Stacked layers

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.

Layer Stacks and Protective Layers. The layer stack of an MO disk consists mainly of an MO layer, a dielectric antirefiection layer, and a metallic reflection layer (Fig. 14). The thickness of the antireflection layer as well as that of the MO layer have to be properly chosen to obtain a maximum magnetooptical figure-of-mefit (FOM). The FOM can be further increased by using a quadfilayer configuration with dielectric layers on both sides of the MO layer. Practical disks use the generalized configuration 50—120-nm dielectric layer, 25—90-nm MO layer, 17—70-nm dielectric layer (for quadfilayer configuration only), and 15—150-nm reflective layer. 

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. 

Ellipsometry is a method of measuring the film thickness, refractive index, and extinction coefficient of single films, layer stacks, and substrate materials with very high sensitivity. Rough surfaces, interfaces, material gradients and mixtures of different materials can be analyzed. 

Spectroscopic dlipsometry is sensitive to the dielectric functions of the different materials used in a layer stack. But it is not a compositional analytical technique. Combination with one of the compositional techniques, e. g. AES or XPS and with XTEM, to furnish information about the vertical structure, can provide valuable additional information enabling creation of a suitable optical model for an unknown complex sample structure. 

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,.

Figure 2. Transmittance spectral profile of a coating consisting of a quarterwave stack of 23 layer stack centered on 800 nm. Light gray without ripple control. Dark gray with ripple control. It can be used either as a intermediate band filter, or a shortwave dichroic beam splitter or a longwave one.

The carbon-based nanofillers are mainly layered graphite, nanotube, and nanofibers. Graphite is an allotrope of carbon, the stmcture of which consists of graphene layers stacked along the c-axis in a staggered array [1], Figure 4.1 shows the layered structure of graphite flakes. 

HRTEM picture (Fig. 1(a)) shows that CNF-R is estimated of a diameter of 30 40 nm and has a hollow core. The graphene layers are about 15-20 inclining to the axis. After heat treatment, CNF-HT, the structure remained, but graphene layers stack more regularly. 

The unit layers stack together face-to-face and are held in place by weak attractive forces. The distance between corresponding planes in adjacent unit layers is called the c-spacing. A clay crystal structure with a unit layer consisting of three sheets typically has a c-spacing of about 9.5 X 10 mm. 

Tetrahedra in hexagonal closest-packing (a) view of the hexagonal layers (b) view parallel to the hexagonal layers (stacking direction upwards)... 

Figure 8.12. The structural entity layer stack with infinite lateral extension (left) results in a ID scattering intensity (right)... 

Equation (8.59) defines the ID interference function of a layer stack material. G (s) is one-dimensional, because p has been chosen in such a way that it extinguishes the decay of the Porod law. Its application is restricted to a layer system, because misorientation has been extinguished by Lorentz correction. If the intensity were isotropic but the scattering entities were no layer stacks, one would first project the isotropic intensity on a line and then proceed with a Porod analysis based on p = 2. For the computation of multidimensional anisotropic interference functions one would choose p = 2 in any case, and misorientation would be kept in the state as it is found. If one did not intend to keep the state of misorientation, one would first desmear the anisotropic scattering data from the orientation distribution of the scattering entities (Sect. 9.7). 

D Structural Entities. In materials science, stmctural entities which can satisfactorily be represented by layer stacks are ubiquitous. In the field of polymers they have been known for a long time [156], Similar is the microfibrillar [157] structure. Compared to the microfibrils, the layer stacks are distinguished by the large lateral extension of their constituting domains. Both entities share the property that their two-phase structure is predominantly described by a ID density function, Ap (r3), which is varying along the principal axis, r3, of the structural entity. 

D Intensity. As already mentioned (cf. p. 126 and Fig. 8.12), the isotropic scattering of a layer-stack structure is easily desmeared from the random orientation of its entities by Lorentz correction (Eq. 8.44). For materials with microfibrillar structure this is more difficult. Fortunately microfibrils are, in general, found in highly oriented fiber materials where they are oriented in fiber direction. In this case the one-dimensional intensity in fiber direction,... 

Opportunities and Limits. If we intend to obtain a clearer look on nanostructure than the one the CLD is able to offer, we can try to get rid of the orientation smearing - either by considering materials with a special topology (layer stacks), or by studying anisotropic materials. 

If the scattering entities in our material are stacks of layers with infinite lateral extension, Eq. (8.47) is applicable. This means that we can continue to investigate isotropic materials, and nevertheless unwrap the ID intensity of the layer stack. To this function Ruland applies the edge-enhancement principle of Merino and Tchoubar (cf. Sect. 8.5.3) and receives the interface distribution function (IDF), gi (x). Ruland discusses isotropic [66] and anisotropic [67] lamellar topologies. 

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. 

Let us consider a nanostructured thin film built from lamellar particles [84], If the principal axis of layer stacks is oriented normal to the film surface, the scattered intensity measured in symmetrical-reflection geometry (SRSAXS) is... 

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. 

In most oxides, the oxygen atoms are present as close-packed layers stacked either to produce cubic symmetry or hexagonal symmetry. Some of the cubic cases have already been discussed. Now some hexagonal cases will be considered. 

Figure 2. HRTEM image analysis, a raw HKTEM image b corresponding skeletonized image c limits of a coherent domain, definition of the structural (L, La, Lc, d) and microtextural (a) parameters N is the number of layers stacked within a domain.

Structure determinations of LiZn2Mo308 and Zn3Mo308 (18) showed that these compounds are isomorphous but the pattern of oxide-layer stacking is different from that of Zn2Mo308. Otherwise the structures are closely related and all contain the cluster units with the same connectivity, [Mo30l+06/203/3]n . 

Figure 9.6. Illustration of the crystallization process (the layered stacks symbolize the nanocrystals) and shrinkage of the mesostructure in thin films upon heat treatment. 

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