The question is with regards to Thermal Expansion at the point of melting.

My basic understanding is that a material will generally undergo linear thermal expansion until some phase change occurs (crystal formation, melt, etc) that changes the material behavior. Take Aluminum, for example. It has a linear expansion coefficient of ~23E-6 /K when solid, but might go as high as ~98E-6 /K when melted. What I can't find, however, is how much expansion occurs over the process of the melting transition itself? It seems like if a solid metal with a poisson ratio of 0.35 (compressible material) transitions to a liquid with poisson's ratio of ~0.5 (incompressible), there must be some large amount of expansion as it fully "decompresses" to that point. Kind of how water which we all learned in elementary school counter-intuitively expands when frozen, I would assume metal behaves more intuitively with a large expansion when melted.

Is there any formula to predict this expansion amount during melt, assuming all heat is contributing to phase transition and not increasing temperature?

  • $\begingroup$ A quick reading on the articles on the web, my impression is not all metals are created equal, while almost all metals expand under heat, there are exceptions. Also, metals with a higher melting point tend to have lower thermal expansion. Interesting topic, but I doubt there is a precise answer to it. $\endgroup$
    – r13
    Commented Jul 29, 2021 at 22:51
  • $\begingroup$ Pattern makers shrinkage factors are easy enough to find for any engineering metal . Just reverse it for expansion. $\endgroup$ Commented Jul 30, 2021 at 1:30

1 Answer 1


Phase transitions are isothermal processes, so I think your best bet would be to calculate a weighted average of the molar volumes of the two phases. These values can be easily looked up.

  • $\begingroup$ Correct: phase transitions are isothermal as I said ("all heat is contributing to phase transition and not increasing temperature"). Do you know a resource that supplies the molar volumes of metals immediately before melting onset and immediately after? Common ones like aluminum and copper I can locate, but for unusual alloys I was hoping there was some predictive formula. $\endgroup$ Commented Nov 1, 2020 at 23:51
  • 2
    $\begingroup$ @TrevorBuckner if you know the P-T phase diagram of the system, you can use the Clausius-Clapeyron equation to calculate the specific volume change of the phase transition. For exotic alloys these may not be available, but the volume change on melting is a relatively easy experimental measurement. For a solid-state transformation, you could measure the lattice parameter via XRD, perhaps. A back-of-the-envelope calculation could use the packing of hard spheres. For example, close-packed spheres (FCC, HCP) fill 74% of available space, while random packing (liquid) is closer to 62%. $\endgroup$
    – Chris
    Commented Nov 2, 2020 at 4:07

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