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The invention relates to a method for producing break-proof, large-size calcium fluoride monocrystals, which are suited for optical components used in the low UV range. The CaF2 starting material is firstly melted. Afterwards, the melt is solidified while cooling it to form a monocrystal. In order to increase the breaking strength, Th, Ba, W, Sb, Y and/or rare earths are added by doping to the CaF2 starting material that can contain small amounts of impurities.