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Aerogel
Aerogel - synthetic porous ultralight material derived from a gel, in which the liquid component of the gel has been replaced with a gas. The result is a solid with extremely low density[1] and low thermal conductivity. Picture: a 2 gram sample of aerogel supporting a 2,5 kg brick.

Amorphous metal -  a solid metallic material, usually an alloy, with a disordered atomic-scale structure. Most metals are crystalline in their solid state, which means they have a highly ordered arrangement of atoms.  Batches of amorphous steel have been produced that demonstrate strengths much greater than conventional steel alloys.

Damascus
Damascus steel - a type of steel used in Middle Eastern swordmaking. Damascus steel was created from wootz steel, a steel developed in India around 300 BC.[1] These swords are characterized by distinctive patterns of banding and mottling reminiscent of flowing water. Such blades were reputed to be tough, resistant to shattering and capable of being honed to a sharp, resilient edge.[2] A research team in Germany published a report in 2006 revealing nanowires and carbon nanotubes in a blade forged from Damascus steel.[6] This finding was covered by National Geographic[7] and the New York Times.[8] Although certain types of modern steel outperform these swords, chemical reactions in the production process made the blades extraordinary for their time, as damascus steel was superplastic and very hard at the same time. Picture: a watered pattern characteristic of a Damascus steel. This is an XVIII century blade from Iran.

Conductive Polymers -  organic polymers that conduct electricity. One possible application is an organic solar cell, a type of polymer solar cell that uses organic electronics, a branch of electronics that deals with conductive organic polymers or small organic molecules,[1] for light absorption and charge transport to produce electricity from sunlight by the photovoltaic effect. 

Graphene - a one-atom thick layer of graphite. A nice video of the person who discovered this material, and others, can be seen at BBC's "Tomorrow's world", 2013. 

High-temperature superconductivity - materials that behave as superconductors at unusually[1] high temperatures.  The first high-Tc superconductor was discovered in 1986 by IBM researchers Karl Müller and Johannes Bednorz,[2][3] who were awarded the 1987 Nobel Prize in Physics "for their important break-through in the discovery of superconductivity in ceramic materials". Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion of magnetic fields occurring in certain materials when cooled below a characteristic critical temperature. It was discovered by Dutch physicist Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum mechanical phenomenon. It is characterized by the Meissner effect, the complete ejection of magnetic field lines from the interior of the superconductor as it transitions into the superconducting state. The occurrence of the Meissner effect indicates that superconductivity cannot be understood simply as the idealization of perfect conductivity in classical physics. 

Metamaterials -  cellular assemblies of multiple elements fashioned from materials including metals and plastics, arranged in periodic patterns. Metamaterials gain their properties not from their constituents, but from their exactingly-designed structures. Their precise shape, geometry, size, orientation and arrangement can affect light or sound in a manner that is unachievable with conventional materials.

Metal foam - a cellular structure consisting of a solid metal, frequently aluminium, containing a large volume fraction of gas-filledpores. The pores can be sealed (closed-cell foam), or they can form an interconnected network (open-cell foam). The defining characteristic of metal foams is a very high porosity: typically 75–95% of the volume consists of void spaces making these ultralight materials.

Graphete
Composite materials - materials made from two or more constituent materials with significantly different physical or chemical properties, that when combined, produce a material with characteristics different from the individual components. Picture: graphite composite part. 

Self healing material - a class of smart materials that have the structurally incorporated ability to repair damage caused by mechanical usage over time. The inspiration comes from biological systems, which have the ability to heal after being wounded. Initiation of cracks and other types of damage on a microscopic level has been shown to change thermalelectrical, and acoustical properties, and eventually lead to whole scale failure of the material. Usually, cracks are mended by hand, which is unsatisfactory because cracks are often hard to detect. A material (polymersceramics, etc.) that can intrinsically correct damage caused by normal usage could lower production costs of a number of different industrial processes through longer part lifetime, reduction of inefficiency over time caused by degradation, as well as prevent costs incurred by material failure.[1] For a material to be defined strictly as self-healing, it is necessary that the healing process occurs without human intervention.

Smart materials -  designed materials that have one or more properties that can be significantly changed in a controlled fashion by external stimuli

Nanomateirals - materials the single units of which is sized (in at least one dimension) between 1 and 1000nanometers (10−9 meter) but is usually 1—100 nm (the usual definition of nanoscale[1]).

Nanomaterial research is a field that takes a materials science-based approach on nanotechnology. It studies materials with morphological features on the nanoscale, and especially those that have special properties stemming from their nanoscale dimensions.

Silicene - a two-dimensional allotrope of silicon, similar to graphene. The material was discovered in 2012. 

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