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 (CrFeMnNi and CrFeMnNi), 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-CrFe and L1-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).
Highlights
Multicomponent systems, called High Entropy Alloys (HEAs), are crystalline solids that form predominantly in a single phase
We develop a matrix formalism to study multi-body ordering probabilities beyond pair approximation previously used for investigating the short-range order (SRO) and configuration entropy in multi-component alloys by using a hybrid combination of Cluster Expansion (CE) and Monte Carlo methods
The cluster probabilities are worked out by explicit inversion within the orthonormal sets of the point functions adopted in the ATAT package and a direct product of a matrix formulation obtained from symmetrically independent correlation functions
Summary
Multicomponent systems, called High Entropy Alloys (HEAs), are crystalline solids that form predominantly in a single phase. A hybrid approach taking the Monte Carlo calculated correlation functions at temperature and computing the configuration entropy value from analytic CVM expression has been used in a binary FCC lattice model [23]. It is shown that accurate free energies can be obtained for ordered and disordered phases at arbitrary chemical concentration and temperature without thermodynamic integration provided that use is made of high-order CVM entropy expressions. We close this gap by developing a new methodology based on matrix formulation to calculate analytically the cluster probabilities for arbitrary K-component alloys from the correlation functions obtained by the hybrid Monte Carlo and CE Hamiltonian. The changes in configuration entropy are attributed to the presence of ordered phases that are more stable at low temperatures and the complementary tendency towards disordered random solution of the alloy at the given average composition.
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