Thin films of CaF2 containing layers of Si and Ge nanocrystallites were grown epitaxially on Si( 111) substrates by MBE while varying the substrate temperature. The sticking coefficient of both Si and Ge to CaF2 are less than unity at the temperatures studied. Evidence that chemical reactions are minimal between Si and CaF2 leading to the formation of volatile species such as SiFx is presented and it is surmised that the dominant mechanism for re-evaporation is thermal desorption. Both Si and Ge sticking coefficients vary exponentially with 1/T and activation energies are determined. A cluster growth model describing the evolution of the amount of Si in clusters over time is given. Solving in the limit of low cluster coverage, a solution that varies linearly with time and exponentially with 1/T is obtained. Weak room temperature photoluminescence from Si nanocrystallites in CaF2 is seen, however, it is unclear whether the luminescence is coming from the Si nanocrystallites or the CaF2. Second harmonic generation is observed from samples containing single layers of Ge in CaF2.