A kinetic model of diffusional phase transformations in ternary line compounds and determination of diffusion coefficients: Application to the Nb–Mo–Si system

The diffusional phase transformations in inhomogeneous multicomponent systems play an important role in affecting the material properties. Ternary line compounds, which are ternary phases with components that have both large and small solid solubility, are often observed in applications. They are different from solid solutions with variable composition ratios and stoichiometric compounds with fixed composition ratios. However, the existing models cannot quantitatively characterize the diffusional phase transformations in ternary line compounds. Therefore, by introducing the state equation related to the chemical potential and mole fraction, a kinetic model of diffusional phase transformations was established for the first time to describe the mole fraction evolution and phase growth in ternary line compounds. Furthermore, a method to determine the tracer diffusion coefficients of components related to the mole fraction and crystal phase structure in ternary line compounds was proposed, and applied to the diffusion of Nb-Mo-Si ternary system composed of the MoSi ₂ and Nb. During the high-temperature diffusion process of Nb-MoSi ₂, the silicide-poor phase (Mo, Nb) ₅Si ₃ is formed, which is a typical ternary line compound. Based on the diffusion experiments and inverse calculations, the tracer diffusion coefficients of components in ternary line compound (Mo, Nb) ₅Si ₃ were experimentally obtained. Moreover, ab-initio calculations of defect energetics clarified the microscopic diffusion mechanisms in the silicide-poor phase, and explained the reason why that the diffusion coefficient of Si decreases significantly with the increase of Nb mole fraction in ternary line compound (Mo, Nb) ₅Si ₃. The research provides valuable guidance for modeling and analyzing the diffusional phase transformation of multi-component systems.