We have studied the orientational epitaxy of Al films evaporated on Si(001) using surface x-ray scattering techniques. Although the Al primarily grows as two (011) domains, separated by 90 o azimuthal rotations, we find four additional domains which are rotated ±18.9 o away from the two primary domains. The selection of this set of epitaxial configurations by the growing film is explained by a simple rigid-lattice model. This model produces distinct minima in a plot of Si-Al interfacial energy versus in-plane orientation, with positions and depth which are fully consistent with the experimentally observed domains