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Configurational Entropy in Multicomponent Alloys: Matrix Formulation from Ab Initio Based Hamiltonian and Application to the FCC Cr-Fe-Mn-Ni System

1
School of Mechanical Aerospace and Civil Engineering, University of Manchester, Manchester M13 9PL, UK
2
CCFE, United Kingdom Atomic Energy Authority, Abingdon OX14 3DB, UK
3
Faculty of Materials Science and Engineering, Warsaw University of Technology, Woloska 141, 02-507 Warsaw, Poland
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(1), 68; https://doi.org/10.3390/e21010068
Received: 7 November 2018 / Revised: 10 January 2019 / Accepted: 11 January 2019 / Published: 15 January 2019
(This article belongs to the Special Issue New Advances in High-Entropy Alloys)
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Abstract

Configuration entropy is believed to stabilize disordered solid solution phases in multicomponent systems at elevated temperatures over intermetallic compounds by lowering the Gibbs free energy. Traditionally, the increment of configuration entropy with temperature was computed by time-consuming thermodynamic integration methods. In this work, a new formalism based on a hybrid combination of the Cluster Expansion (CE) Hamiltonian and Monte Carlo simulations is developed to predict the configuration entropy as a function of temperature from multi-body cluster probability in a multi-component system with arbitrary average composition. The multi-body probabilities are worked out by explicit inversion and direct product of a matrix formulation within orthonomal sets of point functions in the clusters obtained from symmetry independent correlation functions. The matrix quantities are determined from semi canonical Monte Carlo simulations with Effective Cluster Interactions (ECIs) derived from Density Functional Theory (DFT) calculations. The formalism is applied to analyze the 4-body cluster probabilities for the quaternary system Cr-Fe-Mn-Ni as a function of temperature and alloy concentration. It is shown that, for two specific compositions (Cr 25Fe 25Mn 25Ni 25 and Cr 18Fe 27Mn 27Ni 28), the high value of probabilities for Cr-Fe-Fe-Fe and Mn-Mn-Ni-Ni are strongly correlated with the presence of the ordered phases L1 2 -CrFe 3 and L1 0-MnNi, respectively. These results are in an excellent agreement with predictions of these ground state structures by ab initio calculations. The general formalism is used to investigate the configuration entropy as a function of temperature and for 285 different alloy compositions. It is found that our matrix formulation of cluster probabilities provides an efficient tool to compute configuration entropy in multi-component alloys in a comparison with the result obtained by the thermodynamic integration method. At high temperatures, it is shown that many-body cluster correlations still play an important role in understanding the configuration entropy before reaching the solid solution limit of high-entroy alloys (HEAs). View Full-Text
Keywords: multicomponent; ab initio; configuration entropy; matrix formulation; cluster expansion; cluster variation method; monte carlo; thermodynamic integration multicomponent; ab initio; configuration entropy; matrix formulation; cluster expansion; cluster variation method; monte carlo; thermodynamic integration
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Fernández-Caballero, A.; Fedorov, M.; Wróbel, J.S.; Mummery, P.M.; Nguyen-Manh, D. Configurational Entropy in Multicomponent Alloys: Matrix Formulation from Ab Initio Based Hamiltonian and Application to the FCC Cr-Fe-Mn-Ni System. Entropy 2019, 21, 68.

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