  The role of stoichiometry and growth temperature in the preferential
nucleation of material phases in the Li-Nb-O family are explored yielding an
empirical growth phase diagram. It is shown that while single parameter
variation often produces multi-phase films, combining substrate temperature
control with the previously published lithium flux limited growth allows the
repeatable growth of high quality single crystalline films of many different
oxide phases. Higher temperatures (800-1050 {\deg}C) than normally used in MBE
were necessary to achieve high quality materials. At these temperatures the
desorption of surface species is shown to play an important role in film
composition. Using this method single phase films of NbO, NbO$_{2}$,
LiNbO$_{2}$, Li$_{3}$NbO$_{4}$, LiNbO$_{3}$, and LiNb$_{3}$O$_{8}$ have been
achieved in the same growth system, all on c-plane sapphire. Finally, the
future of these films in functional oxide heterostructures is briefly
discussed.
