[Paper Review] Accurate ab initio modeling of solid solution strengthening in high entropy alloys

Franco Moitzi, Lorenz Romaner+2 more|arXiv (Cornell University)|Sep 26, 2022

High Entropy Alloys Studies4 citations

TL;DR

This paper presents a computationally efficient, parameter-free ab initio methodology based on the coherent potential approximation (CPA) and density functional theory (DFT) with element-specific exchange-correlation pressure corrections to accurately model solid solution strengthening in high entropy alloys (HEAs). The approach accounts for thermal effects, including magnetism and phonons, and achieves quantitative agreement with experimental critical resolved shear stress (CRSS) data for FeNiCoCr and NiCoCr, revealing non-monotonic misfit volume trends due to complex component interactions.

ABSTRACT

High entropy alloys (HEA) represent a class of materials with promising properties, such as high strength and ductility, radiation damage tolerance, etc. At the same time, a combinatorially large variety of compositions and a complex structure render them quite hard to study using conventional methods. In this work, we present a computationally efficient methodology based on ab initio calculations within the coherent potential approximation. To make the methodology predictive, we apply an exchange-correlation correction to the equation of state and take into account thermal effects on the magnetic state and the equilibrium volume. The approach shows good agreement with available experimental data on bulk properties of solid solutions. As a particular case, the workflow is applied to a series of iron-group HEA to investigate their solid solution strengthening within a parameter-free model based on the effective medium representation of an alloy. The results reveal intricate interactions between alloy components, which we analyze by means of a simple model of local bonding. Thanks to its computational efficiency, the methodology can be used as a basis for an adaptive learning workflow for optimal design of HEA.

Motivation & Objective

• To overcome the limitations of conventional DFT in predicting equilibrium volumes and misfit parameters in high entropy alloys due to systematic errors in standard exchange-correlation functionals.
• To develop a predictive, parameter-free workflow for modeling solid solution strengthening (SSS) in multi-component HEAs, particularly those based on iron-group elements with complex magnetic behavior.
• To incorporate finite-temperature effects—such as thermal expansion, spin fluctuations, and phonon contributions—into the DFT-based calculation of alloy properties.
• To validate the model against experimental data on CRSS and misfit volumes for selected fcc HEAs, including NiCoCr and FeNiCoCr.
• To analyze the non-intuitive concentration dependence of misfit volumes and identify key interactions between alloy components using a local bonding model.

Proposed method

• Employing the coherent potential approximation (CPA) to model the effective medium of multi-component HEAs, enabling accurate treatment of disordered solid solutions.
• Applying element-specific exchange-correlation (XC) pressure corrections to DFT-calculated equations of state to correct systematic errors in equilibrium lattice parameters and volumes.
• Including finite-temperature effects via phonon contributions and spin fluctuations, particularly important for magnetic 3d transition metals like Fe and Mn.
• Calculating key SSS parameters—lattice constant, misfit parameter δ, elastic moduli—self-consistently at relevant temperatures using CPA-DFT.
• Using the Varvenne-Curtin (VC) model to compute temperature-dependent critical resolved shear stress (CRSS) from the ab initio-derived parameters.
• Proposing a simple local bonding model to interpret and predict non-monotonic trends in misfit volumes as functions of composition.

Experimental results

Research questions

• RQ1 Can a DFT-based approach with CPA and XC corrections accurately predict the equilibrium volume and misfit volume of high entropy alloys, especially when standard functionals fail?
• RQ2 How do finite-temperature effects—particularly magnetism and thermal expansion—affect the prediction of solid solution strengthening in iron-group HEAs?
• RQ3 To what extent do component interactions lead to non-monotonic concentration dependencies of misfit volumes, and can these be captured by a simple local bonding model?
• RQ4 Does the proposed parameter-free workflow yield quantitatively accurate predictions of temperature-dependent critical resolved shear stress (CRSS) for fcc HEAs?
• RQ5 Can the model explain why equimolar compositions are not always optimal for maximizing yield strength in HEAs, based on misfit volume and elastic property trade-offs?

Key findings

• The element-specific XC pressure correction significantly improves the accuracy of equilibrium lattice constants and misfit volumes, with excellent agreement between calculated and experimental values for NiCoCr.
• The model predicts temperature-dependent CRSS for NiCoCr and FeNiCoCr with good quantitative agreement to experimental data, validating the approach for practical alloy design.
• For the five-component FeMnNiCoCr alloy, the model underestimates CRSS slightly, likely due to increased structural complexity and strong magnetic interactions.
• The misfit parameter δ is identified as the dominant factor determining strength trends across the three studied HEAs, with non-monotonic concentration dependence arising from intricate inter-component interactions.
• The local bonding model qualitatively captures the evolution of misfit volumes in FeMnNiCoCr with Ni concentration, indicating that component-specific electronic structure effects are critical.
• Thermal effects, especially spin fluctuations in Fe and Mn, are shown to be essential for accurate prediction of alloy properties at elevated temperatures, which are often neglected in standard DFT workflows.