Omnidirectional Photonic Bandgap in Two-dimensional Photonic Quasicrystal Made of Near-Transparent Dielectric Material

Complete bandgap for all-dielectric photonic crystals in the microwave region can be obtained only by using high-contrast materials. This requires the usage of dielectric materials with high relative permittivity coefficient. In this paper, we study, both numerically and experimentally, a two-dimensional all-dielectric photonic quasicrystal made of polyurethane foam, which is considered in all microwave applications as a transparent material. The quasicrystal structure having an omnidirectional two-dimensional bandgap is mathematically generated by the direct inscription of Bragg’s peaks of the structure in the reciprocal space. The sample of the quasicrystal was manufactured on CNC (computer numerical controlled) milling machine out of foam with very low dielectric permittivity of 1.254. The numerical simulations and the experimental study are in good agreement with the theoretical model.

Formation of Fractal Dendrites by Laser-Induced Melting of Aluminum Alloys

We report on the fabrication of fractal dendrites using laser-induced melting of aluminum alloys. We target boron carbide (B4C), which is one of the most effective radiation-absorbing materials characterized by a low coefficient of thermal expansion. Due to the high fragility of B4C crystals, we were able to introduce its nanoparticles into a stabilization aluminum matrix of AA385.0. The high-intensity laser field action led to the formation of composite dendrite structures under the effect of local surface melting. Modelling the dendrite cluster growth confirms its fractal nature and sheds light on the pattern behavior of the resulting quasicrystal structure.

The Quasicrystal Model as a Framework for Order to Disorder Transitions in 2D Systems

Order to disorder transitions are important for 2D objects such as oxide films with a cellular porous structure, honeycomb, graphene, and Bénard cells in liquid and artificial systems consisting of colloid particles on a plane. For instance, solid films of the porous alumina represent an almost regular quasicrystal structure (perfect aperiodic quasicrystals discovered in 1991 is not implied here). We show that, in this case, the radial distribution function is well described by the quasicrystal model, i.e., the smeared hexagonal lattice of the two-dimensional ideal crystal by inserting a certain amount of defects into the lattice. Another example is a system of hard disks in a plane, which illustrates the order to disorder transitions. It is shown that the coincidence with the distribution function, obtained by the solution of the Percus-Yevick equation, is achieved by the smoothing of the square lattice and injecting the defects of the vacancy type into it. However, a better approximation is reached when the lattice is a result of a mixture of the smoothened square and hexagonal lattices. Impurity of the hexagonal lattice is considerable at short distances. Dependences of the lattices constants, smoothing widths, and impurity on the filling parameter are found. Transition to the order occurs upon an increasing of the hexagonal lattice contribution and decreasing of smearing.

Quasicrystals: What do we know? What do we want to know? What can we know?

More than 35 years and 11 000 publications after the discovery of quasicrystals by Dan Shechtman, quite a bit is known about their occurrence, formation, stability, structures and physical properties. It has also been discovered that quasiperiodic self-assembly is not restricted to intermetallics, but can take place in systems on the meso- and macroscales. However, there are some blank areas, even in the centre of the big picture. For instance, it has still not been fully clarified whether quasicrystals are just entropy-stabilized high-temperature phases or whether they can be thermodynamically stable at 0 K as well. More studies are needed for developing a generally accepted model of quasicrystal growth. The state of the art of quasicrystal research is briefly reviewed and the main as-yet unanswered questions are addressed, as well as the experimental limitations to finding answers to them. The focus of this discussion is on quasicrystal structure analysis as well as on quasicrystal stability and growth mechanisms.