Lattice structure, crystal

The factors given in both 2.2.4. and Table 2-1 arise due to the unit-cell axes, intercepts and angles involved for a given crystal lattice structure. Also given are the lattice symbols which are generally used. The axes and angles given for each system are the restrictions on the unit cell to make... 

Recognizing Cause and Effect In a crystal lattice structure, the electrons are held tightly by the ions, which are rigidly held in place by electrostatic attraction. Discuss how this characteristic explains why ionic compounds generally (a) have high melting points and (b) do not conduct electricity in the solid state. 

Comparing and Contrasting Nonionic compounds do not exist in crystal lattice structures but rather as individual particles, which are affected by other particles. In other words, nonionic compounds experience forces between particles. Based on what you learned in Part B about the melting points of ionic versus nonionic compounds, how do you think the attractive energy between particles compares with the energy of the crystal lattice ... 

Pictures taken from Crystal Lattice Structures Web page cst-www.nrl.navy.mil/lattice/ provided by Center for Computational Materials Science of United States Naval Research Laboratory... 

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]. 

Nevertheless, the chemical potentials of SE s are frequently used instead of the chemical potentials of (independent) components of a crystalline system. Obviously, a crystal with its given crystal lattice structure is composed of SE s. They are characterized much more specifically than the crystal s chemical components, namely with regard to lattice site and electrical charge. The introduction of these two additional reference structures leads to additional balanced equations or constraints (beside the mass balances) and, therefore, SE s are not independent species in the sense of chemical thermodynamics, as are, for example, ( - 1) chemical components in an n-component system. 

Table 1.1 Crystal lattice structures of some transition metals and their compounds...

Shown below are commonly encountered crystal lattice structures The lattice type depends on the radius ratio favoring a particular coordination number for the structure type. ( )... 

We would expect this trend for increasing atomic mass within a group. We might also expect the density of KF to be less than 2.0 g/cm3, but it is actually 2.5 g/cm3 due to a change in crystal lattice structure. 

The forces holding ions together in ionic solids are electrostatic forces. Opposite charges attract each other. These are the strongest intermolecular forces. Ionic forces hold many ions in a crystal lattice structure... 

In all of this work there was little suggestion that the surface states of the palladium might behave differently from bulk states. Selwood (17) indicated that, from some sorption-magnetic susceptibility data for hydrogen sorbed on palladium which was finely dispersed on alumina gel, the ultimate sorption capacity was approximately at the ratio 2H/Pd. Trzebiatowsky and coworkers (25) deposited palladium on alumina gel in amounts ranging from 0.46 to 9.1% of gel weight. They found the palladium to be present in a normal crystal lattice structure, but its susceptibility was less than for the bulk metal. This suggested to the present authors that the first layer of palladium atoms laid down on the alumina gel underwent an interaction with the alumina, which has some of the properties of a semiconductor. Such behavior was definitely shown in this laboratory (22) in the studies on the sorption of NO by alumina gel. Much of this... 

The measured crystal optical activity, in general, can be either of molecular origin or due to the chiral helical arrangement of chiral or achiral molecules in the crystal, or both. The two factors are difficult to separate. Kobayashi defined a chirality factor r = (pc — ps)/pc = 1 — pslpc, where pc is the rotatory power per molecule of a randomly oriented crystal aggregate derived from the gyration tensors determined by HAUP, and ps that in solution [51]. It is a measure of the 4 crystal lattice structural contribution to the optical activity and represents the severity of the crystal lattice structural contribution to the optical activity, and represents the severity of the restriction of the freedom of molecular orientation by forming a crystal lattice. Quartz is a typical example of r = 1, as it does not contain chiral molecules or ions and its optical activity vanishes in random orientation (ps = 0). 

But just what causes the pairing in the high-Tc superconductors is unclear, and scientists disagree on the mechanism. Some researchers believe that the phonon-electron interaction is important, as it is in the BCS theory. But a growing number now believe that something else is at work. The intermediary, many feel, is some sort of magnetic, electronic excitation in the crystal lattice structure, a... 

These are sodium and calcium aluminosilicates which have cage-like crystal lattice structures containing pores of various sizes, depending on their constitution. They can absorb small molecules, such as water, which can fit into the pores. The most commonly used types 3A, 4A, and 5A have pore sizes of approximately 3A, 4A, and 5A respectively, and they are available in bead or powder form. After activation at 250-320°C for a minimum of 3h they are probably the most powerful desiccants available.iC ) They can... 

Earlier work by Matsuura et al. reported that there was a difference in the photochemical behaviour of santonin dependent on whether the reactions were carried out in the liquid or solid phase. - More recent work has demonstrated that the dienones (273) and (274) do not exhibit this difference in behaviour. Irradiation of these compounds yields the same products (275) and (276) respectively whether the reactions are in solution or in the crystal. The authors - suggest that this similarity in behaviour is due to loose crystal lattice structures. The solid state irradiation of the dienone (277) results in the formation of the normal products for such systems, namely the corresponding photoketone, photophenol, and lumiketone. The ratio of these three products was sensitive to temperature. In solution no temperature dependence was detected. Interestingly when the dienone is irradiated in the solid with wavelengths > 400 nm a quantitative yield of the lumiketone is obtained. ... 

As the formula for sodium chloride, NaCl, indicates, there is a 1 1 ratio of sodium cations and chlorine anions. Recall that the attractions in sodium chloride involve more than a single cation and a single anion. Figure I2a illustrates the crystal lattice structure of sodium chloride. Within the crystal, each Na" ion is surrounded by six CP ions, and, in turn, each CP ion is surrounded by six Na" ions. Because this arrangement does not hold for the edges of the crystal, the edges are locations of weak points. 

Figure 2.2 Three-dimensional hex onal close-packed crystal lattice structure. The atoms of the third layer are positioned above those of the first layer. The atoms of all following layers repeat the positions of every second preceding layer. The structure is denoted as an ABAB. . . structure. The basal face, (0001), has a 2D hep structure. The layered structure of the prismatic faces is also clearly seen. The unit cell of a hep crystal containing 17 atoms is given on the r ht-hand side.

In the second case every third consecutive layer occupies a concavity lying above a concavity of the first layer. Therefore, an ABCABC. . . sequence of planes results, forming a face-centered cubic (fee) 3D Me bulk lattice, Fig. 2.3. The unit cells of both crystal lattice structures are also given in Figs. 2.2 and 2.3. 

Figure 2,3 Three-dimensional face-centered cubic crystal lattice structure. The atoms of every third and all consecutive third layers are positioned above an empty B or C place of the first layer. A crystal with cubic and octahedral faces results. The structure of the octahedral (111) faces is a hep structure. The smooth quadratic structure of the cubic (100) faces is also clearly seen, The unit cell containing 14 atoms is shown on the right-hand side. The (111) plane is given by the hatched surface.

The OOA was not designed for and does not apply to temperature dependencies of any kind in JT crystals. In particular, one cannot expect a reasonable estimate of the temperature of phase transitions in crystal lattice (structural), electron orbital, and/or spin system. This follows from the partitioning procedure that includes averaging over vibrational degrees of freedom. One can see the same reason from another perspective. The pseudo spin of a JT site, as the basic concept used in the OOA, operates in the basis of degenerate ground state wave functions. Excited vibronic states are beyond the pseudo spin setup. Therefore, in the OOA, by its very definition, temperature population of excited states does not make sense. 

HCP (hexagonal close packing) A type of crystal lattice structure found in zinc, titanium, and cobalt, for example. 

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