Interpretable Machine Learning in Solid-State Chemistry, with Applications to Perovskites, Spinels, and Rare-Earth Intermetallics: Finding Descriptors Using Decision Trees.

Machine-learning methods have exciting potential to aid materials discovery, but their wider adoption can be hindered by the opaqueness of many models. Even if these models are accurate, the inability to understand the basis for the predictions breeds skepticism. Thus, it is imperative to develop machine-learning models that are explainable and interpretable so that researchers can judge for themselves if the predictions are consistent with their own scientific understanding and chemical insight. In this spirit, the sure independence screening and sparsifying operator (SISSO) method was recently proposed as an effective way to identify the simplest combination of chemical descriptors needed to solve classification and regression problems in materials science. This approach uses domain overlap (DO) as the criterion to find the most informative descriptors in classification problems, but sometimes a low score can be assigned to useful descriptors when there are outliers or when samples belonging to a class are clustered in different regions of the feature space. Here, we present a hypothesis that the performance can be improved by implementing decision trees (DT) instead of DO as the scoring function to find the best descriptors. This modified approach was tested on three important structural classification problems in solid-state chemistry: perovskites, spinels, and rare-earth intermetallics. In all cases, the DT scoring gave better features and significantly improved accuracies of ≥0.91 for the training sets and ≥0.86 for the test sets.

Machine-learning prediction of thermal expansion coefficient for perovskite oxides with experimental validation.

Perovskite oxides have been of high-interest and relatively well studied over the last 20 years due to their various applications, specifically for solid oxide fuel cells (SOFCs) and solid oxide electrolysis cells (SOECs). One of the key properties for a perovskite to perform well as a component in SOFCs, SOECs, and other high-temperature applications is its thermal expansion coefficient (TEC). The use of machine learning (ML) to predict material properties has greatly increased over the years and has proven to be a very useful tool for materials screening. The process of synthesizing and testing perovskite oxides is laborious and costly, and the use of physics-based models is often highly computationally expensive. Due to the amount of elements able to be accommodated in the ABO3 structure and the ability for crystallographic mixing in both the A and B-sites, there are a massive amount of possible ABO3 perovskites. In this paper, a ML model for the prediction of the TECs of AA'BB'O3 perovskites is produced and applied to millions of potential compositions resulting in reliable TEC predictions for 150 451 of the compositions.

Ternary Rare-Earth-Metal Nickel Indides RE23Ni7In4 (RE = Gd, Tb, Dy) with Yb23Cu7Mg4-Type Structure.

The ternary rare-earth-metal nickel indides RE23Ni7In4 (RE = Gd, Tb, Dy) were prepared by arc-melting mixtures of the elements followed by annealing at 870 K. They adopt the Yb23Cu7Mg4-type structure (space group P63/mmc, Pearson symbol hP68, Z = 2), as determined by laboratory and synchrotron powder diffraction methods for RE = Gd (a = 9.6435(10) Å, c = 22.118(3) Å) and Tb (a = 9.5695(8) Å, c = 21.983(3) Å), and single-crystal X-ray diffraction methods for RE = Dy (a = 9.533(5) Å, c = 21.890(13) Å). The centrosymmetric Yb23Cu7Mg4-type structure is closely related to the noncentrosymmetric Pr23Ir7Mg4-type structure. Triangular In3 clusters within RE23Ni7In4 represent a rare type of cluster found among metal-rich indides; the reasons for their formation were investigated by density functional theory methods.

Tailorable Indirect to Direct Band-Gap Double Perovskites with Bright White-Light Emission: Decoding Chemical Structure Using Solid-State NMR.

Efficient white-light-emitting single-material sources are ideal for sustainable lighting applications. Though layered hybrid lead-halide perovskite materials have demonstrated attractive broad-band white-light emission properties, they pose a serious long-term environmental and health risk as they contain lead (Pb2+) and are readily soluble in water. Recently, lead-free halide double perovskite (HDP) materials with a generic formula A(I)2B'(III)B″(I)X6 (where A and B are cations and X is a halide ion) have demonstrated white-light emission with improved photoluminescence quantum yields (PLQYs). Here, we present a series of Bi3+/In3+ mixed-cationic Cs2Bi1-xInxAgCl6 HDP solid solutions that span the indirect to direct band-gap modification which exhibit tailorable optical properties. Density functional theory (DFT) calculations indicate an indirect-direct band-gap crossover composition when x > 0.50. These HDP materials emit over the entire visible light spectrum, centered at 600 ± 30 nm with full-width at half maxima of ca. 200 nm upon ultraviolet light excitation and a maximum PLQY of 34 ± 4% for Cs2Bi0.085In0.915AgCl6. Short-range structural insight for these materials is crucial to unravel the unique atomic-level structural properties which are difficult to distinguish by diffraction-based techniques. Hence, we demonstrate the advantage of using solid-state nuclear magnetic resonance (NMR) spectroscopy to deconvolute the local structural environments of these mixed-cationic HDPs. Using ultrahigh-field (21.14 T) NMR spectroscopy of quadrupolar nuclei (115In, 133Cs, and 209Bi), we show that there is a high degree of atomic-level B'(III)/B″(I) site ordering (i.e., no evidence of antisite defects). Furthermore, a combination of XRD, NMR, and DFT calculations was used to unravel the complete atomic-level random Bi3+/In3+ cationic mixing in Cs2Bi1-xInxAgCl6 HDPs. Briefly, this work provides an advance in understanding the photophysical properties that correlate long- to short-range structural elucidation of these newly developed solid-state white-light emitting HDP materials.

Significant Variability in the Photocatalytic Activity of Natural Titanium-Containing Minerals: Implications for Understanding and Predicting Atmospheric Mineral Dust Photochemistry.

The billions of tons of mineral dust released into the atmosphere each year provide an important surface for reaction with gas-phase pollutants. These reactions, which are often enhanced in the presence of light, can change both the gas-phase composition of the atmosphere and the composition and properties of the dust itself. Because dust contains titanium-rich grains, studies of dust photochemistry have largely employed commercial titanium dioxide as a proxy for its photochemically active fraction; to date, however, the validity of this model system has not been empirically determined. Here, for the first time, we directly investigate the photochemistry of the complement of natural titanium-containing minerals most relevant to mineral dust, including anatase, rutile, ilmenite, titanite, and several titanium-bearing species. Using ozone as a model gas-phase pollutant, we show that titanium-containing minerals other than titanium dioxide can also photocatalyze trace gas uptake, that samples of the same mineral phase can display very different reactivity, and that prediction of dust photoreactivity based on elemental/mineralogical analysis and/or light-absorbing properties is challenging. Together, these results show that the photochemistry of atmospheric dust is both richer and more complex than previously considered, and imply that a full understanding of the scope and impact of dust-mediated processes will require the community to engage with this complexity via the study of ambient mineral dust samples from diverse source regions.

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(Ru0.4Ge0.6) 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.

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.

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, ZrAu0.5Os0.5 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.

Machine Learning Directed Search for Ultraincompressible, Superhard Materials.

In the pursuit of materials with exceptional mechanical properties, a machine-learning model is developed to direct the synthetic efforts toward compounds with high hardness by predicting the elastic moduli as a proxy. This approach screens 118 287 compounds compiled in crystal structure databases for the materials with the highest bulk and shear moduli determined by support vector machine regression. Following these models, a ternary rhenium tungsten carbide and a quaternary molybdenum tungsten borocarbide are selected and synthesized at ambient pressure. High-pressure diamond anvil cell measurements corroborate the machine-learning prediction of the bulk modulus with less than 10% error, as well as confirm the ultraincompressible nature of both compounds. Subsequent Vickers microhardness measurements reveal that each compound also has an extremely high hardness exceeding the superhard threshold of 40 GPa at low loads (0.49 N). These results show the effectiveness of materials development through state-of-the-art machine-learning techniques by identifying functional inorganic materials.

Polyanionic Gold-Tin Bonding and Crystal Structure Preference in REAu1.5Sn0.5 (RE = La, Ce, Pr, Nd).

During a systematic search of the RE-Au-Sn (RE = La, Ce, Pr, Nd) ternary phase space, a series of compounds with the general formula REAu1.5Sn0.5 have been identified. These phases can be synthesized by arc melting the elemental metals, followed by annealing. The crystal structures were solved using single-crystal X-ray diffraction, with the composition confirmed by energy-dispersive X-ray spectroscopy. All four compounds crystallize in orthorhombic space group Imma with the CeCu2-type structure. Most notable in these compounds is the polyanionic backbone composed of a single statistically mixed Au/Sn position, which creates a puckered hexagonal bonding network separated by the rare-earth atoms. Electronic structure calculations indicate that the Au 5d bands are dominant in the density of states, while the crystal orbital Hamilton population (-COHP) curves demonstrate Au-Au and Au-Sn interactions, which stabilize the crystal structure. Likewise, a qualitative electron localization function analysis supports the existence of a polyanionic network, and a Bader charge analysis implies anionic character on Au and Sn. The preference for these compounds to adopt the simple CeCu2-type structure is also determined using density functional theory calculations and compared to related compounds to establish a better picture of the unusual behavior of Au in polar intermetallic compounds.

Searching for Missing Binary Equiatomic Phases: Complex Crystal Chemistry in the Hf-In System.

There remain 21 systems (out of over 3500 possible combinations of the elements) in which the existence of the simple binary equiatomic phases AB has not been established experimentally. Among these, the presumed binary phase HfIn is predicted to adopt the tetragonal CuAu-type structure (space group P4/ mmm) by a recently developed machine-learning model and by structure optimization through global energy minimization. To test this prediction, the Hf-In system was investigated experimentally by reacting the elements in a 1:1 stoichiometry at 1070 K. Under the conditions investigated, the bulk and surface of the sample correspond to different crystalline phases but have nearly the same equiatomic composition, as revealed by energy-dispersive X-ray analysis. The structure of the bulk sample, which was solved from powder X-ray diffraction data through simulated annealing, corresponds to the γ-brass (Cu5Zn8) type (space group I4̅3 m) with Hf and In atoms disordered over four sites. The structure of crystals selected from the surface, which was solved using single-crystal X-ray diffraction data, corresponds to the CuPt7 type (space group Fm3̅ m) with Hf and In atoms partially disordered over three sites. The discrepancy between the predicted CuAu-type structure and the two experimentally refined crystal structures is reconciled through close inspection of structural relationships, which reveal that the γ-brass-type structure of the bulk HfIn phase is indeed derived through small distortions and defect formation within the CuAu-type structure.

Not Just Par for the Course: 73 Quaternary Germanides RE4 M2 XGe4 ( RE = La-Nd, Sm, Gd-Tm, Lu; M = Mn-Ni; X = Ag, Cd) and the Search for Intermetallics with Low Thermal Conductivity.

A total of 73 new quaternary rare-earth germanides RE4 M2 XGe4 ( RE = rare-earth metal; M = Mn-Ni; X = Ag, Cd) were prepared through reactions of the elements. The solid solution Nd4Mn2Cd(Ge1- ySi y)4 was also prepared under the same conditions and found to be complete over the entire range. All of these compounds adopt the monoclinic Ho4Ni2InGe4-type structure (space group C2/ m, a = 14.2-16.7 Å, b = 4.0-4.6 Å, c = 6.8-7.5 Å, ß = 106-109°), as revealed by powder X-ray diffraction analysis and single-crystal X-ray diffraction analysis on selected members. The structure determination of Nd4(Mn0.78(1)Ag0.22(1))2Ag0.83(1)Ge4 disclosed disorder of Mn and Ag atoms within the tetrahedral site and Ag deficiencies within the square planar site. Within the solid solution Nd4Mn2Cd(Ge1- ySi y)4, the end-members and two intermediate members were structurally characterized; as the Si content increases, the Cd sites become less deficient and the individual [Mn2 Tt2] layers contract but become further apart from each other. Electronic band structure calculations confirm that the Ag-Ge or Cd-Ge bonds are the weakest in the structure and thus prone to distortion. Thermal property measurements confirm expectations from machine-learning predictions that these quaternary germanides should exhibit low thermal conductivity, which was found to be <10 W m-1 K-1 for Nd4Mn2AgGe4.

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

A method to predict the crystal structure of equiatomic ternary compositions based only on the constituent elements was developed using cluster resolution feature selection (CR-FS) and support vector machine (SVM) classification. The supervised machine-learning model was first trained with 1037 individual compounds that adopt the most populated ternary 1:1:1 structure types (TiNiSi-, ZrNiAl-, PbFCl-, LiGaGe-, YPtAs-, UGeTe-, and LaPtSi-type) and then validated using an additional 519 compounds. The CR-FS algorithm improves class discrimination and indicates that 113 variables including size, electronegativity, number of valence electrons, and position on the periodic table (group number) influence the structure preference. The final model prediction sensitivity, specificity, and accuracy were 97.3%, 93.9%, and 96.9%, respectively, establishing that this method is capable of reliably predicting the crystal structure given only its composition. The power of CR-FS and SVM classification is further demonstrated by segregating the crystal structure of polymorphs, specifically to examine polymorphism in TiNiSi- and ZrNiAl-type structures. Analyzing 19 compositions that are experimentally reported in both structure types, this machine-learning model correctly identifies, with high confidence (>0.7), the low-temperature polymorph from its high-temperature form. Interestingly, machine learning also reveals that certain compositions cannot be clearly differentiated and lie in a "confused" region (0.3-0.7 confidence), suggesting that both polymorphs may be observed in a single sample at certain experimental conditions. The ensuing synthesis and characterization of TiFeP adopting both TiNiSi- and ZrNiAl-type structures in a single sample, even after long annealing times (3 months), validate the occurrence of the region of structural uncertainty predicted by machine learning.

Gd12Co5.3Bi and Gd12Co5Bi, Crystalline Doppelgänger with Low Thermal Conductivities.

Attempts to prepare Gd12Co5Bi, a member of the rare-earth (RE) intermetallics RE12Co5Bi, which were identified by a machine-learning recommendation engine as potential candidates for thermoelectric materials, led instead to formation of the new compound Gd12Co5.3Bi with a very similar composition. Phase equilibria near the Gd-rich corner of the Gd-Co-Bi phase diagram were elucidated by both lab-based and variable-temperature synchrotron powder X-ray diffraction, suggesting that Gd12Co5.3Bi and Gd12Co5Bi are distinct phases. The higher symmetry structure of Gd12Co5.3Bi (cubic, space group Im3̅, Z = 2, a = 9.713(6) Å), as determined from single-crystal X-ray diffraction, is closely related to that of Gd12Co5Bi (tetragonal, space group Immm). Single Co atoms and Co-Co dumbbells are disordered with occupancies of 0.78(2) and 0.22(2), respectively, in Gd12Co5.3Bi, but they are ordered in Gd12Co5Bi. Consistent with this disorder, the electrical resistivity shows less dependence on temperature for Gd12Co5.3Bi than for Gd12Co5Bi. The thermal conductivity is low and reaches 2.8 W m(-1) K(-1) at 600 °C for both compounds; however, the temperature dependence of the thermal conductivity differs, decreasing for Gd12Co5.3Bi and increasing for Gd12Co5Bi as the temperature increases. The unusual trends in thermal properties persist in the heat capacity, which decreases below 2R, and in the thermal diffusivity, which increases at higher temperatures.

Many metals make the cut: quaternary rare-earth germanides RE4M2InGe4 (M = Fe, Co, Ni, Ru, Rh, Ir) and RE4RhInGe4 derived from excision of slabs in RE2InGe2.

The formation of quaternary rare-earth (RE) germanides containing transition metals (M's) from groups 6 to 10 was investigated through arc-melting and annealing reactions at 800 °C; about 50 new compounds were obtained. These include several new series of quaternary germanides RE4M2InGe4 (M = Fe, Co, Ru, Rh, Ir), previously known only for M = Mn and Ni; additional members of RE4Ni2InGe4 extended to other RE substituents; and a different but closely related series RE4RhInGe4. Detailed crystal structures were determined by single-crystal X-ray diffraction studies for 20 compounds. Monoclinic structures in space group C2/m are adopted by RE4M2InGe4 (Ho4Ni2InGe4-type, a = 15.1-16.5 Å, b = 4.1-4.4 Å, c = 6.9-7.3 Å, ß = 106.2-108.6°) and RE4RhInGe4 (own type, a = 20.0-20.2 Å, b = 4.2-4.3 Å, c = 10.1-10.2 Å, ß = 105.0-105.3°). Both structures contain frameworks built from MGe4 tetrahedra, InGe4 square planes, and Ge2 dimers, delimiting tunnels occupied by RE atoms. These structures can also be derived by cutting slabs along different directions from the more symmetrical RE2InGe2 structure. Although the Ge2 dimers are relatively invariant, the InGe4 square planes can undergo distortion to form two sets of short versus long In-Ge distances. This distortion results from a competition between M-Ge bonding in the MGe4 tetrahedra and In-Ge bonding in the InGe4 square planes.

Quaternary germanides RE4Mn2InGe4 (RE = La-Nd, Sm, Gd-Tm, Lu).

The quaternary germanides RE4Mn2InGe4 (RE = La-Nd, Sm, Gd-Tm, Lu) have been prepared by arc-melting reactions of the elements and annealing at 800 °C and represent the second example of the RE4M2InGe4 series previously known only for M = Ni. Single-crystal X-ray diffraction studies conducted on the earlier RE members of RE4Mn2InGe4 confirmed that they adopt the monoclinic Ho4Ni2InGe4-type structure [space group C2/m, a = 16.646(2)-15.9808(9) Å, b = 4.4190(6)-4.2363(2) Å, c = 7.4834(10)-7.1590(4) Å, ß = 106.893(2)-106.304(1)° in the progression of RE from La to Gd]. The covalent framework contains Mn-centered tetrahedra and Ge2 dimers that build up [Mn2Ge4] layers, which are held weakly together by four-coordinate In atoms and outline tunnels filled by the RE atoms. This bonding picture is supported by band-structure calculations. An alternative description based on Ge-centered trigonal prisms reveals that RE4Mn2InGe4 is closely related to RE2InGe2. The electrical resistivity behavior of Pr4Mn2InGe4 is similar to that of Pr2InGe2.

Phase equilibria in the Mo-Fe-P system at 800 °C and structure of ternary phosphide (Mo(1-x)Fe(x))3P (0.10 ≤ x ≤ 0.15).

Construction of the isothermal section in the metal-rich portion (<67 atom % P) of the Mo-Fe-P phase diagram at 800 °C has led to the identification of two new ternary phases: (Mo(1-x)Fe(x))(2)P (x = 0.30-0.82) and (Mo(1-x)Fe(x))(3)P (x = 0.10-0.15). The occurrence of a Co(2)Si-type ternary phase (Mo(1-x)Fe(x))(2)P, which straddles the equiatomic composition MoFeP, is common to other ternary transition-metal phosphide systems. However, the ternary phase (Mo(1-x)Fe(x))(3)P is unusual because it is distinct from the binary phase Mo(3)P, notwithstanding their similar compositions and structures. The relationship has been clarified through single-crystal X-ray diffraction studies on Mo(3)P (α-V(3)S-type, space group I42m, a = 9.7925(11) Å, c = 4.8246(6) Å) and (Mo(0.85)Fe(0.15))(3)P (Ni(3)P-type, space group I4, a = 9.6982(8) Å, c = 4.7590(4) Å) at -100 °C. Representation in terms of nets containing fused triangles provides a pathway to transform these closely related structures through twisting. Band structure calculations support the adoption of these structure types and the site preference of Fe atoms. Electrical resistivity measurements on (Mo(0.85)Fe(0.15))(3)P reveal metallic behavior but no superconducting transition.

Finding the Next Superhard Material through Ensemble Learning.

An ensemble machine-learning method is demonstrated to be capable of finding superhard materials by directly predicting the load-dependent Vickers hardness based only on the chemical composition. A total of 1062 experimentally measured load-dependent Vickers hardness data are extracted from the literature and used to train a supervised machine-learning algorithm utilizing boosting, achieving excellent accuracy (R2  = 0.97). This new model is then tested by synthesizing and measuring the load-dependent hardness of several unreported disilicides and analyzing the predicted hardness of several classic superhard materials. The trained ensemble method is then employed to screen for superhard materials by examining more than 66 000 compounds in crystal structure databases, which show that 68 known materials have a Vickers hardness ≥40 GPa at 0.5 N (applied force) and only 10 exceed this mark at 5 N. The hardness model is then combined with the data-driven phase diagram generation tool to expand the limited number of reported high hardness compounds. Eleven ternary borocarbide phase spaces are studied, and more than ten thermodynamically favorable compositions with a hardness above 40 GPa (at 0.5 N) are identified, proving this ensemble model's ability to find previously unknown materials with outstanding mechanical properties.

Dehydrocoupling - an alternative approach to functionalizing germanium nanoparticle surfaces.

Surface functionalization is an essential aspect of nanoparticle design and preparation; it can impart stability, processability, functionality, as well as tailor optoelectronic properties that facilitate future applications. Herein we report a new approach toward modifying germanium nanoparticle (GeNP) surfaces and for the first time tether alkyl chains to the NP surfaces through Si-Ge bonds. This was achieved via heteronuclear dehydrocoupling reactions involving alkylsilanes and Ge-H moieties on the NP surfaces. The resulting solution processable RR'2Si-GeNPs (R = octadecyl or PDMS; R' = H or CH3) were characterized using FTIR, Raman, 1H-NMR, XRD, TEM, HAADF, and EELS and were found to retain the crystallinity of the parent GeNP platform.

Alkaline Earth Metal-Organic Frameworks with Tailorable Ion Release: A Path for Supporting Biomineralization.

An innovative application of metal-organic frameworks (MOFs) is in biomedical materials. To treat bone demineralization, which is a hallmark of osteoporosis, biocompatible MOFs (bioMOFs) have been proposed in which various components, such as alkaline-earth cations and bisphosphonate molecules, can be delivered to maintain normal bone density. Multicomponent bioMOFs that release several components simultaneously at a controlled rate thus offer an attractive solution. We report two new bioMOFs, comprising strontium and calcium ions linked by p-xylylenebisphosphonate molecules that release these three components and display no cytotoxic effects on human osteosarcoma cells. Varying the Sr2+/Ca2+ ratio in these bioMOFs causes the rate of ions dissolving into simulated body fluid to be unique; along with the ability to adsorb proteins, this property is crucial for future efforts in drug-release control and promotion of mineral formation. The one-pot synthesis of these bioMOFs demonstrates the utility of MOF design strategies.