Predicting metastable phase boundaries in

Metastable precipitate phase boundaries are difficult to ascertain experimentally and yet are important for controlling the microstructure of precipitation-hardenable alloys. We demonstrate how first-principles calculations of configurational and vibrational free energies can be used to predict precipitate phase boundaries of stable and metastable phases in $\chem{Al\tx{-}Cu}$ alloys. Surprisingly, the formation entropy of a Cu impurity is found to be hugely positive (+2.7 kB/atom), leading to a dramatic enhancement in the solubility. The large entropy is dominated by the very low-frequency vibration of the small impurity atom (Cu) inside the large cage of the host (Al). The agreement between the GGA and experimental data is within 100$\un{K}$ for all phases, showing that accurate first-principles determination of metastable phase boundaries is now possible