Phase diagrams of the Blume-Emery-Griffiths model for semiconducting alloy systems (${\mathit{ABD}}_2$${)}_{1\mathrm{-}\mathit{x}}$(CD${)}_{2\mathit{x}}$ or [(AB${)}_{1\mathrm{-}\mathit{x}}$${\mathit{C}}_{2\mathit{x}}$]${\mathit{D}}_2$

The Blume-Emery-Griffiths model is used to model the ordering of semiconducting alloy systems with chalcopyrite structure and zinc-blende structure as the parents, such as the alloy systems (${\mathit{ABD}}_2$ ${)}_{1\mathrm{-}\mathit{x}}$(CD${)}_{2\mathit{x}}$ or [(AB${)}_{1\mathrm{-}\mathit{x}}$ ${\mathit{C}}_{2\mathit{x}}$]${\mathit{D}}_2$. The ground states are determined to classify the types of ordering and phase diagrams of the system. The new ordered phases are found at composition x=3/4 and x=1/4 besides the x=1/2 stannite phase for a range of energy parameters. The phase diagrams of the compounds are calculated by the cluster-variation method. Several features of the phase diagrams are discussed and compared with experiment.