The full performance of GaN devices for high power applications is not exploited due to their self-heating. Possible solutions are the integration of materials with high heat conductivity i.e., single crystalline diamond and graphene layers. We report the growth of single crystalline (0001)-oriented GaN thin films on (100), (110) and (111) diamond single crystals studied by transmission electron microscopy (TEM) in cross-sections. As for graphene, we show a high quality GaN layer that was deposited on patterned graphene layers and 6H-SiC. The atomic structures of the interfaces in the heterostructure are studied using aberration-corrected scanning TEM combined with energy dispersive x-ray and electron energy-loss spectroscopy.