Crystal lattice/shape

J) The extreme fineness of iadividual clay particles, which may be of colloidal size ia at least one dimension. Clay minerals are usually platy ia shape, and less often lathlike and tubular or scroU shaped (13). Because of this fineness clays exhibit the surface chemical properties of coUoids (qv) (14). Some clays possess relatively open crystal lattices and show internal surface colloidal effects. Other minerals and rock particles, which are not hydrous aluminosihcates but which also show colloidal dimensions and characteristics, may occur intimately intermixed with the clay minerals and play an essential role. 

The SEM can also be used to provide crystallographic information. Surfaces that to exhibit grain structure (fracture surfaces, etched, or decorated surfaces) can obviously be characterized as to grain size and shape. Electrons also can be channeled through a crystal lattice and when channeling occurs, fewer backscattered electrons can exit the surface. The channeling patterns so generated can be used to determine lattice parameters and strain. 

To find the equilibrium form of a crystal, the following Wullf construction [20] can be used, which will be explained here, for simplicity, in two dimensions. Set the centre of the crystal at the origin of a polar coordinate system r,6. The radius r is assumed proportional to the surface tension 7( ), where 6 defines the angle between the coordinate system of the crystal lattice and the normal direction of a point at the surface. The anisotropy here is given through the angular dependence. A cubic crystal, for example, shows in a two-dimensional cut a clover-leaf shape for 7( ). Now draw everywhere on this graph the normals to the radius vector r = The... 

The cytoplasmic domains reconstructed from negatively stained [90] and from frozen-hydrated samples [91,177] have similar shapes. Both include the protruding lobe and the bridge region that links the Ca " -ATPase molecules into dimers. The intramembranous peptide domains of the two ATPase molecules which make up a dimer spread apart as they pass through the bilayer toward the luminal side of the membrane, establishing contacts with the Ca -ATPase molecules in the neighboring dimer chains. The lateral association of dimer chains into extended crystal lattice is... 

Therefore we have two extremes in crystal habit in sodium chloride, the octahedron and the skeleton, the prevailing shape depending upon the relative rates of growth in different directions in the crystal lattice. The common cube shape is formed when a balance in the two rates of growth prevails. 

The structures of ionic compounds comprising complex ions can in many cases be derived from the structures of simple ionic compounds. A spherical ion is substituted by the complex ion and the crystal lattice is distorted in a manner adequate to account for the shape of this ion. 

The electrocrystallization on an identical metal substrate is the slowest process of this type. Faster processes which are also much more frequent, are connected with ubiquitous defects in the crystal lattice, in particular with the screw dislocations (Fig. 5.25). As a result of the helical structure of the defect, a monoatomic step originates from the point where the new dislocation line intersects the surface of the crystal face. It can be seen in Fig. 5.48 that the wedge-shaped step gradually fills up during electrocrystallization after completion it slowly moves across the crystal face and winds up into a spiral. The resultant progressive spiral cannot disappear from the crystal surface and thus provides a sufficient number of growth... 

The hydrocarbons 54 and 5551) which are functional group-free analogues of 26 and 38 display no activities of inclusion formation, either with polar or with apolar solvents371. This result is another proof that mostly for the roof-shaped type of compounds, functional groups play a fundamental role in the construction of a low-density packed crystal lattice. 

A polymorph is a solid crystalline phase of a compound resulting from the possibility of at least two different crystal lattice arrangements of that compound in the solid state [42], Polymorphs of a compound are, however, identical in the liquid and vapor states. They usually melt at different temperatures but give melts of identical composition. Two polymorphs of a compound may be as different in structure and properties as crystals of two different compounds [43,44], Apparent solubility, melting point, density, hardness, crystal shape, optical and electrical properties, vapor pressure, etc. may all vary with the polymorphic form. The polymorphs that are produced depend upon factors such as storage temperature, recrystallization solvent, and rate of cooling. Table 2 suggests the importance of polymorphism in the field of pharmaceutics [45],... 

A large number of compounds of pharmaceutical interest are capable of being crystallized in either more than one crystal lattice structure (polymorphs), with solvent molecules included in the crystal lattice (solvates), or in crystal lattices that combine the two characteristics (polymorphic solvates) [122,123]. A wide variety of structural explanations can account for the range of observed phenomena, as has been discussed in detail [124,125]. The pharmaceutical implications of polymorphism and solvate formation have been recognized for some time, with solubility, melting point, density, hardness, crystal shape, optical and electrical properties, vapor pressure, and virtually all the thermodynamic properties being known to vary with the differences in physical form [126]. 

In order to achieve efficient build-up to heavy depths when dyeing cellulose acetate at 80 °C it is customary, particularly for navy blues, to use a mixture of two or more components of similar hue. If these behave independently, each will give its saturation solubility in the fibre. In practice, certain mixtures of dyes with closely related structures are 20-50% less soluble in cellulose acetate than predicted from the sum of their individual solubilities [87]. Dyes of this kind form mixed crystals in which the components are able to replace one another in the crystal lattice. The melting point depends on composition, varying gradually between those of the components, and the mixed crystals exhibit lower solubility than the sum of solubilities of the component dyes [88]. Dyes of dissimilar molecular shape do not form mixed crystals, the melting point curve of the mixture shows a eutectic point and they behave additively in mixtures with respect to solubility in water and in the fibre. 

Recently, various kinds of porous POMs have been synthesized (Table 13. 2). They have controlled pores between particles (crystallites) [169-183], in their crystal lattices [184-192], or in the molecules [193-201], and show unique sorption and catalytic properties. Worthy targets of future research are shape- and stereo-selective oxidations using porous POMs. 

Matter (anything that has mass and occupies space) can exist in one of three states solid, liquid, or gas. At the macroscopic level, a solid has both a definite shape and a definite volume. At the microscopic level, the particles that make up a solid are very close together and many times are restricted to a very regular framework called a crystal lattice. Molecular motion (vibrations) exists, but it is slight. 

In general, the shape and character of etch pits may reveal information about the impurity content of the crystal. "Beaked pits (pits with curved apexes, see 12) can indicate impurity haloes. Some forms of the arcuate etching we observed in quartz (16) may be examples of beaking. Very shallow pits can form at aged dislocations while very deep pits form at new dislocations. "Aging" may be related to impurity diffusion in the crystal lattice. 

A crystal lattice is made up of identical repeating unit cells that give the crystal its characteristic shape. Figure 4.21 shows a three-dimensional representation of a simple cubic arrangement of unit cells. 

An important advantage of the inclusion complexes of the cyclodextrins over those of other host compounds, particularly in regard to their use as models of enzyme-substrate complexes, is their ability to be formed in aqueous solution. In the case of clathrates, gas hydrates, and the inclusion complexes of such hosts as urea and deoxycholic acid, the cavity in which the guest molecule is situated is formed by the crystal lattice of the host. Thus, these inclusion complexes disintegrate when the crystal is dissolved. The cavity of the cyclodextrins, however, is a property of the size and shape of the molecule and hence it persists in solution. In fact, there is evidence that suggests that the ability of the cyclodextrins to form inclusion complexes is dependent on the presence of water. Once an inclusion complex has formed in solution, it can be crystallized however, in the solid state, additional cavities appear in the lattice, as in the case of the hosts previously mentioned, which enable the inclusion of further guest molecules. ... 

In the case of potassium nitrate the Vickers hardness indentations have not a quadratic shape. This is due to a direction dependent hardness in the crystal lattice of this material. The direction dependency can be explained with an anisotropic effect in the lat-... 

Two different types of crystals were obtained by cooling crystallization of qulzalofop-ethyl dissolved In ethyl alcohol at room temperature. As shown In Photograph 1, one type consists of plate-llke crystal of 20-50 jum In size and another one Is halrllke crystal of 1-2 pm In short axis size. As shown In Figure 1, different X-ray patterns were obtained for the two crystals. Melting points and heats of fusion were also measured for the two crystal types by DTA and DSC, which are listed In Table I. These results Indicate that the different shapes of the two crystal types are related to differences In crystal lattice. 

Crystalline substances exhibit a defined shape and volume on the atomic or molecular scale where the crystal symmetry is repeated to form a clearly defined geometrical, three-dimensional form, called a crystal lattice. 

The addition of a wax crystal modifier to diesel fuel is a common and well-accepted alternative to kerosene dilution. Wax crystal modifiers are typically polymeric compounds which have the ability to co-crystallize with wax to alter the size, shape, and structure of the wax crystal lattice. 

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