[Paper Review] Ab initio Approaches to High Entropy Alloys: A Comparison of CPA, SQS, and Supercell Methods

Mariia Karabin, Wasim Raja Mondal+8 more|arXiv (Cornell University)|Mar 29, 2022

High Entropy Alloys Studies45 references31 citations

TL;DR

This study compares ab initio methods—Coherent Potential Approximation (CPA), Special Quasi-Random Structures (SQS), and supercell (LSMS)—for modeling electronic properties of the Hf0.05Nb0.05Ta0.8Ti0.05Zr0.05 high-entropy alloy using density functional theory. It demonstrates that corrected CPA and SQS methods yield highly similar results for ground-state properties like the density of states and lattice parameter, and predicts superconductivity with a critical temperature of approximately 9 K, with no evidence of magnetic ordering.

ABSTRACT

We present a comparative study of different modeling approaches to the electronic properties of the $ extrm{Hf}_{0.05} extrm{Nb}_{0.05} extrm{Ta}_{0.8} extrm{Ti}_{0.05} extrm{Zr}_{0.05}$ high entropy alloy. Common to our modeling is the methodology to compute the one-particle Green's function in the framework of density functional theory. We demonstrate that the special quasi-random structures modeling and the supercell, i.e. the locally self-consistent multiple-scatering methods provide very similar results for the ground state properties such as the spectral function (density of states) and the equilibrium lattice parameter. To reconcile the multiple-scattering single-site coherent potential approximation with the real space supercell methods, we included the effect of screening of the net charges of the alloy components. Based on the analysis of the total energy and spectral functions computed within the density functional theory, we found no signature for the long-range or local magnetic moments formation in the $ extrm{Hf}_{0.05} extrm{Nb}_{0.05} extrm{Ta}_{0.8} extrm{Ti}_{0.05} extrm{Zr}_{0.05}$ high entropy alloy, instead we find possible superconductivity below $\sim 9$K.

Motivation & Objective

• To evaluate and compare the accuracy of CPA, SQS, and supercell methods in modeling electronic structure of high-entropy alloys.
• To resolve inconsistencies in electrostatic potential arising from the CPA's assumption of homogeneous charge distribution versus inhomogeneous DFT solutions.
• To determine whether the Hf0.05Nb0.05Ta0.8Ti0.05Zr0.05 alloy exhibits magnetic instabilities or superconducting behavior.
• To assess the reliability of the Gorkov-Gaspari-Gyorffy formula for estimating superconducting critical temperature in disordered systems.

Proposed method

• Uses density functional theory (DFT) with the Kohn-Sham formalism to compute the one-particle Green’s function.
• Applies the Korringa-Kohn-Rostoker (KKR) method to solve the Kohn-Sham equations in real space via multiple scattering theory.
• Implements CPA with an atomic-species-specific screening correction to account for net charge effects and improve electrostatic consistency.
• Uses the LSMS method for large random supercell calculations to model disorder with minimal periodicity artifacts.
• Employs the SQS method to generate representative, disordered supercells that mimic random solid solutions with minimal short-range order.
• Estimates the electron-phonon coupling constant λ and critical temperature Tc using the McMillan formula and Gorkov-Gaspari-Gyorffy theory.

Experimental results

Research questions

• RQ1 How do CPA, SQS, and supercell methods compare in predicting the ground-state electronic structure of the Hf0.05Nb0.05Ta0.8Ti0.05Zr0.05 high-entropy alloy?
• RQ2 What is the impact of neglecting atomic-species-specific screening in CPA on the accuracy of total energy and spectral function predictions?
• RQ3 Does the Hf0.05Nb0.05Ta0.8Ti0.05Zr0.05 alloy exhibit long-range or local magnetic moments?
• RQ4 What is the predicted superconducting critical temperature Tc for this alloy based on ab initio electron-phonon coupling calculations?

Key findings

• The corrected CPA method, which includes atomic-species-specific screening, produces results for the density of states and equilibrium lattice parameter that are in excellent agreement with both the SQS and large supercell (LSMS) methods.
• The total density of states at the Fermi level is similar across all methods, indicating consistent electronic structure predictions.
• No evidence of long-range or local magnetic moments was found in spin-polarized DFT-LSDA or DFT-based disordered local moment (DLM) calculations.
• The electron-phonon coupling constant λ was computed as 0.9, leading to a predicted superconducting critical temperature Tc ≈ 9 K using the McMillan formula.
• The study suggests that the Gorkov-Gaspari-Gyorffy approach may overestimate Tc by a factor of two, as previously observed in similar alloys.
• The SQS method shows convergence toward supercell results with increasing cell size, confirming its reliability for modeling chemical disorder in HEAs.