Decahedra and Icosahedra Everywhere: The Anomalous Crystallization of Au and Other Metals at the Nanoscale

Abstract

Throughout history, objects with fivefold symmetry have been a popular topic of interest for artists, philosophers, and scientists. This may be because fivefold symmetry is very conspicuous in nature. In the case of crystals, fivefold rotational symmetry is mathematically forbidden, and macroscopic crystals exhibiting fivefold symmetry have never been shown to exist. Nevertheless, in the nanoworld, nanoparticles are often found with decahedral and icosahedral shapes that have an overall pseudo-fivefold symmetry. These structures are observed at many length scales, from 1 nm up to 1 µm. In this review, several reasons for the stability of fivefold nanoparticles are discussed. These include the formation of twin boundaries, surface reconstruction faceting, and other factors.

Icosahedral supracrystal assembly from polymer-grafted nanoparticles via interplay of interfacial energy and confinement effect

“…In an emulsion-based system involving polymers, the overall free energy arises from a combination of the oil-water (emulsion droplet-surrounding aqueous medium) interfacial energy ( E int ) and the stretching energy ( E str ) induced by conformational changes of the polymers ( 49 ). In addition, the presence of multiple twin planes in icosahedral supracrystals can lead to an increase in both twinning energy and strain energy essential for bridging the gaps between tetrahedrons ( 50 ). Nevertheless, the substantial interparticle distances resulting from the use of long polymer ligands effectively reduce the twinning energy ( 42 ).…”

Following structural changes in iridium nanoparticles during oxygen evolution electrocatalysis with operando X-ray total scattering

“…Decahedral particles are constructed from fcc-shaped crystals separated by twin boundaries, resembling stacking faults. 70 Decahedral metal nanoparticles are readily obtained in many systems, 73 and the formation of decahedral Ir nanoparticles has been reported via a similar synthesis route. 74 To validate our modeling approach further, we used a brute-force structure-mining algorithm 69,70 as presented in the SI in Table S2 and Figure S10.…”

Following structural changes in iridium nanoparticles during oxygen evolution electrocatalysis with operando X-ray total scattering

“…Decahedral particles are constructed from fcc-shaped crystals separated by twin boundaries, resembling stacking faults. 70 Decahedral metal nanoparticles are readily obtained in many systems, 73 and the formation of decahedral Ir nanoparticles has been reported via a similar synthesis route. 74 Therefore, we model the experimental PDF with an Ir 192 decahedral particle, see the structure inset in Figure 2.…”