Stacking Principle and Magic Sizes of Transition Metal Nanoclusters Based on Generalized Wulff Construction

Abstract

Nanoclusters with extra stability at certain cluster sizes are known as magic clusters with exotic properties. The classic Wulff construction principle, which stipulates that the preferred structure of a cluster should minimize its total surface energy, is often invoked in determining the cluster magicity, resulting in close-shelled Mackay icosahedronal clusters with odd-numbered magic sizes of 13, 55, 147, etc. Here we use transition metal clusters around size 55 as prototypical examples to demonstrate that, in the nanometer regime, the classic Wulff construction principle needs to be generalized to primarily emphasize the edge atom effect instead of the surface energy. Specifically, our detailed calculations show that nanoclusters with much shorter total edge lengths but substantially enlarged total surface areas are energetically much more stable. As a consequence, a large majority of the nanoclusters within the 3d-, 4d-, and 5d-transition metal series are found to be fcc or hcp crystal fragments with much lower edge energies, and the widely perceived magic size of 55 is shifted to its nearby even numbers.

Stacking-controllable interlayer coupling and symmetric configuration of multilayered MoS2

“…By varying the Mo:S ratio, the shapes of the MoS 2 crystals evolve from a triangle to a truncated triangle and finally become hexagonal 29,30 , as shown in Figure 1e. The shape transformation process along the direction perpendicular to the carrier-gas flow stipulates that the Mo:S ratio change is the primary reason for the shape transformation.…”

“…The confined Mo:S atomic ratio controls the final shape of the MoS 2 crystals, as explained by the Wulff construction principle, 29,30 which states that specific crystal shapes are preferred over others depending on their surface energies. In other words, the surface energy and its dependence on the crystallographic orientation can define the equilibrium shape of a crystal.…”

“…When the growth temperature increases above 850°C, the stacking order increases, forming bilayer seeded crystals with some layers reaching up to~15-20L with the formation of completely grown 3L or 4L AA(A…)-and AB(A…)-stacked MoS 2 crystals. 30 Furthermore, this growth is governed by a terrace-growth mechanism, wherein the triangles stack up layer by layer and shrink gradually to the center. During this growth process, the upper layers are formed later and have a shorter time to grow.…”

Investigação <i>ab initio</i> dos mecanismos de formação de nanoligas <i>core-shell</i> com platina e metais de transição dos períodos 3<i>d</i>, 4<i>d</i> e 5<i>d</i>

“…Apesar do estudo mencionado envolver tanto metais simples (i.e., metais que possuem apenas orbitas s e p) quanto metais de transição, apenas as seguintes estruturas referentes aos nanoclusters pGMC de MT 55 integram o presente trabalho: estrutura icosaédrica (ICO); 85 fragmentos de fcc (FCCf); 86 fragmentos de hcp (HCPf); 86 estrutura politetraédrica (PTH); 87, 88 estrutura distorcida de núcleo reduzido (DRC); 89 estrutura do tipo-roda (WHE). 88 Dentre as estruturas investigadas, a estrutura ICO regular de simetria I h é uma configuração especial, uma vez que possui alta compactação e maximiza a esfericidade, o que tende a aumentar a estabilidade das partículas finitas em nanoescala. Por este motivo, optou-se por reproduzir nesse projeto de pesquisa não somente as estruturas pGMC observadas por Piotrowski et al 70 como também a estrutura ICO para cada MT 55 .…”

“…Nesse estudo, essa estrutura foi observada como a pGMC para um um único nanocluster,Ir 55 , que possui 7 átomos na região do caroço (48 na superfície). Assim como para as estruturas DRC, a maximização de átomos na superfície leva a um abaixamento da energia total do sistema, tal como apontaram Li et al 88 em seu estudo.…”