Close packing deviations from

The deviation from the Einstein equation at higher concentrations is represented in Figure 13, which is typical of many systems (88,89). The relative viscosity tends to infinity as the concentration approaches the limiting volume fraction of close packing ( ) (0 = - 0.7). Equation 10 has been modified (90,91) to take this into account, and the expression for becomes (eq. 11) ... 

Various phases have been described55 for thiolates adsorbed at Au(lll) surfaces starting from ( /3x /3) i 30° at low coverage and including the 3 x 2 /3, 3x4 and p x 3. All of these are commensurate with the Au(lll) surface. In sharp contrast, with Ag(lll) an incommensurate ( /7x /7) i 19.1° structure forms for carbon chains longer than 2. The deviation from commensurate behaviour is thought to be due to repulsive interactions between the close-packed alkyl chains and the reduction in strength of the Ag-Ag bonds to... 

The ratio d3a of the lattice constants is a direct measure of the deviation of the lattice from a perfect cubic close-packed lattice, which is it measures the layeredness of the lattice. An ideal ccp lattice has a d3a ratio of 1.633, whereas a pure layered lattice with no transition metal in the lithium layer has a... 

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. 

It is important to emphasize that the above discussion does not take into account the optical anisotropy of the oriented films (5), and assuming the same refractive index for all the sample. However, if the films have the same molecular density, such as, for the first approximation, complete monolayers (5-7), these constraints are not critical. On the other hand, these considerations may be important in partial monolayers, since significant deviations may arise when going down in surface concentration. The refractive index of the film, n2, is a monotonic function of the molecular density, varying from 1.00, in the limit of zero surface coverage, to about 1.50, in a complete closely-packed monolayer. 

The most important causes of deviation of k from the normal value will, however, be those properties of the molecules which cause the rate of increase of F with temperature to differ from the rate of increase of gaseous pressure. These may be very large, as the molecules are closely packed in the surface, and will no doubt be determined by details of the shape and size of the molecules, as well as by the lateral attractions between them. Unfortunately, evaluation of these factors is quite impossible at present. 

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