Zero-dimensional materials

There is nothing intrinsically superior about non-zero-dimensional materials compared to lanthanide cages as magnetocaloric materials, but, thus far, synthetic chemists have been unable to realize as many of the required properties in cages simultaneously, as they have done with some chains and lattices. The key advantage is cramming in as many metals as possible into a structure with as few ligands as possible. 

The quantized silver clusters can be considered as metal quantum dots , because these are zero-dimensional materials where the band gap is formed by... 

Matrix-stabilized (glass, NaCl) CuCl nanocrystals is a typical zero-dimensional material, which constitutes a quantum dot system in which excitons are weakly confined [4]. Small angle X-ray scattering study has established that the resultant... 

In addition to structural and electronic properties that are explored in zero-dimensional materials, one-dimensional materials also exhibit rather interesting elastic properties. We shall begin this section with a brief review of elastic considerations regarding one-dimensional nanomaterials and afterward move onto structural and electronic properties. 

Carbon nanotubes have the same range of diameters as fullerenes, and are expeeted to show various kinds of size effeets in their struetures and properties. Carbon nanotubes are one-dimensional materials and fullerenes are zero-dimensional, whieh brings different effects to bear on their structures as well as on their properties. A whole range of issues from the preparation, structure, properties and observation of quantum effeets in carbon nanotubes in eomparison with 0-D fullerenes are diseussed in this book. 

The problem of accessibility in microporous solids is extreme in zero-dimensional zeolite structures such as clathrasils, that is, zeolite-related materials consisting of window-connected cages. The pore openings in these caged structures are restricted to six-membered rings of [Si04] units at most, which corresponds to pore diameters of approximately 0.2 nm [58]. These pores are too small for the removal of templates and, afterward, are impenetrable to typical sorptive molecules for characterization such as N2 and Ar or reactants such as hydrocarbons. Therefore, the intrinsic... 

The majority of MCE materials have been zero dimensional. More recently, MOFs have emerged as superior alternatives, relative to lanthanide cages, as... 

Tables 9.1 and 9.2 show how non-zero-dimensional compounds can have the largest MCEs. Even amongst this non-exhaustive selection, these compounds have larger Gd(III) percentages and densities. It is possible, of course, to synthesize polymeric compounds with inferior performance. However, these represent a new tool in the arsenal of magnetocaloric research, which, as we will see below, has been extremely successful, including in 3d-4f materials.

Point defects are only notionally zero dimensional. It is apparent that the atoms around a point defect must relax (move) in response to the defect, and as such the defect occupies a volume of crystal. Atomistic simulations have shown that such volumes of disturbed matrix can be considerable. Moreover, these calculations show that the clustering of point defects is of equal importance. These defect clusters can be small, amounting to a few defects only, or extended over many atoms in non-stoichiometric materials (Section 4.4). 

A block model of defects on a single-crystal surface is depicted in Figure 2.4.17 The surface itself in reality is a two-dimensional defect of the bulk material. In addition, one-dimensional defects in the form of steps which have zero-dimensional defects in the form of kink sites. Terraces, which are also shown in the figure, have a variety of surface sites and may also exhibit vacancies, adatoms, and point defects. Surface boundaries may be formed as a result of surface reconstruction of several equivalent orientations on terraces. 

The simplest way to classify nanomaterials used in combination with liquid crystal materials or the liquid crystalline state is by using their shape. Three shape families of nanomaterials have emerged as the most popular, and sorted from the highest to the lowest frequency of appearance in published studies these are zero-dimensional (quasi-spherical) nanoparticles, one-dimensional (rod or wirelike) nanomaterials such as nanorods, nanotubes, or nanowires, and two-dimensional (disc-like) nanomaterials such as nanosheets, nanoplatelets, or nanodiscs. 

In a Si zero-dimensional system the strong quantum confinement can increase the optical infrared gap of bulk Si and consequently shift the optical transition energies towards the visible range [65,66]. This is the reason for which silicon nanocrystals (Si-NCs) with a passivated surface are used as the natural trial model for theoretical simulations on Si based light emitting materials, such as porous Si or Si nanocrystals dispersed in a matrix. In this section we present a comprehensive analysis of the structural, electronic and optical properties of Si-NCs as a function of size, symmetry and surface passivation. We will also point out the main changes induced... 

Another aspect that is interesting to note concerns the dependence of the DFT gap on the orientation of the wire, indeed, for each wire size the following relation holds g[100] > g[lll] > Eg [110]. As has been pointed out in Ref. [121], this is related to the different geometrical structure of the wires in the [100], [111] and [110] directions. Indeed the [100], [111] wires appear as a collection of small clusters connected along the axis, while the [110] wires resemble a linear chain. So we expect that quantum confinement effects are much bigger in the [100], [111] wires, due to their quasi zero-dimensionality, with respect to the [110] wires. Further, the orientation anisotropy reduces with the wire width and it is expected to disappear for very large wires, where the band gap approaches that of the bulk material. 

These important, but not completely understood, problems are considered here by using the novel, quantum chemical, approach to the microscopical theory of ferroelectrics and related materials [1], The isomorphous H-bonded crystals M3(H/D)(A04)2 (M = K, Rb A = S, Se) are taken as examples. There are two reasons of such choice. This family is investigated actively at present. Moreover, it is a suitable subject of theoretical examination because of simple chemical constitution of the TKHS-like compounds (zero-dimensional H-bond network). 

The special effects associated with materials made up of nanosized particles are also due to non-local interactions. Such effects were first noticed in the field of micro-electronics during efforts to decrease the size of devices to quasi one-dimensional or zero-dimensional structures [236]. One possibility for obtaining zero-dimensional structures is the inclusion of spherical semiconductor particles in a transparent dielectric medium. Such isolated microcrystals, typically of nanometer size are known as quantum dots. Best-known examples include particles of CdS and CdSe isolated in silicate glasses. 

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