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Single crystals of germanium have been prepared by two methods using a vacuum furnace (~5Ã10-6 mm Hg pressure) with induction heating. In the first method nucleation is induced at the upper surface of the melt by producing the necessary heat gradient, and a single crystal is grown in the crucible by controlling the rate of cooling. In the second method molten germanium is seeded with a single crystal and is withdrawn as it solidifies in the orientation of the seed crystal. Seeds orientated with the (111), (100), and (110) planes parallel to the surface of the melt have been used and well-developed crystal faces are obtained. Single crystals of pure germanium and Sb or In-doped germanium does not wet the crucible; Al-doped germanium adheres to the crucible. Resistivity gradients may be greatly reduced by repeated recrystallizations. Pure germanium of about 55 ohm-cm resistivity can be obtained in this way.