Machine-learned interatomic potentials for alloys and alloy phase diagrams

Abstract

We introduce machine-learned potentials for Ag-Pd to describe the energy of alloy configurations over a wide range of compositions. We compare two different approaches. Moment tensor potentials (MTPs) are polynomial-like functions of interatomic distances and angles. The Gaussian approximation potential (GAP) framework uses kernel regression, and we use the smooth overlap of atomic position (SOAP) representation of atomic neighborhoods that consist of a complete set of rotational and permutational invariants provided by the power spectrum of the spherical Fourier transform of the neighbor density. Both types of potentials give excellent accuracy for a wide range of compositions, competitive with the accuracy of cluster expansion, a benchmark for this system. While both models are able to describe small deformations away from the lattice positions, SOAP-GAP excels at transferability as shown by sensible transformation paths between configurations, and MTP allows, due to its lower computational cost, the calculation of compositional phase diagrams. Given the fact that both methods perform nearly as well as cluster expansion but yield off-lattice models, we expect them to open new avenues in computational materials modeling for alloys.

Gaussian Process Regression for Materials and Molecules

“…As a result, rather than merely inspecting energy and force errors, a more reliable way to assess transferability of ML potentials is by performing extensive and wide-ranging explorations of atomistic configurations, such as random structure searches, 139 MD simulations at high temperatures, 122 or transition path calculations. 198 …”

Bandgap Engineering in the Configurational Space of Solid Solutions via Machine Learning: (Mg,Zn)O Case Study

“… 10 , 11 Rosenbrock et al have recently proposed ML potentials as an alternative to cluster expansions for the investigation of alloy phase diagrams. 12 Natarajan and van der Ven employed ML tools including neural networks to generalize the cluster expansion approach by relaxing the condition of linearity on the CCFs. 13 An alternative approach, which we follow in this work, is to use a different descriptor altogether, one that is not constrained by the locality of the CCFs, like the CME mentioned above.…”

Nested sampling for materials

“…If inter-atom correlations are important, it may be useful to propose moves jointly swapping the species of compact clusters of atoms, but this has not appeared to be necessary so far. While atom swap moves are sufficient for constant composition simulations, it is also possible to vary the composition in a semi-grand-canonical (s-GC) ensemble, where the total number of particles is fixed, but not the number of any particular chemical species [49,50]. In this case, the energy or enthalpy is augmented by a chemical potential term i n i μ i , where i indicates chemical species, n i is the number of atoms of species i, and μ i is its applied chemical potential.…”

“…The semi-grand-canonical ensemble was used to simulate the temperature-composition phase diagram for a machine-learning potential of the AgPd alloy [50]. In this case, the composition is an output observable of the NS simulation, as plotted in Fig.…”

“…5 in Ref. [50] ies of the hard-core double-ramp Jagla model revealed a previously unknown thermodynamically stable crystalline phase, drawing surprising similarities to water [94].…”