Interactive Exploration of High-Dimensional Phase Diagrams

High-dimensional thermodynamic phase stability databases are becoming increasingly common due to the convergence of three recent trends: (1) the widespread interest in so-called "high-entropy" alloys, (2) the availability of high-throughput computational assessments of phase stability in broad composition spaces, and (3) the ongoing development of ever-increasingly broad, multicomponent, multiphase CALPHAD databases. Although automated computational tools can readily process such high-dimensional data, scientists are often unable to visualize the relevant phase relationships, an ability that is crucial to gaining an intuitive understanding of the stability constraints governing materials design. The present work addresses this need by providing algorithms that enable the interactive exploration of phase equilibria in high-dimensional spaces. These algorithms concentrate the complex nonlinear nonsmooth optimization needed into a preprocessing step that generates a large number of high-dimensional yet elementary graphical primitives. These primitives can then be cross-sectioned to yield 3-dimensional views in a computationally efficient manner that enables an interactive exploration of high-dimensional spaces. All of these operations are highly parallelizable, thus facilitating scaling of this method to large datasets.