Uncertainty quantification of phase boundary in a composition-phase map via Bayesian strategies

Phase boundary indicates the conditions of transition between phase regions, which is a key constituent of a phase diagram. We propose an approach to determine the phase boundary and its uncertainty in a phase-composition map based on the data from high-throughput experimentation. Bayesian logistics regression combined with the domain knowledge of phase diagrams was applied in the approach. For a typical ternary isothermal section, both the linear and nonlinear phase boundaries as well as the vertices of a ternary tie triangle were modeled to quantify the uncertainty with consideration of a couple of affecting factors such as data-point density, noise in the data, data coverage, etc. The effectiveness of the present approach was demonstrated by the Fe-Cr-Ni isothermal section data from database and the Fe-Co-Ni composition-phase map data by experiment. Moreover, the uncertainty of the phase boundary in the ternary system can be further reduced by incorporating the available data from the subbinary systems. The data-driven nature of the developed approach can further guide the efficient implementation of high-throughput experiments and provide confidence measures for decision-making in materials design and further Computer Coupling of Phase Diagrams and Thermochemistry (CALPHAD) method modeling.