Pentagonal Symmetry and Disclinations in Small Particles

Abstract

A comprehensive review is given on experimental studies of small particles with fivefold symmetry accompanied by an in-depth theoretical description of their characteristics and computer modeling. The cases of uniform and nonuniform deformations (disclination model), stability and relaxation of elastic stresses in pentagonal particles and needle-like crystals, models of their formation are discussed.

Generation of subsurface voids and a nanocrystalline surface layer in femtosecond laser irradiation of a single-crystal Ag target

“…Closing the gap in the packing of the fcc domains introduces inhomogeneous strain into the system and is equivalent to the introduction of a positive wedge disclination with a power of 7.35º [79,80]. The strong quadratic dependence of the elastic strain energy of a disclination on the size of the crystal precludes the five-fold twinned structures from appearing in bulk crystals and largely limits their habitat to nanoparticles and nanowires with sizes up to several tens of nanometers [79,[80][81][82][83].…”

“…The strong quadratic dependence of the elastic strain energy of a disclination on the size of the crystal precludes the five-fold twinned structures from appearing in bulk crystals and largely limits their habitat to nanoparticles and nanowires with sizes up to several tens of nanometers [79,[80][81][82][83]. The pentagonal twinned structures have also been reported for nanocrystalline metals synthesized by severe plastic deformation techniques [84][85][86], where the formation of the fivefold deformation twins is attributed to a sequential twinning occurring under conditions of changing orientation of external stresses [87,88].…”

Structural distortions in 5–10 nm silver nanoparticles under high pressure

“…1,2 The properties exhibited by particles with multiply twinned polycrystalline structures are often far different from those of single-crystalline particles or from the bulk. The exposure of specific surfaces and the presence of particular grain boundaries facilitates interesting mechanical and chemical behaviors and alters the surface properties.…”

“…2,6 The Dh and Ih are constructed of irregular tetrahedral grains that have body-centered orthorhombic and rhombohedral crystal symmetries, respectively. The corresponding orthorhombic and rhombohedral distortions of the fcc lattice introduce small but uniform strains within each tetrahedral grain.…”

Многообразие Форм Роста Пентагональных Кристаллов При Электрокристаллизации Меди

“…Однако наибольших размеров такие кристаллы достигали лишь при электролити-ческом способе их получения [1]. Среди разнообразных моделей образования и роста пентаго-нальных кристаллов наиболее приемлемой и объясняющей известные экспериментальные фак-ты является дисклинационная модель [2,3]. В то же время энергетически выгодным образова-ние дисклинаций, как показано в [2,4] , может быть только в случае частиц размером не более сотен нм; поэтому наличие дисклинаций в более крупных пентагональных кристаллах (иногда до сотен мкм [1]), полученных электрохимическим осаждением, является дискуссионным.…”