2017
DOI: 10.1103/physrevb.96.014107
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Robustness of the cluster expansion: Assessing the roles of relaxation and numerical error

Abstract: Cluster expansion (CE) is effective in modeling the stability of metallic alloys, but sometimes cluster expansions fail. Failures are often attributed to atomic relaxation in the DFT-calculated data, but there is no metric for quantifying the degree of relaxation. Additionally, numerical errors can also be responsible for slow CE convergence. We studied over one hundred different Hamiltonians and identified a heuristic, based on a normalized mean-squared displacement of atomic positions in a crystal, to determ… Show more

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Cited by 43 publications
(37 citation statements)
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“…Indeed, Fig. 1 shows that when the atomic sizes are significantly different, the accuracy of fitting the energy of the relaxed configurations is significantly less than that of the unrelaxed configurations-this is similar to how cluster expansion behaves [8]. This can be rectified in part by introducing, for instance, the explicit dependence of the energy on the average compositiondependent equilibrium volume of the lattice [7].…”
Section: Discussionmentioning
confidence: 94%
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“…Indeed, Fig. 1 shows that when the atomic sizes are significantly different, the accuracy of fitting the energy of the relaxed configurations is significantly less than that of the unrelaxed configurations-this is similar to how cluster expansion behaves [8]. This can be rectified in part by introducing, for instance, the explicit dependence of the energy on the average compositiondependent equilibrium volume of the lattice [7].…”
Section: Discussionmentioning
confidence: 94%
“…Accurate computational prediction of the mixing enthalpy and configuration entropy would be very instrumental in studying HEAs, as it is hard to experimentally explore different compositions of five or more elements due to combinatorial complexity. The state-of-the-art methodology of computationally assessing the stability of multicomponent crystalline alloys is based on cluster expansion [5,6,7,8], allowing to fit formation energies of binary systems over the entire range of compositions, ternary and quaternary systems [9,10,11,12] over, typically, some subrange of the composition range, and quinary systems at specific points of the composition range [13].…”
Section: Introductionmentioning
confidence: 99%
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“…but is not useful when this is not the case. Its accuracy also converges slowly when atomic size mismatch is not negligible 20 . Additionally, more classical machine-learning algorithms such as decision trees 21 , support vector machines 22 , and other ML algorithms 23,24 have been tried.…”
Section: Introductionmentioning
confidence: 94%
“…that only a small fraction of clusters is relevant for describing the property of interest (e.g. energy) [40]. Conversely, SAMPLE's energy model is not sparse.…”
Section: The Energy Modelmentioning
confidence: 99%