We demonstrate how three "state-of-the-art" techniques may be combined to build a bridge between atomistics and microstructure: (1) first-principles calculations, (2) a mixed-space cluster expansion approach, and (3) the diffuse-interface phase-field model. The first two methods are used to construct the driving forces for a phase-field microstructural model of theta'- Al2Cu precipitates in Al: bulk, interfacial, and elastic energies. This multiscale approach allows one to isolate the physical effects responsible for precipitate microstructure evolution.