Tangible symmetry elements and space-group models to guide from molecular to solid-state composition

The ability to imagine symmetry and the spatial arrangement of atoms and molecules is crucial in chemistry in general. Teaching and understanding crystallography and the composition of the solid state therefore require understanding of symmetry elements and their relationships. To foster the student's spatial imagination, models representing a range of concepts from individual rotation axes to complete space groups have been designed and built. These models are robust and large enough to be presented and operated in a lecture hall, and they enable students to translate conventional 2D notations into 3D objects and vice versa. Tackling them hands-on means understanding them.

Syntheses and crystal structures of 2-(p-tolyl)-1H-perimidine hemihydrate and 1-methyl-2-(p-tolyl)-1H-perimidine

The title compounds, 2-(4-methylphenyl)-1H-perimidine hemihydrate (1, C18H14N2·0.5H2O) and 1-methyl-2-(4-methylphenyl)-1H-perimidine (2, C19H16N2), were prepared and characterized by 1H NMR and single-crystal X-ray diffraction. The organic molecule of the hemihydrate lies on a twofold rotation axis while the water molecule lies on the intersection of three twofold rotation axes (point group symmetry 222). As a consequence, the hydrogen atoms that are part of the N—H group and the water molecule as well as the CH3 group of the p-tolyl ring are disordered over two positions. In compound 1, the perimidine and the 2-aryl rings are slightly twisted while its N-methylated derivative 2 has a more distorted conformation because of the steric repulsion between the N-methyl group and the 2-aryl ring. In the crystal structures, molecules of perimidine 2 are held together only by C—H...π contacts while the parent perimidine 1 does not exhibit this type of interaction. Its crystal packing is established by intermolecular N—H...O hydrogen bonds with the solvent water molecules and additionally stabilized by π–π stacking.

Synthesis, crystal structure and thermal properties of bis(1,3-dicyclohexylthiourea-κS)bis(isothiocyanato-κN)cobalt(II)

Crystals of the title compound, [Co(NCS)2(C13H24N2S)2], were obtained by the reaction of Co(NCS)2 with 1,3-dicyclohexylthiourea in ethanol. Its crystal structure consists of discrete complexes that are located on twofold rotation axes, in which the CoII cations are tetrahedrally coordinated by two terminal N-bonded thiocyanate anions and two 1,3-dicyclohexylthiourea ligands. These complexes are linked via intermolecular N—H...S and C—H...S hydrogen bonding into chains, which elongate in the b-axis direction. These chains are closely packed in a pseudo-hexagonal manner. The CN stretching vibration of the thiocyanate anions located at 2038 cm−1 is in agreement with only terminal bonded anionic ligands linked to metal cations in a tetrahedral coordination. TG–DTA measurements prove the decomposition of the compound at about 227°C. DSC measurements reveal a small endothermic signal before decomposition at about 174°C, which might correspond to melting.

Visual Measurement and Calibration of Geometric Errors of Rotating Axes for Five-axis Platform

In this paper, a method for identifying and decoupling geometric errors of rotation axes using vision measurement is proposed. Based on screw theory and exponential product formula, identification equations of position-dependent geometric errors (PDGEs) and position-independent geometric errors (PIGEs) of the rotation axes are established. The mapping relationships between the error twist and geometric errors are established. The error model provides the coupling mechanism of PDGEs and PIGEs. Furthermore, a progressive decoupling method is proposed to separate PDGEs and PIGEs without additional assumptions. The pose parameters, required for solving the identification equations, are obtained by visual measurement. Then, the error terms of PIGEs and PDGEs are determined. Lastly, the error calibration of the rotation axes is investigated, thus providing an average rotary table orientation error reduction of 28.1% compared to the situation before calibration.

Effects of rotation errors on goniometric measurements

Goniometric measurements are essential for the determination of many optical quantities, and quantifying the effects of errors in the rotation axes on these quantities is a complex task. In this paper, we show how a measurement model for a four-axis goniometric system can be developed to allow the effects of alignment and rotation errors to be included in the uncertainty of the measurement. We use three different computational methods to propagate the uncertainties due to several error sources through the model to the rotation angles and then to the measurement of bidirectional reflectance and integrated diffuse reflectance, a task that would otherwise be intractable. While all three methods give the same result, the GTC Python package is the simplest and intrinsically provides a full uncertainty budget, including all correlations between measurement parameters. We then demonstrate how the development of a measurement model and the use of GTC has improved our understanding of the system. As a consequence, taking advantage of negative correlations between measurements in different geometries allows us to minimise the total uncertainty in integrated diffuse reflectance, lowering the standard uncertainty from 0.0029 to 0.0015.

Predicting individual acclimation to the cross-coupled illusion for artificial gravity

BACKGROUND: The cross-coupled (CC) illusion and associated motion sickness limits the tolerability of fast-spin-rate centrifugation for artificial gravity implementation. Humans acclimate to the CC illusion through repeated exposure; however, substantial inter-individual differences in acclimation exist, which remain poorly understood. To address this, we investigated several potential predictors of individual acclimation to the CC illusion. METHODS: Eleven subjects were exposed to the CC illusion for up to 50 25-minute acclimation sessions. The metric of acclimation rate was calculated as the slope of each subject’s linear increase in spin rate across sessions. As potential predictors of acclimation rate, we gathered age, gender, demographics, and activity history, and measured subjects’ vestibular perceptual thresholds in the yaw, pitch, and roll rotation axes. RESULTS: We found a significant, negative correlation (p = 0.025) between subjects’ acclimation rate and roll threshold, suggesting lower thresholds yielded faster acclimation. Additionally, a leave-one-out cross-validation analysis indicated that roll thresholds are predictive of acclimation rates. Correlations between acclimation and other measures were not found but were difficult to assess within our sample. CONCLUSIONS: The ability to predict individual differences in CC illusion acclimation rate using roll thresholds is critical to optimizing acclimation training, improving the feasibility of fast-rotation, short-radius centrifugation for artificial gravity.

Spatial Orientations of Angular Momentum Vectors of Galaxies in Supercluster S [195+027+0022] and Substructure

This paper presents an analysis of the spin vector orientations of SDSS (Sloan Digital Sky Survey) galaxies in the Supercluster S [195+027+0022] using the seventh data release (2008 October). By using the spectroscopic database of galaxies, identified number density map in the region of Superclusters. Several density enhancements are observed, suggesting the possibility of substructure in the Supercluster. Two-dimensional observed parameters that we received from the database are used to compute three-dimensional galaxy rotation axes by applying `position angle-inclination' method. Apply the selection effects by performing the random simulation method. The expected distribution curves are obtained from the simulation. Chi-square, auto-correlation, and Fourier tests are used to examine non-random effects in the polar and azimuthal angle distributions of the galaxy rotation axes. To check these results with the different galaxy evolution models namely Hierarchy, Primordial, and Pancake model. The result supports the Hierarchy model.

Spherulitic and rotational crystal growth of Quartz thin films

To obtain crystalline thin films of alpha-Quartz represents a challenge due to the tendency for the material towards spherulitic growth. Thus, understanding the mechanisms that give rise to spherulitic growth can help regulate the growth process. Here the spherulitic type of 2D crystal growth in thin amorphous Quartz films was analyzed by electron back-scatter diffraction (EBSD). EBSD was used to measure the size, orientation, and rotation of crystallographic grains in polycrystalline SiO2 and GeO2 thin films with high spatial resolution. Individual spherulitic Quartz crystal colonies contain primary and secondary single crystal fibers, which grow radially from the colony center towards its edge, and fill a near circular crystalline area completely. During their growth, individual fibers form so-called rotational crystals, when some lattice planes are continuously bent. The directions of the lattice rotation axes in the fibers were determined by an enhanced analysis of EBSD data. A possible mechanism, including the generation of the particular type of dislocation(s), is suggested.

Accurate Clamping Method of Multipoint Flexible Fixture for Large Complex Surface

In the field of aviation and astronautics, large complex surface parts such as aircraft cabin cover are complex, varying in model, and produced in small batch. In order to reduce fixture cost and improve production efficiency, a variable multipoint and multi-DOF supporting fixture is designed. The coordinate system of the complex structure fixture is defined, and the kinematics of the multibody structures driven by air cylinders are modeled according to the topological principle. With the help of this data structure, fast and optimal search for clamping state can be realized. With the dichotomy method, the driving amount of the electric cylinder of the suction cups and the two rotation angles of two rotation axes at the end of the linkages are solved accurately. Based on the digital twin simulation method, the precise clamping motion of flexible fixture is calculated for an aircraft cockpit cover with a software developed by the authors in C++ language on the Visual studio platform. The distance between the clamping point and the surface was verified with a laser tracker. Finally, the practical experiment of a real cockpit cover clamping proves the practicability and effectiveness of the proposed method.

Geometric Calibration of Rotational Vision System for Dynamic Exterior Orientation

Rotational vision system (RVS) is a common type of active vision with only rotational freedom. Typically, the rotational freedom is provided by turntable and pan-tilt-zoom (PTZ). Or eye in hand (EIH) structure in an articulated arm robot. The ideal assumption that rotation axes are perfectly aligned with the coordinate axes of the local camera is mostly violated due to assembling deviations and limitations of manufacturing accuracy. To solve this problem, we propose a generalized deviation model for a specified rotation axis that relates the rotation motion of the platform to the exterior orientation (EO) of the camera. Based on it we put heuristic estimation algorithms through minimizing global reprojection error and fitting a circle in space respectively for rotating platform with or without accurate angle measurements with constrained global optimization. Implemented experiments on a servo pan-tilt turntable validate the accuracy and efficiency of the above models and calibration technique.