Examination of Solid-Solution Phase Formation Rules for High Entropy Alloys from Atomistic Monte Carlo Simulations

Abstract

In this study, we used atomistic simulation methods to examine solid-solution phase formation rules for CoCrFeNi high entropy alloy. Using the Monte Carlo simulations based on the modified embedded atom method (MEAM) potentials, we sampled the thermodynamically equilibrium structures of the CoCrFeNi alloy and further predicted that the CoCrFeNi alloy could form a solid solution phase with high configurational entropy of 1.329R at 1373 K. Furthermore, we examined the stability of this solid solution phase of the CoCrFeNi alloy against the well-recognized solid-solution phase formation rules by varying the MEAM potentials and thus tuning the atom size and mixing enthalpy in the alloy. Our simulation results revealed that it required atom size difference effect d j j < 0:05 and mixing enthalpy effect À10 kJ/mol < DH % 0 kJ/mol for the modeled CoCrFeNi alloy to remain a single solid solution phase.

Computationally aided, entropy-driven synthesis of highly efficient and durable multi-elemental alloy catalysts

“…S1). We launched a composition prescreening process to identify solid solution structures based on the phase formation rules derived in well-studied bulk high-entropy alloy materials (8,25,26), where the solid solution phase usually meets the following criteria: (i) atomic differences ( ≤ 6.5%), (ii) mixing enthalpy (−11.6 < H mix < Fig. 1.…”

“…To screen the possible structures for the MEA-NPs, two sets of rules, derived from well-studied high-entropy alloy materials, were applied for size mismatch, mixing enthalpy, and Gibbs free energy (details in the Supplementary Materials) (8,25,26,37). We scanned all possible alloys by selecting n (3 ≤ n ≤ 10) of the 10 active metal elements (Ru, Rh, Co, Ni, Ir, Pd, Cr, Fe, Cu, and Mo) and changing the composition of each element from 5 up to 50%, with a 5% step size increment.…”

Modeling the structure and thermodynamics of high-entropy alloys

“…We gave several examples of their application to HEAs and related compounds. Specifically, we discussed the application of the CPA, 14,41,96,100,101,[113][114][115][116][117][118][119] supercell and SQS methods, 38,40,66,[120][121][122][123] empirical pair-and embedded atom-potentials, [124][125][126][127][128][129][130][131] and the Miedema approximation. 6,56,[58][59][60][61][132][133][134] We explained how these may be combined for direct free energy calculation, 65,85,103,135 incorporated into cluster expansions, 69,70,85,88,109,136 used as the basis for computer simulation, [84]…”

Extreme mixing in nanoscale transition metal alloys

“…The thermal and structural stability may come from the entropy stabilization effect, whereby a high-entropy structure is stabilized both thermodynamically (DG mix = DH mix À TDS mix ) and kinetically (sluggish diffusion due to large distortions). 16,28,30,42 The 4D-STEM result in particular clearly illustrated strain and distortions in the lattice of entropy-stabilized 15-HEA nanoparticles, which could serve as local diffusion barriers for phase separation and therefore improve the structural stability. Additionally the strain inside the nanoparticles could largely tune the performance, especially for catalysis.…”

“…10 Similar empirical single-phase selection rules have been established in multielement highentropy alloys (HEAs), again by restricting the possible alloy elements to a range of approximately À15 kJ/mol < DH mix < 5 kJ/mol and 0 < d < 5%, or similar confinement. [10][11][12][14][15][16][17][18] As a result, facile alloying is generally found under restricted conditions for elements with a small mixing enthalpy and oxidation potential, as shown in the range within the green line in Figure 1B. Nevertheless, these existing phase selection rules render very limited alloys and largely restricted compositional spaces for material discovery.…”