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Bi2Sr2CaCu2Oy (Bi-2212) superconducting single crystals were prepared by a modified vertical Bridgman method using large alumina crucibles of a 26 mm bore diameter with cone-shaped bottom. In order to obtain large and high quality single crystals, we optimized growth conditions using the large crucibles. We obtained a large plate-like single crystal with a size of 17.0 mm × 5.5 mm when the crystal growth was carried out with the rotation speed of 50 rpm and at the temperature for starting the crystal growth of 1000°C. In the single crystal, the FWHM value of the (0010) x-ray diffraction peak which was assigned to a Bi-2212 superconductor was small and about 0.06°. Tc of the single crystal was about 87 K, which was higher than Tc=82 K of the single crystals grown with smaller crucibles whose bore diameter is 35% less than the large crucibles.