Disentangling Structural Confusion through Machine Learning: Structure Prediction and Polymorphism of Equiatomic Ternary Phases ABC

Data-Driven Score-Based Models for Generating Stable Structures with Adaptive Crystal Cells

The discovery of new functional and stable materials is a big challenge due to its complexity. This work aims at the generation of new crystal structures with desired properties, such as chemical stability and specified chemical composition, by using machine learning generative models. Compared with the generation of molecules, crystal structures pose new difficulties arising from the periodic nature of the crystal and from the specific symmetry constraints related to the space group. In this work, score-based probabilistic models based on annealed Langevin dynamics, which have shown excellent performance in various applications, are adapted to the task of crystal generation. The novelty of the presented approach resides in the fact that the lattice of the crystal cell is not fixed. During the training of the model, the lattice is learned from the available data, whereas during the sampling of a new chemical structure, two denoising processes are used in parallel to generate the lattice along with the generation of the atomic positions. A multigraph crystal representation is introduced that respects symmetry constraints, yielding computational advantages and a better quality of the sampled structures. We show that our model is capable of generating new candidate structures in any chosen chemical system and crystal group without any additional training. To illustrate the functionality of the proposed method, a comparison of our model to other recent generative models based on descriptor-based metrics is provided.

Data quantity governance for machine learning in materials science

Data-driven machine learning (ML) is widely employed in the analysis of materials structure-activity relationships, performance optimization and materials design due to its superior ability to reveal latent data patterns and make accurate prediction. However, because of the laborious process of materials data acquisition, ML models encounter the issue of the mismatch between a high dimension of feature space and a small sample size (for traditional ML models) or the mismatch between model parameters and sample size (for deep-learning models), usually resulting in terrible performance. Here, we review the efforts for tackling this issue via feature reduction, sample augmentation and specific ML approaches, and show that the balance between the number of samples and features or model parameters should attract great attention during data quantity governance. Following this, we propose a synergistic data quantity governance flow with the incorporation of materials domain knowledge. After summarizing the approaches to incorporating materials domain knowledge into the process of ML, we provide examples of incorporating domain knowledge into governance schemes to demonstrate the advantages of the approach and applications. The work paves the way for obtaining the required high-quality data to accelerate materials design and discovery based on ML.

Halide-driven polymorph selectivity in the synthesis of MnX (X = S, Se) nanoparticles

Devising synthetic strategies to control crystal structure is of great importance as materials properties are governed by structure. MnS is a great model system as it has three known stable polymorphs. Herein, we show the selective synthesis of colloidal wurtzite- and rock-salt-type MnS under identical reactions conditions changing only the manganese halide precursor. Mixtures of Mn halides or halide surrogate (e.g., NH₄Cl) also enabled polymorph control. Powder X-ray diffraction aliquot studies of the reactions revealed the crystal structure at the onset of nucleation and that of the final product is the same, unlike the Ostwald ripening transformation observed in other systems. The halide-driven selectivity was also observed in the synthesis of manganese selenide nanoparticles. In this system, variation of the Mn halide precursor allowed access to the wurtzite- and rock salt-type polymorphs of MnSe, as well as the pyrite-MnSe₂ phase. Based on this work, the mixing of metal salts might be a simple and effective strategy towards polymorph control and access materials with new crystal structures.

Synthesis and Crystal Structure of the Zintl Phases NaSrSb, NaBaSb and NaEuSb

This work details the synthesis and the crystal structures of the ternary compounds NaSrSb, NaBaSb and NaEuSb. They are isostructural and adopt the hexagonal ZrNiAl-type structure (space group P6¯2m; Pearson code hP9). The structure determination in all three cases was performed using single-crystal X-ray diffraction methods. The structure features isolated Sb^3- anions arranged in layers stacked along the crystallographic c-axis. In the interstices, alkali and alkaline-earth metal cations are found in tetrahedral and square pyramidal coordination environments, respectively. The formal partitioning of the valence electrons adheres to the valence rules, i.e., Na⁺Sr²⁺Sb^3-, Na⁺Ba²⁺Sb^3- and Na⁺Eu²⁺Sb^3- can be considered as Zintl phases with intrinsic semiconductor behavior. Electronic band structure calculations conducted for NaBaSb are consistent with this notion and show a direct gap of approx. 0.9 eV. Additionally, the calculations hint at possible inverted Dirac cones, a feature that is reminiscent of topological quantum materials.

Machine Learning for Electrocatalyst and Photocatalyst Design and Discovery

Electrocatalysts and photocatalysts are key to a sustainable future, generating clean fuels, reducing the impact of global warming, and providing solutions to environmental pollution. Improved processes for catalyst design and a better understanding of electro/photocatalytic processes are essential for improving catalyst effectiveness. Recent advances in data science and artificial intelligence have great potential to accelerate electrocatalysis and photocatalysis research, particularly the rapid exploration of large materials chemistry spaces through machine learning. Here a comprehensive introduction to, and critical review of, machine learning techniques used in electrocatalysis and photocatalysis research are provided. Sources of electro/photocatalyst data and current approaches to representing these materials by mathematical features are described, the most commonly used machine learning methods summarized, and the quality and utility of electro/photocatalyst models evaluated. Illustrations of how machine learning models are applied to novel electro/photocatalyst discovery and used to elucidate electrocatalytic or photocatalytic reaction mechanisms are provided. The review offers a guide for materials scientists on the selection of machine learning methods for electrocatalysis and photocatalysis research. The application of machine learning to catalysis science represents a paradigm shift in the way advanced, next-generation catalysts will be designed and synthesized.

Accelerate Synthesis of Metal-Organic Frameworks by a Robotic Platform and Bayesian Optimization

Synthesis of materials with desired structures, e.g., metal-organic frameworks (MOFs), involves optimization of highly complex chemical and reaction spaces due to multiple choices of chemical elements and reaction parameters/routes. Traditionally, realizing such an aim requires rapid screening of these nonlinear spaces by experimental conduction with human intuition, which is quite inefficient and may cause errors or bias. In this work, we report a platform that integrates a synthesis robot with the Bayesian optimization (BO) algorithm to accelerate the synthesis of MOFs. This robotic platform consists of a direct laser writing apparatus, precursor injecting and Joule-heating components. It can automate the MOFs synthesis upon fed reaction parameters that are recommended by the BO algorithm. Without any prior knowledge, this integrated platform continuously improves the crystallinity of ZIF-67, a demo MOF employed in this study, as the number of operation iterations increases. This work represents a methodology enabled by a data-driven synthesis robot, which achieves the goal of material synthesis with targeted structures, thus greatly shortening the reaction time and reducing energy consumption. It can be easily generalized to other material systems, thus paving a new route to the autonomous discovery of a variety of materials in a cost-effective way in the future.

Machine Learning Driven Synthesis of Few-Layered WTe2 with Geometrical Control

Reducing the lateral scale of two-dimensional (2D) materials to one-dimensional (1D) has attracted substantial research interest not only to achieve competitive electronic applications but also for the exploration of fundamental physical properties. Controllable synthesis of high-quality 1D nanoribbons (NRs) is thus highly desirable and essential for further study. Here, we report the implementation of supervised machine learning (ML) for the chemical vapor deposition (CVD) synthesis of high-quality quasi-1D few-layered WTe₂ NRs. Feature importance analysis indicates that H₂ gas flow rate has a profound influence on the formation of WTe₂, and the source ratio governs the sample morphology. Notably, the growth mechanism of 1T' few-layered WTe₂ NRs is further proposed, which provides new insights for the growth of intriguing 2D and 1D tellurides and may inspire the growth strategies for other 1D nanostructures. Our findings suggest the effectiveness and capability of ML in guiding the synthesis of 1D nanostructures, opening up new opportunities for intelligent materials development.

Element selection for crystalline inorganic solid discovery guided by unsupervised machine learning of experimentally explored chemistry

The selection of the elements to combine delimits the possible outcomes of synthetic chemistry because it determines the range of compositions and structures, and thus properties, that can arise. For example, in the solid state, the elemental components of a phase field will determine the likelihood of finding a new crystalline material. Researchers make these choices based on their understanding of chemical structure and bonding. Extensive data are available on those element combinations that produce synthetically isolable materials, but it is difficult to assimilate the scale of this information to guide selection from the diversity of potential new chemistries. Here, we show that unsupervised machine learning captures the complex patterns of similarity between element combinations that afford reported crystalline inorganic materials. This model guides prioritisation of quaternary phase fields containing two anions for synthetic exploration to identify lithium solid electrolytes in a collaborative workflow that leads to the discovery of Li3.3SnS3.3Cl0.7. The interstitial site occupancy combination in this defect stuffed wurtzite enables a low-barrier ion transport pathway in hexagonal close-packing.

Coordination Polymers Constructed from Pyrogallol[4]arene-Assembled Metal-Organic Nanocapsules

Coordination polymers, commonly known as infinite crystalline lattices, are versatile networks and have diverse potential applications in the fields of gas storage, molecular separation, catalysis, optics, and drug delivery, among other areas. Secondary building blocks, mainly incorporating rigid polydentate organic linkers and metal ions or clusters, are commonly employed to construct coordination polymers. Recently, novel building blocks such as coordination polyhedra have been utilized as metal nodes to fabricate coordination polymers. Benefiting from the rigid porous structure of the coordination polyhedron, prefabricated designer "pores" can be incorporated in this type of coordinate polymer. In this Account, coordination polymers built by pyrogallol[4]arene-assembled metal-organic nanocapsules are summarized. This class of metal-organic nanocapsule possesses the following advantages that make them excellent candidates in the construction of coordination polymers: (i) Various geometrical shapes with different volumes of the inner cavities can be obtained from these capsules. Among them, the two main categories illustrated are dimeric and hexameric capsules, which comprise two and six pyrogallol[4]arenes units, respectively. (ii) A wide range of possible metal ions ranging from main group metals to transition metals and even lanthanides have been demonstrated to seam the capsules. Therefore, these coordination polymers can be endowed with fascinating functionalities such as magnetism, semiconductivity, luminescence, and radioactivity. (iii) Up to 24 metal ions have been successfully embedded on the surface of the nanocapsule, each a potential reaction site in the construction of coordination polymers, opening up pathways for the formation of multidimensional frameworks.In this Account, we focus primarily on the synthesis and the structural information on pyrogallol[4]arene-derived coordination polymers. Coordination polymers can be formed by introducing linkers with two coordination sites, using pyrogallol[4]arenes with coordination sites on the tail, or even via metal ions cross-linking with each other. Machine learning was recently developed to help us predict and screen the structures of the coordination polymers. With single crystal analysis in hand, detailed structural information provides a molecular-level perspective. Significantly, following the formation of coordination polymers, the overall shape and structure of the discrete metal-organic nanocapsules remains essentially unchanged, with full retention of the prefabricated pores. If a rigid linker is used to connect capsules, more than one lattice void with different volumes can be found within the framework. Thus, molecules with different sizes could potentially be encapsulated within these coordination polymers. In addition, flexible ligands can also be employed as linkers. For example, polymers have been employed as large linkers that transform the crystalline coordination polymers into polymer matrices, paving the way toward the synthesis of advanced functional materials. Overall, coordination polymers constructed with pyrogallol[4]arene-assembled metal-organic nanocapsules show wide diversity and tunability in structure and fascinating properties, as well as the promise of built-in functionality in the future.

A data-driven XRD analysis protocol for phase identification and phase-fraction prediction of multiphase inorganic compounds

A CNN model with 6 convolution layers is used for phase identification.

Navigating the design space of inorganic materials synthesis using statistical methods and machine learning

Data-driven approaches have brought about a revolution in manufacturing; however, challenges persist in their applications to synthetic strategies. Their application to the deterministic navigation of reaction trajectories to stabilize crystalline solids with precise composition, atomic connectivity, microstructural dimensionality, and surface structure remains a frontier in inorganic materials research. The design of synthetic methodologies for the preparation of inorganic materials is often inefficient in terms of exploration of potentially vast design spaces spanning multiple process variables, reaction sequences, as well as structural parameters and reactivities of precursors and structure-directing agents. Reported synthetic methods are further limited in terms of the insight they provide into underlying chemical and physical principles. The recent surge in interest in accelerating the discovery of new materials can be considered as an opportunity to re-evaluate our approach to materials synthesis, and for considering new frameworks for exploration that are systematic and strategic in approach. Herein, we outline with the help of several illustrative examples, the challenges, opportunities, and limitations of data-driven synthesis design. The account collates discussion of design-of-experiments sampling methods, machine learning modeling, and active learning to develop experimental workflows that accelerate the experimental navigation of synthetic landscapes.

Feature vector clustering molecular pairs in computer simulations

A clustering framework is introduced to analyze the microscopic structural organization of molecular pairs in liquids and solutions. A molecular pair is represented by a representative vector (RV). To obtain RV, intermolecular atom distances in the pair are extracted from simulation trajectory as components of the key feature vector (KFV). A specific scheme is then suggested to transform KFV to RV by removing the influence of permutational molecular symmetry on the KFV as the predicted clusters should be independent of possible permutations of identical atoms in the pair. After RVs of pairs are obtained, a clustering analysis technique is finally used to classify all the RVs of molecular pairs into the clusters. The framework is applied to analyze trajectory from molecular dynamics simulations of an ionic liquid (trihexyltetradecylphosphonium bis(oxalato)borate ([P_6,6,6,14 ][BOB])). The molecular pairs are successfully categorized into physically meaningful clusters, and their effectiveness is evaluated by computing the product moment correlation coefficient (PMCC). (Willett, Winterman, and Bawden, J. Chem. Inf. Comput. Sci. 1986, 26, 109-118; Downs, Willett, and Fisanick, J. Chem. Inf. Comput. Sci. 1994, 34, 1094-1102) It is observed that representative configurations of two clusters are related to two energy local minimum structures optimized by density functional theory (DFT) calculation, respectively. Several widely used clustering analysis techniques of both nonhierarchical (k-means) and hierarchical clustering algorithms are also evaluated and compared with each other. The proposed KFV technique efficiently reveals local molecular pair structures in the simulated complex liquid. It is a method, which is highly useful for liquids and solutions in particular with strong intermolecular interactions. © 2019 Wiley Periodicals, Inc.

Single-Crystal Automated Refinement (SCAR): A Data-Driven Method for Determining Inorganic Structures

Single-crystal diffraction is one of the most common experimental techniques in chemistry for determining a crystal structure. However, the process of crystal structure determination and refinement is not always straightforward. Methods for simplifying and rationalizing the path to the most optimal crystal structure model have been incorporated into various data processing and crystal structure solution software, with the focus generally on aiding macromolecular or protein structure determination. In this work, we propose a new method that uses single-crystal data to determine the crystal structures of inorganic, extended solids called "single-crystal automated refinement" (SCAR). The approach was developed using data mining and machine learning methods and considers several structural features common in inorganic solids, like atom assignment based on physically reasonable distances, atomic statistical mixing, and crystallographic site deficiency. The output is a tree of possible solutions for the data set with a corresponding fit score indicating the most reasonable crystal structure. Here, the foundation for SCAR is presented followed by the implementation of SCAR to determine two newly synthesized and previously unreported phases, ZrAu_0.5Os_0.5 and Nd₄Mn₂AuGe₄. The structure solutions are found to be comparable with those produced by manually solving the data set, including the same refined mixed occupancies and atomic deficiency, supporting the validity of this automatic structure solution method. The proposed SCAR program is thus verified as being a fast and reliable assistant in determining even complex single-crystal diffraction data for extended inorganic solids.

Solving the Coloring Problem in Half-Heusler Structures: Machine-Learning Predictions and Experimental Validation

The site preferences within the structures of half-Heusler compounds have been evaluated through a machine-learning approach. A support-vector machine algorithm was applied to develop a model which was trained on 179 experimentally reported structures and 23 descriptors based solely on the chemical composition. The model gave excellent performance, with sensitivity of 93%, selectivity of 96%, and accuracy of 95%. As an illustration of data sanitization, two compounds (GdPtSb, HoPdBi) flagged by the model to have potentially incorrect site assignments were resynthesized and structurally characterized. The predictions of the correct site assignments from the machine-learning model were confirmed by single-crystal and powder X-ray diffraction analysis. These site assignments also corresponded to the lowest total energy configurations as revealed from first-principles calculations.

How To Optimize Materials and Devices via Design of Experiments and Machine Learning: Demonstration Using Organic Photovoltaics

Most discoveries in materials science have been made empirically, typically through one-variable-at-a-time (Edisonian) experimentation. The characteristics of materials-based systems are, however, neither simple nor uncorrelated. In a device such as an organic photovoltaic, for example, the level of complexity is high due to the sheer number of components and processing conditions, and thus, changing one variable can have multiple unforeseen effects due to their interconnectivity. Design of Experiments (DoE) is ideally suited for such multivariable analyses: by planning one's experiments as per the principles of DoE, one can test and optimize several variables simultaneously, thus accelerating the process of discovery and optimization while saving time and precious laboratory resources. When combined with machine learning, the consideration of one's data in this manner provides a different perspective for optimization and discovery, akin to climbing out of a narrow valley of serial (one-variable-at-a-time) experimentation, to a mountain ridge with a 360° view in all directions.

Discovery of Intermetallic Compounds from Traditional to Machine-Learning Approaches

Intermetallic compounds are bestowed by diverse compositions, complex structures, and useful properties for many materials applications. How metallic elements react to form these compounds and what structures they adopt remain challenging questions that defy predictability. Traditional approaches offer some rational strategies to prepare specific classes of intermetallics, such as targeting members within a modular homologous series, manipulating building blocks to assemble new structures, and filling interstitial sites to create stuffed variants. Because these strategies rely on precedent, they cannot foresee surprising results, by definition. Exploratory synthesis, whether through systematic phase diagram investigations or serendipity, is still essential for expanding our knowledge base. Eventually, the relationships may become too complex for the pattern recognition skills to be reliably or practically performed by humans. Complementing these traditional approaches, new machine-learning approaches may be a viable alternative for materials discovery, not only among intermetallics but also more generally to other chemical compounds. In this Account, we survey our own efforts to discover new intermetallic compounds, encompassing gallides, germanides, phosphides, arsenides, and others. We apply various machine-learning methods (such as support vector machine and random forest algorithms) to confront two significant questions in solid state chemistry. First, what crystal structures are adopted by a compound given an arbitrary composition? Initial efforts have focused on binary equiatomic phases AB, ternary equiatomic phases ABC, and full Heusler phases AB₂C. Our analysis emphasizes the use of real experimental data and places special value on confirming predictions through experiment. Chemical descriptors are carefully chosen through a rigorous procedure called cluster resolution feature selection. Predictions for crystal structures are quantified by evaluating probabilities. Major results include the discovery of RhCd, the first new binary AB compound to be found in over 15 years, with a CsCl-type structure; the connection between "ambiguous" prediction probabilities and the phenomenon of polymorphism, as illustrated in the case of TiFeP (with TiNiSi- and ZrNiAl-type structures); and the preparation of new predicted Heusler phases MRu₂Ga and RuM₂Ga (M = first-row transition metal) that are not obvious candidates. Second, how can the search for materials with desired properties be accelerated? One particular application of strong current interest is thermoelectric materials, which present a particular challenge because their optimum performance depends on achieving a balance of many interrelated physical properties. Making use of a recommendation engine developed by Citrine Informatics, we have identified new candidates for thermoelectric materials, including previously unknown compounds (e.g., TiRu₂Ga with Heusler structure; Mn(Ru_0.4Ge_0.6) with CsCl-type structure) and previously reported compounds but counterintuitive candidates (e.g., Gd₁₂Co₅Bi). An important lesson in these investigations is that the machine-learning models are only as good as the experimental data used to develop them. Thus, experimental work will continue to be necessary to improve the predictions made by machine learning.