This study reports the first identification of continuous invariant and univariant monotectic equilibria in the Fe–Sn–Ti ternary system exhibiting liquid–liquid phase separation (LLPS), characterized through a comprehensive CALPHAD-based thermodynamic analysis of newly acquired experimental data. These equilibria display features of second- and higher-order phase transitions consistent with the Ehrenfest classification and were revealed through detailed evaluation of entropy, heat capacity, tin distribution in demixed liquids, and their derivatives. Unlike classical degenerate equilibria that may appear to challenge the Gibbs phase rule, the continuous equilibria identified here provide a coherent thermodynamic interpretation and were precisely mapped across selected isopleths, liquidus and solidus projections, isothermal sections, and the Scheil reaction scheme. We further propose that certain univariant first-order transformations originating or terminating at tricritical points analogous to the Nishizawa horn may be accompanied by previously unrecognized continuous univariant transitions, offering predictive potential for similar phenomena in other ternary alloy systems. These findings are expected to stimulate further research within the materials science and condensed matter communities, particularly into the thermodynamic nature and broader implications of continuous transitions in LLPS-bearing systems.
Witusiewicz et al. (Sat,) studied this question.