Pressure dependent phase diagrams of alloys: Integrating thermodynamic modeling with experimental validation

Alloy phase diagrams define phase boundaries, transformations, and invariant points, providing key insights into thermodynamic stability and microstructural evolution. Experimental determination of alloy phase diagrams (PD) requires careful thermophysical measurements to establish equilibrium conditions coupled with structural analysis of the phases. At ambient pressure, mapping binary alloy PDs took decades and that of ternary alloys continues to date. Application of high pressure alters interatomic interactions, stabilizing novel elemental and alloy phases, thus reshaping PDs and requiring re-mapping of PDs. While structural characterization under pressure at ambient temperatures is well-developed, extension to higher temperatures and performing thermophysical measurements remain technically challenging. Thus, pressure PDs remain unknown for most alloys.

To address this gap, we integrate experimental techniques with thermodynamic modeling. We construct high-pressure alloy phase diagrams from a thermodynamic model, incorporating sound velocity and density measurements and first-principles data. The predicted transitions are then validated by high-pressure x-ray diffraction in a diamond anvil cell (DAC) and resistivity measurements in a Paris-Edinburgh (PE) press. We have applied our approach to alloy systems of several types, including: isomorphous Bi-Sb, eutectic Ga-In, monotectic Bi-Ga with a liquid miscibility gap, and ternary Bi-Sb-Pb in pressure ranges of up to 10 GPa. Our findings reveal multiple phenomena, such as pressure-driven transformations of PD from isomorphous or monotectic to eutectic forms, pressure shifts in eutectic, and other, invariant points. The PD model allows to distinguish and isolate the different contributions to the pressure dependence of the phase diagrams, e.g., the pressure dependence of the melting temperatures of the elements and that of the interatomic interactions. This integrated approach offers a robust framework for predicting and experimentally verifying high-pressure alloy phase behavior, advancing the understanding of phase stability under extreme conditions.