Analytical Model for Liquid/Liquid Interfacial Energy of Microalloyed Monotectic Alloys

An analytical model is proposed for the calculation of the interfacial energy γ_L₁/L₂ between an A-rich matrix liquid and B-rich droplets in an A-B monotectic alloy microalloyed by element <i>I</i>, based on the Gibbs absorption isotherm. The model is applicable to the microalloying element segregated to the liquid/liquid interface or impoverished in the interface. Solidification experimental results validated the model. Calculation results demonstrate that the variation of γ_L₁/L₂ with <i>I</i> concentration <i>x</i>_<i>I</i> is not always monotonic. It is determined by the dependence of <i>I</i> chemical potential μ_<i>I</i> on <i>x</i>_<i>I</i>, which is closely related to the interaction parameter <i>L</i>_A<i>I</i> in the A-rich corner of the liquid A-<i>I</i> alloy. μ_<i>I</i> increases with <i>x</i>_<i>I</i> monotonically when <i>L</i>_A<i>I</i> < 2<i>R</i>_g<i>T</i>_b,A-B (<i>T</i>_b,A-B is the binodal line temperature), and it shows a tendency with <i>x</i>_<i>I</i> of first increase and then decrease, followed by an increase when <i>L</i>_A<i>I</i> ≥ 2<i>R</i>_g<i>T</i>_b,A-B. The variation trends of γ_L₁/L₂ and μ_<i>I</i> with <i>x</i>_<i>I</i> are opposite for an element <i>I</i> segregated to the liquid/liquid interface and similar for an element <i>I</i> impoverished in the liquid/liquid interface.