The famous sequence of precipitates which form upon heat treating Al-Cu is part of nearly every metallurgical textbook. Numerous precipitation (and other) experiments have led to a long-standing belief that the energetic ground state of ${\mathrm{Al}}_2\mathrm{Cu}$ is the $\theta$ phase. Modern first-principles calculations at $T=0\mathrm{}\mathrm{K}$ surprisingly predict the energy of the observed ${\mathrm{Al}}_2\mathrm{Cu}-\theta$ phase to be higher than that of its metastable counterpart, ${\theta }^{\prime }$. We show that vibrational entropy reverses this energetic preference at $T\sim 150–200°\mathrm{C}$, resolves the apparent discrepancy between theory and experiment, and hence plays a critical (but previously unsuspected) role in the precipitation sequence.

• Received 7 November 2000

DOI:https://doi.org/10.1103/PhysRevLett.86.5518