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Active learning of ternary alloy structures and energies

Abstract Machine learning models with uncertainty quantification have recently emerged as attractive tools to accelerate the navigation of catalyst design spaces in a data-efficient manner. Here, we combine active learning with a dropout graph convolutional network (dGCN) as a surrogate model to explore the complex materials space of high-entropy alloys (HEAs). We train the dGCN on the formation energies of disordered binary alloy structures in the Pd-Pt-Sn ternary alloy system and improve predictions on ternary structures by performing reduced optimization of the formation free energy, the target property that determines HEA stability, over ensembles of ternary structures constructed based on two coordinate systems: (a) a physics-informed ternary composition space, and (b) data-driven coordinates discovered by the Diffusion Maps manifold learning scheme. Both reduced optimization techniques improve predictions of the formation free energy in the ternary alloy space with a significantly reduced number of DFT calculations compared to a high-fidelity model. The physics-based scheme converges to the target property in a manner akin to a depth-first strategy, whereas the data-driven scheme appears more akin to a breadth-first approach. Both sampling schemes, coupled with our acquisition function, successfully exploit a database of DFT-calculated binary alloy structures and energies, augmented with a relatively small number of ternary alloy calculations, to identify stable ternary HEA compositions and structures. This generalized framework can be extended to incorporate more complex bulk and surface structural motifs, and the results demonstrate that significant dimensionality reduction is possible in thermodynamic sampling problems when suitable active learning schemes are employed.

Chemistry↗

Materials Data on Sn2(PdPt)3 by Materials Project

Sn2(PtPd)3 crystallizes in the orthorhombic Pmmm space group. The structure is three-dimensional. there are three inequivalent Pt sites. In the first Pt site, Pt is bonded to four equivalent Pt, four equivalent Pd, and four equivalent Sn atoms to form PtSn4Pd4Pt4 cuboctahedra that share corners with four equivalent PtSn4Pd4Pt4 cuboctahedra, corners with eight equivalent PdSn4Pd4Pt4 cuboctahedra, edges with eight equivalent PtSn4Pd8 cuboctahedra, edges with eight equivalent PdSn4Pd2Pt6 cuboctahedra, edges with eight equivalent SnPd6Pt6 cuboctahedra, faces with four equivalent SnPd6Pt6 cuboctahedra, faces with six PdSn4Pd2Pt6 cuboctahedra, and faces with eight PtSn4Pd4Pt4 cuboctahedra. All Pt–Pt bond lengths are 2.87 Å. All Pt–Pd bond lengths are 2.86 Å. All Pt–Sn bond lengths are 2.87 Å. In the second Pt site, Pt is bonded to eight Pd and four equivalent Sn atoms to form PtSn4Pd8 cuboctahedra that share corners with twelve PtSn4Pd8 cuboctahedra, edges with eight equivalent PtSn4Pd4Pt4 cuboctahedra, edges with eight equivalent PdSn4Pd2Pt6 cuboctahedra, edges with eight equivalent SnPd6Pt6 cuboctahedra, faces with four equivalent SnPd6Pt6 cuboctahedra, faces with six PtSn4Pd8 cuboctahedra, and faces with eight PdSn4Pd2Pt6 cuboctahedra. All Pt–Pd bond lengths are 2.87 Å. All Pt–Sn bond lengths are 2.85 Å. In the third Pt site, Pt is bonded to four equivalent Pt, four equivalent Pd, and four equivalent Sn atoms to form PtSn4Pd4Pt4 cuboctahedra that share corners with twelve PtSn4Pd8 cuboctahedra, edges with eight equivalent SnPd6Pt6 cuboctahedra, edges with sixteen PdSn4Pd2Pt6 cuboctahedra, faces with four equivalent PdSn4Pd2Pt6 cuboctahedra, faces with four equivalent SnPd6Pt6 cuboctahedra, and faces with ten PtSn4Pd4Pt4 cuboctahedra. All Pt–Pd bond lengths are 2.87 Å. All Pt–Sn bond lengths are 2.87 Å. There are two inequivalent Pd sites. In the first Pd site, Pd is bonded to six Pt, two equivalent Pd, and four equivalent Sn atoms to form PdSn4Pd2Pt6 cuboctahedra that share corners with twelve equivalent PdSn4Pd2Pt6 cuboctahedra, edges with four equivalent PdSn4Pd4Pt4 cuboctahedra, edges with eight equivalent SnPd6Pt6 cuboctahedra, edges with twelve PtSn4Pd4Pt4 cuboctahedra, faces with four equivalent SnPd6Pt6 cuboctahedra, faces with six PtSn4Pd4Pt4 cuboctahedra, and faces with eight PdSn4Pd2Pt6 cuboctahedra. Both Pd–Pd bond lengths are 2.86 Å. All Pd–Sn bond lengths are 2.87 Å. In the second Pd site, Pd is bonded to four equivalent Pt, four equivalent Pd, and four equivalent Sn atoms to form PdSn4Pd4Pt4 cuboctahedra that share corners with four equivalent PdSn4Pd4Pt4 cuboctahedra, corners with eight equivalent PtSn4Pd4Pt4 cuboctahedra, edges with eight equivalent PtSn4Pd4Pt4 cuboctahedra, edges with eight equivalent PdSn4Pd2Pt6 cuboctahedra, edges with eight equivalent SnPd6Pt6 cuboctahedra, faces with four equivalent SnPd6Pt6 cuboctahedra, faces with six PtSn4Pd4Pt4 cuboctahedra, and faces with eight PdSn4Pd2Pt6 cuboctahedra. All Pd–Sn bond lengths are 2.86 Å. Sn is bonded to six Pt and six Pd atoms to form SnPd6Pt6 cuboctahedra that share corners with twelve equivalent SnPd6Pt6 cuboctahedra, edges with twelve PtSn4Pd4Pt4 cuboctahedra, edges with twelve PdSn4Pd2Pt6 cuboctahedra, faces with six PtSn4Pd4Pt4 cuboctahedra, faces with six PdSn4Pd2Pt6 cuboctahedra, and faces with six equivalent SnPd6Pt6 cuboctahedra.

36 MATERIALS SCIENCE↗