Estimating the temperature dependent zero-phase-fraction features in ternary phase diagram via Bayesian approach

A complete ternary phase diagram under constant pressure describes conditions of phase regions in the composition-temperature space, where the zero-phase-fraction (ZPF) features are in the form of point, curve, or surface. In this work, we propose an approach to determine the ZPF features and their uncertainty from the discrete data points on the isothermal sections at different temperatures. Domain knowledge of phase diagrams was used as prior in Bayesian statistics. The schematic and effectiveness of the developed method were demonstrated by two model systems and two actual systems. Besides, an experimentally determined Fe-Co-Ni system has been employed to demonstrate how to determine the phase boundary surfaces of the ternary system with combination of experimental data and information from the sub-binary systems. Phase boundary surfaces of the ternary system can be satisfactorily determined even with the data of only one isothermal section when coupled with the information from the sub-binary systems.