Lattice gas model is presented for rhombohedral lattice. Seven ordered structure types and four perfectly ordered structures are determined using concentration wave theory. The ordered structures of cation in corundum-type dimetal trioxides are predicted and reasonable explanations for typical experimental results are given.rhombohedral crystal, concentration wave, ordered structure, corundumRhombohedral system is one of the seven crystal systems. In recent years, many materials with rhombohedral structure have attracted many researcher's attention. For instance, sapphire (α-Al 2 O 3 ) is an infrared window material with excellent comprehensive performance [1] , and it is also a substrate material for the epitaxial preparation of ferroelectric materials [2,3] ; α-Al 2 O 3 is the main composition phase of scale on the surface of TiAl-based alloy, which contributes to the oxidation resistance at high temperature [4,5] ; ruby, based on α-Al 2 O 3 , is an important laser material; Ti-doped sapphire is widely used as important working crystal for tunable lasers and ultra-fast, high power light pumping. Zr-or Hf-doped BaTiO 3 is a new type of piezoelectric ceramic with stable rhombohedral phase above room temperature [6] . The r-BN is the precursor of new superhard materials c-BN [7] ; metastable rhombohedral α-Ga 2 O 3 has a smaller energy gap indicating very different photoelectric performance [8] . Recently, multi-component ordered solid solution has become one of the important fields for the investigation of these materials, for the performances of materials are determined by their structures. For instance, transition metal doped corundum type of α-Al 2-x T x O 3 (T = Sc, Y, La, Ac; x=0.5) crystals are high k-gate dielectric materials [9,10] ; corundum type solid solution α-FeAlO 3 were reported [11] . The investigations on multi-component coatings and composite coatings for oxidation resistance at high temperature [12][13][14] as well as on the property of other corundum type solid solution [15,16] are all hot points of materials research.Theoretically, while the main ordered structure types of cubic system [17][18][19] and hexagonal system [20,21] have been determined, the results about rhombohedral system have seldom been reported. Therefore, it is necessary to study the ordered structure types of rhombohedral system theoretically, which can give useful instruction to the research of related materials.