Single crystals of Li6Y(BO3)3 have been grown by both the Bridgman and Czochralski methods. It was found that the complex nature of the melt solidifications affects the efficiency of the crystallization process and the composition of the grown crystals. High supercooling favored melt dissociation and the formation of thermodynamically unstable phases Li3Y(BO3)2 and Li3Y2(BO3)3. Applying X-ray phase analysis for air-quenched ceramic samples it was shown that the room temperature stability region of the off-stoichiometric Li6Y(BO3)3 phase is extended towards the B2O3 rich, Y2O3 deficient compositions.