Compositional phase stability in medium-entropy and high-entropy Cantor-Wu alloys from an ab initio all-electron Landau-type theory and atomistic modeling

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Compositional phase stability in medium-entropy and high-entropy Cantor-Wu alloys from an ab initio all-electron Landau-type theory and atomistic modeling

Christopher D. Woodgate and Julie B. Staunton

Phys. Rev. B 105, 115124 – Published 17 March 2022

Abstract

We describe the implementation and analysis of a first-principles theory, derived in an earlier work, for the leading terms in an expansion of a Gibbs free energy of a multicomponent alloy in terms of order parameters that characterize potential, compositional phases. The theory includes the effects of rearranging charge and other electronics from changing atomic occupancies on lattice sites. As well as the rigorous description of atomic short-range order in the homogeneously disordered phase, pairwise interaction parameters suited for atomistic modeling in a multicomponent setting can be calculated. From our study of an indicative series of the Cantor-Wu alloys, NiCo, NiCoCr, NiCoFeCr, and NiCoFeMnCr, we find that the interactions are not approximated well either as pseudobinary or restricted to nearest-neighbor range. Our computed order-disorder transition temperatures are low, consistent with experimental observations, and the nature of the ordering is dominated by correlations between Ni, Co, and Cr, while Fe and Mn interact weakly. Further atomistic modeling suggests that there is no true single-phase low-temperature ground state for these multicomponent systems. Instead the single-phase solid solution is kept stable to low temperatures by the large configurational entropy and the Fe and Mn dilution effects. The computational cost-effectiveness of our method makes it a good candidate for further exploration of the space of multicomponent alloys.

Received 6 January 2022
Accepted 2 March 2022

DOI:https://doi.org/10.1103/PhysRevB.105.115124

Physics Subject Headings (PhySH)

Electronic structure Solid-solid transformations

Transition metal alloys

Density functional calculations Monte Carlo methods

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Christopher D. Woodgate and Julie B. Staunton

Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom

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Vol. 105, Iss. 11 — 15 March 2022

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Images

Figure 1
Examples of ordered structures based on the fcc lattice which can be described by concentration waves. $A 1$ represents a disordered alloy. $L 1_{0}$ can be described by modes $k = {(0, 0, 1), (0, 0, - 1)}$ , while $L 1_{2}$ is described by a combination of all six $k$ vectors, $k = {0, 0, 1}$ .
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Figure 2
Comparison of the species-resolved density of states of the systems considered in this work. We use the CPA to average over disorder, and the DLM picture to reflect that we expect these systems to be in a paramagnetic state when prepared. This results in fine detail being smeared out. The most notable feature is how the addition of Cr completely changes the DoS curves for both Ni and Co when compared to the binary NiCo, indicating that the Ni-Co interaction is likely to be poorly approximated as pseudobinary in multicomponent systems.
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Figure 3
Eigenvalues of the chemical stability matrix along symmetry lines around the Brillouin zone. All are computed at a temperature of 1000 K, above any predicted ordering temperature. For an $s$ -species alloy there are $s - 1$ physically meaningful eigenvalues due to the conservation of overall concentrations. In line with the trends shown in the density of states plots, the contrast between the binary alloys and those with three, four, or five components can clearly be seen. It should also be noted that the addition of Fe and Mn does not significantly alter the shape of the two modes present in NiCoCr. Rather, Fe and Mn introduce two essentially flat modes which, in concentration space, are polarized along the Fe and Mn directions indicating that these elements dilute the other interactions in the system. The upward trend in the lowest-lying eigenvalue from the three-component through to the five-component system is a result of the increasing contribution from the configurational entropy stabilizing the solid solution.
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Figure 4
Visualizations of indicative atomic configurations, specific heat capacity curves, and short-range order parameters for NiCoCr, NiCoFeCr, and NiCoFeMnCr. Ni, Co, Fe, Mn, and Cr are indicated by green, pink, red, purple, and blue, respectively. Each visualization is of a sample configuration of 2048 atoms equilibrated at the denoted temperature. The visualized configurations, taken in combination with the SRO parameters visualized in Fig. 5 show that the low-temperature ground state of the system as multiphase, with some regions Ni rich and some regions Ni deficient, although this occurs at comparatively low temperatures and may not be experimentally accessible.
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Figure 5
Specific heat capacity curves (SHCs) and short-range order (SRO) parameters for NiCoCr, NiCoFeCr, and NiCoFeMnCr. (Details of how SHC values and SRO parameters are calculated are given in Sec. 2d.) In all three systems at low temperatures we find a predominance towards Ni-Ni and Co-Cr nearest-neighbor pairs, and away from Ni-Co nearest-neighbor and Co-Cr second-nearest-neighbor pairs. Very little ordering emerges between Fe, Mn, and the other species present in either the quarternary or quinary, confirming that these elements interact weakly and stabilize the solid solution. Where multiple curves lie on top of each other at high temperatures it indicates little to no SRO.
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