On the Nb-Ge Binary System

First-principles calculations were used to study intermetallic compounds in the Nb-Ge system, to gain a better understanding of the phase diagram and resolve conflicts reported in the literature. The enthalpy of formation with regard to temperature was calculated for all the intermetallic compounds, to investigate phase stabilities and phase equilibria at low and elevated temperatures. These results, combined with the electronic DOS, suggest that the tI32 (W₅Si₃-type) Nb₅Ge₃ and NbGe₂ compounds are stable over the whole temperature range. The stoichiometric cP8 Nb₃Ge becomes stable close to its melting temperature. Regarding different compositions of the cP8 Nb₃Ge, the calculations suggest the (Nb)_0.75(Nb,Ge)_0.25 model for the Nb₃Ge phase instead of the proposed model, (Nb)_0.75(Nb,Ge,Va)_0.25, where Va represents vacancy. The calculations show that the tI32 (Cr₅B₃-type) Nb₅Ge₃, hP16 (Mn₅Si₃-type) Nb₅Ge₃ and Nb₁₀Ge₇ compounds should be considered metastable. The elastic constants, bulk, shear, and Young’s modulus, Poisson’s ratio, and Debye temperature of the Nb, Ge, cP8 Nb₃Ge, tP32 Nb₃Ge, tI32 (Cr₅B₃-type) Nb₅Ge₃, tI32 (W₅Si₃-type) Nb₅Ge₃, hP16 (Mn₅Si₃-type) Nb₅Ge₃, Nb₁₀Ge₇ and NbGe₂ were calculated. These phases were found to be mechanically stable. Using the Cauchy pressure, Pugh’s index of ductility, and the Poisson’s ratio as criteria, the calculations suggest that the tI32 (Cr₅B₃-type) Nb₅Ge₃ and NbGe₂ intermetallics should be brittle (with the latter being the most brittle) and the cP8 Nb₃Ge, tP32 Nb₃Ge, hP16 Nb₅Si₃ and Nb₁₀Ge₇ ductile (with cP8 Nb₃Ge being the most ductile).