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It is significant to study the problems how the tetragonal and orthorhombic structures of YBa2Cu3Oy generate, since the structures closely relate to superconductivity. To deal with these problems, we approach the generation of tetragonal and orthorhombicity and their morphologies by SEM, TEM, and X-ray diffraction analysis, respectively. For interpreting the experimental phenomena, we put forward a crystal growth modal: the tetragonal grows at sintering temperatures, and the tetragonal transits to orthorhombicity and forms twins along  faces at annealing temperatures. This model agrees with experimental results well.