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The phase transition in YBa2Cu3O7-x (123 phase) from high temperature to low temperature has been theoretically analyzed by crystal symmetry group as well as group-subgroup theory. The result shows that the space group of the orthorhombic 123 phase should be Pmmm, not Pm2m, which is consistent with the type of domain boundaries detected in the 123 phase so far. The analysis also reveals that the phase transition from the tetragonal 123 phase to the orthorhombic 123 phase follows the crystallographic relationship between group and subgroup with the order being 2.

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