Predicting metastable phase boundaries in alloys from first-principles calculations of free energies: The role of atomic vibrationsC. Ravi1, 2, C. Wolverton1 and V. Ozolins3
1 Ford Research and Advanced Engineering, MD 3083/SRL Dearborn, MI 48121-2053, USA
2 Department of Materials Science and Engineering, The Pennsylvania State University - University Park, PA 16802-5006, USA
3 Department of Materials Science and Engineering, University of California Los Angeles, CA 90095-1595, USA
received 12 August 2005; accepted in final form 12 January 2006
published online 1 February 2006
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 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 for all phases, showing that accurate first-principles determination of metastable phase boundaries is now possible.
65.40.Gr - Entropy and other thermodynamical quantities.
63.20.Dj - Phonon states and bands, normal modes, and phonon dispersion.
81.30.Bx - Phase diagrams of metals and alloys.
© EDP Sciences 2006