A unified approach to phase and microstructural stability for Fe-ETM alloys through Miedemaʹs model

Alloying behavior and phase stability of nine Fe-ETM (Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W) binary, five ternary (Fe–Zr–Nb, Fe–Ti–Nb, Fe–Cr–Zr, Fe–Cr–Ti, Fe–V–Ti) alloy systems have been analyzed by Miedemaʹs model. It is observed that Fe with V, Cr, Mo, W would tend to form solid solutions over entire composition range when the molten alloy is supercooled to a large extend below its melting point. With Ti, Zr, Hf, Ta and Nb there exists a terminal solid solubility beyond which liquid alloy will tend to freeze in the glassy state than crystallizing as a solid solution phase. The composition where glassy state will be most stable compared to the solid solution phase coincides with that of the Laves phase as reported in the equilibrium phase diagram. In ternary systems also similar trend is observed. Independent calculation of elastic and chemical enthalpy for all the systems indicates that low contribution of the enthalpies favors solid solution formation. Whereas, highly negative chemical and the positive elastic energy contribution tends to destabilize the parent lattice favoring intermetallics and amorphous phase formation. This leads to a theoretical convergence of Hume-Rothery rule and Inoueʹs empirical criteria of amorphous phase formation. Laves phase being a Frank-Kasper phase, further structural similarity could be drawn between complex crystalline and liquid phases. This opens up new possibilities in alloy design of glasses and predicting phase stability, which is extended to microstructure analysis in Fe based binary and multicomponent systems.