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I know that the disordered CuAu structure is based around FCC whereas the ordered CuAu structure is tetragonal. Why would the FCC structure be more stable at high temperatures?

For context, I was asked to explain this with the aid of a graph. I don't really know where to start

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    $\begingroup$ Pretty much all disordered things are more stable at high temperatures. Think of liquids vs solids, to begin with. $\endgroup$ Apr 8, 2021 at 12:06
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    $\begingroup$ That makes sense. But why would a closely packed structure ever be more disordered than one which isn't? $\endgroup$
    – user85551
    Apr 8, 2021 at 12:27
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    $\begingroup$ Because every single atomic position in that close-packed structure has some freedom: it may be Cu, or it may be Au. That's a lot of disorder. $\endgroup$ Apr 8, 2021 at 12:40
  • $\begingroup$ Fabulous , I understand this. Thank you! $\endgroup$
    – user85551
    Apr 8, 2021 at 12:56

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I'm not a metallurgist or even not a good physical chemist. However, I'd like to explain what's happening in $\ce{AuCu}$ alloy with temperature and any expert can intervene.

According to Ref.1, $\ce{Cu}$ and $\ce{Au}$ are both univalent group IB metals with the atomic size difference ~12%. The $\ce{AuCu}$ alloy forms the tetragonally distorted fcc lattice where alternate (00h) planes contain either $\ce{Cu}$ or $\ce{Au}$ atoms and cause a contraction in c-direction. Resulting tetragonal face-centered structure has c/a ratio of 0.92 $(\frac{c}{a} = \frac{\pu{367 pm}}{\pu{396 pm}} = 0.93)$. In the temperature range ~$\pu{380 ^\circ C}$ to $\pu{410 ^\circ C}$, the superlattice $\ce{CuAu}$-II is formed, which consist of $\ce{CuAu}$-bct unit cells with the antiphase domains along the b-direction (Ref.2). There is a lattice shift of $\frac12(a+c)$ at each five unit-cell length. The superlattice $\ce{CuAu}$-II is described as orthorhombic cell with 10 cells along one of a direction, $oI40$.

Phase diagram of AuCu alloy

Calculated diffraction patterns

Suggested reading: Ref.3 and 4.


References:

  1. Valentina F. Degtyareva, Nataliya S. Afonikova, "Simple Metal and Binary Alloy Phases Based on the fcc Structure: Electronic Origin of Distortions, Superlattices and Vacancies," Crystals 2017, 7(2), 34 (13 pages) (DOI: https://doi.org/10.3390/cryst7020034).
  2. V. Ozoliņš, C. Wolverton, Alex Zunger, "Cu-Au, Ag-Au, Cu-Ag, and Ni-Au intermetallics: First-principles study of temperature-composition phase diagrams and structures," Phys. Rev. B 1998, 57(11), 6427 (DOI: https://doi.org/10.1103/PhysRevB.57.6427).
  3. M. Sanati, L. G. Wang, Alex Zunger, "Adaptive Crystal Structures: $\ce{CuAu}$ and $\ce{NiPt}$," Phys. Rev. Lett. 2003, 90(4), 045502 (DOI: https://doi.org/10.1103/PhysRevLett.90.045502).
  4. S. -H. Wei, A. A. Mbaye, L. G. Ferreira, Alex Zunger, "First-principles calculations of the phase diagrams of noble metals: Cu-Au, Cu-Ag, and Ag-Au," Phys. Rev. B 1987, 36(8), 4163 (DOI: https://doi.org/10.1103/PhysRevB.36.4163).
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