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Atom arrangement plays a critical role in determining material properties. It is, therefore, essential for materials science and engineering to identify and characterize distinct atom configurations. Currently, crystal structures can be…
A general theory of topological classification of defects is introduced. We illustrate the application of tools from algebraic topology, including homotopy and cohomology groups, to classify defects including several explicit calculations…
Conventionally, high-throughput computational materials searches start from an input set of bulk compounds extracted from material databases, and this set is screened for candidate materials for specific applications. In contrast, many…
Subgroup discovery (SGD) is presented here as a data-mining approach to help find interpretable local patterns, correlations, and descriptors of a target property in materials-science data. Specifically, we will be concerned with data…
A systematic search for multicomponent crystal structures is carried out for five different ternary systems of nuclei in a polarizable background of electrons, representative of accreted neutron star crusts and some white dwarfs. Candidate…
Electronic-structure theory is a strong pillar of materials science. Many different computer codes that employ different approaches are used by the community to solve various scientific problems. Still, the precision of different packages…
Machine-learning models are capable of capturing the structure-property relationship from a dataset of computationally demanding ab initio calculations. Over the past two years, the Organic Materials Database (OMDB) has hosted a growing…
Entangled embedded periodic nets and crystal frameworks are defined, along with their dimension type, homogeneity type, adjacency depth and periodic isotopy type. We obtain periodic isotopy classifications for various families of embedded…
Oxidation states are well-established in chemical science teaching and research. We data-mine more than 168,000 crystallographic reports to find an optimal allocation of oxidation states to each element. In doing so we uncover discrepancies…
This paper presents a set of general strategies for the analysis of structure in amorphous materials and a general approach to assessing the utility of a selected structural description. Measures of structural diversity and utility are…
The prediction of energetically stable crystal structures formed by a given chemical composition is a central problem in solid-state physics. In principle, the crystalline state of assembled atoms can be determined by optimizing the energy…
We introduce a phase-field crystal model that creates an array of complex three- and two-dimensional crystal structures via a numerically tractable three-point correlation function. The three-point correlation function is designed in order…
Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in $R^d$. It is shown that natural parametrizations provide affine section…
We have analysed structural motifs in the Deem database of hypothetical zeolites, to investigate whether the structural diversity found in this database can be well-represented by classical descriptors such as distances, angles, and ring…
The zeolitic imidazolate frameworks (ZIF) have emerged as a promising candidate for catalysis, carbon-dioxide (CO$_{2}$) capture and storage as well as flue gas separation due to their tunable porosity and chemical stability. ZIFs consists…
The generation of plausible crystal structures is often the first step in predicting the structure and properties of a material from its chemical composition. Quickly generating and predicting inorganic crystal structures is important for…
Metal-organic frameworks (MOFs) are porous materials composed of metal ions and organic linkers. Due to their chemical diversity, MOFs can support a broad range of applications in chemical separations. However, the vast amount of structural…
A total of 126 isotopes with Z $\le$ 10 have been identified to date. The discovery of these isotopes which includes the observation of unbound nuclei, is discussed. For each isotope a brief summary of the first refereed publication,…
High-entropy alloys (HEAs) have attracted growing attention for their exceptional mechanical and thermal properties arising from complex atomic configurations. In this paper, we propose crystal fractional graph neural network for predicting…
We formulate topological crystalline materials on the basis of the twisted equivariant $K$-theory. Basic ideas of the twisted equivariant $K$-theory is explained with application to topological phases protected by crystalline symmetries in…