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For instance, suppose it is a 50-50 alloy of two metals that is BCC at room temperature $T_0$. If I raise (or lower) the temperature, is it possible for the bonds in the crystal to rearrange and form a new structure (say, FCC) that is more energetically favourable at the new $T$?

I saw a question on an engineering forum (here) that seemed to suggest the only thing that affected the structure was the % composition of the alloy. Could temperature play a role, too?

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The microstructure of an alloy depends on such variables as the alloying elements present, their concentrations, and the heat treatment of the alloy (i.e., the temperature, the heating time at temperature, and the rate of cooling to room temperature). -Materials Science and Engineering: An Introduction 9th, Wiley, Calister, Rethwisch

Look up phase diagrams for different alloys

Here is a phase diagram for iron and carbon (steel). Depending on the composition of the alloy and the temperature it is at different crystal structures will form and multiple phases can be present at the same time. $\alpha$ is ferrite and has BCC structure, austenite ($\gamma$) has FCC.

By User A1 at en.wikipedia [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], from Wikimedia Commons

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  • $\begingroup$ Is it possible to change the structure without changing the composition (ie. only change the temperature)? This isn't clear from the phase diagram. $\endgroup$ – Wise Owl Mar 4 '16 at 2:55
  • $\begingroup$ if you keep the concentration of the alloy the same and you raise the temperature the structure will change. For instance at the eutectic composition of 0.76% carbon the ferrite and perlite (alternating layers of ferrite and cementite) transform into FCC austenite when you increase the temperature above 730 degrees celsius $\endgroup$ – Devin Crossman Mar 4 '16 at 3:02
  • $\begingroup$ Phase changes based on temperature and pressure can also occur in pure metals; you can see the x-ray diffraction pattern change with the conditions, e.g., bismuth, which has bcc, fcc, hcp phases: books.google.com/… $\endgroup$ – Peter Diehr Mar 4 '16 at 3:05
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    $\begingroup$ Perhaps the most dramatic example of this is in the two "common" allotropes of Carbon. $\endgroup$ – Aron Mar 4 '16 at 9:16
  • $\begingroup$ @Aron: indeed, and not everybody knows that diamond is unstable at STP. It's possible for the bonds to re-arrange into a more favourable structure, exactly as the questioner asks, it's just a really really slow process. $\endgroup$ – Steve Jessop Mar 4 '16 at 10:41
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Yes, it is very possible. Even water goes through such different structures

enter image description here

Two lines in particular from the wikipedia article on Ice:

  • Ice II A rhombohedral crystalline form with highly ordered structure. Formed from ice Ih by compressing it at temperature of 190–210 K. When heated, it undergoes transformation to ice III.
  • Ice III A tetragonal crystalline ice, formed by cooling water down to 250 K at 300 MPa. Least dense of the high-pressure phases. Denser than water.
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  • $\begingroup$ " Formed from ice Ih by compressing it at temperature of 190–210 K" - at first I misread that as Celsius and I thought "that must take a lot of pressure". $\endgroup$ – John Dvorak Mar 5 '16 at 21:00
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No alloy is required. Plutonium is an example: Phase diagram of plutonium

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There is certainly far more to metallurgy than % composition of the alloy. Devin Crossman's answer hints a little at the processes involved. Hardness is strongly affected by heat treatments, for example, though this does not have much to do directly with the subject of this question https://en.wikipedia.org/wiki/Hardening_(metallurgy).

A classic (and very relevant) example of a phase change in metallurgy occurs with tin. Tin changes from a tetragonal metallic structure (density 7.365 g/cm3) to a diamond type nonmetallic structure (density 5.769 g/cm3) at temperatures below 13.2C.

The transformation is said to be "autocatalytic" (though I think it may be more a case of crystal nucleation) and is referred to as "tin pest." Tin objects will become brittle and simply fall apart at low enough temperatures.

https://en.wikipedia.org/wiki/Tin_pest

https://www.youtube.com/watch?v=FUoVEmHuykM

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