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.
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