POLARIZATION AND FREQUENCY-POLARIZATION DEPENDENCES OF THREE-PHOTON INTERBAND LINEAR-CIRCULAR DICHROISM IN SEMICONDUCTORS OF CUBIC SYMMETRY

The polarization and frequency-polarization dependences of the linear-circular dichroism and light absorption coefficients in semiconductors of cubic symmetry, caused by vertical three-photon optical transitions between the states of the spin-orbit splitting and conduction bands, are calculated. KEY WORDS: three-photon optical transitions, spin-orbit splitting band, conduction band, linear-circular dichroism, light absorption, semiconductor.

Solution of the random field XY magnet on a fully connected graph

We use large deviation theory to obtain the free energy of the XY model on a fully connected graph on each site of which there is a randomly oriented field of magnitude $h$. The phase diagram is obtained for two symmetric distributions of the random orientations: (a) a uniform distribution and (b) a distribution with cubic symmetry. In both cases, the ordered state reflects the symmetry of the underlying disorder distribution. The phase boundary has a multicritical point which separates a locus of continuous transitions (for small values of $h$) from a locus of first order transitions (for large $h$). The free energy is a function of a single variable in case (a) and a function of two variables in case (b), leading to different characters of the multicritical points in the two cases.

Rietveld Refinement and X-ray Absorption Study on the Bonding States of Lanthanum-Based Perovskite-Type Oxides La1-xCexCoO3

Metal-oxygen bonding of the Ce-doped LaCoO3 system remains largely unexplored despite extensive studies on its magnetic properties. Here, we investigate the structure and local structure of nanoscale La1-xCexCoO3, with x = 0, 0.2, and 0.4, using the Rietveld refinement and synchrotron X-ray absorption techniques, complemented by topological analysis of experimental electron density and electron energy distribution. The Rietveld refinement results show that LaCoO3 subject to Ce addition is best interpretable by a model of cubic symmetry in contrast to the pristine LaCoO3, conventionally described by either a monoclinic model or a rhombohedral model. Ce4+/Co2+ are more evidently compatible dopants than Ce3+ for insertion into the main lattice. X-ray absorption data evidence the partially filled La 5d-band of the pristine LaCoO3 in accordance with the presence of La–O bonds with the shared-type atomic interaction. With increasing x, the increased Ce spectroscopic valence and enhanced La–O ionic bonding are noticeable. Characterization of the local structures around Co species also provides evidence to support the findings of the Rietveld refinement analysis.

Resonant Ultrasound Spectroscopy: Sensitivity Analysis for Anisotropic Materials with Hexagonal Symmetry

Resonance ultrasound spectroscopy (RUS) is a non-destructive technique for evaluating elastic and an-elastic material properties. The frequencies of free vibrations for a carefully crafted sample are measured, and material properties can be extracted from this. In one popular application, the determination of monocrystal elasticity, the results are not always reliable. In some cases, the resonant frequencies are insensitive to changes in certain elastic constants or their linear combinations. Previous work has been done to characterize these sensitivity issues in materials with isotropic and cubic symmetry. This work examines the sensitivity of elastic constant measurements by the RUS method for materials with hexagonal symmetry, such as titanium-diboride. We investigate the reliability of RUS data and explore supplemental measurements to obtain an accurate and complete set of elastic constants.

Facile self-assembly of colloidal diamond from tetrahedral patchy particles via ring selection

Diamond-structured crystals, particularly those with cubic symmetry, have long been attractive targets for the programmed self-assembly of colloidal particles, due to their applications as photonic crystals that can control the flow of visible light. While spherical particles decorated with four patches in a tetrahedral arrangement—tetrahedral patchy particles—should be an ideal building block for this endeavor, their self-assembly into colloidal diamond has proved elusive. The kinetics of self-assembly pose a major challenge, with competition from an amorphous glassy phase, as well as clathrate crystals, leaving a narrow widow of patch widths where tetrahedral patchy particles can self-assemble into diamond crystals. Here we demonstrate that a two-component system of tetrahedral patchy particles, where bonding is allowed only between particles of different types to select even-member rings, undergoes crystallization into diamond crystals over a significantly wider range of patch widths conducive for experimental fabrication. We show that the crystallization in the two-component system is both thermodynamically and kinetically enhanced, as compared to the one-component system. Although our bottom-up route does not lead to the selection of the cubic polytype exclusively, we find that the cubicity of the self-assembled crystals increases with increasing patch width. Our designer system not only promises a scalable bottom-up route for colloidal diamond but also offers fundamental insight into crystallization into open lattices.

Mechanical Properties and Energy Absorption Characteristics of Additively Manufactured Lightweight Novel Re-Entrant Plate-Based Lattice Structures

In this work, three novel re-entrant plate lattice structures (LSs) have been designed by transforming conventional truss-based lattices into hybrid-plate based lattices, namely, flat-plate modified auxetic (FPMA), vintile (FPV), and tesseract (FPT). Additive manufacturing based on stereolithography (SLA) technology was utilized to fabricate the tensile, compressive, and LS specimens with different relative densities (ρ). The base material’s mechanical properties obtained through mechanical testing were used in a finite element-based numerical homogenization analysis to study the elastic anisotropy of the LSs. Both the FPV and FPMA showed anisotropic behavior; however, the FPT showed cubic symmetry. The universal anisotropic index was found highest for FPV and lowest for FPMA, and it followed the power-law dependence of ρ. The quasi-static compressive response of the LSs was investigated. The Gibson–Ashby power law (≈ρn) analysis revealed that the FPMA’s Young’s modulus was the highest with a mixed bending–stretching behavior (≈ρ1.30), the FPV showed a bending-dominated behavior (≈ρ3.59), and the FPT showed a stretching-dominated behavior (≈ρ1.15). Excellent mechanical properties along with superior energy absorption capabilities were observed, with the FPT showing a specific energy absorption of 4.5 J/g, surpassing most reported lattices while having a far lower density.

A Generalized Strain Energy-Based Homogenization Method for 2-D and 3-D Cellular Materials with and without Periodicity Constraints

A generalized strain energy-based homogenization method for 2-D and 3-D cellular materials with and without periodicity constraints is proposed using Hill’s Lemma and the matrix method for spatial frames. In this new approach, the equilibrium equations are enforced at all boundary and interior nodes and each interior node is allowed to translate and rotate freely, which differ from existing methods where the equilibrium conditions are imposed only at the boundary nodes. The newly formulated homogenization method can be applied to cellular materials with or without symmetry. To illustrate the new method, four examples are studied: two for a 2-D cellular material and two for a 3-D pentamode metamaterial, with and without periodic constraints in each group. For the 2-D cellular material, an asymmetric microstructure with or without periodicity constraints is analyzed, and closed-form expressions of the effective stiffness components are obtained in both cases. For the 3-D pentamode metamaterial, a primitive diamond-shaped unit cell with or without periodicity constraints is considered. In each of these 3-D cases, two different representative cells in two orientations are examined. The homogenization analysis reveals that the pentamode metamaterial exhibits the cubic symmetry based on one representative cell, with the effective Poisson’s ratio v¯ being nearly 0.5. Moreover, it is revealed that the pentamode metamaterial with the cubic symmetry can be tailored to be a rubber-like material (with v¯ ≅0.5) or an auxetic material (with v¯< 0).

Cubic microlattices embedded in nematic liquid crystals: a Landau-de Gennes study

We consider a Landau-de Gennes model for a connected cubic lattice scaffold in a nematic host, in a dilute regime. We analyse the homogenised limit for both cases in which the lattice of embedded particles presents or not cubic symmetry and then we compute the free effective energy of the composite material. In the cubic symmetry case, we impose different types of surface anchoring energy densities, such as quartic, Rapini-Papoular or more general versions, and, in this case, we show that we can tune any coefficient from the corresponding bulk potential, especially the phase transition temperature. In the case with loss of cubic symmetry, we prove similar results in which the effective free energy functional has now an additional term, which describes a change in the preferred alignment of the liquid crystal particles inside the domain. Moreover, we compute the rate of convergence for how fast the surface energies converge to the homogenised one and also for how fast the minimisers of the free energies tend to the minimiser of the homogenised free energy.

Application of Bi12ZnO20 Sillenite as an Efficient Photocatalyst for Wastewater Treatment: Removal of Both Organic and Inorganic Compounds

This work aims to synthesize and characterize a material that can be used as an effective catalyst for photocatalytic application to remove both organic and inorganic compounds from wastewater. In this context, sillenite Bi12ZnO20 (BZO) in a pure phase was synthesized using the sol–gel method. Before calcination, differential scanning calorimetry (DSC) analysis was done to determine the temperature of the formation of the sillenite phase, which was found to be 800 °C. After calcination, the phase was identified by X-ray diffraction (XRD) and then refined using the Rietveld refinement technique. The results prove that BZO crystals have a cubic symmetry with the space group I23 (N°197); the lattice parameters of the structure were also determined. From the crystalline size, the surface area was estimated using the Brunauer-Emmett-Teller (BET) method, which was found to be 11.22 m2/g. The formation of sillenite was also checked using the Raman technique. The morphology of the crystals was visualized using electron scanning microscope (SEM) analysis. After that, the optical properties of BZO were investigated by diffuse reflectance spectroscopy (DRS) and photoluminescence (PL); an optical gap of 2.9 eV was found. In the final step, the photocatalytic activity of the BZO crystals was evaluated for the removal of inorganic and organic pollutants, namely hexavalent chromium Cr(VI) and Cefixime (CFX). An efficient removal rate was achieved for both contaminants within only 3 h, with a 94.34% degradation rate for CFX and a 77.19% reduction rate for Cr(VI). Additionally, a kinetic study was carried out using a first-order model, and the results showed that the kinetic properties are compatible with this model. According to these findings, we can conclude that the sillenite BZO can be used as an efficient photocatalyst for wastewater treatment by eliminating both organic and inorganic compounds.