The rule of four: anomalous distributions in the stoichiometries of inorganic compounds.

Why are materials with specific characteristics more abundant than others? This is a fundamental question in materials science and one that is traditionally difficult to tackle, given the vastness of compositional and configurational space. We highlight here the anomalous abundance of inorganic compounds whose primitive unit cell contains a number of atoms that is a multiple of four. This occurrence-named here the rule of four-has to our knowledge not previously been reported or studied. Here, we first highlight the rule's existence, especially notable when restricting oneself to experimentally known compounds, and explore its possible relationship with established descriptors of crystal structures, from symmetries to energies. We then investigate this relative abundance by looking at structural descriptors, both of global (packing configurations) and local (the smooth overlap of atomic positions) nature. Contrary to intuition, the overabundance does not correlate with low-energy or high-symmetry structures; in fact, structures which obey the rule of four are characterized by low symmetries and loosely packed arrangements maximizing the free volume. We are able to correlate this abundance with local structural symmetries, and visualize the results using a hybrid supervised-unsupervised machine learning method.

Placental Lesions Associated With Stillbirth by Gestational Age, as Related to Cause of Death: Follow-Up Results From the Stillbirth Collaborative Research Network.

BACKGROUND: We previously identified placental lesions associated with stillbirths of varying gestational ages (GA) using advanced feature analysis. We further investigated the relationships between placental lesions and cause of death in stillbirths within these GA ranges. METHODS: Using data from the Stillbirth Collaborative Research Network, we derived a sample of stillbirths who underwent placental examination and Initial Causes of Fetal Death (INCODE) evaluation for determining cause of death. We then compared the rates of causes of death within and among GA ranges (extreme preterm stillbirth [PTSB] [<28 weeks], early PTSB [28-336/7 weeks], late PTSB [34-366/7 weeks], term stillbirth [≥37 weeks]) according to the presence of these lesions. RESULTS: We evaluated 352 stillbirths. In extreme PTSB, obstetric complications and infections were associated with acute funisitis. In early PTSB, uteroplacental insufficiency was associated with parenchymal infarcts. In term stillbirth (vs early PTSB), increased syncytial knots were associated with umbilical cord causes and infection. CONCLUSIONS: Placental lesions of high importance in distinguishing stillbirths at different GAs are associated with specific causes of death. This information is important in relating the presence of placental lesions and fetal death and in helping to understand etiologies of stillbirths at different GAs.

Placental lesions associated with stillbirth by gestational age, according to feature importance: Results from the stillbirth collaborative research network.

INTRODUCTION: Previous studies have identified lesions commonly found in placentas associated with stillbirth but have not distinguished across a range of gestational ages (GAs). The objective of this study was to identify lesions associated with stillbirths at different GAs by adapting methods from the chemical machine learning field to assign lesion importance based on correlation with GA. METHODS: Placentas from the Stillbirth Collaborative Research Network were examined according to standard protocols. GAs at stillbirth were categorized as: <28 weeks (extreme preterm stillbirth [PTSB]), 28-33'6 weeks (early PTSB), 34-36'6 weeks (late PTSB), ≥37 weeks (term stillbirth). We identified and ranked the most discriminating placental features, as well as those that were similar across GA ranges, using Kernel Principal Covariates Regression (KPCovR). RESULTS: These analyses included 210 (47.2%) extreme PTSB, 85 (19.1%) early PTSB, 62 (13.9%) late PTSB, and 88 (19.8%) term stillbirths. When we compute the KPCovR, the first principal covariate indicates that there are four lesions (acute funisitis & nucleated fetal red blood cells found in extreme PTSB; multifocal reactive amniocytes & multifocal meconium found in term stillbirth) that distinguish GA ranges among all stillbirths. DISCUSSION: There are distinct placental lesions present across GA ranges in stillbirths; these lesions are identifiable using sophisticated feature selection. Further investigation may identify histologic changes across gestations that relate to fetal mortality.

A data-driven interpretation of the stability of organic molecular crystals.

Due to the subtle balance of intermolecular interactions that govern structure-property relations, predicting the stability of crystal structures formed from molecular building blocks is a highly non-trivial scientific problem. A particularly active and fruitful approach involves classifying the different combinations of interacting chemical moieties, as understanding the relative energetics of different interactions enables the design of molecular crystals and fine-tuning of their stabilities. While this is usually performed based on the empirical observation of the most commonly encountered motifs in known crystal structures, we propose to apply a combination of supervised and unsupervised machine-learning techniques to automate the construction of an extensive library of molecular building blocks. We introduce a structural descriptor tailored to the prediction of the binding (lattice) energy and apply it to a curated dataset of organic crystals, exploiting its atom-centered nature to obtain a data-driven assessment of the contribution of different chemical groups to the lattice energy of the crystal. We then interpret this library using a low-dimensional representation of the structure-energy landscape and discuss selected examples of the insights into crystal engineering that can be extracted from this analysis, providing a complete database to guide the design of molecular materials.

A route to hierarchical assembly of colloidal diamond.

Photonic crystals, appealing for their ability to control light, are constructed from periodic regions of different dielectric constants. Yet, the structural holy grail in photonic materials, diamond, remains challenging to synthesize at the colloidal length scale. Here we explore new ways to assemble diamond using modified gyrobifastigial (mGBF) nanoparticles, a shape that resembles two anti-aligned triangular prisms. We investigate the parameter space that leads to the self-assembly of diamond, and we compare the likelihood of defects in diamond self-assembled via mGBF vs. the nanoparticle shape that is the current focus for assembling diamond, the truncated tetrahedra. We introduce a potential route for realizing mGBF particles by dimerizing triangular prisms using attractive patches, and we report the impact of this superstructure on the photonic properties.

The diversity of three-dimensional photonic crystals.

Many butterflies, birds, beetles, and chameleons owe their spectacular colors to the microscopic patterns within their wings, feathers, or skin. When these patterns, or photonic crystals, result in the omnidirectional reflection of commensurate wavelengths of light, it is due to a complete photonic band gap (PBG). The number of natural crystal structures known to have a PBG is relatively small, and those within the even smaller subset of notoriety, including diamond and inverse opal, have proven difficult to synthesize. Here, we report more than 150,000 photonic band calculations for thousands of natural crystal templates from which we predict 351 photonic crystal templates - including nearly 300 previously-unreported structures - that can potentially be realized for a multitude of applications and length scales, including several in the visible range via colloidal self-assembly. With this large variety of 3D photonic crystals, we also revisit and discuss oft-used primary design heuristics for PBG materials.

Relevance of packing to colloidal self-assembly.

Since the 1920s, packing arguments have been used to rationalize crystal structures in systems ranging from atomic mixtures to colloidal crystals. Packing arguments have recently been applied to complex nanoparticle structures, where they often, but not always, work. We examine when, if ever, packing is a causal mechanism in hard particle approximations of colloidal crystals. We investigate three crystal structures composed of their ideal packing shapes. We show that, contrary to expectations, the ordering mechanism cannot be packing, even when the thermodynamically self-assembled structure is the same as that of the densest packing. We also show that the best particle shapes for hard particle colloidal crystals at any finite pressure are imperfect versions of the ideal packing shape.