Accelerating computational modeling and design of high-entropy alloys

Abstract

With huge design spaces for unique chemical and mechanical properties, we remove a roadblock to computational design of high-entropy alloys using a metaheuristic hybrid Cuckoo Search (CS) for "on-the-fly" construction of Super-Cell Random APproximates (SCRAPs) having targeted atomic site and pair probabilities on arbitrary crystal lattices. Our hybrid-CS schema overcomes large, discrete combinatorial optimization by ultrafast global solutions that scale linearly in system size and strongly in parallel, e.g. a 4-element, 128-atom model [a 10 73+ space] is found in seconds -a reduction of 13,000+ over current strategies. With model-generation eliminated as a bottleneck, computational alloy design can be performed that is currently impossible or impractical. We showcase the method for real alloys with varying short-range order. Being problem-agnostic, our hybrid-CS schema offers numerous applications in diverse fields. I. INTRODUCTIONComplex solid-solution alloys (CSAs), a subset of which are near-equiatomic high-entropy alloys, 1-7 show remarkable properties for number of elements N ≥ 4 and set of elemental compositions {c α=1,N }, 8 even for mediumentropy (N =3). These findings have encouraged research into CSAs for applications in aerospace and defense, like adding refractory elements for higher operational temperatures. For higher-melting refractory CSAs, vacancy defects -ubiquitous when processing -can have a profound influence on stability and phase selection 9 , adding another design "element". Thus, CSAs have a vast design space to create materials with novel or improved properties (e.g., structural strength or resistance to fatigue, oxidation, corrosion, and wear), while other properties (e.g., resistivity, thermoelectricity, elasticity, and yield strength) can alter rapidly with a set of {c α }. [6][7][8][9][10][11][12][13][14][15] As such, accurate "on-the-fly" constructed CSA models are needed to enable computational design and to identify trends in {c α }-derived properties and thermal stability. Yet, models of CSAs have a design space that grows exponentially -a NP-hard combinatorial problem.To remove this design roadblock, we establish a hybrid Cuckoo Search (CS), an evolutionary algorithm 16 inspired by Yang and Deb 17 based on the brood parasitism of a female Cuckoo bird (mimicking color and pattern of a few host species). Importantly, the CS advantages are: (a) guaranteed global convergence, (b) local and global searches controlled by a switching parameter, and (c) Lévy flights scan solution space more efficiently -no random walks, so better than a Gaussian process. 17-19 A CS yields approximate solutions ("nests") for intractable or gradient-free problems 20 with little problem-specific knowledge -often only a solution "fitness" function. 21 For complex cases, fitness can be discontinuous, non-differentiable to noisy. Related methods 18 are genetic-algorithm, 22 simulated-annealing, 23 particleswarm, 24 and ant-colony 25 optimization.