The use of highly efficient and solarblind GaN photocathodes as part of multichannel plate UV detectors for applications in astronomy would strongly benefit from the direct growth of GaN on typical window materials with high transmission down to the deep UV range. GaN growth on MgF2 substrates by plasma-assisted molecular beam epitaxy has recently been demonstrated. Here, we report an extensive scanning transmission electron microscopy study of the thin film microstructure for growth at 525 • C and 650 • C on (100) MgF2. For the lower growth temperature, cubic as well as hexagonal GaN are observed with no preferred nucleation of either phase on the substrate and typical grain size for both variants of 100-200 nm. The higher growth temperature leads to predominant growth of hexagonal GaN in two different orientations with the same range of grain size and cubic GaN with grain sizes of about 20 nm. Furthermore, in-diffusion of Mg and F into the GaN is observed, which is accompanied by the formation of cavities in the MgF2 directly at the interface.