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Short-Range Order in High Entropy Alloys: Theoretical Formulation and Application to Mo-Nb-Ta-V-W System

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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 Monte-Carlo simulations within the combined CE and first-principles formalism. The strongest chemical SRO parameter is predicted for the first nearest-neighbor Mo-Ta pair that is in consistent agreement with high value of enthalpy of mixing in the B2 structure for this binary system. The prediction of B2 phase presence for Mo-Ta pairs in the considered bcc HEAs is reinforced by the positive contribution to the average SRO from the second nearest-neighbor shell. Interestingly, it is found that the average SRO parameter for the first and second nearest-neighbor shells of V-W pairs is also strongly negative in a comparison with the Mo-Ta pairs. This finding in the HEAs can be rationalized and discussed by the presence of the ordered-like B32 phase which has been predicted as the ground-state structure in binary bcc V-W system at the equimolar composition.

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Acknowledgments

This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under Grant Agreement No. 633053 and funding from the RCUK Energy Programme [Grant Number EP/P012450/1]. The views and opinions expressed herein do not necessarily reflect those of the European Commission. AFC acknowledges financial support from EPSRC (EP/L01680X/1) through the Materials for Demanding Environments Centre for Doctoral Training. JSW acknowledges the financial support from the Foundation of Polish Science grant HOMING (No. Homing/2016-1/12). The HOMING programme is co-financed by the European Union under the European Regional Development Fund. The simulations were partially carried out by JSW with the support of the Interdisciplinary Centre for Mathematical and Computational Modelling (ICM), University of Warsaw, under grant no GA65-14. DNM would like to acknowledge the support from Marconi-Fusion, the High Performance Computer at the CINECA headquarters in Bologna (Italy) for its provision of supercomputer resources.

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Authors and Affiliations

  1. CCFE, United Kingdom Atomic Energy Authority, Abingdon, OX14 3DB, UK

    A. Fernández-Caballero & D. Nguyen-Manh

  2. School of Mechanical Aerospace and Civil Engineering, University of Manchester, Manchester, M13 9PL, UK

    A. Fernández-Caballero & P. M. Mummery

  3. Faculty of Materials Science and Engineering, Warsaw University of Technology, Woloska 141, 02-507, Warsaw, Poland

    J. S. Wróbel

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  1. A. Fernández-Caballero
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  4. D. Nguyen-Manh
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Correspondence to D. Nguyen-Manh.

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Fernández-Caballero, A., Wróbel, J.S., Mummery, P.M. et al. Short-Range Order in High Entropy Alloys: Theoretical Formulation and Application to Mo-Nb-Ta-V-W System. J. Phase Equilib. Diffus. 38, 391–403 (2017). https://doi.org/10.1007/s11669-017-0582-3

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