Icosahedral twins

The simplest form of these clusters is twenty interlinked tetrahedral crystals joined along triangular (e.g. cubic-(111)) faces, although more complex variants of the outer surface also occur.

A variety of different methods (e.g. condensing metal nanoparticles in argon, deposition on a substrate, wet chemical synthesis) lead to the icosahedral form, and they also occur in virus capsids.

Icosahedral arrangements, typically because of their smaller total surface energy,[4] can be preferred for small nanoparticles.

For face centered cubic (fcc) materials such as gold or silver these structures can be considered as being built from twenty different single crystal units all with three twin facets arranged in icosahedral symmetry, and mainly the low energy {111} external facets.

Roland De Wit pointed out that these can be thought of in terms of disclinations,[9] an approach later extended to three dimensions by Elisabeth Yoffe.

[13] The most common approach to understand the formation of these particles, first used by Shozo Ino in 1969,[4] is to look at the energy as a function of size comparing these icosahedral twins, decahedral nanoparticles and single crystals.

[18] There is no general consensus on the exact sizes when there is a transition in which type of particle is lowest in energy, as these vary with material and also the environment such as gas and temperature; the coupling surface stress term and also the surface energies of the facets are very sensitive to these.

[20][21][22] In addition, as first described by Michael Hoare and P Pal[23] and R. Stephen Berry[24][25] and analyzed for these particles by Pulickel Ajayan and Laurence Marks[26] as well as discussed by others such as Amanda Barnard,[27] David J. Wales,[28][29][30] Kristen Fichthorn[31] and Francesca Baletto and Riccardo Ferrando,[32] at very small sizes there will be a statistical population of different structures so many different ones will exist at the same time.

In many cases nanoparticles are believed to grow from a very small seed without changing shape, and hence what is found reflects the distribution of coexisting structures.

An example is shown in the figure, with probability in the lower part and energy above with axes of an order parameter

Using transmission electron microscopy and diffraction these authors demonstrated the presence of the units in the particles, and also the twin relationships.

) point group symmetry.These forms occur for both elemental nanoparticles[36][37] as well as alloys[38][39] and colloidal crystals.

[40] A related form also exists in icosahedral viruses as shown in the electron micrograph images.

[41][42] Quasicrystals are un-twinned structures with long range rotational but not translational periodicity, that some initially tried to explain away as icosahedral twinning.