Quasicrystals

PART:1-

Regular crystals have translational symmetry, where the same unit part is repeated over and over again with no rotation. Quasicrystals have rotational symmetry, where the same unit part is repeated over and over, but with a rotation about an angle.

Quasicrystals are structural forms that are both ordered and nonperiodic. They form patterns that fill all the space but lack translational symmetry. The term and the concept were introduced originally to denote a specific arrangement observed in solids which can be said to be in a state intermediary between crystal and glass. Producing Bragg diffraction, they share a defining property with crystals, but differ from them by lacking a simple repeating structure.

Mathematical artefacts known as 'aperiodic tilings' were invented in the early 1960s, but some twenty years later physical experiments gave conclusive evidence of their material existence. Within the field of crystallography and solid state physics the discovery has produced a paradigm shift which is indeed a minor scientific revolution.

[1] It was realized that quasicrystals had been investigated and observed earlier

[2] but until then the prevailing views about atomic structure of matter lead to their being explained away.

PART:2-

An ordering is nonperiodic if it lacks translational symmetry, which means that a shifted copy will never match exactly with its original. The ability to diffract comes from the existence of an indefinitely large number of elements with a regular spacing, a property loosely described as long-range order. Experimentally the aperiodicity is revealed in the unusual symmetry of the diffraction pattern.

The first officially reported case of what came to be known as quasicrystals was made by Dan Shechtman and coworkers in 1984. Between a mathematical model of a quasicrystal, such as the Penrose tiling, and the corresponding physical systems, the distinction is taken to be evident and usually does not have to be emphasized.

The study of the physical and optical properties of photonic crystals has generated a burst of new ideas for optical devices and systems. Special mention needs to be made here of photonic crystal silica fibres, which appear as the first application of photonic crystals to the real world of optical communications.

In the field of semiconductors and metals, the fabrication of photonic crystals has represented an important challenge for micro- and nanotechnology. In turn, these technologies have benefited from the validation of processes which has thus been completed. In this respect, the evolution of photonics has paralleled the revolution which has been taking place in the field of electronics with the development of nanotransistors and quantum dot memories.

PART:3-

Nanophotonics are now being recognized as a special branch of optics, in much the same way as nanoelectronics form a special branch of electronics. Some of the technological problems that had appeared at the time of the first studies on photonic crystals, are currently in the process of being solved. However, it should be stressed that future development and applications of photonic crystals are definitively dependent on the degree of accuracy which can be achieved in the fabrication of micro- and nanostructures, and thus on the overall dimensions of the corresponding devices.

One of the most striking illustrations of the fruitfulness of research on metallo-dielectric photonic crystals is probably the development of the so-called metamaterials, which are expected to provide a new approach towards negative refraction, through the simultaneous control of the effective permittivity and the effective permeability.

Since metamaterials are dependent upon the structure of the material rather than the properties of the atoms that make up it's composition, it is possible to build photonic metamaterials using packed nanospheres. Recently major breakthroughs have occurred in Nonlinear Liquid Crystal Nano-Metamaterials which use nanosphere- and nanoshell-doped liquid crystals can produce metamaterials with a tunable refractive index!