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One of the biggest unsolved problems in condensed matter physics is what mechanism causes high-temperature superconductivity and if there is a material that can exhibit superconductivity at both room temperature and atmospheric pressure. Among the many important properties of a superconductor, the critical temperature (Tc) or transition temperature is the point at which a material transitions into a superconductive state. In this implementation, machine learning is used to predict the critical temperatures of chemically unique compounds in an attempt to identify new chemically novel, high-temperature superconductors. The training data set (SuperCon) consists of known superconductors and their critical temperatures, and the testing data set (NOMAD) consists of around 700,000 novel chemical formulae. The chemical formulae in these data sets are first passed through a collection of rapid screening tools, SMACT, to check for chemical validity. Next, the DiSCoVeR algorithm is used to train on the SuperCon data to form a model, and then screens through batches of the formulae in the NOMAD data set. Having a combination of a chemical distance metric, density-aware dimensionality reduction, clustering, and a regression model, the DiSCoVeR algorithm serves as a tool to identify and assess these superconducting compositions [1]. This research and implementation resulted in the screening of chemically novel compositions exhibiting critical temperatures upwards of 150 K, which correlates to superconductors in the cuprate class. This implementation demonstrates a process of performing machine learning-assisted superconductor screening (while exploring chemically distinct spaces) which can be utilized in the materials discovery process.

Capturing structure-property relationships of materials for property prediction using machine learning requires the representation or featurization of the structural aspects of materials at different levels, including atomic, crystal, and microscales. While crystal structure-based modeling techniques are effective for materials informatics, many materials datasets do not have complete structural information. On the other hand, when it comes to discovering novel materials, structural information of the chemical compounds is not known beforehand. These two cases make the application of structure-based learning techniques limited. Tools for the automated generation of structural features are limited in materials science. Indeed, most structural descriptions of materials are done via human analysis and then stored as text entries in scientific documents. One way to extract a structure-based feature vector from this corpus of knowledge would be to leverage natural language processing to create word embeddings trained on these structural descriptions. This approach could encode the information about the kind of structures any individual element of the periodic table forms which can be leveraged to tackle both the situation mentioned above: lack of structural details in a dataset, structural information for novel materials. In this work, we created word embeddings by training models on automatically generated text descriptions of crystal structure from Robocrystallographer and assess the utility of these structure-based feature vectors in predicting materials properties by comparing the performance against mat2vec and one-hot encoded features.

Benchmarks are crucial for driving progress in scientific disciplines. To be effective, benchmarks should closely mimic real-world tasks while being computationally efficient, allowing for accessibility and repeatability. Developing surrogate models that can be indistinguishable from the ground truth observation within the explored dataset bounds dramatically reduces the computational burden of running benchmarks without sacrificing quality, but this requires a large amount of initial data. In the fields of materials science and chemistry, relevant optimization tasks can be challenging due to their complexity, which includes hierarchical, noisy, multi-fidelity, multi-objective, high-dimensional, and non-linearly correlated variables. Additionally, they may include mixed numerical and categorical variables that are subject to linear and non-linear constraints. Simulating or experimentally verifying such tasks can be difficult, which is why benchmarks are essential. This study aimed to overcome these challenges by generating 173219 quasi-random hyperparameter combinations across 23 hyperparameters and using them to train CrabNet on the Matbench experimental band gap dataset (Computational runtime: 387 RTX-2080-Ti GPU days). The results were stored in a free-tier shared MongoDB Atlas dataset, creating a regression dataset that maps hyperparameter combinations to metrics such as MAE, RMSE, computational runtime, and model size for the CrabNet model trained on the Matbench experimental band gap benchmark task. To simulate the actual simulations, heteroskedastic noise was incorporated into the regression dataset, and bad hyperparameter combinations were excluded. Percentile ranks were computed within each group of identical parameter sets to capture heteroskedastic noise, rather than assuming Gaussian noise as is done in traditional approaches. This approach can be applied to other benchmark datasets, bridging the gap between optimization benchmarks with low computational overhead and realistically complex, real-world optimization scenarios.

Would you rather search for a line inside a cube or a point inside a square? Physics-based simulations and wet-lab experiments often have symmetries (degeneracies) that allow reducing problem dimensionality or search space, but constraining these degeneracies is often unsupported or difficult to implement in many optimization packages, requiring additional time and expertise. So, are the possible improvements in efficiency worth the cost of implementation? We demonstrate that the compactness of a search space (to what extent and how degenerate solutions and non-solutions are removed) affects Bayesian optimization search efficiency. Here, we use the Adaptive Experimentation (Ax) Platform by Meta and a physics-based particle packing simulation with eight or nine tunable parameters, depending on the search space compactness. These parameters represent three truncated log-normal distributions of particle sizes which exhibit compositional-invariance and permutation-invariance characteristic of formulation problems (e.g., chemical formulas, composite materials, alloys). We assess a total of four search space types which range from none up to both constraint types imposed simultaneously. In general, the removal of degeneracy through problem reformulation (as seen by the optimizers surrogate model) improves optimization efficiency. We recommend that optimization practitioners in the physical sciences carefully consider the trade-off between implementation cost and search efficiency before running expensive optimization campaigns.

A large collection of element-wise planar densities for compounds obtained from the Materials Project is calculated using brute force computational geometry methods, where the planar density is given by the total fractional area of atoms intersecting a supercell's crystallographic plane divided by the area of the supercell's crystallographic plane. It is demonstrated that the element-wise maximum lattice plane densities can be useful as machine learning features. The methods described here are implemented in an open-source Mathematica package hosted at https://github.com/sgbaird/LatticePlane.

We present the DiSCoVeR algorithm (https://github.com/sparks-baird/mat_discover), a Python tool for identifying and assessing high-performing, chemically unique compositions relative to existing compounds.

Benchmarks are an essential driver of progress in scientific disciplines. Ideal benchmarks mimic real-world tasks as closely as possible, where insufficient difficulty or applicability can stunt growth in the field. Benchmarks should also have sufficiently low computational overhead to promote accessibility and repeatability. The goal is then to win a “Turing test” of sorts by creating a surrogate model that is indistinguishable from the ground truth observation (at least within the dataset bounds that were explored), necessitating a large amount of data. In materials science and chemistry, industry-relevant optimization tasks are often hierarchical, noisy, multi-fidelity, multi-objective, high-dimensional, and non-linearly correlated while exhibiting mixed numerical and categorical variables subject to linear and non-linear constraints. To complicate matters, unexpected, failed simulation or experimental regions may be present in the search space. In this study, 438371 random hard-sphere packing simulations representing 279 CPU days’ worth of computational overhead were performed across nine input parameters with linear constraints and two discrete fidelities each with continuous fidelity parameters and results were logged to a free-tier shared MongoDB Atlas database. Two core tabular datasets resulted from this study: 1. a failure probability dataset containing unique input parameter sets and the estimated probabilities that the simulation will fail at each of the two steps, and 2. a regression dataset mapping input parameter sets (including repeats) to particle packing fractions and computational runtimes for each of the two steps. These two datasets can be used to create a surrogate model as close as possible to running the actual simulations by incorporating simulation failure and heteroskedastic noise. For the regression dataset, percentile ranks were computed within each of the groups of identical parameter sets to enable capturing heteroskedastic noise. This contrasts with a more traditional approach that imposes a-priori assumptions such as Gaussian noise, e.g., by providing a mean and standard deviation. A similar approach can be applied to other benchmark datasets to bridge the gap between optimization benchmarks with low computational overhead and realistically complex, real-world optimization scenarios.

Closed-loop Spectroscopy Lab: Light-mixing Demo (CLSLab:Light) is a teaching and prototyping platform for autonomous scientific discovery. It consists of a set of LEDs and a light sensor while encapsulating key principles for "self-driving" (i.e., autonomous) research laboratories, including sending commands, receiving sensor data, physics-based simulation, and advanced optimization. CLSLab:Light is a "Hello, World!" introduction to these topics, accessible by students, educators, hobbyists, and researchers for less than 100 USD, a small footprint, and under an hour of setup time.

Traditional, data-driven materials discovery involves screening chemical systems with machine learning algorithms and selecting candidates that excel in a target property. The number of screening candidates grows infinitely large as the fractional resolution of compositions the number of included elements increases. The computational infeasibility and probability of overlooking a successful candidate grow likewise. Our approach shifts the optimization focus from model parameters to the fractions of each element in a composition. Using a pretrained network, CrabNet, and writing a custom loss function to govern a vector of element fractions, compositions can be optimized such that a predicted property is maximized or minimized. Single and multi-property optimization examples are presented that highlight the capabilities and robustness of this approach to inverse design.

We present work on the application of sequential supervised machine learning for a reduced-dimension, ballistic deposition, Monte Carlo particle packing. Calculations are carried out for a combination of three distinguishable hard spheres representing different materials. Each set of spheres has a distribution of particle sizes in order to mimic realistic milling conditions of raw ingredients. Since infinite combinations of particle size, distribution, fraction, and density exist, we employ machine learning to aid in the design optimization of new high packing density mixtures. Previously calculated binary packs of particle radius ratios of 80:1 were analyzed, but this work highlights results of ternary packs with radius ratios greater than 300:1. We demonstrate a sequential learning approach where iterative experiments are performed based on minimizing the uncertainty in the target regime of high packing density. New candidate mixtures are identified via classification rather than regression which provides superior ability to extrapolate into high packing density mixtures.

In recent years, multi-phase materials capable of multi-ion transport have emerged as attractive candidates for a variety of electrochemical devices. Here, we provide experimental results for fabricating a composite electrolyte made up of a one-dimensional fast sodium-ion conductor, sodium zirconogallate, and an oxygen-ion conductor, yttria-stabilized zirconia. The composite is synthesized through a vapor phase conversion mechanism, and the kinetics of this process are discussed in detail. The samples are characterized using diffraction, electron microscopy, and electrochemical impedance spectroscopy techniques. Samples with a finer grain structure exhibit higher kinetic rates due to larger three-phase boundaries (TPBs) per unit area. The total conductivity is fitted to an Arrhenius type equation with activation energies ranging from 0.23 eV at temperatures below 550 °C to 1.07 eV above 550 °C. The electrochemical performance of multi-phase multi-species, mixed sodium- and oxygen-ion conductors, is tested under both oxygen chemical potential gradient as well as sodium chemical potential gradient, before and after reaching equilibrium, are discussed using the Goldman-Hodgkin-Kats (GHK) and the Nernst equation. The total conductivity of the degraded cathode and anode terminals is investigated using electrochemical impedance spectroscopy. The degradation investigation of samples indicates a decrease in conductivity adjacent to the anode terminal, the loss of sodium content, and the formation of β-gallia adjacent to the fuel electrode after ~396h at 1463 K.

Nickel and Cobalt based superalloys are commonly used as turbine materials for high-temperature applications. However, their maximum operating temperature is limited to about 1100oC. Therefore, to improve turbine efficiency, current research is focused on designing materials that can withstand higher temperatures. Niobium-based alloys can be considered as promising candidates because of their exceptional properties at elevated temperatures. The conventional approach to alloy design relies on phase diagrams and structure-property data of limited alloys and extrapolates this information into the unexplored compositional space. In the present work, we harness machine learning and provide a design strategy for finding an Nb-based alloy composition with optimized yield strength and ultimate tensile strength at high temperatures. We use a Bayesian optimization algorithm combined with domain knowledge-based material descriptors to find an optimal Nb-based quaternary and quinary alloy composition for the targeted value of mechanical strengths. Furthermore, we extend our study to multi-objective optimization to suggest an optimal alloy candidate by integrating yield strength and ultimate tensile strength into a single composite property. We developed a detailed design flow and python programming code, which could be helpful for accelerating alloy design in a limited alloy data regime.

Would you rather search for a line inside a cube or a point inside a square? This type of solution degeneracy often exists in physics-based simulations and wet-lab experiments, but constraining these degeneracies is often unsupported or difficult to implement in many optimization packages, requiring additional time and expertise. So, are the possible improvements in efficiency worth the cost of implementation? We demonstrate that the compactness of a search space (to what extent and how degenerate solutions and non-solutions are removed) can significantly affect Bayesian optimization search efficiency via the Ax platform. We use a physics-based particle packing simulation with seven to nine tunable parameters, depending on the search space compactness, that represent three truncated, discrete log-normal distributions of particle sizes. This physics-based simulation exhibits three qualitatively different degeneracy types: size-invariance, compositional-invariance, and permutation-invariance. We assess a total of eight search space types which range from none up to all three constraint types imposed simultaneously. We find that leaving the search space unconstrained leads to a large variance in the outcome and that on average, the most constrained search space is not always the most efficient. Likewise, the least constrained search space is not always the least efficient. We recommend that optimization practitioners in the physical sciences carefully consider the impact of removing search space degeneracies on search efficiency before running expensive optimization campaigns.

We demonstrate advantages of samples made by mechanical stacking of exfoliated van der Waals materials for controlling the topological surface state of a 3-dimensional topological insulator (TI) via interaction with an adjacent magnet layer. We assemble bilayers with pristine interfaces using exfoliated flakes of the TI BiSbTeSe2 and the magnet Cr2Ge2Te6, thereby avoiding problems caused by interdiffusion that can affect interfaces made by top-down deposition methods. The samples exhibit an anomalous Hall effect (AHE) with abrupt hysteretic switching. For the first time in samples composed of a TI and a separate ferromagnetic layer, we demonstrate that the amplitude of the AHE can be tuned via gate voltage with a strong peak near the Dirac point. This is the signature expected for the AHE due to Berry curvature associated with an exchange gap induced by interaction between the topological surface state and an out-of-plane-oriented magnet., submitted version

Short-range magnetic correlations can significantly increase the thermopower of magnetic semiconductors, representing a noteworthy development in the decades-long effort to develop high-performance thermoelectric materials. Here, we reveal the nature of the thermopower-enhancing magnetic correlations in the antiferromagnetic semiconductor MnTe. Using magnetic pair distribution function analysis of neutron scattering data, we obtain a detailed, real-space view of robust, nanometer-scale, antiferromagnetic correlations that persist into the paramagnetic phase above the N\'eel temperature $T_{\mathrm{N}}$ = 307 K. The magnetic correlation length in the paramagnetic state is significantly longer along the crystallographic $c$ axis than within the $ab$ plane, pointing to anisotropic magnetic interactions. Ab initio calculations of the spin-spin correlations using density functional theory in the disordered local moment approach reproduce this result with quantitative accuracy. These findings constitute the first real-space picture of short-range spin correlations in a magnetically enhanced thermoelectric and inform future efforts to optimize thermoelectric performance by magnetic means.

Would you rather search for a point inside of a line or a line inside of a rectangle? This is a type of solution degeneracy that often exists physics-based simulations and wetlab experiments, but constraining these degeneracies is often unsupported or difficult-to-implement in many optimization packages, requiring additional time and expertise. So, is the increase in efficiency worth the cost of implementation? We demonstrate that the compactness of a search space (to what extent degenerate solutions and nonsolutions are removed) can have a significant effect on Bayesian optimization search efficiency via the Ax platform. As our optimization task, we use a physics-based particle packing simulation with seven to nine tunable parameters, depending on the search space compactness, that represent three truncated, discrete log-normal distributions of particle sizes. This physics-based simulation exhibits three qualitatively different degeneracy types: size-invariance, compositional-invariance, and permutation-invariance. The degeneracies are reflected in the outcomes being identical when: 1. all particle sizes are multiplied by a constant factor, 2. the fractional prevalences of the particle types sum to unity, and 3. sets of log-normal distribution parameters are swapped with each other, respectively. This simulation provides fertile ground for assessing the impact of multiple constraints on search efficiency, with a total of eight search space types which ranges from none up to all three constraints imposed simultaneously. Contrary to intuition, we find that, on average, the most compact search space performs worse than the least compact search space ((0.692 ± 0.036) vs. (0.699 ± 0.016) , respectively) over 50 iterations due to the interactions of the non-linear size-invariance degeneracy with other degeneracy types. The most efficient search space in terms of both predicted and validated outcomes is the combination of the composition and permutation constraints, resulting in a mean packing fraction of (0.728±0.010) over 50 iterations, where randomly sampled volume fractions are typically no less than 0.6. We recommend that optimization practitioners in the physical sciences carefully consider the impact of removing search space degeneracies on search efficiency prior to running expensive optimization campaigns.

Thermoelectrics (TEs) are an important class of technology that harvest electric power directly from heat sources. When designing both high performance and environmentally friendly TE materials, the pseudo-cubic structure has great theoretical potential to maximize the dimensionless figure of merit ZT. The TE multinary single crystal with a pseudo-cubic structure paves a new path toward manipulating valley degeneracy and anisotropy with low thermal conductivity caused by short-range lattice distortion. Here, we report a record high ZT = 1.6 around 800 K realized in a totally environmentally benign p-type Na-doped Cu2ZnSnS4 (CZTS) single crystal. The exceptional performance comes from a high power factor while maintaining intrinsically low thermal conductivity. The combination of the pseudo-cubic structure and intrinsic properties of the CZTS single crystal takes advantage of simple material tuning without complex techniques.

Humankind’s unparalleled access to computing, data, and materials resources has resulted in the discovery of new, technology enabling materials. This work is a preview of a recent publication wherein predictive and generative machine learning models are applied on the largest polymer dataset to correlate chemical structure with glass transition temperature thereby leading to the discovery of new high-temperature polymers.

New featurization schemes for describing materials as composition vectors in order to predict their properties using machine learning are common in the field of Materials Informatics. However, little is known about the comparative efficacy of these methods. This work sets out to make clear which featurization methods should be used across various circumstances. Our findings include, surprisingly, that simple fractional and random-noise representations of elements can be as effective as traditional and new descriptors when using large amounts of data. However, in the absence of large datasets or for data that is not fully representative, we show that the integration of domain knowledge offers advantages in predictive ability.

The field of materials science has seen an explosion in the amount of accessible high quality data. With this sudden surge of data, the application of machine learning (ML) onto materials data has led to great results. Particular success has been found in training models based on chemical formula. Such models have traditionally focused on learning from density functional theory (DFT) or experimental data. Though some researchers have explored the use of DFT calculated properties as features for learning, this has not gained much traction since the machine learning predictions would be limited by the DFT computation time and accuracy. In this work, we explore the use of a stacked ensemble learning system that combines machine learning from DFT calculations to improve learning on experimental data. This is accomplished by handling the DFT and experimental data separately, training distinct models for each. The DFT models are used to generate a "predicted DFT" value for the formulae in the experimental data. A meta-learner-trained using predictions generated by the experimental models combined with predictions from the DFT models-is shown to improve root-mean-squared-error by over 9% in the test data, when compared to a baseline model that only learns from the training data.

The development of structural materials with outstanding mechanical response has long been sought for innumerable industrial, technological, and even biomedical applications. However, these compounds tend to derive their fascinating properties from a myriad of interactions spanning multiple scales, from localized chemical bonding to macroscopic interactions between grains. This diversity has limited the ability of researchers to develop new materials on a reasonable timeline. Fortunately, the advent of machine learning in materials science has provided a new approach to analyze high-dimensional space and identify correlations among the structure-composition-property-processing relationships that may have been previously missed. In this review, we examine some successful examples of using data science to improve known structural materials by analyzing fatigue and failure, and we discuss approaches to develop entirely new classes of structural materials in complex composition spaces including high-entropy alloys and bulk metallic glasses. Highlighting the recent advancement in this field demonstrates the power of data-driven methodologies that will hopefully lead to the production of market-ready structural materials.

Materials informatics is increasingly finding ways to exploit machine learning algorithms. Techniques such as decision trees, ensemble methods, support vector machines, and a variety of neural network architectures are used to predict likely material characteristics and property values. Supplemented with laboratory synthesis, applications of machine learning to compound discovery and characterization represent one of the most promising research directions in materials informatics. A shortcoming of this trend, in its current form, is a lack of standardized materials data sets on which to train, validate, and test model effectiveness. Applied machine learning research depends on benchmark data to make sense of its results. Fixed, predetermined data sets allow for rigorous model assessment and comparison. Machine learning publications that do not refer to benchmarks are often hard to contextualize and reproduce. In this data descriptor article, we present a collection of data sets of different material properties taken from the AFLOW database. We describe them, the procedures that generated them, and their use as potential benchmarks. We provide a compressed ZIP file containing the data sets and a GitHub repository of associated Python code. Finally, we discuss opportunities for future work incorporating the data sets and creating similar benchmark collections.

This Methods/Protocols article is intended for materials scientists interested in performing machine learning-centered research. We cover broad guidelines and best practices regarding the obtaining...

Materials researchers are paying ever more attention to sustainability, criticality, availability, and other industrial ecology metrics and concepts as they develop new materials. Previous reports for these metrics have typically been either for a few specific compositions or for a single year. In this work, we present a new curated dataset which reports the global elemental production on a per country basis from the years 1998 to 2015 alongside elemental prices over this same time period. The data are taken from United States Geological Survey Minerals Yearbook entries. In addition to the raw data, analysis of the Herfindahl–Hirschman Index has been carried out and is reported alongside market share of each element for each year in the range provided. Lastly, we present a few possible scenarios for data utility such as exploring trends over the time period, correlating volatility with availability, or examining abrupt changes in the Herfindahl–Hirschman Index and how these may or may not relate to geopolitical events such as wars in mineral producing countries.