Structures, lattice

However, the B.E.T. and modificated B.E.T as well as isotherm of d Arcy and Watt fit the experimental data only in some range of the relative humidities up to about 80-85%. At the same time the adsorption in the interval 90-100% is of great interest for in this interval the A— B conformational transition, which is of biological importance, takes place [17], [18]. This disagreement can be the result of the fact that the adsorbed water molecules can form a regular lattice, structure of which depends on the conformation of the NA. To take into account this fact we assume that the water binding constants depend on the conformational variables of the model, i.e ... 

Anuther concept that is extremely powerful when considering lattice structures is the fi i i/imca/ lattice. X-ray crystallographers use a reciprocal lattice defined by three vectors a, b and c in which a is perpendicular to b and c and is scaled so that the scalar juoduct of a and a equals 1. b and c are similarly defined. In three dimensions this leads to the following definitions ... 

The summation is over the different types of ion in the unit cell. The summation ca written as an analytical expression, depending upon the lattice structure (the orij Mott-Littleton paper considered the alkali halides, which form simple cubic lattices) evaluated in a manner similar to the Ewald summation this typically involves a summc over the complete lattice from which the explicit sum for the inner region is subtractec... 

A discussion of the adsorption of water on oxides would be incomplete without some reference to the irreversible effects which are often encountered when samples of oxide, hydroxide or oxide-hydroxide are exposed to the vapour. These effects ( low-temperature ageing ), which manifest themselves in changes in surface area, in pore structure and sometimes in the lattice structure itself, are complex and difficult to reproduce exactly. ... 

Figure 1.13 The grain boundary and interface which can be formed between two crystals with the insertion of dislocations. In the grain boundary the two crystals are identical in lattice structure, but there is a difference in lattice parameters in the formation of the interface...

Extensive computer simulations have been caiTied out on the near-surface and surface behaviour of materials having a simple cubic lattice structure. The interaction potential between pairs of atoms which has frequently been used for inert gas solids, such as solid argon, takes die Lennard-Jones form where d is the inter-nuclear distance, is the potential interaction energy at the minimum conesponding to the point of... 

However, when deliberately employed, channeling is a powerful tool that may be used to determine the lattice positions of specific types of atoms or the number of specific atoms in interstitial positions (out of the lattice structure). Further information on this technique is available. ... 

Filter aids as well as flocculants are employed to improve the filtration characteristics of hard-to-filter suspensions. A filter aid is a finely divided solid material, consisting of hard, strong particles that are, en masse, incompressible. The most common filter aids are applied as an admix to the suspension. These include diatomaceous earth, expanded perlite, Solkafloc, fly ash, or carbon. Filter aids build up a porous, permeable, and rigid lattice structure that retains solid particles and allows the liquid to pass through. These materials are applied in small quantities in clarification or in cases where compressible solids have the potential to foul the filter medium. 

Reactions that are catalyzed by solids occur on the surfaces of the solids at points of high chemical activity. Therefore, the activity of a catalytic surface is proportional to the number of active centers per unit area. In many cases, the concentration of active centers is relatively low. This is evident by the small quantities of poisons present (material that retards the rate of a catalytic reaction) that are sufficient to destroy the activity of a catalyst. Active centers depend on the interatomic spacing of the solid structure, chemical constitution, and lattice structure. 

Another special case of weak heterogeneity is found in the systems with stepped surfaces [97,142-145], shown schematically in Fig. 3. Assuming that each terrace has the lattice structure of the exposed crystal plane, the potential field experienced by the adsorbate atom changes periodically across the terrace but exhibits nonuniformities close to the terrace edges [146,147]. Thus, we have here another example of geometrically induced energetical heterogeneity. Adsorption on stepped surfaces has been studied experimentally [95,97,148] as well as with the help of both Monte Carlo [92-94,98,99,149-152] and molecular dynamics [153,154] computer simulation methods. 

Finally, we assume that the fields 4>, p, and u vary slowly on the length scale of the lattice constant (the size of the molecules) and introduce continuous approximation for the thermodynamical-potential density. In the lattice model the only interactions between the amphiphiles are the steric repulsions provided by the lattice structure. The lattice structure does not allow for changes of the orientation of surfactant for distances smaller than the lattice constant. To assure similar property within the mesoscopic description, we add to the grand-thermodynamical potential a term propor-tional to (V u) - -(V x u) [15], so that the correlation length for the orientational order is equal to the size of the molecules. 

The reason for the formation of a lattice can be the isotropic repulsive force between the atoms in some simple models for the crystalhzation of metals, where the densely packed structure has the lowest free energy. Alternatively, directed bonds often arise in organic materials or semiconductors, allowing for more complicated lattice structures. Ultimately, quantum-mechanical effects are responsible for the arrangements of atoms in the regular arrays of a crystal. 

The theory of crystal growth accordingly starts usually with the assumption that the atoms in the gaseous, diluted, or hquid mother phase will have a tendency to arrange themselves in a regular lattice structure. We ignore here for the moment the formation of poly crystalhne solids. In principle we should start with the quantum-mechanical basis of the formation of such lattice structures. Unfortunately, however, even with the computational effort of present computers with a performance of about 100 megaflops... 

Crystals have spatially preferred directions relative to their internal lattice structure with consequences for orientation-dependent physico-chemical properties i.e., they are anisotropic. This anisotropy is the reason for the typical formation of flat facetted faces. For the configuration of the facets the so-called Wullf theorem [20] was formulated as in a crystal in equihbrium the distances of the facets from the centre of the crystal are proportional to their surface free energies. ... 

The macroscopic appearance of crystals, with their polygonal facets and the underlying lattice structure, is the consequence of quantum mechanical... 

The crystal structure of many compounds is dominated by the effect of H bonds, and numerous examples will emerge in ensuing chapters. Ice (p. 624) is perhaps the classic example, but the layer lattice structure of B(OH)3 (p. 203) and the striking difference between the a- and 6-forms of oxalic and other dicarboxylic acids is notable (Fig. 3.9). The more subtle distortions that lead to ferroelectric phenomena in KH2PO4 and other crystals have already been noted (p. 57). Hydrogen bonds between fluorine atoms result in the formation of infinite zigzag chains in crystalline hydrogen fluoride... 

M +(g)-(-e" this is 7297kJ mol for Li but drops to 2255kJmol for Cs. The largest possible lattice energy to compensate for this would be obtained with the smallest halogen F and (making plausible assumptions on lattice structure and ionic radius) calculations indicate that CsF2 could indeed be formed exothermically from its elements ... 

In203 has the C-type M2O3 structure (p. 1238) and InO(OH) (prepared hydrothermal ly from In(OH)3 at 250-400°C and 100-1500 atm) has a deformed rutile structure (p. 961) rather than the layer lattice structure of AIO(OH) and GaO(OH). Crystalline In(OH)3 is best prepared by addition of NH3 to aqueous InCl3 at 100° and ageing the precipitate for a few hours at this temperature it has the simple Re03-type structure distorted somewhat by multiple H bonds. 

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