This Article reports a mechanistic study on the formation of colloidal UO(2)/In(2)O(3) and FePt/In(2)O(3) heterodimer nanocrystals. These dimer nanocrystals were synthesized via the growth of In(2)O(3) as the epitaxial material onto the seed nanocrystals of UO(2) or FePt. The resulting dimer nanocrystals were characterized using X-ray powder diffraction (XRD), energy dispersion spectroscopy, transmission electron microscopy (TEM), scanning transmission electron microscopy, and high-resolution TEM (HRTEM). The results from XRD and HRTEM clearly show that lattice strains exist in both of these dimer nanocrystals. Interestingly, the lattice of In(2)O(3) expands in UO(2)/In(2)O(3) dimers, whereas FePt/In(2)O(3) dimers exhibit compressed In(2)O(3) lattices. Using HRTEM and nanocrystal structure simulations, we have identified the crystallographic orientation of the attachment of the two segments in these two types of dimers. An unconventional Miller index was introduced to describe the crystallographic orientation of these heterodimer nanocrystals. On the basis of the results herein as well as those from other researchers, we propose an empirical law for the determination of the crystallographic attachment orientation in heterodimers: instead of growth on the facet of the seed nanocrystals where lattice mismatch is minimized, the growth of an epitaxial material often chooses the crystal facets where the first atomic monolayer of this material has the strongest affinity for the seed nanocrystals.