Aperiodic Arrangements Research Articles

Effect of aperiodicity on the broadband reflection of silicon nanorod structures for photovoltaics

We carry out a systematic numerical study of the effects of aperiodicity on silicon nanorod anti-reflection structures. We use the scattering matrix method to calculate the average reflection loss over the solar spectrum for periodic and aperiodic arrangements of nanorods. We find that aperiodicity can either improve or deteriorate the anti-reflection performance, depending on the nanorod diameter. We use a guided random-walk algorithm to design optimal aperiodic structures that exhibit lower reflection loss than both optimal periodic and random aperiodic structures.

Scattering properties of meta-atoms

Metamaterials consist of a periodic or aperiodic arrangement of so-called meta-atoms. Usually their optical properties are derived from the collective response of this ensemble. However, it is highly desirable to deduce them from the scattering properties of individual meta-atoms because frequently the periodic arrangement has a spurious effect on the desired functionality. Moreover, understanding the scattering properties of individual meta-atoms permits introducing guidelines for their design and predicting effective properties of amorphous metamaterials. To achieve this we introduce a genuine approach to quantify the properties of individual meta-atoms. To this end we evaluate spectrally resolved the composition of the rigorously calculated scattered field in terms of contributions of electromagnetic multipoles, such as electric and magnetic dipoles, quadrupoles and, in principle, arbitrary higher order moments. Beyond its direct application to metamaterial's design and characterization, the approach will be significant in the entire field of nanooptics as, for example, for optical nanoantennas.

Understanding complex magnetic order in disordered cobalt hydroxides through analysis of the local structure

In many ostensibly crystalline materials, unit-cell-based descriptions do not always capture the complete physics of the system due to disruption in long-range order. In the series of cobalt hydroxides studied here, Co(OH)${}_{2\ensuremath{-}x}$(Cl)${}_{x}$(H${}_{2}$O)${}_{n}$, magnetic Bragg diffraction reveals a fully compensated N\'eel state, yet the materials show significant and open magnetization loops. A detailed analysis of the local structure defines the aperiodic arrangement of cobalt coordination polyhedra. Representation of the structure as a combination of distinct polyhedral motifs explains the existence of locally uncompensated moments and provides a quantitative agreement with bulk magnetic measurements and magnetic Bragg diffraction.

Diffraction effects due to modulation of orthorhombic crystals by aperiodically arranged twin boundaries

A number of the orthorhombic crystals formed due to diffusionless transformations, of which Ni2MnGa crystal is an example, show diffraction patterns suggesting a modulation along the <110> directions. Nanotwined substructures with aperiodically arranged twin boundaries (TBs) on the (110) planes are found in such crystals. In the work, peculiarities of the diffraction intensity distributions for orthorhombic crystals with the aperiodic TBs arrangement are analyzed. It is shown that the intensity distributions for the twin-modulated structures formed in given orthorhombic crystals differ from those resulted from a wave-modulation of the crystals.

High-Q X-band distributed Bragg resonator utilizing an aperiodic alumina plate arrangement

This paper describes a high-Q X-band distributed Bragg resonator that uses an aperiodic arrangement of non-lambda/4 low loss alumina plates mounted in a cylindrical waveguide. An ABCD parameter waveguide model was developed to simulate and optimize the cavity. The dielectric plates and air waveguide dimensions were optimized to achieve maximum quality factor by redistributing the energy loss within the cavity. An unloaded quality factor (Q(0)) of 196,000 was demonstrated at 9.93 GHz.

The role of nanoparticle shapes and deterministic aperiodicity for the design of nanoplasmonic arrays

In this paper, we study the role of nanoparticle shape and aperiodic arrangement in the scattering and spatial localization properties of plasmonic modes in deterministic-aperiodic (DA) arrays of metal nanoparticles. By using an efficient coupled-dipole model for the study of the electromagnetic response of large arrays excited by an external field, we demonstrate that DA structures provide enhanced spatial localization of plasmonic modes and a higher density of enhanced field states with respect to their periodic counterparts. Finally, we introduce and discuss specific design rules for the engineering and optimization of field enhancement and localization in DA arrays. Our results, which we fully validated by rigorous Generalized Mie Theory (GMT) and transition matrix (T-matrix) theory, demonstrate that DA arrays provide a robust platform for the design of a variety of novel optical devices with enhanced and controllable plasmonic fields.

Mode confinement in photonic quasicrystal point-defect cavities for particle accelerators

In this letter, we present a study of the confinement properties of point-defect resonators in finite-size photonic-bandgap structures composed of aperiodic arrangements of dielectric rods, with special emphasis on their use for the design of cavities for particle accelerators. Specifically, for representative geometries, we study the properties of the fundamental mode (as a function of the filling fraction, structure size, and losses) via two-dimensional and three-dimensional full-wave numerical simulations, as well as microwave measurements at room temperature. Results indicate that for reduced-size structures, aperiodic geometries exhibit superior confinement properties by comparison with periodic ones.

Spectral diffusion and drift: Single chromophore and en masse

We develop a systematic description of spectral diffusion of ideal chromophores interacting with incoherently relaxing two-state, localized environmental degrees of freedom ("spins") for general initial environment configurations. We remedy the existing, incomplete treatments by formulating the problem in terms of the proper correlation function and by obtaining an accurate solution for generic aperiodic arrangements of environmental spins, nearly free of the customary simplifying assumptions on the multiparticle spin coordinate distribution. We report and estimate, for the first time, the effects of the drift and distortion of a narrow spectral line that arise when the line is not in the center of the inhomogeneous band. While the drift turns out to be modest in most ensemble measurements, accounting for its effects is imperative in analyzing single chromophore spectral jumps, to which end the authors propose a novel experiment. Further, we argue that by employing a sufficiently large chromophore one can decouple the concentration of the fluctuating centers from the strength of their interaction with the chromophore. Finally, the additional line broadening, owing to a distribution of the central chromophore frequencies, is evaluated. Upper estimates for an analogous broadening stemming from a nonequilibrium environment are made.

DNA: beyond the double helix

AbstractReciprocal exchange can be used to produce DNA motifs based on branching at the level of secondary structure. These motifs can be combined by sticky‐ended cohesion to produce a variety of structures. Stick polyhedra and nanomechanical devices have been produced by self‐assembly from motifs based on branched DNA. Periodic arrays with tunable surface features has also been produced; aperiodic arrangements have been used for DNA‐based computation.

Coding and geometrical shapes in nanostructures: A fractal DNA-assembly

Fractal patterns represent an important class of aperiodic arrangements. Generating fractal structures by self-assembly is a major challenge for nanotechnology. The specificity of DNA sticky-ended interactions and the well-behaved structural nature of DNA parallelogram motifs has previously led to a protocol that appears likely to be capable of producing fractal constructions [A. Carbone and N.C. Seeman, A route to fractal DNA assembly, Natural Computing 1, 469–480, 2002]. That protocol depends on gluing the set of tiles with special `glue tiles' to produce the fractal structure. It is possible to develop a fractal-assembly protocol that does not require the participation of gluing components. When designed with similar DNA parallelogram motifs, the protocol involves sixteen specific tiles, sixteen closely related tiles, and a series of protecting groups that are designed to be removed by the introduction of specific strands into the solution. One novel aspect of the construction on the theoretical level is the interplay of both geometry and coding in tile design. A second feature, related to the implementation, is the notion of generalized protecting groups.

Biochemistry and structural DNA nanotechnology: an evolving symbiotic relationship.

Structural DNA nanotechnology is derived from naturally occurring structures and phenomena in cellular biochemistry. Motifs based on branched DNA molecules are linked together by sticky ends to produce objects, periodic arrays, and nanomechanical devices. The motifs include Holliday junction analogues, double and triple crossover molecules, knots, and parallelograms. Polyhedral catenanes, such as a cube or a truncated octahedron, have been assembled from branched junctions. Stiff motifs have been used to produce periodic arrays, containing topographic features visible in atomic force microscopy; these include deliberately striped patterns and cavities whose sizes can be tuned by design. Deliberately knotted molecules have been assembled. Aperiodic arrangements of DNA tiles can be used to produce assemblies corresponding to logical computation. Both DNA structural transitions and branch migration have been used as the basis for the operation of DNA nanomechanical devices. Structural DNA nanotechnology has been used in a number of applications in biochemistry. An RNA knot has been used to establish the existence of RNA topoisomerase activity. The sequence dependence of crossover isomerization and branch migration at symmetric sites has been established through the use of symmetric immobile junctions. DNA parallelogram arrays have been used to determine the interhelical angles for a variety of DNA branched junctions. The relationship between biochemistry and structural DNA nanotechnology continues to grow.

Role of aperiodic surface defects on the intensity of electron diffraction spots

A random distribution of two-dimensional gallium arsenide (GaAs) islands is found to effect the intensity of the electron diffraction pattern from the GaAs(001) surface. By utilizing the spontaneous island formation phenomenon as well as submonolayer deposition, the island coverage is systematically changed. It is found that the intensities of the one-, two-, and three-quarter-order diffraction spots of the [11̄0] azimuth decrease as the concentration of islands increases. In addition, only in the presence of islands, does the intensity of the half-order spot decrease as the grazing angle of the electron beam is decreased. A simple quantitative model is developed that provides insight into how an aperiodic arrangement of islands effects the electron diffraction patterns.

Magneto-optical study of the magnetization reversal process of Fe nanowires

We discuss results of magneto-optical Kerr effect (MOKE) measurementsperformed on a thin Fe film of 13 nm thickness, which has been patterned into aperiodic arrangement of nanowires by means of optical interference lithography.The resulting array of nanowires consist of stripes having a width of 150 nm anda periodicity of 300 nm. MOKE hysteresis loops are measured withinmagnetic fields which are aligned in different directions, both parallel andperpendicular with respect to the direction of the nanowires as well as forvarious angles in between. A particular arrangement of the longitudinalKerr effect measurement allows us to identify both the longitudinal andthe transverse component of the magnetization of Fe nanowires. Fromthis both the angle and the magnitude of the magnetization vector M⃗ arederived. For a non-parallel alignment of the nanowires with respect to the direction of theexternal magnetic field, the hysteresis loops consist of a plateau region with two coercivefields Hc1and Hc2,which is discussed as resulting from an anisotropic pinning behaviour ofmagnetic domains in directions along and perpendicular to the nanowires.

Structure of One-Dimensional Al-Co-Ni Quasicrystal Studied by Atomic-Scale Transmission Electron Microscopy

The structure of a one-dimensional Al-Co-Ni quasicrystal in an Al 71 Co 19 Ni 10 alloy annealed at 1100°C for 11 h has been studied by atomic-scale observations of high-angle annular detector scanning transmission electron microscopy and high-resolution transmission electron microscopy. Its structure can be characterized as a two-dimensional aperiodic arrangement of columnar clusters of atoms with a decagonal section of 2.0 nm in diameter and with pentagonal symmetry. In the arrangement of the atomic clusters, pairs of two lattice planes with high density of the atomic clusters are periodically arrayed with an interval of about 3 nm along the one direction. The atomic clusters with two orientations of pentagonal symmetry are randomly arranged with no special ordering manner.

Periodic and aperiodic arrangements of dodecagonal (Ta, V)151Te74 clusters studied by transmission electron microscopy: The method’s merits and limitations

A series of metal-rich tellurides in the ternary system Ta/V/Te crystallizes in closely related structures representing different arrangements of a basic disc-like (Ta, V)151Te74 cluster. The centres of these clusters define various periodic or aperiodic square–triangle tilings on a length scale of about 2nm. The structure of the approximant Ta83V14Te60 with its underlying square tiling has been studied under various imaging conditions by high-resolution transmission electron microscopy and complementary image simulations. At a large defocus ε≈−180nm, a (Ta, V)151Te74 cluster is represented by a bright dot surrounded by 12 others forming a dodecagon. The application of this selective imaging technique allows us to determine the tilings, i.e., the cluster arrangements, of new approximants and of quasicrystalline phases almost unambiguously. More complex contrast features as observed in some regions of the sample and the streaks turning up in reciprocal space are interpreted as stacking faults along the pseudo-12-fold axis.

In Situ TEM Heating of Nanosized ZrO2

In situ TEM heating experiments at temperatures between 820° and 860°C provide significant insights into the atomistics of neck formation during the sintering of nanoscale faceted, single‐crystal particles of ZrO2. High‐resolution TEM was used to observe the crystallography and the relative orientation in a variety of original particle‐pairs and the relative orientation of their evolving necks. Previous studies have determined that unconstrained particles can rotate during neck growth. When there is a significant amount of misalignment, the particles are not able to align completely. In these instances, the neck that forms is epitaxial with one of the particles. Additionally, in particle‐pairs with significant misalignment, the neck stops growing when it forms a crystallographic facet which is continuous with the preexisting facet of the template particle. When the two particles have close to the same orientation, the particles rotate into complete alignment and the neck that forms is consequently epitaxial with both particles. When the neck‐particle system is in complete registry, the growing neck is rounded: there is an aperiodic arrangement of steps, even on the atomic resolution scale. The experimental results are discussed in terms of the random starting state of the two particles, the equilibrium crystal shape of the particle‐neck system, and the operative kinetic mechanisms.

Photonic Band Gaps in Two Dimensional Photonic Quasicrystals

It is generally believed that long range periodic order is instrumental in the formation of a photonic band gap. Using a spectral method that scales linearly with the system size, we found that sizable spectral gaps for each polarization in 2D can be found in aperiodic arrangements of dielectrics that resemble quasicrystalline tiling. Since the aperiodic arrangement has many inequivalent sites, the defect properties of these systems are more complex and interesting than conventional photonic band gap systems.

High-resolution electron microscopy study of the early stage of formation of a Al-Pd-Mn decagonal quasicrystal from its crystalline approximant

The formation process of the decagonal quasicrystalline phase (D-phase) with 1.2 nm periodicity from a crystalline approximant in the Al70Pd13Mn17 alloy has been identified by high-resolution electron microscopy. At the early formation stage, decagonal atom clusters, which are the most important structural units of the D-phase, were observed to segregate from the crystalline matrix with an atomic correlation determined by the structural characteristics of the crystal. A non-equilibrium structural state (a mixture of the segregated atom clusters and the crystalline matrix phase) was also observed, and its structural characteristics clearly revealed. The equilibrium D-phase, whose structure is characterized by an aperiodic arrangement of decagonal atom clusters with definite linkages and a long-range quasiperiodic correlation, was formed by fully annealing at 800degreeC for a long time. The linear phason strain in the equilibrium D-phase formed from the crystalline approximant may be related to the structur...

High-resolution transmission electron microscopy of the Al‒Pd‒Mn decagonal quasicrystal with 1.6 nm periodicity and its crystalline approximants

Abstract The structural characteristics of the decagonal quasicrystal with 1–6 nm periodicity and its various crystalline approximants in the Al70Pd20Mn5 system have been revealed by high-resolution electron microscopy. It is shown that the Al[sbnd]Pd[sbnd]Mn decagonal quasicrystal, formed as a main phase by rapid solidification, contains a kind of atom column with about 1.6 nm periodicity as the most fundamental structural unit. The two-dimensional aperiodic arrangements of the atom columns with definite linkages constructs the main structure of the decagonal quasicrystal. The quasiperiodic structural characteristic of the Al[sbnd]Pd[sbnd]Mn decagonal quasicrystal with 1.6 nm periodicity is compared with that of a Penrose tiling and that of an Al[sbnd]Pd[sbnd]Mn decagonal quasicrystal with 1.2 nm periodicity. Various crystalline approximants of the decagonal quasicrystal with 1.6 nm periodicity, existing in the as-casted and annealed states, are presented. It is shown that their structures can be systema...

The decagonal quasicrystal formed from an Al–Pd–Mn icosahedral quasicrystal

We present a detailed investigation on the decagonal quasicrystal (D-phase) formed from an Al-Pd-Mn icosahedral quasicrystal (I-phase) through a solid-state phase transformation, including its formation, compositional and crystallographical relationships with the matrix I-phase, growth mode, and structural characteristics. The as-melt-spun Al70Pd20Mn10 alloy contains only I-phase. By annealing at 800 °C, the D-phase is found to grow cpitaxially from the I-phase to establish a D/I two-phase equilibrium with distinctly different composition between them. The D-phase exhibits a stepped growth interface, which consists of a facet plane, formed by sharing the tenfold plane with a fivefold plane of the matrix I-phase, and some ledges across it. The growth of the D-phase into the I-phase proceeds through lateral movement of the ledges along the tenfold plane. High-resolution electron microscopy reveals that the structure of the D-phase is constructed by an aperiodic arrangement of decagonal atom clusters with definite linkages and long-range quasiperiodic correlation.