On the Nb-Ge Binary System

Abstract

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).