Interphase energies of hcp precipitates in fcc metals: A density-functional theory study in Al-Ag

Abstract

Density-functional theory (DFT) calculations of interphase boundary energies relevant to hexagonal-close-packed (hcp) $\ensuremath{\gamma}$-precipitate formation were performed within approximate unit cells that mirror the experimental conditions in face-centered-cubic (fcc) Al-Ag solid solutions. In Al-rich, fcc Al-Ag, $\ensuremath{\gamma}$ precipitates are observed to form rapidly with large $(300+)$ aspect ratios even though the Al stacking-fault energy is high (approximately $130\text{ }\text{mJ}/{\text{m}}^{2}$), which should suppress hcp ribbon formation according to standard arguments. Our DFT results show why high-aspect ratio plates occur and why previous estimates based on Wulff construction were orders of magnitude less than observed values. Using DFT, we obtain a Gibbs free-energy diagram that gives the relevant hcp equilibrium precipitate structure occurring at $50\text{ }\text{at}\text{.}\text{ }\mathrm{%}$ Ag. We derive the critical nucleation parameters for $\ensuremath{\gamma}$-precipitate formation, which require our calculated bulk-driving force for nucleation and interphase boundary energies. From our DFT-based nonequilibrium estimate for precipitation that accounts for growth via coarsening by ledge and edge migrations, we obtain time-dependent aspect ratio that agrees well with experiment. The same energetics and growth model are relevant to other phenomena, such as lath morphology in martensites or island coarsening.