First-principles prediction of equilibrium precipitate shapes in Al-Cu alloys

A first-principles thermodynamic approach for studying coherent precipitation in size-mismatched alloys is presented and applied to the well studied (but still controversial) problem of Guinier-Preston (GP) zone formation in Al-Cu alloys. The exceptionally soft anharmonic elastic response of Cu along (100) is crucial in determining the shape of clusters of Cu atoms embedded in the Al matrix which are plate-like (100) structures. First-principles calculations involving both strain and interfacial energies yield two types of disc shaped precipitate, namely GP1 and GP2, which are single Cu monolayers and two monolayers separated by three A1 layers respectively, in agreement with many (but not all) measurements. Competition between the thermodynamic driving force (favouring GP2) and interfacial energy around the perimeter of the zones (favouring GP1) leads to a size-dependent transition „ in the equilibrium precipitate shape from GP1 to GP2 at about 150 Å. This theoretical approach (generally applicable to metals, ceramics and semi¬conductors) should aid in understanding the coherent precipitate shapes in a variety of alloy materials.