Abstract
High entropy alloys contain multiple elements in large proportions that make them prone to phase separation. These alloys generally have shallow enthalpy of mixing which makes the entropy contributions of similar magnitude. As a result, the phase stability of these alloys is equally dependent on enthalpy and entropy of mixing and understanding the individual contribution of thermodynamic properties is critical. In the overall vision of designing high entropy alloys, in this work, using density functional theory calculations, we elucidate the contributions of various entropies, i.e., vibrational, electronic and configurational towards the phase stability of binary alloys. We show that the contribution of electronic entropy is very small compared to the vibrational and configurational entropies, and does not play a significant role in the phase stability of alloys. The configurational and vibrational entropies can either destabilize or can collectively contribute to stabilize the solid solutions. As a result, even those systems that have negative mixing enthalpy can show phase instability, revealed as a miscibility gap; conversely, systems with positive mixing enthalpy can be phase stable due to entropic contributions. We suggest that including entropic contributions are critical in the development of theoretical framework for the computational prediction of stable, single-phase high entropy alloys that have shallow mixing enthalpies, unlike ordered intermetallics.
Highlights
The phase stability of an alloy is guided by Gibbs free energy (ΔGmix) that comprises of enthalpy (ΔHmix) and entropy (ΔSmix) of mixing
ΔSmix contributions have been included in the calculations, albeit selectively; including ΔSmix has shown to improve the accuracy of the predicted thermodynamic quantities, such as the order–disorder phase transformation temperature and miscibility gap temperature.[3,4,10,11,12,13,14,15]
More recently, it has been shown that the contributions of configurational entropy might only be a part of a bigger picture, and it may not be the only quantity to be considered while explaining the stability of high entropy alloys (HEAs).[22,23,24]
Summary
The phase stability of an alloy is guided by Gibbs free energy (ΔGmix) that comprises of enthalpy (ΔHmix) and entropy (ΔSmix) of mixing. Due to the random distribution of multiple elements, the configurational entropy (ΔSconf) is higher in HEAs than in the ordered alloys, which further contributes to the HEA phase stability. More recently, it has been shown that the contributions of configurational entropy might only be a part of a bigger picture, and it may not be the only quantity to be considered while explaining the stability of HEAs.[22,23,24] For example, using the Hume–Rothery rules as a guide, Otto et al.[22] experimentally showed that the configurational entropy may not be enough to explain the stability of NiCrCoMnFe HEAs. In a series of experiments, they systematically replaced one element at a time in NiCrCoMnFe single phase-fcc HEA with a similar element (e.g., Ni with Cu, Co with Ti). While this strategy should not significantly change the configurational entropy contribution, none of the substitutions led to the formation of a single-phase solid solution
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