Method for growing a single crystal, comprises producing a melt from a mixture containing aluminum-

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Use of a method for growing a gallium or aluminum garnet crystal , in particular a single crystal, or from a melt of a gallium garnetaluminum garnet at least one rare earth, preferably Ce, Lu, Sc or Y, or from a melt of a mixture of oxides of formula 3 O 2 Me, wherein the rare earth element or the rare earth elements Me, gallium and/or is aluminium, of aluminium fluoride, gallium and/or fluoride of the rare earth element or the rare earth elements as flux in the melt, wherein the rare earth element in the presence of the fluoride in the melt further 3 in excess with respect to the stoichiometry of the 2 O Al gallium or. aluminum garnet and wherein in the melt at the presence of the gallium or is present. rare earth element oxides in excess with respect to the stoichiometry of the product the rare earth element oxide or the aluminum garnet are present. The use serves the embodiment of processes for growing a gallium or. aluminum garnet crystal and producing optical lenses or. Scintillators from this crystal.