Abstract
High entropy alloys (HEAs) contain near equimolar amounts of five or more elements and are a compelling space for materials design. In the design of HEAs, great emphasis is placed on identifying thermodynamic conditions for single-phase and multi-phase stability regions, but this process is hindered by the difficulty of navigating stability relationships in high-component spaces. Traditional phase diagrams use barycentric coordinates to represent composition axes, which require (N – 1) spatial dimensions to represent an N-component system, meaning that HEA systems with N > 4 components cannot be readily visualized. Here, we propose forgoing barycentric composition axes in favor of two energy axes: a formation-energy axis and a ‘reaction energy’ axis. These Inverse Hull Webs offer an information-dense 2D representation that successfully captures complex phase stability relationships in N ≥ 5 component systems. We use our proposed diagrams to visualize the transition of HEA solid-solutions from high-temperature stability to metastability upon quenching, and identify important thermodynamic features that are correlated with the persistence or decomposition of metastable HEAs.
Highlights
Traditional alloy design consists of one or two principal elements alloyed with small amounts of supplementary elements
Our Inverse Hull Webs display both high-level trends in temperature-dependent phase stability, as well as precise details regarding the thermodynamic competition between compounds
By displaying salient thermodynamic information in 2D for any N-component system, we overcome a major limitation of traditional phase diagrams for analyzing high-component systems—as shown here to rationalize solid-solution stability in high entropy alloys (HEAs)
Summary
Traditional alloy design consists of one or two principal elements alloyed with small amounts of supplementary elements. Past attempts to visualize HEA stability include projecting a five-component phase diagram into three dimensions, or constructing a series of quaternary phase diagrams[23] These approaches do not scale to an arbitrary number of components, and do not quantitatively display relative thermodynamic relationships between phases—especially as a function of temperature. We design a variety of plot features including color, line-width, and marker shape to retain salient compositional information lost by eliminating barycentric composition axes. We name these diagrams Inverse Hull Webs and use them to illustrate temperature-dependent phase-stability during the quenching of HfMoNbTiZr and AlCrFeNi, which are experimentally reported to be a single-phase and a multiphase HEA system, respectively. Our use of energy axes allows our Inverse Hull Webs to offer a complementary perspective to
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