sep 21, 2016 at 10:48
  • $\begingroup$ @JohnRennie: I knew I messed putting the concept into words somehow. $\endgroup$
    – SF.
    Commented Sep 21, 2016 at 11:08
  • $\begingroup$ Moth balls? Basically you could have something that sublimates at either temperature but seems solid to us because of the slow time scale. $\endgroup$
    – JDługosz
    Commented Sep 22, 2016 at 6:54
  • $\begingroup$ Hmm... do we have any example of a pyroelectric liquid that became easier to vaporise as it cool beyond its transition temperature such that it becomes a paraelectric and thus too weak to hold itself together? $\endgroup$
    – Secret
    Commented May 16, 2018 at 19:32

3 Answers 3


Yes, here's the phase diagram for Helium-3:

enter image description here

Notice that around 3 MPa, an increase in temperature causes a transition from liquid to solid.

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    $\begingroup$ How do we know those diagrams? Did we test all combinations of temperature and pressure for all the things, or is there a theoretical result? $\endgroup$
    – njzk2
    Commented Sep 21, 2016 at 14:17
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    $\begingroup$ @njzk2: That's a separate question. But as Helium-3 is the element for extreme-low temperature research, I'd daresay there are lots of data points available for that isotope. $\endgroup$
    – DevSolar
    Commented Sep 21, 2016 at 14:56
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    $\begingroup$ What is the vertical line in the solid phase at a little less than 0.1 mK? $\endgroup$
    – gerrit
    Commented Sep 21, 2016 at 15:41
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    $\begingroup$ @gerrit: According to this paper page 5/figure 3, it's the cutoff between a spin-ordered and spin-disordered solid. $\endgroup$ Commented Sep 21, 2016 at 16:07
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    $\begingroup$ It would be good to clarify, inside the post, whether this is experimentally verified or only theoretical, and ideally also provide some additional information on what actually happens to the material that makes it sublimate as it is cooled down. $\endgroup$ Commented Sep 21, 2016 at 21:12

This question has already been answered pretty thoroughly, but I feel like I should add that all of this is related to something called the Clausius-Clapeyron equation, $$ \frac{\textrm{d} P}{\textrm{d} T} = \frac{\Delta s}{\Delta v} $$ This relates the slope of the phase boundary in a $P-T$ phase diagram to specific entropy change $\Delta s$ and the specific volume change $\Delta v$ of the phase transition. Now, if we talk about going from a solid phase to a liquid phase, $\Delta s$ is always positive, because solids have crystalline order, which is lost when going to the liquid phase. Since the specific volume in this case is usually also positive, we expect the slope of the phase boundary to be positive. In the cases when it is not, we have the very unusual scenario of a substance being more "compact" in liquid phase than in solid phase. That this is true of water is well-known: try putting water in a tight container into your freezer and see how it goes. From lemon's linked image, we see it is also true of helium 3.

  • $\begingroup$ I don't think the question has been pretty thoroughly answered. For instance, the current accepted and top answer does not mention anything about a substance that would boil when cooled down at constant pressure. Everything is focused on the liquid/solid transition, leaving entirely aside the gaseous/liquid one. $\endgroup$ Commented May 16, 2018 at 19:16

Just to follow up John Rennie's comment (because I didn't quite believe it)

water phase diagram from wikipedia

Looks like ice between 0 and -20C will melt at some (rather extreme) range of pressures but only at increasing pressure not with decreasing temperature.

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    $\begingroup$ "only at increasing pressure not with increasing temperature" - I think you misstated that. Increasing the temperature will also cause melting, unless the pressure is low enough that it sublimates instead. $\endgroup$ Commented Sep 21, 2016 at 17:44
  • $\begingroup$ @user2357112 thanks - I knew there was something wrong but couldn't spot it. And phase diagrams have always been a source of confusion ! $\endgroup$ Commented Sep 21, 2016 at 18:18
  • $\begingroup$ It will melt at much lower pressures with pressure growth - because compressing it will heat it too. That's how ice skating works - creating a thin film of water from melting ice with the pressure. But if you artificially maintain the temperature at 0C, this is correct. $\endgroup$
    – SF.
    Commented Sep 22, 2016 at 8:04
  • $\begingroup$ I think the phase diagram shows that melting ice purely by pressure is unlikely. Ice skating works by friction heating $\endgroup$ Commented Sep 23, 2016 at 3:34
  • $\begingroup$ @SF. - That's a myth ("that's how ice skating works"). The pressure under an ice skate blade is far too low to cause ice to melt per the phase transition diagram. A related question on this issue: physics.stackexchange.com/questions/1720/… . $\endgroup$ Commented May 17, 2018 at 21:43

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