Three-dimensional Periodic Arrays Research Articles

Signatures of a magnetic superstructure phase induced by ultrahigh magnetic fields in a breathing pyrochlore antiferromagnet

The mutual coupling of spin and lattice degrees of freedom is ubiquitous in magnetic materials and potentially creates exotic magnetic states in response to the external magnetic field. Particularly, geometrically frustrated magnets serve as a fertile playground for realizing magnetic superstructure phases. Here, we observe an unconventional two-step magnetostructural transition prior to a half-magnetization plateau in a breathing pyrochlore chromium spinel by means of state-of-the-art magnetization and magnetostriction measurements in ultrahigh magnetic fields available up to 600 T. Considering a microscopic magnetoelastic theory, the intermediate-field phase can be assigned to a magnetic superstructure with a three-dimensional periodic array of 3-up-1-down and canted 2-up-2-down spin molecules. We attribute the emergence of the magnetic superstructure to a unique combination of the strong spin-lattice coupling and large breathing anisotropy.

Effect of the metasurface on the electromagnetic wave absorption performance of cementitious materials

• Metasurface can significantly improve the EWAP of cementitious materials. • Integrated electromagnetic absorbing structures and materials method is designed. • MAPC-M exhibits a peak RL of −25.1 dB with a bandwidth of 11.64 GHz below −10 dB. • The effects of metasurface on the EWAP of MAPC are verified by CST simulation. Electromagnetic metasurface can effectively control the electromagnetic wave absorption performance (EWAP) of materials. This study presents an integrated structures and materials design method to improve the EWAP of cementitious materials. Based on a three-dimensional periodic array surface structure, nano-Fe 3 O 4 magnetic fluid is used as an absorber to develop metasurface cementitious electromagnetic absorbing materials. The experimental results show that the metasurface can effectively improve the EWAP of cementitious materials, achieving an excellent EWAP with a maximum reflection loss of −25.1 dB and a bandwidth of 11.64 GHz below −10 dB at 2–18 GHz. In addition, the CST simulation of the EWAP coincides with that obtained experimentally. In addition, the simulated electric and magnetic field distributions and magnetic loss density in the metasurface further demonstrate the synergistic effects of λ/4 resonance, edge diffraction, multiple reflection, and scattering on the dissipation of electromagnetic waves. Overall, these results indicate that electromagnetic metasurface can advance and promote the integrated design of materials and structures and the application of cementitious electromagnetic absorbing materials.

Dodecagonal quasicrystals of oil-swollen ionic surfactant micelles

A delicate balance of noncovalent interactions directs the hierarchical self-assembly of molecular amphiphiles into spherical micelles that pack into three-dimensional periodic arrays, which mimic intermetallic crystals. Herein, we report the discovery that adding water to a mixture of an ionic surfactant and n-decane induces aperiodic ordering of oil-swollen spherical micelles into previously unrecognized, aqueous lyotropic dodecagonal quasicrystals (DDQCs), which exhibit local 12-fold rotational symmetry and no long-range translational order. The emergence of these DDQCs at the nexus of dynamically arrested micellar glasses and a periodic Frank-Kasper (FK) σ phase approximant sensitively depends on the mixing order of molecular constituents in the assembly process and on sample thermal history. Addition of n-decane to mixtures of surfactant and water instead leads only to periodic FK A15 and σ approximants with no evidence for aperiodic order, while extended ambient temperature annealing of the DDQC also reveals its transformation into a σ phase. Thus, these lyotropic DDQCs are long-lived metastable morphologies, which nucleate and grow from a stochastic distribution of micelle sizes formed by abrupt segregation of varied amounts of oil into surfactant micelles on hydration. These findings indicate that molecular building block complexity is not a prerequisite for the formation of aperiodic supramolecular order, while also establishing the generic nature of quasicrystalline states across metal alloys and self-assembled micellar materials.

Hedgehog-lattice spin texture in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice

The hedgehog lattice, a three-dimensional periodic array of magnetic monopoles and antimonopoles, is known to be realized in the presence of the Dzyaloshinskii-Moriya (DM) interaction. Here, we demonstrate by means of Monte Carlo simulations that the hedgehog lattice is induced by not the DM interaction but frustration in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice. In the model, the breathing bond-alternation is characterized by the ratio of the nearest-neighbor (NN) antiferromagnetic exchange interaction for large tetrahedra to that for small ones, J1'/J1. A quadruple-q state with the ordering vector of q=(\pm 1/2,\pm 1/2,\pm 1/2), which is realized for a large third NN antiferromagnetic interaction along the bond direction J3, turns out to become the hedgehog-lattice state in the breathing case of J1'/J1 <1, while in the uniform case of J1'/J1 =1, it is a collinear state favored by thermal fluctuations. It is also found that in a magnetic field, the structure of the (1/2,1/2,1/2) hedgehog lattice is changed from cubic to tetragonal, resulting in a nonzero net spin chirality which in a metalic system, should yield a characteristic topological Hall effect.

Quasiperiodic boundary conditions for three-dimensional superfluids

We derive boundary conditions that allow a three-dimensional periodic array of superfluid vortices to be modeled in a Cartesian domain. The method is applicable to vortices in the Gross-Pitaevskii description of a superfluid and to fluxtubes in the Ginzburg-Landau description of a superconductor. Unlike standard methods for modeling infinite arrays of vortices, the boundary conditions can be used to study the three-dimensional tangling and reconnection of vortex lines expected in superfluid turbulence. In the two-dimensional case, the boundary conditions include two parameters that determine the lattice offset, which for a single superfluid is essentially arbitrary. In the three-dimensional case the boundary conditions include three parameters that must satisfy a particular linear relationship. We present an algorithm for finding all vortex lattice states within a given domain. We demonstrate the utility of the boundary conditions in two specific problems with imperfect or tangled lattices.

Enhanced optical absorbance and fabrication of periodic arrays on nickel surface using nanosecond laser

A hundred-nanosecond pulsed laser was employed to structure the nickel surface. The effects of laser spatial filling interval and laser scanning speed on the optical absorbance capacity and morphologies on the nickel surface were experimentally investigated. The black nickel surface covered with dense micro/nanostructured broccoli-like clusters with strong light trapping capacity ranging from the UV to the near IR was produced at a high laser scanning speed up to v=100mm/s. The absorbance of the black nickel is as high as 98% in the UV range of 200–400nm, more than 97% in the visible spectrum, ranging from 400 to 800nm, and over 90% in the IR between 800 and 2000nm. In addition, when the nickel surface was irradiated in two-dimensional crossing scans by laser with different processing parameters, self-organized and shape-controllable structures of three-dimensional (3D) periodic arrays can be fabricated. Compared with ultrafast laser systems previously used for such processing, the nanosecond fiber laser used in this work is more cost-effective, compact and allows higher processing rates. This nickel surface structured technique may be applicable in optoelectronics, batteries industry, solar/wave absorbers, and wettability materials.

Computation of Flow Through a Three-Dimensional Periodic Array of Porous Structures by a Parallel Immersed-Boundary Method

A parallel implementation of an immersed-boundary (IB) method is presented for low Reynolds number flow simulations in a representative elementary volume (REV) of porous media that are composed of a periodic array of regularly arranged structures. The material of the structure in the REV can be solid (impermeable) or microporous (permeable). Flows both outside and inside the microporous media are computed simultaneously by using an IB method to solve a combination of the Navier–Stokes equation (outside the microporous medium) and the Zwikker–Kosten equation (inside the microporous medium). The numerical simulation is firstly validated using flow through the REVs of impermeable structures, including square rods, circular rods, cubes, and spheres. The resultant pressure gradient over the REVs is compared with analytical solutions of the Ergun equation or Darcy–Forchheimer law. The good agreements demonstrate the validity of the numerical method to simulate the macroscopic flow behavior in porous media. In addition, with the assistance of a scientific parallel computational library, PETSc, good parallel performances are achieved. Finally, the IB method is extended to simulate species transport by coupling with the REV flow simulation. The species sorption behaviors in an REV with impermeable/solid and permeable/microporous materials are then studied.

Scattering of electromagnetic radiation by three-dimensional periodic arrays of identical particles

The generalized multiparticle Mie-solution (GMM), a Lorenz-Mie-type rigorous theory for the scattering of a monochromatic plane wave by an arbitrary configuration of nonintersecting scattering bodies, has lately been revisited and further developed. A recent progress is the initiation of a special version applied to one- and two-dimensional (1D and 2D) periodic arrays (PAs) of identical particles [J. Opt. Soc. Am. A30, 1053 (2013)]. As a continuous advance, the present work extends the initiative PA-type solution from 1D and 2D to the more involved three-dimensional (3D) regular arrays. Analytical formulations applicable to the 3D PAs are derived, including the special PA-type explicit expressions for cross sections of extinction, scattering, backscattering, and radiation pressure. The specific PA-version is a complement to the general formulation and solution process of the standard GMM. In either 1D and 2D or 3D cases, the newly devised PA-approach is capable of providing expeditiously theoretical predictions of radiative scattering characteristics for periodic structures consisting of a huge number of identical unit cells, which the general approach of the GMM is unable to handle in practical calculations, owing to excessive computing time and/or computer memory requirements. To illustrate practical applications, sample numerical solutions obtained via the PA-approach are shown for 3D PAs of finite lengths that have ∼5×10(7) component particles, including structures having a rectangular opening. Also discussed is potential future work on the theory and its tests.

Complex modes and artificial magnetism in three-dimensional periodic arrays of titanium dioxide microspheres at millimeter waves

We characterize the modes with real and complex wavenumbers for both longitudinal and transverse polarization states (with respect to the mode traveling direction) in three dimensional (3D) periodic arrays of titanium dioxide (TiO2) microspheres in the frequency range between 250&#xA0;GHz and 350&#xA0;GHz. Modal results are computed by using a single magnetic dipole approximation (SDA) and an SDA model with correction (SDA-WC) that assumes the array to be embedded in a host with an effective permittivity computed through Maxwell Garnett formulas. Moreover, for the transverse polarization case, modal wavenumbers are computed also by fitting the full-wave simulation magnetic field (one point per unit cell) in a finite thickness structure, and their agreement and disagreement are discussed. The longitudinal polarization is not affected by the artificial correction introduced in the SDA-WC; in the transverse polarization case, instead, the correction is needed to obtain results in better agreement with the full-wave data fit. In the observed frequency range, there are one longitudinal mode and two transverse modes, one forward and one backward, where the forward one is &#x201C;dominant&#x201D; (i.e., it contributes mostly to the field in the array). Therefore, in the case of transverse polarization, we describe the composite material in terms of homogenized refractive index and relative permeability, comparing results from (i)&#xA0;modal analysis (with and without correction), (ii)&#xA0;Maxwell Garnett formulas, and (iii)&#xA0;Nicolson&#x2013;Ross&#x2013;Weir retrieval method from scattering parameters of finite thickness structures. The agreement among the different methods justifies the performed homogenization procedure in the case of transverse polarization. We show that artificial magnetism is generated from a nonmagnetic composite material.

Traveling Waves on Three-Dimensional Periodic Arrays of Two Different Magnetodielectric Spheres Arbitrarily Arranged on a Simple Tetragonal Lattice

Based on Shore and Yaghjian's work (IEEE Trans. Antennas Propag., vol. 57, no. 10, pp. 3077-3091, Oct. 2009), a general theory has been developed to describe traveling waves on three-dimensional (3-D) periodic arrays of two sets of magnetodielectric spheres arbitrarily arranged on a simple tetragonal lattice. This theory is eventually in the form of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -β (dispersion) equations. To improve the computational efficiency, rapidly converging expressions and their double summation form are derived for slowly converging summations in the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -β equations. The dispersion diagrams of seven different arrangements of the spheres are analyzed for three combinations of sphere types: 1) dielectric spheres with equal permittivity but different radius; 2) dielectric spheres with equal radius but different permittivity; and 3) one set of spheres is purely dielectric while the other set is magnetic. Results show that the maximum bandwidths of the double-negative (DNG) region provided by different spheres arrangements for spheres combinations 1-3 are, respectively, 0.21%, 0.069%, and 7.403%. Compared to results reported in previous literature, analysis of these possible arrangements of the spheres shows similar narrow DNG bandwidths for spheres combinations 1 and 2, and wider DNG bandwidths for spheres combination 3. Although purely dielectric materials with relative permittivity much greater than one are readily available, the usefulness of purely dielectric DNG metamaterials still depends on whether the narrow bandwidths achievable are acceptable for the particular applications. Since purely magnetic materials with relative permeability much greater than one above 1 GHz are not currently available, the practicality of fabricating DNG metamaterials using arrays with spheres combination 3 is questionable for radio frequency (RF) applications, at least at present, despite the fact that this combination yields much wider DNG bandwidths than those of spheres combinations 1 and 2.

Gel-immobilized single-crystal-like colloidal crystal films

Colloidal crystals, three-dimensional periodic arrays of monodisperse colloidal particles, have attracted considerable attention in the field of materials science and for technological applications because of their novel optical applications as photonic crystals. Although polycrystalline colloidal crystals can be easily prepared, the fabrication of a large single crystal is a challenging for advanced studies pertaining to optical properties or applications. This review reports a unique method for fabricating gel-immobilized single-crystal-like colloidal crystal films and their excellent optical properties. A suspension of charged colloids is forced to flow in a flat capillary cell using an air-pulse-drive system. Optical characterizations such as ordinary spectroscopy, laser Kossel diffraction, and imaging spectroscopy for the crystals indicate that the strong shear flow generated in the cell induces a single-domain crystal with a fixed crystallographic orientation determined by the cell geometry. The flow-aligned crystal can be subsequently immobilized in a self-standing hydrogel film by a photopolymerization technique. The resultant gel-immobilized colloidal crystal film can be used as tunable photonic crystals in nonvolatile ionic liquids and be converted into a dry film of densely packed colloidal crystals without cracks. The present materials are expected to contribute to the development of novel colloidal photonic crystals and open the door to industrial mass production of colloidal photonic crystals.

TAUB-NUT CRYSTAL

We consider the Gibbons–Hawking metric for a three-dimensional periodic array of multi-Taub-NUT centers, containing not only centers with a positive NUT charge but also ones with a negative NUT charge. The latter are regarded as representing the asymptotic form of the Atiyah–Hitchin metric. The periodic arrays of Taub-NUT centers have close parallels with ionic crystals, where the Gibbons–Hawking potential plays the role of the Coulomb static potential of the ions, and are similarly classified according to their space groups. After a periodic identification and a Z2 projection, the array is transformed by T-duality to a system of NS5-branes with the SU(2) structure, and a further standard embedding yields, though singular, a half-BPS heterotic 5-brane background with warped compact transverse dimensions. A discussion is given on the possibility of probing the singular geometry by two-dimensional gauge theories.

Corrections to “Traveling Waves on Three-Dimensional Periodic Arrays of Two Different Alternating Magnetodielectric Spheres” [Oct 09 3077-3091

In the above titled paper (ibid., vol. 57, no. 10, pp. 3077-3091, Oct. 2009), there were a number of errors. These errors are remedied here.

Alignment and optical polarization of InGaAs quantum wires on GaAs high index surfaces

Highly ordered three-dimensional periodic arrays of In 0.40Ga 0.60As quantum wires (QWRs) on GaAs (311)A and GaAs (331)A have been achieved by molecular beam epitaxy and revealed by high-resolution X-ray diffraction. Polarization dependent photoluminescence measurements demonstrated high optical anisotropy of 40% in (331)A QWRs and 16% in (311)A QWRs. Such a difference in polarization value could be caused by the differences in geometry, ordering, and high piezoelectric field between (331)A and (311)A samples.

Analysis of Double-Negative (DNG) Bandwidths for Metamaterials Composed of Three-Dimensional Periodic Arrays of Two Different Magnetodielectric Spheres Arbitrarily Arranged on a Simple Tetragonal Lattice

Based on the theory describing traveling waves on three-dimensional (3-D) periodic arrays of two sets of magnetodielectric spheres arbitrarily arranged on a simple tetragonal lattice, dispersion diagrams of seven different arrangements of the spheres are analyzed for three combinations of sphere types: I) dielectric spheres with equal permittivity but different radius; II) dielectric spheres with equal radius but different permittivity; and III) one set of spheres is purely dielectric while the other set is magnetic. Results show that the maximum bandwidths of the DNG region provided by different spheres arrangements for spheres combinations I-III are, respectively, 0.21%, 0.069%, and 7.403%. Compared to results reported in previous literature, analysis of these possible arrangements of the spheres shows similar narrow double-negative (DNG) bandwidths for spheres combinations I and II, and wider DNG bandwidths for spheres combination III. Although purely dielectric materials with relative permittivity much greater than one are readily available, the usefulness of purely dielectric DNG metamaterials still depends on whether the narrow bandwidths achievable are acceptable for the particular applications. Since purely magnetic materials with relative permeability much greater than one above 1 GHz are not currently available, the practicality of fabricating DNG metamaterials using arrays with spheres combination III is questionable for radio frequency (RF) applications, at least at present, despite the fact that this combination yields much wider DNG bandwidths than those of spheres combinations I and II.

The Crystalline Nanocluster Phase as a Medium for Structural and Spectroscopic Studies of Light Absorption of Photosensitizer Dyes on Semiconductor Surfaces

The crystalline nanocluster phase, in which nanoscale metal oxide clusters are self-assembled in three-dimensional periodic arrays, is described. The crystalline assembly of nanoparticles functionalized with technologically relevant ligands offers the opportunity to obtain unambiguous structural information that can be combined with theoretical calculations based on the known geometry and used to interpret spectroscopic and other information. A series of Ti/O clusters up to approximately 2.0 nm in diameter have been synthesized and functionalized with the adsorbents catechol and isonicotinic acid. Whereas the isonicotinate is always adsorbed in a bridging monodentate mode, four different adsorption modes of catechol have been identified. The particles show a significantly larger variation of the Ti-O distances than observed in the known TiO(2) phases and exhibit both sevenfold overcoordination and five- and fourfold undercoordination of the Ti atoms. Theoretical calculations show only a moderate dependence of the catecholate net charge on the geometry of adsorption. All of the catechol-functionalized clusters have a deep-red color due to penetration of the highest occupied catechol levels into the band gap of the Ti/O particles. Spectroscopic measurements of the band gap of the Ti(17) cluster are in good agreement with the theoretical values and show a blue shift of approximately 0.22 eV relative to those reported for anatase nanoparticles.

Plasmonic nanostructures and optical metamaterials: Studies by the layer-multiple-scattering method

We apply the layer-multiple-scattering method to study the optical properties of different plasmonic architectures; namely two- and three-dimensional periodic arrays of metallic nanocylinders and of metallodielectric nanosandwiches. These structures exhibit various types of collective plasmonic resonances, tunable over a broad spectral range from infrared to visible frequencies, which cause large enhancement of the local field and give rise to interesting phenomena that we discuss and provide a consistent interpretation of the underlying physics. We analyze extinction spectra of finite slabs of the structures under consideration and explain the different spectral features. In relation to optical metamaterials, we deduce effective electromagnetic parameters by the S-matrix retrieval procedure for single- and multi-layer slabs of periodic arrays of metallodielectric nanosandwiches and propose a method to resolve ambiguities in the determination of the effective refractive index, which become prominent for thick slabs, based on the complex band structure of the corresponding infinite crystal.

A New Photoactive Crystalline Highly Porous Titanium(IV) Dicarboxylate

Titanium is a very attractive candidate for MOFs due to its low toxicity, redox activity, and photocatalytic properties. We present here MIL-125, the first example of a highly porous and crystalline titanium(IV) dicarboxylate (MIL stands for Materials of Institut Lavoisier) with a high thermal stability and photochemical properties. Its structure is built up from a pseudo cubic arrangement of octameric wheels, built up from edge- or corner-sharing titanium octahedra, and terephthalate dianions leading to a three-dimensional periodic array of two types of hybrid cages with accessible pore diameters of 6.13 and 12.55 A. X-ray thermodiffractometry and thermal analysis show that MIL-125 is stable up to 360 degrees C under air atmosphere while nitrogen sorption analysis indicates a surface area (BET) of 1550 m(2) x g(-1). Moreover, under nitrogen and alcohol adsorption, MIL-125 exhibits a photochromic behavior associated with the formation of stable mixed valence titanium-oxo compounds. The titanium oxo cluster are back oxidized in the presence of oxygen. This photochemical phenomenon is analyzed through the combined use of Electron Spin Resonance (ESR) and UV-visible absorption spectroscopies. The photogenerated electrons are trapped as Ti(III) centers, while a concomitant oxidation of the adsorbed alcohol molecules occurs. This new microporous hybrid is a very promising candidate for applications in smart photonic devices, sensors, and catalysis.

An issue to remember

Thumbing through a recent copy of a journal reveals unexpected riches.

X-ray scattering from periodic arrays of quantum dots

Three-dimensional periodic arrays of self-organized quantum dots in semiconductormultilayers are investigated by high-resolution x-ray scattering. We demonstratethat the statistical parameters of the dot array can be determined directly fromthe scattering data without performing a numerical simulation of the scatteredintensity.