First-principles theory of 250 000-atom coherent alloy microstructure

Microstructural issues in alloys such as precipitation have largely been outside the realm of first-principles electronic structure calculations due to the length scales involved in precipitation microstructure (typically nanometres to micrometres) and the inherent thermodynamic/statistical nature of the problem. Here, we show that modem, first-principles total energy calculations can be combined with a mixed-space cluster expansion approach (a generalized real/reciprocal space Ising model) and Monte Carlo simulations to yield a method capable of describing equilibrium coherent precipitate shapes in alloys with system sizes up to 250 000 atoms. Both the (anisotropic) interfacial free energies and the coherency strain between precipitate and matrix are accounted for in this method as well as the short-range atomic-scale ordering of the solid solution. Illustrations of the technique are given for several famous examples of coherent precipitation in aluminium alloys: Al-Mg, Al-Cu and Al-Ni.