Tilt Descriptions

The comer connectivity of the BX octahedra means that the tilt of one octahedron completely determines the tilting in the plane perpendicular to the tilt axis 

In the simplest case, and considering only a two-octahedron repeat along each of the cubic or pseudocubic axes, 10 possible tilt combinations are possible  

In order to relate these to crystallographic structures, it is necessary to take into account the relative magnitudes of the tilts. In this case, three unequal tilts produce three unequal pseudocubic axes, two equal tilts and one different tilt produce two equal pseudocubic axes and one different and three equal tilts produce three equal pseudocubic axes. Moreover, whenever a superscript is 0 or +, a mirror plane must exist perpendicular to the tilt axis. By examination of the 10 tilt combinations described in terms of these and related constraints, 23 different tilt systems can be derived together with the pseudocubic unit cell dimensions and the ideal space group of the four octahedra unit cell (Table 1.2). It is, though, important to 

The lattice parameters of many of the resulting unit cells can be related to the B—O bond distance, d, and the angles of rotation, p about a tetrad axis [001 ], 9 about a diad axis [110] and cp about a triad axis [111]. The simplest of these are given in Table 1.3. 

Number Symbol Pseudocubic unit cell Space group 

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Lead azide is manufactured on a technical scale by the action of sodium azide on an aqueous solution of lead nitrate. According to a description of manufacture in the Wolfratshausen factory in Germany [109], the reaction is conducted in an open reactor of stainless steel, provided with a jacket warmed by hot water and a stirrer which may be lifted out of the reactor (Fig. 49). The reactor is emptied by tilting. Its upper edge is therefore fitted with a spout so that the contents pour easily. The size of the reactor is such that 4.5 kg of lead nitrate in the form of a 9-10% solution can be used in each batch. This solution is poured into the reactor, warmed to 50°C and neutralized with sodium hydroxide to a pH of about 4.0 (in the presence of methyl orange) and 150 g of dextrin mixed with a small amount of water, is added. The suspension or solution of dextrin in water should be decanted before use to separate mechanical impurities, such as sand. 

See Appendix B for descriptions of tilt, twist, and mixed grain boundaries. 

Chiral molecules which form smectic liquid crystals are often capable of forming structures in which the electric dipoles associated with the molecules all point approximately in the same direction in a particular region but in which this direction rotates as one moves in a direction normal to the smectic planes. Such materials are rather misleadingly referred to as ferroelectric liquid crystals. The mechanism responsible for this effect is illustrated in Figure 7.3. The molecules tilt into a smectic-C phase due to their structure as illustrated. Dipoles associated with the molecules are supposed to point in a direction normal to the page. Thus, if the molecules all have the same handedness the dipoles all point in he same direction. This description is an oversimplification as the molecules rotate about their long axes but point preferentially in the manner indicated. This phenomenon has been successfully applied to... 

In the previous sections we have shown that the inclusion of the director of the underlying nematic order in the description of a smectic A like system leads to some important new features. In general, the behavior of the director under external fields differs from the behavior of the layer normal. In this chapter we have only discussed the effect of a velocity gradient, but the effects presented here seem to be of a more general nature and can also be applied to other fields. The key results of our theoretical treatment are a tilt of the director, which is proportional to the shear rate, and an undulation instability which sets in above a threshold value of the tilt angle (or equivalently the shear rate). 

In addition, a tactoid containing n sheets in such a disordered state is separated from an adjacent tactoid containing n sheets by inter-tactoid pores. If two adjacent tactoids are tilted with respect to one another, very complicated architecture may exist within the suspension. The description of such architectures should be performed in terms of correlation functions relating the spaces occupied by solids or by voids. Such an analysis is difficult for anisotropic objects. 

Despite the experimental results and theoretical calculations reported so far, a conclusive description of the ligand packing for homoligand nanoparticles cannot be drawn. The present idea is that the real structure of the ligand shell results from the interplay between van der Waals interactions and the tendency of the thiolates to reach the optimal tilt angle on each facet, as discussed by Stellacci and coworkers on the basis of STM analyses.214,215... 

Robinson et al. [69] studied the influence of cholesterol on molecular ordering of phospholipids by MD simulation. They used a more detailed description of the phospholipids including the head groups and charges. The simulated system contained two cholesterol molecules and 18 DMPC molecules in each leaflet of the bilayer (10 mol% cholesterol) and was simulated after equilibrium for 400 ps employing NVT conditions. They observed an increase in the fraction of trans conformations of the lipid alkyl chains with a decrease in kinks. Also, the dynamic and conformation of the flexible cholesterol side chains was characterized and it was found that they had a smaller tilt angle than the lipid chains with respect to the bilayer normal. 

More recently, Glazer developed a very influential notation for describing the 23 different tilt systems that have been observed (Glazer, 1972). The description is based on the rotations of the octahedra about each of the three Cartesian axes. The direction of the rotation about any one axis, relative to the rotations about the other two axes, is specified by a letter with a superscript that indicates whether the rotations in adjacent layers, which are coupled to the other layers via the vertex-sharing octahedra, are in the same (-I-) or opposite ( —) directions. For example, signifies an equivalent... 

In an attempt to reconcile the microfibrillar structure and the X-ray diffraction pattern with the coiled-coil hypothesis Swanbeck (1961) proposed a model in which a central three-strand coiled coil was surrounded further by four concentric layers of a-helices, the tilt increasing progressively up to a value of 50° in the outer layer of nineteen chains. In a later more detailed description (Swanbeck, 1963) it was proposed that the three inner layers consisted of a-helices of pitch 5.25, 5.65, and 6.40 A, that the fourth layer consisted of 3.0w helices (Donohue, 1953) and the outer layer was a 3-structure. 

A consistent description of the structure of alkanethiol monolayers on gold has emerged from an array of spectroscopic and diffraction studies. X-ray photoelectron spectroscopic (XPS) studies support the presence of anisotropically chemisorbed alkanethiolates on gold [24-29]. Ellipsometric measurements [24-27, 30], capacitance studies [30] and XPS measurements [31] confirm monolayer film thickness. Fourier transform infrared external reflective spectroscopy (FTIR-ERS) shows that the chains tilt at about 30° off the surface normal, and the plane containing the carbon backbone is twisted out of the plane of tilt by about 50° [25-27, 30, 32, 33]. 

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