Cubic packed arrays

MHX-Ni batteries 219 crystallography 365 cubic close packing 47 cubic packed arrays 293 curing, lead oxides 167... 

Low strain soil behavior can be illustrated by considering the soil as an assemblage of discrete elastic particles. A cubically packed array of spheres loaded along one of the packing axes is shown in Figure 9.4. A packing axis is the preferred orientation of the majority of the particles. 

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. 

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]

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. 

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. 

For estimation purposes, consider the 7-AI2O3 surface phase to be similar to the bulk structure—a cubic close-packed array of oxygen atoms with aluminum atoms in interstices. With this model there is one AF nucleus of... 

III. Cation arrays derived from body-centred cubic packing... 

An alternative way of viewing this structure is to think of it as a cubic close-packed array of chloride Ions with sodium Ions filling all the octahedral holes. The conventional unit cell of a ccp array Is an F face-centred cube (hence the cubic in ccp) the close-packed layers lie at right angles to a cube diagonal (Figure 1.32). Filling all the... 

Below 146°C, two phases of Agl exist y-Agl, which has the zinc blende structure, and (3-Agl with the wurtzite structure. Both are based on a close-packed array of iodide ions with half of the tetrahedral holes filled. However, above 146°C a new phase, a-AgI, is observed where the iodide ions now have a body-centred cubic lattice. If you look back to Figure 5.7, you can see that a dramatic increase in conductivity is observed for this phase the conductivity of a-Agl is very high, 131 S m , a factor of 10 higher than that of (3- or y-AgI, comparable with the conductivity of the best conducting liquid electrolytes. How can we explain this startling phenomenon ... 

The spinel structure is a common mixed oxide structure, typified by spinel itself MgAl204, in which the oxide ions are in a face-centred cubic close packed array (see Section 1.6.3 and Figure 1.43). For an array of TV oxide ions, there are TVoctahedral holes, and the trivalent ions (AP" ) occupy half of the octahedral sites (Figure 9.10). 

Spinels. Several ternary oxides of AB2O4 composition have the structure of the mineral spinel, MgAl204, the unit cell containing eight formula units (Mgg A1, g03 2). The structure (Fig. 1.12) consists of a cubic close-packed array of oxide ions in which the magnesium ions occupy of the tetrahedral (A) sites and the... 

In the sphalerite structure the anions form a cubic close packed array. The structure has a single adjustable parameter, the cubic cell edge. The 0 ions are too small for them to be in contact in this structure (see Fig. 6.4) so ZnO adopts the lower symmetry hexagonal wurtzite structure which has three adjustable parameters, the a and c unit cell lengths and the z coordinate of the 0 ion, allowing the environment around the Zn " ion to deviate from perfect tetrahedral symmetry. In the sphalerite structure the ZnX4 tetrahedron shares each of its faces with a vacant octahedral cavity (one is shown in Fig. 2.6(a)), while in the wurtzite structure one of these faces is shared with an empty tetrahedral cavity which places an anion directly over the shared face as seen in Fig. 2.6(b). The primary coordination number of Zn " in sphalerite is 4 and there are no tertiary bonds, but in wurtzite, which has the same primary coordination number, there is an additional tertiary bond with a flux of 0.02 vu through the face shared with the vacant tetrahedron. 

Wurtzite structure. Zinc sulfide can also crystallize in a hexagonal form called wurtzite that is formed slightly less exothermically than the cubic zinc blende (sphalerite) modification (Afff = —192.6 and —206.0 kJ mol-1, respectively) and hence is a high temperature polymorph of ZnS. The relationship between the two structures is best described in terms of close packing (Section 4.3) in zinc blende, the anions (or cations) form a cubic close-packed array, whereas in wurtzite they form hexagonal close-packed arrays. This relationship is illustrated in Fig. 4.13 note, however, that this does not represent the actual unit cell of either form. 

The structure of the sodium selenide crystal may be described as a cubic close-packed array of Se2- ions, with an Na+ ion in every tetrahedral hole. 

Spinel Mixed Metal Oxide Pigments. The crystal structure of spinel, MgAl204, is made up of an approximately cubic closely packed array of oxygen ions (Fig. 26). The unit cell contains 32 oxygen ions. Of the 64 possible tetrahedral sites, 8 are occupied by magnesium ions of the 32 possible octahedral sites, 16 are occupied by aluminum ions. 

Fig. 4.14 Unit cells in the cubic closest packed systems, (a) A face-ccntcred array of atoms. Note that the exposed layer consists of a closest packed array of fifteen atoms. Consider this the A layer , (b) A closest packed layer of six atoms placed on (a). Consider this the B layer, (c) The final atom, a member of the C layer, is added to complete the cube. The fee unit cell is redrawn in (d. Note that the single atom that composes the C layer does net lie above any atom in the A layer (as it would if ths were hep).

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