Temperature-Dependent Configurational Entropy Calculations for Refractory High-Entropy Alloys

Abstract

The cluster expansion formalism for alloys is used to construct surrogate models for three refractory high-entropy alloys (NbTiVZr, HfNbTaTiZr, and AlHfNbTaTiZr). These cluster expansion models are then used along with Monte Carlo methods and thermodynamic integration to calculate the configurational entropy of these refractory high-entropy alloys as a function of temperature. Many solid solution alloy design guidelines are based on the ideal entropy of mixing, which increases monotonically with $$N$$ N , the number of elements in the alloy. However, our results show that at low temperatures, the configurational entropy of these materials is largely independent of $$N$$ N , and the assumption described above only holds in the high-temperature limit. This suggests that alloy design guidelines based on the ideal entropy of mixing require further examination.

Mixed Enthalpy–Entropy Descriptor for the Rational Design of Synthesizable High-Entropy Materials Over Vast Chemical Spaces

“…The ⟨|Δ E D |⟩ parameter for assessing the entropy forming ability is also fundamentally different from commonly used methods such as EFA descriptor and direct entropy estimation methods like Monte Carlo method, , cluster expansion method, − and molecular dynamics simulations. ,, These classical methods typically rely on sampling a vast array of possible alloy configurations or chemically ordered clusters. In contrast, ⟨|Δ E D |⟩ does not require any such sampling, depending solely on the defect-formation energies of substitutional defects in the chemically ordered constituent materials in the host HEM structure.…”

Towards quantifying (meta-)stability of multi-principal element alloys: from configurational entropy to characteristic temperatures

“…All these empirical descriptors have the advantage of being simple to calculate, since they essentially express component-weighted elemental properties, and they bare some success in understanding binary solid-state solutions. Yet, when applied to metastability-related phase transformations and local chemical ordering, their efficacy is frequently questioned due to limited reliability (25)(26)(27). For instance, by fitting the elemental properties of a large dataset containing 1,252 multi-component alloys, a machine-learning informed model was extracted, suggesting that empirical rules typically predict with a success ratio between 71∼82% (26).…”