Layer stacking order

FIGURE 29.3 XRD pattern of partially purified UC2 nanocapsules. The highest double peak corresponds to capsules and graphite interlayer spacings. The ampUfied zone between 42° and 46° evidences the layer stacking order different than in graphite. 

Figure C2.2.4. Types of smectic phase. Here tire layer stacking (left) and in-plane ordering (right) are shown for each phase. Bond orientational order is indicated for tire hexB, SmI and SmF phases, i.e. long-range order of lattice vectors. However, tliere is no long-range translational order in tliese phases.

Zirconium chloride and bromide have closely related but dissimilar stmctures. Both contain two metal layers enclosed between two nonmetal layers which both have hexagonal stmcture. In ZrCl, the four-layer sandwich repeats in layers stacked up according to /abca/bcab/cabc/, whereas the ZrBr stacking order is /abca/cabc/bcab/ (188). Both are metallic conductors, but the difference in packing results in different mechanical properties the bromide is much more brittle. 

Figure 5. Structure of LiC6. (a) Left schematic drawing showing the AA layer stacking sequence and the aa interlayer ordering of the intercalated lithium. Right Simplified representation [21. (b) In-plane distribution of Li in LiC6. (c) In-plane distribution of Li in LiC,.

A glance at the structure of graphite, illustrated in Fig. 1, reveals the presence of voids between the planar, sp -hybridized, carbon sheets. Intercalation is the insertion of ions, atoms, or molecules into this space without the destruction of the host s layered, bonding network. Stacking order, bond distances, and, possibly, bond direction may be altered, but the characteristic, lamellar identity of the host must in some sense be preserved. 

For a layer-stack material like polyethylene or other semicrystalline polymers the IDF presents clear hints on the shape of the layer thickness distributions, the range of order, and the complexity of the stacking topology. Based on these findings inappropriate models for the arrangement of the layers can be excluded. Finally the remaining suitable models can be formulated and tested by trying to fit the experimental data. 

If meridional streaks are found for materials built from layer stacks, these patterns can be analyzed analogously [259]. An application to data sets combined from series of reflections with increasing order is possible, as well. 

Water on Smectites. Compared to vermiculites, smectites present a more difficult experimental system because of the lack of stacking order of the layers. For these materials, the traditional technique of X-ray diffraction, either using the Bragg or non-Bragg intensities, is of little use. Spectroscopic techniques, especially nuclear magnetic resonance and infrared, as well as neutron and X-ray scattering have provided detailed information about the position of the water molecules, the dynamics of the water molecule motions, and the coordination about the interlayer cations. 

From Deer, R. A., W. A. Howie, and J. Zussman (1963). Rock-Forming Minerals, Polylype = the crystallographic designation of the stacking order of tetranedral and Layers display 4.35-nm corregation periods. 

Imagine two parallel plates of area A between which is sandwiched a liquid of viscosity r). If a force F parallel to the x direction is applied to one of these plates, it will move in the x direction as shown in Figure 4.1. Our concern is the description of the velocity of the fluid enclosed between the two plates. In order to do this, it is convenient to visualize the fluid as consisting of a set of layers stacked parallel to the boundary plates. At the boundaries, those layers in contact with the plates are assumed to possess the same velocities as the plates themselves that is, v = 0 at the lower plate and equals the velocity of the moving plate at that surface. This is the nonslip condition that we described in Chapter 2, Section 2.3. Intervening layers have intermediate velocities. This condition is known as laminar flow and is limited to low velocities. At higher velocities, turbulence sets in, but we do not worry about this complication. 

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