Structure of (Ga2O3)2(ZnO)13 and a unified description of the homologous series (Ga2O3)2(ZnO)(2n + 1).

The structure of (Ga(2)O(3))(2)(ZnO)(13) has been determined by a single-crystal X-ray diffraction technique. In the monoclinic structure of the space group C2/m with cell parameters a = 19.66 (4), b = 3.2487 (5), c = 27.31 (2) Å, and β = 105.9 (1)°, a unit cell is constructed by combining the halves of the unit cell of Ga(2)O(3)(ZnO)(6) and Ga(2)O(3)(ZnO)(7) in the homologous series Ga(2)O(3)(ZnO)(m). The homologous series (Ga(2)O(3))(2)(ZnO)(2n + 1) is derived and a unified description for structures in the series is presented using the (3+1)-dimensional superspace formalism. The phases are treated as compositely modulated structures consisting of two subsystems. One is constructed by metal ions and another is by O ions. In the (3 + 1)-dimensional model, displacive modulations of ions are described by the asymmetric zigzag function with large amplitudes, which was replaced by a combination of the sawtooth function in refinements. Similarities and differences between the two homologous series (Ga(2)O(3))(2)(ZnO)(2n + 1) and Ga(2)O(3)(ZnO)(m) are clarified in (3 + 1)-dimensional superspace. The validity of the (3 + 1)-dimensional model is confirmed by the refinements of (Ga(2)O(3))(2)(ZnO)(13), while a few complex phenomena in the real structure are taken into account by modifying the model.