In the Nd-Fe-B permanent magnet materials, several elements such as C, B, Cu, Dy, etc. are added to the main phase in order to improve the properties of the magnets from various aspects. The formation, mixing properties within various binary systems relevant to the multi-component phase have important effect on the microstructure formation so as to the coercivity of the magnets. First-principles calculations combined with the cluster expansion method (CEM) have been performed on series of binary systems such as Nd-O, Fe-Nd, Nd-Dy, Fe-Dy, Cu-Nd, Cu-Fe to investigate the ground state stability of ordered phases as well as solid solutions, in order to reveal the characteristic features of electronic structures and atomic interactions of the systems with intrinsic stability and intrinsic instability. Such information is significant in understanding the properties of the multi-component phase, also provides the basic data for further study of the thermodynamic properties.