[Paper Review] Short-range order in high entropy alloys:Theoretical formulation and application to Mo-Nb-Ta-V-W system

A. Fernández-Caballero, Jan Wróbel+2 more|arXiv (Cornell University)|May 4, 2017

High Entropy Alloys Studies3 citations

TL;DR

This study develops a theoretical framework based on cluster expansion and first-principles calculations to model short-range chemical ordering in the refractory high-entropy alloy Mo-Nb-Ta-V-W. It predicts strong chemical short-range order (SRO) for Mo-Ta and V-W pairs due to favorable B2 and B32-type ordering, respectively, with SRO parameters indicating phase stability trends beyond pairwise interactions.

ABSTRACT

In high-entropy alloys (HEAs), the local chemical fluctuations from disordered solute solution state into segregation, precipitation and ordering configurations are complex due to the large number of elements. In this work, the cluster expansion (CE) Hamiltonian for multi-component alloy systems is developed in order to investigate the dependence of chemical ordering of HEAs as a function of temperature dependence due to derivation of configuration entropy from the ideal solute solution. Analytic expressions for Warren-Cowley short-range order (SRO) parameters are derived for a five component alloy system. The theoretical formulation is used to investigate the evolution of the ten different SRO parameters in the MoNbTaVW and the sub-quaternary systems obtained by MonteCarlo simulations within the combined CE and first-principles formalism.

Motivation & Objective

• To develop a theoretical formulation for Warren-Cowley short-range order (SRO) parameters in five-component high-entropy alloys.
• To investigate the temperature-dependent chemical ordering in Mo-Nb-Ta-V-W and sub-quaternary systems using Monte Carlo simulations.
• To determine the role of configurational entropy and mixing enthalpy in driving local chemical segregation and ordering.
• To assess the stability of B2 and B32-type ordered phases in the HEA through SRO parameter analysis.
• To provide a predictive model for local atomic structure in complex multi-component alloys beyond nearest-neighbor approximations.

Proposed method

• Derivation of analytic expressions for Warren-Cowley SRO parameters in a five-component system using statistical mechanics and ideal solution approximation.
• Application of the cluster expansion (CE) Hamiltonian to model enthalpy and entropy contributions to free energy in multi-component alloys.
• Integration of first-principles calculations with Monte Carlo simulations to sample atomic configurations and compute SRO parameters.
• Use of thermodynamic integration to compute free energy differences between disordered (A2) and ordered (B2) phases.
• Inclusion of both first and second nearest-neighbor shells in SRO analysis to capture long-range ordering effects.
• Comparison of SRO trends with binary mixing enthalpies and known ground-state structures (e.g., B32 in V-W system).

Experimental results

Research questions

• RQ1 How do SRO parameters evolve with temperature in the Mo-Nb-Ta-V-W high-entropy alloy system?
• RQ2 What is the role of mixing enthalpy and configurational entropy in driving local chemical ordering in multi-component HEAs?
• RQ3 Which element pairs exhibit the strongest short-range order, and what structural phases do they favor?
• RQ4 How do second nearest-neighbor interactions influence the stability of B2-type ordered phases in bcc HEAs?
• RQ5 Why do V-W pairs show strong negative SRO despite having less favorable binary mixing enthalpy than Mo-Ta?

Key findings

• The strongest chemical SRO is predicted for Mo-Ta pairs in the first nearest-neighbor shell, consistent with high negative mixing enthalpy in the B2 structure.
• The B2 phase formation for Mo-Ta pairs is reinforced by a positive contribution from the second nearest-neighbor shell, indicating long-range ordering tendencies.
• The average SRO parameter for V-W pairs is strongly negative and comparable in magnitude to Mo-Ta pairs, indicating a tendency toward B32-type ordering.
• The B32 phase is predicted to be stable for V-W pairs at temperatures below 100 K in the quinary system and below 200 K in the quaternary system.
• At higher temperatures, both first and second nearest-neighbor SRO parameters for V-W pairs become negative, indicating a local environment resembling the B32 ground state.
• Positive SRO parameters for Mo-W, Nb-Ta, Nb-V, and Ta-V pairs indicate phase segregation tendencies, which cannot be explained by binary mixing enthalpies alone and require cluster expansion beyond pairwise approximations.