Icosahedral twins
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icosahedral In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...
twin Twins are two offspring produced by the same pregnancy.MedicineNet > Definition of TwinLast Editorial Review: 19 June 2000 Twins can be either ''monozygotic'' ('identical'), meaning that they develop from one zygote, which splits and forms two em ...
is a nanostructure appearing for atomic clusters and also nanoparticles with some thousands of atoms. These clusters are twenty-faced, made of twenty interlinked
tetrahedra In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the o ...
crystals, typically joined along triangular (e.g. cubic-(111)) faces having three-fold symmetry. One can think of their formation as a kind of atom-scale
self-assembly Self-assembly is a process in which a disordered system of pre-existing components forms an organized structure or pattern as a consequence of specific, local interactions among the components themselves, without external direction. When the ...
. A related, more common structure has five units similarly arranged with twinning, which were known as "fivelings" in the 19th centuryH. Hofmeister (2004) "Fivefold twinned nanoparticles" in ''Encyclopedia of Nanoscience and Nanotechnology'' (ed. H. S. Nalwa, Amer. Sci. Publ., Stevenson Ranch CA) vol. 3, pp. 431-452
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, more recently as "decahedral multiply twinned particles", "pentagonal particles" or "star particles". A variety of different methods (e.g. condensing argon, metal atoms, and virus capsids) lead to icosahedral form at size scales where surface energies are more important those from the bulk.


Causes

When interatom bonding does not have strong directional preferences, it is not unusual for atoms to gravitate toward a
kissing number In geometry, the kissing number of a mathematical space is defined as the greatest number of non-overlapping unit spheres that can be arranged in that space such that they each touch a common unit sphere. For a given sphere packing (arrangement of ...
of 12 nearest neighbors. The three most symmetric ways to do this are by
icosahedral In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...
clustering, or by crystalline face-centered-cubic ( cuboctahedral) and/or hexagonal (tri- orthobicupolar)
close packing In geometry, close-packing of equal spheres is a dense arrangement of congruent spheres in an infinite, regular arrangement (or lattice). Carl Friedrich Gauss proved that the highest average density – that is, the greatest fraction of space occu ...
. Icosahedral arrangements, typically because of their smaller
Surface energy In surface science, surface free energy (also interfacial free energy or surface energy) quantifies the disruption of intermolecular bonds that occurs when a surface is created. In solid-state physics, surfaces must be intrinsically less energe ...
, may be preferred for small clusters. However, the
Achilles' heel An Achilles' heel (or Achilles heel) is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to ...
for icosahedral clustering is that it cannot fill space over large distances in a way that is translationally ordered, so there is some distortion of the atomic positions, that is elastic strain which DeWit pointed out can be thought of in terms of Disclinations, an approach later extended to 3D by Yoffe. The shape is also not always that of a simple icosahedron, and there are now several software codes that make it easy to calculate these, for instance references. At larger sizes the energy to distort becomes larger than the gain in surface energy, and bulk materials (i.e. sufficiently large clusters) generally revert to one of the crystalline close-packing configurations instead. In other words, when icosahedral clusters get sufficiently large, the bulk-atom vote wins out over the surface-atom vote, and the nanoparticles can reduce their energy by converting to simple
Single crystal In materials science, a single crystal (or single-crystal solid or monocrystalline solid) is a material in which the crystal lattice of the entire sample is continuous and unbroken to the edges of the sample, with no grain boundaries.RIWD. "Re ...
with a
Wulff construction The Wulff construction is a method to determine the equilibrium shape of a droplet or crystal of fixed volume inside a separate phase (usually its saturated solution or vapor). Energy minimization arguments are used to show that certain crystal pl ...
shape. This occurs typically in the range where the particles are 10-30
Nanometers 330px, Different lengths as in respect to the molecular scale. The nanometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: nm) or nanometer (American and British English spelling differences#-re ...
in diameter, but it does not always happen and the particles can grow to millimeter sizes.


Ubiquity

Icosahedral twinning has been seen in face-centered-cubic metal nanoparticles that have nucleated: (i) by evaporation onto surfaces, (ii) out of solution, and (iii) by reduction in a polymer matrix.
Quasicrystals A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical ...
are ''un-twinned'' structures with long range rotational but not translational periodicity, that some initially tried to explain away as icosahedral twinning. Quasi-crystals let non-space-filling coordination persist to larger size scales. However, they generally form only when the compositional makeup (e.g. of two dissimilar metals like Ti and Mn) serves as an antagonist to formation of one of the more common close-packed space-filling but twinned crystalline forms.


See also

{{Portal, Science, Technology *
Crystal twinning Crystal twinning occurs when two or more adjacent crystals of the same mineral are oriented so that they share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals that are tightly ...
*
Icosahedron In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...
* Nanomaterial based catalyst *
Nanotechnology Nanotechnology, also shortened to nanotech, is the use of matter on an atomic, molecular, and supramolecular scale for industrial purposes. The earliest, widespread description of nanotechnology referred to the particular technological goal o ...
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Quasicrystals A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical ...
*
Self-assembly of nanoparticles Nanoparticles are classified as having at least one of three dimensions be in the range of 1-100 nm. The small size of nanoparticles allows them to have unique characteristics which may not be possible on the macro-scale. Self-assembly is t ...


Footnotes

Nanoparticles