# Why is the disordered CuAu structure more stable at high temperatures?

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

• Pretty much all disordered things are more stable at high temperatures. Think of liquids vs solids, to begin with. – Ivan Neretin Apr 8 at 12:06
• That makes sense. But why would a closely packed structure ever be more disordered than one which isn't? – Marina Calder Apr 8 at 12:27
• 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. – Ivan Neretin Apr 8 at 12:40
• Fabulous , I understand this. Thank you! – Marina Calder Apr 8 at 12:56

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, $$oI40$$.

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).