The impact of Ti and temperature on the stability of Nb₅Si₃ phases: a first-principles study

Nb-silicide based alloys could be used at T > 1423 K in future aero-engines. Titanium is an important additive to these new alloys where it improves oxidation, fracture toughness and reduces density. The microstructures of the new alloys consist of an Nb solid solution, and silicides and other intermetallics can be present. Three Nb₅Si₃ polymorphs are known, namely αNb₅Si₃ (tI32 Cr₅B₃-type, D8_l), βNb₅Si₃ (tI32 W₅Si₃-type, D8_m) and γNb₅Si₃ (hP16 Mn₅Si₃-type, D8₈). In these 5-3 silicides Nb atoms can be substituted by Ti atoms. The type of stable Nb₅Si₃ depends on temperature and concentration of Ti addition and is important for the stability and properties of the alloys. The effect of increasing concentration of Ti on the transition temperature between the polymorphs has not been studied. In this work first-principles calculations were used to predict the stability and physical properties of the various Nb₅Si₃ silicides alloyed with Ti. Temperature-dependent enthalpies of formation were computed, and the transition temperature between the low (α) and high (β) temperature polymorphs of Nb₅Si₃ was found to decrease significantly with increasing Ti content. The γNb₅Si₃ was found to be stable only at high Ti concentrations, above approximately 50 at. % Ti. Calculation of physical properties and the Cauchy pressures, Pugh's index of ductility and Poisson ratio showed that as the Ti content increased, the bulk moduli of all silicides decreased, while the shear and elastic moduli and the Debye temperature increased for the αNb₅Si₃ and γNb₅Si₃ and decreased for βNb₅Si₃. With the addition of Ti the αNb₅Si₃ and γNb₅Si₃ became less ductile, whereas the βNb₅Si₃ became more ductile. When Ti was added in the αNb₅Si₃ and βNb₅Si₃ the linear thermal expansion coefficients of the silicides decreased, but the anisotropy of coefficient of thermal expansion did not change significantly.