Uncertainty Quantification of Phase Boundaries in Ternary Phase Diagram Assisted by Combinatorial Materials Chip Approach

Biao Wu, Yuanxun Zhou, Haihui Zhang, Lanting Zhang*, Hong Wang

Materials Genome Initiative Center and the School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

ABSTRACT: Combinatorial materials chip method, featuring high-throughput synthesis and the characterization of materials libraries containing 102–104 samples on one small substrate, has proven to be effective in rapid data generation for phase diagram construction. For phase diagram constructed by calculation or experiment, there exists certain degree of uncertainty on the location of phase boundaries. Understanding and quantification of the uncertainties is an important step to make confident decision in property- or performance-based design. In this study, a method based on Bayesian analysis is developed to evaluate the uncertainty of the possible phase boundaries under the principle of Gibbs phase rule. In a ternary isothermal section, only two types of phase boundary are present: the straight line separating the two-phase and three-phase region and the curved line between the single-phase and two-phase region. Mathematical models to evaluate these two types of phase boundary are established and applied to Fe-Co-Ni ternary system to benchmark the approach. Pixel-by-pixel XRD patterns from Fe-Co-Ni combinatorial chips are automatically pre-processed, phase-identified and categorized by hierarchical clustering algorithm, resulting in isothermal sections which are qualitatively consistent with the ones reported in the ASM Alloy Phase Diagram DatabaseTM. Taking advantage of substantial amount of data obtained by combinatorial approach, Bayesian analysis is then employed to analyze the data near the boundary of the phase regions. The result provides a probability distribution of phase boundary, which is a more quantitative description on the uncertainty of phase boundary compared with a single line as one usually perceived. Such information offers a more confident guidance to the design of new materials especially close to the phase boundary.

Figure 1. Quantified uncertainty of the phase boundaries determined in experiment. 

Keywords: phase boundary, uncertainty quantification, Bayes’ theorem, combinatorial materials chip