Closely packed arrays

Figure C2.17.3. Close-packed array of sub-micrometre silica nanoparticles. Wlren nanoparticles are very monodisperse, they will spontaneously arrange into hexagonal close-packed stmcture. This scanning electron micrograph shows an example of this for very monodisperse silica nanoparticles of -250 nm diameter, prepared in a thin-film fonnat following the teclmiques outlined in [236].

Bismuth Triiodlde. Bismuth(Ill) iodide is a greenish black crystalline powder. The iodines are in a hexagonal close-packed array with each bismuth having six nearest-neighbor iodines at 0.32 nm (21). This suggests that the lone pair on bismuth is stereochemicaHy inactive and that the compound is largely ionic in character. 

The essence of this idea is that there is a limit to which particles of like-size can occupy a given space, even when arranged in closely packed arrays (e.g., cubic or tetrahedral arrays). The voids that are left are usually smaller than the parent particles and may be filled by particles of smaller size to increase the concentrations of particles in space. Thus, polydispersity can give a lower viscosity at the same volume fraction or permit higher volume loading at the equivalent monodisperse viscosity. 

As shown in Figure 9.18, Li+ ions fit into a closely packed array of Cl-ions, but Na+ ions do not. What is the value of the r tion/ranioi, ratio at which a cation just fits into a structure of this type ... 

The rock-salt structure is a common ionic structure that takes its name from the mineral form of sodium chloride. In it, the Cl- ions lie at the corners and in the centers of the faces of a cube, forming a face-centered cube (Fig. 5.39). This arrangement is like an expanded ccp arrangement the expansion keeps the anions out of contact with one another, thereby reducing their repulsion, and opens up holes that are big enough to accommodate the Na+ ions. These ions fit into the octahedral holes between the Cl ions. There is one octahedral hole for each anion in the close-packed array, and so all the octahedral holes are occupied. If we look carefully at the structure, we can see that each cation is surrounded by six anions and each anion is surrounded by six cations. The pattern repeats over and over, with each ion surrounded by six other ions of the opposite charge (Fig. 5.40). A crystal of sodium chloride is a three-dimensional array of a vast number of these little cubes. 

Buckminsterfullerene is an allotrope of carbon in which the carbon atoms form spheres of 60 atoms each (see Section 14.16). In the pure compound the spheres pack in a cubic close-packed array, (a) The length of a side of the face-centered cubic cell formed by buckminsterfullerene is 142 pm. Use this information to calculate the radius of the buckminsterfullerene molecule treated as a hard sphere, (b) The compound K3C60 is a superconductor at low temperatures. In this compound the K+ ions lie in holes in the C60 face-centered cubic lattice. Considering the radius of the K+ ion and assuming that the radius of Q,0 is the same as for the Cft0 molecule, predict in what type of holes the K ions lie (tetrahedral, octahedral, or both) and indicate what percentage of those holes are filled. 

Further effects seen with the substitution of Cl for T in the [(Zr6Z)Ii2] type are a reduction of inter-cluster I I repulsions which allows for a reduction in Zr-I inter-cluster bond lengths. The [110] section of this rhombohedral structure is shown in Fig. 5.3 and illustrates that the clusters can be described as a cubic-close-packed array, with the 3 axes running vertically through Z. Phase widths found are 0[Pg.63]

Among MC lattice models of the double layer, it is also worth mentioning the work of Nazmutdinov et al. (1988), who used a lattice model involving two mono-layers of water molecules on the surface of an electrode, forming a hexagonal close-packed array. The interaction of each water molecule in contact with the metal surface (assumed to be Hg) was taken from quantum-mechanical calculations. Information was obtained concerning the relative numbers of molecules with different numbers of hydrogen bonds, and it was concluded that the hypothesis of an icelike state of water in a monolayer on Hg is rather unlikely. 

Measuring static granular structures by MRI incurs some complications. The majority of NMR/MRI experiments to date use heterogeneous particles, specifically, solid particles with liquid cores. Thus, a close packed array of such particles would not image as close packed but would show gaps because the solid shells would yield weak or no NMR signal. 

Fig. 8.5 SEM images of (A) close packed array of latex beads (scale bar= 1 tm) and (B) macroporous aminopropyl-functionalized magnesium phyllosilicate monolith obtained after infiltration and extraction of colloidal template (scale bar= 1 pm).

Mono- or single-crystal materials are undoubtedly the most straightforward to handle conceptually, however, and we start our consideration of electrochemistry by examining some simple substances to show how the surface structure follows immediately from the bulk structure we will need this information in chapter 2, since modern single-crystal studies have shed considerable light on the mechanism of many prototypical electrochemical reactions. The great majority of electrode materials are either elemental metals or metal alloys, most of which have a face-centred or body-centred cubic structure, or one based on a hexagonal close-packed array of atoms. 

Twin geometry may refer to just one set of atoms in the crystal rather than all. This type of twinning is met, for example, in cases where a fraction of octahedral or tetrahedral cation sites in a close-packed array of anions are occupied in an ordered fashion. The close-packed anion array remains unchanged by the twin plane, which applies to the cation array alone (Fig. 3.24). These boundaries are of low energy and are often curved rather than planar. In oxides such as spinel, MgAl204, in which cations are distributed in an ordered fashion over some of the octahedral and tetrahedral sites, boundaries may separate regions that are twinned with respect to the tetrahedral cations only, the octahedral cations only or both. 

Similar antiphase boundaries form in metals with structures based upon a hexagonal close-packed array of metal atoms, such as magnesium. Condensation of vacancies upon one of the close-packed metal atom planes to form a vacancy loop, followed by subsequent collapse, will result in a hypothetical sequence. . ABABBABAB This arrangement will be unstable because of the juxtaposition... 

As in the case of twin planes, the antiphase relationship may affect only one part of the structure, for example, the cation substructure, while leaving the anion substructure unchanged. This is particularly common when the anion array can be considered to consist of a close-packed array of ions, which remains unchanged by the antiphase boundary (Fig. 3.28). 

In the closely related compound AgCuS, the sulfur atoms form a slightly distorted hexagonal close-packed array. The Cu+ ions are located in positions within this framework to form layers, while the Ag+ ions lie between the sulfur-copper layers. These Ag+ ions show a progressively greater anisotropic thermal motion as the temperature rises, until, above 93°C, they are essentially completely mobile, leading to extremely high silver ion conductivity. 

The unit cell of corundum is rhombohedral, but the structure is usually described with respect to hexagonal axes. Each of the cations is surrounded by six oxygen ions in a slightly distorted octahedral coordination. The anions are close to a hexagonal close-packed array and the cations occupy two-thirds of the available octahedral positions in this array in an ordered fashion. The structure is also adopted by a-Fe203 and Q2O3. 

Intuitively, one would expect a volume contraction on forming a strongly bonded compound from the elements. Indeed, Richards 190, 191) regarded heats of formation as heats of compression. The fractional volume contraction, AV = (molecular volume - 2 atomic vol-ume)/2(atomic volume), has been related to formation heats for NaCl or CsCl type structures 151). Even nonpolar compounds in the condensed state cohere in close-packed arrays. The packing density of difluorine, derived from the ratio of the van der Waals envelope to the molecular volume, is especially low, and a larger contraction would be expected for fluorides than for other halides. This approach has yet to be systematically examined. 

The majority of clusters Mm represent fragments of a close-packed array of metal atoms hep or ccp. The triangle, tetrahedron, square-... 

Another important structure is the fluorite structure exhibited by oxides with the formula M02. The coordination of the cation/anion is 8 4. The fluorite structure shown in Figure 2.2d consists of a cubic close-packed array of cations in which all the tetrahedral sites are occupied by anions. The fluorite structure corresponding to the mineral CaF2 is exhibited in oxides such as ZrOz, HfD2, U02, and Tb02. 

This structure could also be described as derived from a cubic close-packed array of atoms (Bi atoms) by filling all the tetrahedral and octahedral holes with Li atoms. 

The structure can be described as composed by a hexagonal close-packed array of oxide ions with aluminium ordered on two-thirds of the octahedral interstices. Along the [001] direction there are six oxygen sheets. 

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