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Computational exploration of the compositional spaces of materials can provide guidance for synthetic research and thus accelerate the discovery of novel materials. Most approaches employ high-throughput sampling and focus on reducing the time for energy evaluation for individual compositions, often at the cost of accuracy. Here, we present an alternative approach focusing on effective sampling of the compositional space. Learning algorithm PhaseBO optimizes the stoichiometry of the potential target material and accelerates its discovery without compromising the accuracy of energy evaluation.

Clustering is a common task in machine learning, but clusters of unlabelled data can be hard to quantify. The application of clustering algorithms in chemistry is often dependant on material representation. Ascertaining the effects of different representations, clustering algorithms, or data transformations on the resulting clusters is difficult due to the dimensionality of these data. We present a thorough analysis of measures for isotropy of a cluster, including a novel implantation based on an existing derivation. Using fractional anisotropy, a common method used in medical imaging for comparison, we then expand these measures to examine the average isotropy of a set of clusters. A use case for such measures is demonstrated by quantifying the effects of kernel approximation functions on different representations of the Inorganic Crystal Structure Database. Broader applicability of these methods is demonstrated in analysing learnt embedding of the MNIST dataset. Random clusters are explored to examine the differences between isotropy measures presented, and to see how each method scales with the dimensionality. Python implementations of these measures are provided for use by the community., Comment: 31 pages, 6 figures

Fundamental differences between materials originate from the unique nature of their constituent chemical elements. Before specific differences emerge according to the precise ratios of elements in a given crystal structure, a material can be represented by the set of its constituent chemical elements. By working at the level of the periodic table, assessment of materials at the level of their phase fields reduces the combinatorial complexity to accelerate screening, and circumvents the challenges associated with composition-level approaches such as poor extrapolation within phase fields, and the impossibility of exhaustive sampling. This early stage discrimination combined with evaluation of novelty of phase fields aligns with the outstanding experimental challenge of identifying new areas of chemistry to investigate, by prioritising which elements to combine in a reaction. Here, we demonstrate that phase fields can be assessed with respect to the maximum expected value of a target functional property and ranked according to chemical novelty. We develop and present PhaseSelect, an end-to-end machine learning model that combines the representation, classification, regression and ranking of phase fields. First, PhaseSelect constructs elemental characteristics from the co-occurrence of chemical elements in computationally and experimentally reported materials, then it employs attention mechanisms to learn representation for phase fields and assess their functional performance. At the level of the periodic table, PhaseSelect quantifies the probability of observing a functional property, estimates its value within a phase field and also ranks a phase field novelty, which we demonstrate with significant accuracy for three avenues of materials applications for high-temperature superconductivity, high-temperature magnetism, and targeted bandgap energy.

The structures of Zr and Hf metal-organic frameworks (MOFs) are very sensitive to small changes in synthetic conditions. One key difference affecting the structure of UiO MOF phases is the shape and nuclearity of Zr or Hf metal clusters acting as nodes in the framework; although these clusters are crucial, their evolution during MOF synthesis is not fully understood. In this paper, we explore the nature of Hf metal clusters that form in different reaction solutions, including in a mixture of DMF, formic acid, and water. We show that the choice of solvent and reaction temperature in UiO MOF syntheses determines the cluster identity and hence the MOF structure. Using in situ X-ray pair distribution function measurements, we demonstrate that the evolution of different Hf cluster species can be tracked during UiO MOF synthesis, from solution stages to the full crystalline framework, and use our understanding to propose a formation mechanism for the hcp UiO-66(Hf) MOF, in which first the metal clusters aggregate from the M6 cluster (as in fcu UiO-66) to the hcp-characteristic M12 double cluster and, following this, the crystalline hcp framework forms. These insights pave the way toward rationally designing syntheses of as-yet unknown MOF structures, via tuning the synthesis conditions to select different cluster species.

International audience; Neutron diffraction and X-ray pair distribution function (XPDF) experiments were performed in order to investigate the magnetic and local crystal structures of Ba2FeSbSe5 and to compare them to the average (i.e. long-range) structural model, previously obtained by single crystal X-ray diffraction. Changes in the local crystal structure (i.e. in the second coordination sphere) are observed upon cooling from 295 K to 95 K resulting in deviations from the average (i.e. longrange) crystal structure. This work demonstrates, that these observations cannot be explained by local or long-range magnetoelastic effects involving Fe-Fe correlations. Instead, we found, that the observed differences between local and average crystal structure can be explained by Sb-5s lone pair dynamics. We also find, that below the Néel temperature (TN = 58 K), the two distinct magnetic Fe 3+ sites order collinearly, such that a combination of antiparallel and parallel spin arrangements along the b-axis results. The nearest-neighbor arrangement (J1 = 6 Å) is fully antiferromagnetic, while next-nearest-neighbor interactions are ferromagnetic in nature.

Following the recent discovery of a new family of hybrid ABX3 perovskites where X=(H2 POO)- (hypophosphite), this work reports a facile synthesis for mixed X-site formate perovskites of composition [GUA]Mn(HCOO)3-x (H2 POO)x , with two crystallographically distinct, partially ordered intermediate phases with x=0.84 and 1.53, corresponding to ca. 30 and 50 mol % hypophosphite, respectively. These phases are characterised by single-crystal XRD and solid-state NMR spectroscopy, and their magnetic properties are reported.

We report a hafnium-containing MOF, hcp UiO-67(Hf), which is a ligand-deficient layered analogue of the face-centered cubic fcu UiO-67(Hf). hcp UiO-67 accommodates its lower ligand:metal ratio compared to fcu UiO-67 through a new structural mechanism: the formation of a condensed “double cluster” (Hf12O8(OH)14), analogous to the condensation of coordination polyhedra in oxide frameworks. In oxide frameworks, variable stoichiometry can lead to more complex defect structures, e.g., crystallographic shear planes or modules with differing compositions, which can be the source of further chemical reactivity; likewise, the layered hcp UiO-67 can react further to reversibly form a two-dimensional metal–organic framework, hxl UiO-67. Both three-dimensional hcp UiO-67 and two-dimensional hxl UiO-67 can be delaminated to form metal–organic nanosheets. Delamination of hcp UiO-67 occurs through the cleavage of strong hafnium-carboxylate bonds and is effected under mild conditions, suggesting that defect-ordered MOFs could be a productive route to porous two-dimensional materials.

Motivated by the famous and pioneering mathematical works by Perelman, Hamilton, and Thurston, we introduce the concept of using modern geometrical mathematical classifications of multi-dimensional manifolds to characterize electronic structures and predict non-trivial electron transport phenomena. Here we develop the Fermi Surface Geometry Effect (FSGE), using the concepts of tangent bundles and Gaussian curvature as an invariant. We develop an index, $\mathbb{H}_F$, for describing the the "hyperbolicity" of the Fermi Surface (FS) and show a universal correlation (R$^2$ = 0.97) with the experimentally measured intrinsic anomalous Hall effect of 16 different compounds spanning a wide variety of crystal, chemical, and electronic structure families, including where current methods have struggled. This work lays the foundation for developing a complete theory of geometrical understanding of electronic (and by extension magnonic and phononic) structure manifolds, beginning with Fermi surfaces. In analogy to the broad impact of topological physics, the concepts begun here will have far reaching consequences and lead to a paradigm shift in the understanding of electron transport, moving it to include geometrical properties of the E vs k manifold as well as topological properties., Comment: 9 pages, 4 figures

Low-dimensional magnetic materials with spin-12 moments can host a range of exotic magnetic phenomena due to the intrinsic importance of quantum fluctuations to their behavior. Here, we report the structure, magnetic structure and magnetic properties of copper(II) thiocyanate, Cu(NCS)2, a one-dimensional coordination polymer which displays low-dimensional quantum magnetism. Magnetic susceptibility, electron paramagnetic resonance (EPR) spectroscopy, 13C magic-angle spinning nuclear magnetic resonance (MASNMR) spectroscopy, and density functional theory (DFT) investigations indicate that Cu(NCS)2 behaves as a two-dimensional array of weakly coupled antiferromagnetic spin chains (J2=133(1) K, ?=J1/J2=0.08). Powder neutron-diffraction measurements confirm that Cu(NCS)2 orders as a commensurate antiferromagnet below TN=12 K, with a strongly reduced ordered moment (0.3 ?B) due to quantum fluctuations.

Carbon capture and storage (CCS) offers a possible solution to curb the CO2 emissions from stationary sources in the coming decades, considering the delays in shifting energy generation to carbon neutral sources such as wind, solar and biomass. The most mature technology for post-combustion capture uses a liquid sorbent, amine scrubbing. However, with the existing technology, a large amount of heat is required for the regeneration of the liquid sorbent, which introduces a substantial energy penalty. The use of alternative sorbents for CO2 capture, such as the CaO-CaCO3 system, has been investigated extensively in recent years. However there are significant problems associated with the use of CaO based sorbents, the most challenging one being the deactivation of the sorbent material. When sorbents such as natural limestone are used, the capture capacity of the solid sorbent can fall by as much as 90 mol% after the first 20 carbonation-regeneration cycles. In this study a variety of techniques were employed to understand better the cause of this deterioration from both a structural and morphological standpoint. X-ray and neutron PDF studies were employed to understand better the local surface and interfacial structures formed upon reaction, finding that after carbonation the surface roughness is decreased for CaO. In situ synchrotron X-ray diffraction studies showed that carbonation with added steam leads to a faster and more complete conversion of CaO than under conditions without steam, as evidenced by the phases seen at different depths within the sample. Finally, in situ X-ray tomography experiments were employed to track the morphological changes in the sorbents during carbonation, observing directly the reduction in porosity and increase in tortuosity of the pore network over multiple calcination reactions.

We report a hafnium-containing MOF, hcp UiO-67(Hf), which is a ligand-deficient layered analogue of the face-centered cubic fcu UiO-67(Hf). hcp UiO-67 accommodates its lower ligand:metal ratio compared to fcu UiO-67 through a new structural mechanism: the formation of a condensed “double cluster” (Hf12O8(OH)14), analogous to the condensation of coordination polyhedra in oxide frameworks. In oxide frameworks, variable stoichiometry can lead to more complex defect structures, e.g., crystallographic shear planes or modules with differing compositions, which can be the source of further chemical reactivity; likewise, the layered hcp UiO-67 can react further to reversibly form a two-dimensional metal–organic framework, hxl UiO-67. Both three-dimensional hcp UiO-67 and two-dimensional hxl UiO-67 can be delaminated to form metal–organic nanosheets. Delamination of hcp UiO-67 occurs through the cleavage of strong hafnium-carboxylate bonds and is effected under mild conditions, suggesting that defect-ordered MOFs could be a productive route to porous two-dimensional materials.

The experimental search for new thermoelectric materials remains largely confined to a limited set of successful chemical and structural families, such as chalcogenides, skutterudites, and Zintl phases. In principle, computational tools such as density functional theory (DFT) offer the possibility of rationally guiding experimental synthesis efforts toward very different chemistries. However, in practice, predicting thermoelectric properties from first principles remains a challenging endeavor, and experimental researchers generally do not directly use computation to drive their own synthesis efforts. To bridge this practical gap between experimental needs and computational tools, we report an open machine learning-based recommendation engine (http://thermoelectrics.citrination.com) for materials researchers that suggests promising new thermoelectric compositions, and evaluates the feasibility of user-designed compounds. We show that this engine can identify interesting chemistries very different from known thermoelectrics. Specifically, we describe the experimental characterization of one example set of compounds derived from our engine, RE12Co5Bi (RE = Gd, Er), which exhibits surprising thermoelectric performance given its unprecedentedly high loading with metallic d and f block elements, and warrants further investigation as a new thermoelectric material platform., 8 pages, 4 figures

A structural phase transition from cubic $Fd\bar{3}m$ to tetragonal $I$4$_1$/$amd$ symmetry with $c/a >$ 1 is observed at $T_{\rm{S}}$ = 16 K in spinel GeCo$_2$O$_4$ below the N\'eel temperature $T_N$ = 21 K. Structural and magnetic ordering appear to be decoupled with the structural distortion occurring at 16 K while magnetic order occurs at 21 K as determined by magnetic susceptibility and heat capacity measurements. An elongation of CoO$_6$ octahedra is observed in the tetragonal phase of GeCo$_2$O$_4$. We present the complete crystallographic description of GeCo$_2$O$_4$ in the tetragonal $I$4$_1$/$amd$ space group and discuss the possible origin of this distortion in the context of known structural transitions in magnetic spinels. GeCo$_2$O$_4$ exhibits magnetodielectric coupling below $T_{\rm{N}}$. The related spinels GeFe$_2$O$_4$ and GeNi$_2$O$_4$ have also been examined for comparison. Structural transitions were not detected in either compound down to $T \approx$ 8 K. Magnetometry experiments reveal in GeFe$_2$O$_4$ a second antiferromagnetic transition, with $T_{\rm{N1}}$ = 7.9 K and $T_{\rm{N2}}$ = 6.2 K, that was previously unknown, and that bear a similarity to the magnetism of GeNi$_2$O$_4$.

A structural phase transition from cubic $Fd\bar{3}m$ to tetragonal $I$4$_1$/$amd$ symmetry with $c/a >$ 1 is observed at $T_{\rm{S}}$ = 16 K in spinel GeCo$_2$O$_4$ below the N��el temperature $T_N$ = 21 K. Structural and magnetic ordering appear to be decoupled with the structural distortion occurring at 16 K while magnetic order occurs at 21 K as determined by magnetic susceptibility and heat capacity measurements. An elongation of CoO$_6$ octahedra is observed in the tetragonal phase of GeCo$_2$O$_4$. We present the complete crystallographic description of GeCo$_2$O$_4$ in the tetragonal $I$4$_1$/$amd$ space group and discuss the possible origin of this distortion in the context of known structural transitions in magnetic spinels. GeCo$_2$O$_4$ exhibits magnetodielectric coupling below $T_{\rm{N}}$. The related spinels GeFe$_2$O$_4$ and GeNi$_2$O$_4$ have also been examined for comparison. Structural transitions were not detected in either compound down to $T \approx$ 8 K. Magnetometry experiments reveal in GeFe$_2$O$_4$ a second antiferromagnetic transition, with $T_{\rm{N1}}$ = 7.9 K and $T_{\rm{N2}}$ = 6.2 K, that was previously unknown, and that bear a similarity to the magnetism of GeNi$_2$O$_4$.

The fast and affordable development of novel materials is needed in order to enable technological advancements in application areas such as clean energy, healthcare, sustainable transport, and climate-friendly consumption. However, the development of novel materials is not a trivial task. One of the biggest challenges in materials design and discovery is the enormous search space of possible material compositions available, also referred to as the “chemical whitespace”. Faced with the high risk, high reward nature of materials exploration, materials scientists have increasingly moved away from traditional trial and error methods and instead adapted new data-driven methods of materials discovery. The rapid development of data science, machine learning (ML), and deep learning (DL) as well as the influx of high-quality materials property datasets have led to the development of the new field of materials informatics (MI). This new paradigm has drastically changed the way in which materials are understood, predicted, discovered, and designed. Despite promising developments in this relatively young field, there are several open issues that need to be addressed. The lack of guidelines and established procedures to ensure high quality research in MI impedes the pace of further development in this field. Furthermore, the current techniques for representing and modeling chemical compositions are flawed and unsuitable to be used in the search of novel materials. Lastly, the prevalence of black-box DL models without model interpretability limits the trust and adoption of these models in academia and industry. Accordingly, the main aims of this work are (1) to propose a set of best practices and protocols for conducting and reporting MI studies, and (2) to improve the state of the art in materials property predictions by introducing interpretable DL techniques for representing and modeling chemical compounds. In the first work described in this thesis, the fundamental ideas and considerations of using data-driven methods for materials science are introduced. A broad set of guidelines and protocols for ensuring the reliable, reproducible, and comparable reporting of research results in MI studies is established. Common software tools, methodologies, and materials data repositories are presented. Lastly, the full procedure of an ML study including data processing, feature engineering, model training, evaluation and comparison is demonstrated using the prediction of heat capacity for solid inorganic compounds as an example. In the second work, a novel DL model named “Compositionally Restricted Attention-Based network” (CrabNet), based on the Transformer self-attention mechanism, is introduced. CrabNet is benchmarked on 28 materials property datasets and is shown to match or exceed state-of-the-art models in the prediction of inorganic material properties. The benefits of learning element-element interactions within chemical compounds using the self-attention mechanism are discussed. Furthermore, a new way of representing chemical composition which overcomes some of the limitations present in current techniques is developed. Lastly, the opportunities to study model interpretability methods in CrabNet are previewed. Continuing in the third work described in this thesis, the model interpretability of CrabNet is further examined. Intrinsic model interpretability methods are added to CrabNet and used to extract additional information about the model and data representations during the modeling process. The extracted information is processed and visualized into static and interactive figures as well as video animations. The examination of these visualizations and additional information reveals well-known chemical patterns about the elements and compounds, intuitively suggesting that CrabNet is able to learn the element properties, element interactions, and how they together dictate materials properties. Furthermore, the dataset quality as well as the self-attention mechanism are also discussed for their significance towards an improved and interpretable modeling of materials properties. Lastly, the potential benefits of applying interpretable modeling methods in academia and industry are discussed. Overall, the methods, results, and considerations discussed in this dissertation are presented in a way to educate and empower interested materials science researchers to undertake their own materials informatics research. Die schnelle und erschwingliche Entwicklung neuartiger Materialien wird benötigt, um technologische Fortschritte in Anwendungsbereichen wie der sauberen Energie, dem Gesundheitswesen, dem nachhaltiger Verkehr und dem klimafreundlichen Konsum zu ermöglichen. Die Entwicklung neuartiger Materialien ist jedoch keine triviale Aufgabe. Eine der größten Herausforderungen bei Materialdesign und -entdeckung ist der enorme Suchraum möglicher Materialzusammensetzungen, der auch als „chemical whitespace“ bezeichnet wird. Angesichts der risikointensiven aber aussichtsreichen Natur der Materialerforschung ziehen Materialwissenschaftler zunehmend von herkömmlichen Versuchs-und-Irrtums- Methoden weg und adaptieren stattdessen neue datengetriebene Methoden der Materialentdeckung. Die schnelle Entwicklung von Data Science, maschinellem Lernen (ML) und Deep Learning (DL) sowie der Zustrom hochwertiger Materialdatensätze haben zu der Entwicklung des neuen Gebiets der Materialinformatik (MI) geführt. Dieses neue Paradigma hat die Art und Weise mit der Materialien verstanden, vorhergesagt, entdeckt und entworfen werden drastisch verändert. Trotz vielversprechender Entwicklungen in diesem relativ neuen Bereich gibt es mehrere offene Probleme, die behoben werden müssen. Der Mangel an Richtlinien und etablierten Verfahren zur Gewährleistung hochwertiger Forschung in der MI behindert das Tempo der Weiterentwicklung in diesem Bereich. Darüber hinaus sind die derzeitigen Techniken zur Darstellung und Modellierung chemischer Zusammensetzungen fehlerhaft und ungeeignet, um bei der Suche nach neuartigen Materialien verwendet zu werden. Schließlich begrenzt die Prävalenz von Black-Box-DL-Modellen ohne Modellinterpretierbarkeit das Vertrauen und die Akzeptanz dieser Modelle in der Wissenschaft und Industrie. Dementsprechend sind die Hauptziele dieser Arbeit (1) einen Satz bewährter Verfahren und Protokolle zur Durchführung und Berichterstellung von MI-Studien vorzuschlagen und (2) den Stand der Technik in der Vorhersage von Materialeigenschaften durch die Einführung von interpretierbaren DL-Techniken zur Darstellung und Modellierung chemischer Verbindungen zu verbessern. In der ersten in dieser Dissertation beschriebenen Arbeit werden die grundlegenden Ideen und Überlegungen zur Verwendung von datengetriebenen Methoden für die Materialwissenschaft eingeführt. Eine breite Reihe von Richtlinien und Protokollen, um die zuverlässige, reproduzierbare und vergleichbare Berichterstattung von Forschungsergebnissen in MI-Studien zu gewährleisten, wird etabliert. Gängige Software-Tools, Methoden und Repositorien für Materialdaten werden dargestellt. Schließlich wird das vollständige Verfahren einer ML-Studie für die Vorhersage der Wärmekapazität fester anorganischer Verbindungen, einschließlich Datenverarbeitung, Feature Engineering, Modelltraining, -auswertung und -vergleich, als Beispiel gezeigt. In der zweiten Arbeit wird ein neuartiges DL-Modell namens „Compositionally Restricted Attention-Based network“ (CrabNet), basierend auf dem Transformer Self- Attention-Mechanismus, eingeführt. CrabNet wird anhand von 28 Materialdatensätzen evaluiert und kann den Stand der Technik bei der Vorhersage anorganischer Materialeigenschaften erreichen oder übertreffen. Die Vorteile, Wechselwirkungen zwischen Elementen in chemischen Verbindungen unter Verwendung des Self-Attention Mechanismus zu lernen, werden ebenfalls diskutiert. Darüber hinaus wird eine neue Art der Repräsentation für chemische Zusammensetzungen, die einige der in aktuellen Techniken vorhandenen Einschränkungen überwindet, präsentiert. Schließlich wird eine Vorschau der Möglichkeiten Modellinterpretationsmethoden in CrabNet zu untersuchen gezeigt. Fortgesetzt in der dritten Arbeit wird die Modellinterpretierbarkeit von CrabNet weiter untersucht. Intrinsische Modellinterpretationsmethoden werden zu CrabNet hinzugefügt und verwendet, um zusätzliche Informationen über das Modell und die Datenrepräsentationen während des Modellierungsprozesses zu extrahieren. Die extrahierten Informationen werden in statischen und interaktiven Abbildungen sowie Videoanimationen verarbeitet und visualisiert. Die Untersuchung dieser Visualisierungen und der zusätzlichen Informationen ergibt bekannte chemische Muster hinsichtlich der Elemente und deren Verbindungen, die intuitiv darauf hindeuten, dass CrabNet die Elementeigenschaften, -wechselwirkungen und deren Einfluss auf die Materialeigenschaften, lernen kann. Darüber hinaus werden die Qualität des Datensatzes und der Self-Attention-Mechanismus hinsichtlich ihrer Bedeutung für eine verbesserte und interpretierbare Modellierung von Materialeigenschaften diskutiert. Schließlich werden die potenziellen Vorteile der Anwendung interpretierbarer Modellierungsmethoden in der Wissenschaft und der Industrie diskutiert. Insgesamt sind die in dieser Dissertation diskutierten Methoden, Ergebnisse und Erwägungen so dargestellt, dass sie interessierte Materialwissenschaftler dazu ermächtigen sich auf diesem Gebiet weiterzubilden, um ihre eigene Forschung in der Materialinformatik durchzuführen.