Homologous compounds, In2O3(ZnO)(m) (m greater than or equal to 3), (InGaO3)(2) ZnO, InGaO3(ZnO)(m) (m greater than or equal to 1), and Ga2O3(ZnO)(m) (m greater than or equal to 7) phases (m = natural number) in the In2O3-ZnGa2O4-ZnO system were synthesized at 1150-1550 degrees C from In2O3, Ga2O3, and ZnO powders. The homologous compounds with smaller m are synthesized as temperature is elevated higher. Single crystals of In2O3(ZnO)(m) (m = 3, 4, and 5), InGaO3(ZnO)(3), and Ga2O3(ZnO)(m) (m greater than or equal to 7, 8, 9, and 16) were grown by means of solid-state reactions in the mixtures of the starting compound powders with mixing ratio of In2O3:ZnO = 1:m at 1550 degrees C, In2O3:Ga2O3:ZnO = 1:1:6 at 1550 degrees C, and Ga2O3:ZnO = 1:m (in a mole ratio) at 1450-1550 degrees C. The crystal data determined by means of a Weissenberg camera are as follows: In2O3(ZnO)(3); a = 3.34 Angstrom; and c = 42.6 Angstrom; In2O3(ZnO)(4), a = 3.33 Angstrom and c = 33.5 Angstrom; In2O3(ZnO)(5), a = 3.32 Angstrom and c = 58.4 Angstrom; and InGaO3(ZnO)(3), a = 3.29 Angstrom and c = 41.8 Angstrom. The crystal data determined by means of a single-crystal X-ray diffractometer are as follows: Ga2O3(ZnO)(7), a = 3.2512(1)Angstrom, b = 19.654(3)Angstrom, and c = 27.754(4)Angstrom; Ga2O3(ZnO)(8), a = 3.2497(1)Angstrom, b = 19.682(3)Angstrom, and c = 30.684(3)Angstrom; Ga2O3(ZnO)(9), a = 3.2520(1)Angstrom, b = 19.707(4)Angstrom, and c = 33.603(5)Angstrom; and Ga2O3(ZnO)(16), a = 3.2534(1)Angstrom, b = 19.764(3)Angstrom, and c = 54.208(5)Angstrom, orthorhombic crystal system in Cmcm space group (No. 63). In2O3(ZnO)(m) and InGaO3(ZnO)(m) belong to R(3) over barm$ for m = odd or P6(3)/mmc for m = even, and their lattice constants are given in a hexagonal form. The crystal data for In2O3(ZnO)(m), InGaO3(ZnO)(m), and Ga2O3(ZnO)(m) are discussed based upon the wurtzite-type crystal structure. (C) 1995 Academic Press, Inc.