Layers of InN and GaN have been successfully grown on GaAs(001) and GaP(001) substrates using a modified molecular beam epitaxy technique. X-ray diffraction data reveals that these layers are, in fact, separated into binary components of GaAs and mixtures of GaN in its hexagonal or zinc-blende form. The same composite layers have also been studied with scanning electron microscopy, and we find a close correlation between the grain size measured from the scanning electron microscopy images and those determined from the full width at half-maximum of the x-ray diffraction spectra. This key observation demonstrates for the first time that there is a direct relationship between the measured x-ray half-widths and the microstructure of the films for both hexagonal and zinc-blende polytypes. In addition, we have been able to control the growth conditions of GaN such that we can now selectively grow either exclusively hexagonal or zinc-blende material.