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.55. Jk, 81.05.Dz, 81.15.Hi Mg x Zn 1-x O (0 ≤ x ≤ 1) layers without wurzite-rocksalt phase mixing have been successfully grown by MBE on a-plane sapphire substrates with ZnO buffer layers. The layers of x < 0.5 take wurzite (0001) structure eliminating the problem of wurzite-rocksalt phase mixing reported previously between x = 0.35 and 0,45, while those of x > 0.5 rocksalt (001) with wurzite (0001) structure only at the initial stage of the growth (<25 nm). The rocksalt (001) rather than (111) which has been generally seen on sapphire without ZnO buffer layers can be explained by the model showing successive transition from wurzite (0001) to rocksalt (001) with the tensile and compressive deformation of the lattices along a-and b-axes, respectively. The band gap energy of Mg x Zn 1-x O has been continuously tuned without the problem of unstable phase mixing.