Catalystless growth of InxAl(1-x)N core-shell nanorods have been realized by reactive magnetron sputter epitaxy onto Si(111) substrates. The samples were characterized by scanning electron microscopy, x-ray diffraction, scanning transmission electron microscopy, and energy dispersive x-ray spectroscopy. The composition and morphology of InxAl(1-x)N nanorods are found to be strongly influenced by the growth temperature. At lower temperatures, the grown materials form well-separated and uniform core-shell nanorods with high In-content cores, while a deposition at higher temperature leads to the formation of an Al-rich InxAl(1-x)N film with vertical domains of low In-content as a result of merging Al-rich shells. The thickness and In content of the cores (domains) increase with decreasing growth temperature. The growth of the InxAl(1-x)N is traced to the initial stage, showing that the formation of the core-shell nanostructures starts very close to the interface. Phase separation due to spinodal decomposition is suggested as the origin of the resultant structures. Moreover, the in-plane crystallographic relationship of the nanorods and substrate was modified from a fiber textured to an epitaxial growth with an epitaxial relationship of InxAl(1-x)N[0001]//Si[111] and InxAl(1-x)N[1120]//Si[110 by removing the native SiOx layer from the substrate.