Structure found in atomic clusters and nanoparticles
Annular dark-field image of a 5-fold twinned Au nanoparticle with a shape similar to a pentagonal bipyramid.FCC icosahedral model projected down the 5-fold on the left and 3-fold zone axis orientation on the right.Examples of digital dark field bowtie/butterfly images of an icosahedral particle.Dark field analysis of dual-tetrahedron crystal pairs.
An icosahedral twin is a nanostructure appearing in atomic clusters and also nanoparticles with some thousands of atoms. These clusters are twenty-faced, with twenty interlinked tetrahedral crystals joined along triangular (e.g. cubic-(111)) faces having three-fold symmetry. A related, more common structure has five units similarly arranged with twinning, which were known as "fivelings" in the 19th century,[1][2][3] 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 the icosahedral form at size scales where surface energies are more important than those from the bulk.
^Hofmeister, H. (1998). <3::aid-crat3>3.0.co;2-3 "Forty Years Study of Fivefold Twinned Structures in Small Particles and Thin Films". Crystal Research and Technology. 33 (1): 3–25. Bibcode:1998CryRT..33....3H. doi:10.1002/(sici)1521-4079(1998)33:1<3::aid-crat3>3.0.co;2-3. ISSN 0232-1300.
^H. 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 ISBN 1-58883-059-4 pdf.
^Marks, L D; Peng, L (2016). "Nanoparticle shape, thermodynamics and kinetics". Journal of Physics: Condensed Matter. 28 (5): 053001. Bibcode:2016JPCM...28e3001M. doi:10.1088/0953-8984/28/5/053001. ISSN 0953-8984. PMID 26792459. S2CID 12503859.
An icosahedraltwin is a nanostructure appearing in atomic clusters and also nanoparticles with some thousands of atoms. These clusters are twenty-faced...
in 1969, is to look at the energy as a function of size comparing icosahedraltwins, decahedral nanoparticles and single crystals. The total energy for...
redirect targets Fiveling – Five crystals arranged round a common axis Icosahedraltwins – Structure found in atomic clusters and nanoparticles Phason – Collective...
such as the triclinic system. Simple twinned crystals may be contact twins or penetration twins. Contact twins meet on a single composition plane, often...
It is an example of the Platonic solid and of the deltahedron. The icosahedral graph represents the skeleton of a regular icosahedron. Many polyhedrons...
be used as a snub tetrahedron.) Aperiodic tiling Archimedean graph Icosahedraltwins List of uniform polyhedra Prince Rupert's cube#Generalizations Quasicrystal...
stabilization of decahedral nanoparticle and icosahedraltwins. In both cases an arrangement of internal twin boundaries leads to lower energy surface energy...
hyperdiamond Detonation nanodiamond Fiveling, twinned structure common in nanodiamonds Icosahedraltwins, structure common in nanodiamonds Wikimedia Commons...
suboxide (B6Ox, x<0.9) might form icosahedral particles, which are neither single crystals nor quasicrystals, but twinned groups of twenty tetrahedral crystals...
several types of twins, including contact twins, reticulated twins, geniculated twins, penetration twins, cyclic twins, and polysynthetic twins. Contact, or...
and antiprisms: the tetrahedral group, the octahedral group, and the icosahedral group. In dimensions n {\displaystyle n} ⩾ 5, there are only three regular...
dodecahedron. It can be constructed by arranging five tetrahedra in rotational icosahedral symmetry (I), as colored in the upper right model. It is one of five...
symmetry embedded in octahedral or icosahedral symmetry, 46-67: Tetrahedral symmetry embedded in octahedral or icosahedral symmetry, 68-75: enantiomorph pairs...
integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, that there are infinitely many pairs of primes that differ...
compound of five cubes, compound of five octahedra, and stella octangula. Icosahedral symmetry I h {\displaystyle \mathrm {I} _{h}} is isomorphic to the alternating...
including solids with axes of five-fold symmetry and three-dimensional icosahedral symmetry. The first reported example of a synthetic quasicrystal: Working...
been extended to them. There are infinitely many lucky numbers. Twin lucky numbers and twin primes also appear to occur with similar frequency. However,...
uniform polyhedra: the tetrahedral group, the octahedral group, the icosahedral group, and a dihedral group (of orders 24, 48, 120, and 4 n {\displaystyle...
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