Propelled partly by the Materials Genome Initiative, and partly by the algorithmic developments and the resounding successes of data-driven efforts in other domains, informatics strategies are beginning to take shape within materials science. These approaches lead to surrogate machine learning models that enable rapid predictions based purely on past data rather than by direct experimentation or by computations/simulations in which fundamental equations are explicitly solved. Data-centric informatics methods are becoming useful to determine material properties that are hard to measure or compute using traditional methods—due to the cost, time or effort involved—but for which reliable data either already exists or can be generated for at least a subset of the critical cases. Predictions are typically interpolative, involving fingerprinting a material numerically first, and then following a mapping (established via a learning algorithm) between the fingerprint and the property of interest. Fingerprints, also referred to as “descriptors”, may be of many types and scales, as dictated by the application domain and needs. Predictions may also be extrapolative—extending into new materials spaces—provided prediction uncertainties are properly taken into account. This article attempts to provide an overview of some of the recent successful data-driven “materials informatics” strategies undertaken in the last decade, with particular emphasis on the fingerprint or descriptor choices. The review also identifies some challenges the community is facing and those that should be overcome in the near future.

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Machine learning in materials informatics: recent applications and prospects

Although the formalism that allows the calculation of alloy thermodynamic properties from
first-principles has been known for decades, its practical implementation has so far remained a tedious
process. The Alloy Theoretic Automated Toolkit (ATAT) drastically simplifies this procedure by implementing
decision rules based on formal statistical analysis that frees the researchers from a constant
monitoring during the calculation process and automatically “glues” together the input and the output of
various codes, in order to provide a high-level interface to the calculation of alloy thermodynamic properties
from first-principles. ATAT implements the Structure Inversion Method (SIM), also known as the
Connolly-Williams method, in combination with semi-grand-canonical Monte Carlo simulations. In order
to make this powerful toolkit available to the wide community of researchers who could benefit from it,
this article present a concise user guide outlining the steps required to obtain thermodynamic information
from ab initio calculations.

/pdf/the-alloy-theoretic-automated-toolkit-a-user-guide-3hlxchpv7x.pdf

The Alloy Theoretic Automated Toolkit: A User Guide

Devising a computational tool that assesses the thermodynamic stability of materials is among the most important steps required to build a “virtual laboratory,” where materials could be designed from first principles without relying on experimental input. Although the formalism that allows the calculation of solid-state phase diagrams from first principles is well established, its practical implementation remains a tedious process. The development of a fully automated algorithm to perform such calculations serves two purposes. First, it will make this powerful tool available to a large number of researchers. Second, it frees the calculation process from arbitrary parameters, guaranteeing that the results obtained are truly derived from the underlying first-principles calculations. The proposed algorithm formalizes the most difficult step of phase diagram calculations, namely the determination of the “cluster expanison,” which is a compact representation of the configurational dependence of the alloy’s energy. This is traditionally achieved by a fit of the unknown interaction parameters of the cluster expansion to a set of structural energies calculated from first principles. We present a formal statistical basis for the selection of both the interaction parameters to include in the cluster expansion and the structures to use to determine them. The proposed method relies on the concepts of cross-validation and variance minimization. An application to the calculation of the phase diagram of the Si-Ge, CaO-MgO, Ti-Al, and Cu-Au systems is presented.

/pdf/automating-first-principles-phase-diagram-calculations-350f6h5nan.pdf

Automating first-principles phase diagram calculations

Devising a computational tool that assesses the thermodynamic stability of materials is among the most important steps required to build a ``virtual laboratory'', where materials could be designed from first-principles without relying on experimental input. Although the formalism that allows the calculation of solid state phase diagrams from first principles is well established, its practical implementation remains a tedious process. The development of a fully automated algorithm to perform such calculations serves two purposes. First, it will make this powerful tool available to large number of researchers. Second, it frees the calculation process from arbitrary parameters, guaranteeing that the results obtained are truly derived from the underlying first-principles calculations. The proposed algorithm formalizes the most difficult step of phase diagram calculations, namely the determination of the ``cluster expansion'', which is a compact representation of the configurational dependence of the alloy's energy. This is traditionally achieved by a fit of the unknown interaction parameters of the cluster expansion to a set of structural energies calculated from first-principles. We present a formal statistical basis for the selection of both the interaction parameters to include in the cluster expansion and of the structures to use in order to determine them. The proposed method relies on the concepts of cross-validation and variance minimization. An application to the calculation of the phase diagram of the Si-Ge, CaO-MgO, Ti-Al, and Cu-Au systems is presented.

https://arxiv.org/pdf/cond-mat/0201511.pdf

Automating First-Principles Phase Diagram Calculations

Semiempirical interatomic potentials have been developed for Al, $\ensuremath{\alpha}\ensuremath{-}\mathrm{Ti},$ and $\ensuremath{\gamma}\ensuremath{-}\mathrm{TiAl}$ within the embedded atom method (EAM) formalism by fitting to a large database of experimental as well as ab initio data. The ab initio calculations were performed by the linearized augmented plane wave (LAPW) method within the density functional theory to obtain the equations of state for a number of crystal structures of the Ti-Al system. Some of the calculated LAPW energies were used for fitting the potentials while others for examining their quality. The potentials correctly predict the equilibrium crystal structures of the phases and accurately reproduce their basic lattice properties. The potentials are applied to calculate the energies of point defects, surfaces, and planar faults in the equilibrium structures. Unlike earlier EAM potentials for the Ti-Al system, the proposed potentials provide a reasonable description of the lattice thermal expansion, demonstrating their usefulness for molecular-dynamics and Monte Carlo simulations at high temperatures. The energy along the tetragonal deformation path (Bain transformation) in $\ensuremath{\gamma}\ensuremath{-}\mathrm{TiAl}$ calculated with the EAM potential is in fairly good agreement with LAPW calculations. Equilibrium point defect concentrations in $\ensuremath{\gamma}\ensuremath{-}\mathrm{TiAl}$ are studied using the EAM potential. It is found that antisite defects strongly dominate over vacancies at all compositions around stoichiometry, indicating that $\ensuremath{\gamma}\ensuremath{-}\mathrm{TiAl}$ is an antisite disorder compound, in agreement with experimental data.

/pdf/interatomic-potentials-for-atomistic-simulations-of-the-ti-2tzzi90d3e.pdf

Interatomic potentials for atomistic simulations of the Ti-Al system

We demonstrate a cluster expansion technique that is capable of accurately predicting formation energies in binary substitutional systems---even for those with large atomic relaxations. Conventional cluster expansions converge rapidly only in the absence of atomic relaxations, and they fail for long-period lattice-mismatched superlattices. When combined with first-principles total-energy methods, our method allows for very fast calculations for structures containing hundreds or thousands of atoms. The convergence and effectiveness of the cluster expansion are enhanced in two ways. First, the expansion is recast into reciprocal space, which allows for the inclusion of all important pair interactions. Second, a reciprocal space formulation for elastic strain energy is introduced, allowing accurate predictions for both long- and short-period superlattices. We illustrate the power of the method by performing a cluster expansion that requires total-energy calculations for only 12 simple input structures, with at most eight atoms per unit cell. We then correctly predict the formation energies of relaxed long-period superlattices, low-symmetry intermixed superlattices, structures with varied compositions, substitutional impurities, and a [ital im]1000 atom/cell simulation of the random alloy.

Efficient cluster expansion for substitutional systems.

We present a general and simple method for obtaining accurate, local density approximation (LDA-) quality interatomic potentials for a large class of bulk metallic alloys. The method is based on our analysis of atomic relaxation, which reveals that the energy released in the relaxation process can be approximated by calculating the epitaxially constrained energies of the constituents {ital A} and {ital B}. Therefore, the pair potential is fitted to the LDA-calculated epitaxial energies of the constituents (to capture the relaxation energies), and to the unrelaxed energies of ordered A{sub n}B{sub m} compounds (to capture the fixed-lattice {open_quotes}chemical{close_quotes} energy). The usefulness of our approach is demonstrated by carrying out this procedure for the Cu{sub 1{minus}x}Au{sub x} alloy system. The resulting pair potential reproduces the relaxed LDA formation energies of ordered compounds rather accurately, even though we used only unrelaxed energies as input. We also predict phonon spectra of the elements and ordered compounds in very good agreement with the LDA results. From the calculations for {approx}10000 atom supercells representing the random alloy, we obtain the bond lengths and relaxation energies of the random phase that are not accessible to direct LDA calculations. We predict that, while in Cu-rich alloys the Cu-Cumore » bond is shorter than the Cu-Au bond, at higher Au compositions this order is switched. Furthermore, we find that Au-rich Cu{sub 1{minus}x}Au{sub x} alloys have ground states that correspond to (001) superlattices of {ital n} monolayers of fcc Au stacked on {ital m} monolayers of the L1{sub 0} CuAu-I structure. The potential developed in this work is available at the site http://www.sst.nrel.gov/data/download.html for interested users. {copyright} {ital 1999} {ital The American Physical Society}« less

Fitting of accurate interatomic pair potentials for bulk metallic alloys using unrelaxed LDA energies

The success of the “cluster variation method” (CVM) in reproducing quite accurately the free energies of Monte Carlo (MC) calculations on Ising models is explained in terms of identifying a cancellation of errors: We show that the CVM produces correlation functions that are too close to zero, which leads to an overestimation of the exact energy, E, and at the same time, to an underestimation of −TS, so the free energy F=E−TS is more accurate than either of its parts. This insight explains a problem with “hybrid methods” using MC correlation functions in the CVM entropy expression: They give exact energies E and do not give significantly improved −TS relative to CVM, so they do not benefit from the above noted cancellation of errors. Additionally, hybrid methods suffer from the difficulty of adequately accounting for both ordered and disordered phases in a consistent way. A different technique, the “entropic Monte Carlo” (EMC), is shown here to provide a means for critically evaluating the CVM entropy. Ins...

Luiz G. Ferreira

Papers

Efficient cluster expansion for substitutional systems.

Fitting of accurate interatomic pair potentials for bulk metallic alloys using unrelaxed LDA energies

Evaluating and improving the cluster variation method entropy functional for Ising alloys