Reimagining Phase Diagrams and Phase Formation Through Graph Theory

ABSTRACT Understanding phase transitions and structure formation in metal alloys is essential to relating structure to properties, development of new phases, defining out‐of‐equilibrium states/processes, and discovering new alloy systems. Structural relaxation and phase formation in alloys often entail complex processes that require interpretation beyond equilibrium conditions. Conventional phase diagrams do not often capture processing history, emergent minor states/phases, or variables that affect nonequilibrium structure formation. Herein, we introduce ParameterGT , a graph‐based framework that maps differences in element properties onto composition‐dependent descriptors. We use atomic radius, electronegativity, and lattice parameters to construct weighted edges, then transform those descriptors into estimates of liquidus temperature limits for select binary eutectic alloys. We compare the estimates with CALPHAD calculations and correlate predictions with differential scanning calorimetry (DSC) measurements with associated eutectics as reference points. This work illustrates that a graph‐based descriptor can predict composition‐dependent equilibrium trends (e.g., melting point), while highlighting that with additional calibration or corrections, nonequilibrium behavior (such as undercooling) can be predicted. Effect of intrinsic (e.g., composition) or extrinsic influences (such as interfacial stresses) can also be abstracted, a fete absent in commonly used phase diagrams or equilibrium calculations.