Crystals positional disorder

That is, S —> 0 as T - 0. The perfect crystal part of this statement of the third law refers to a substance in which all the atoms are in a perfectly orderly array, and so there is no positional disorder. The T— 0 part of the statement implies the absence of thermal motion-—thermal disorder vanishes as the temperature approaches zero. As the temperature of a substance is raised from zero, more orientations become available to the molecules and their thermal disorder increases. Thus we can expect the entropy of any substance to he greater than zero above T = 0. 

The defects of the matrix play an important role on luminescent performances in these materials. Taking into consideration the preparation process of these compounds with the solid-state reaction of mixtures of BaC03, H3BO3, and NH4H2PO4 at different molar ratio, non-equal evaporation during the sintering process of these powders is inevitable and thus results in the formation of intrinsic defects, such as cation and oxygen vacancies. Positional disorder of B and Vacant B (Vb)" have been reported in SrBPOs crystals on the basis of... 

The notion of point defects in an otherwise perfect crystal dates from the classical papers by Frenkel88 and by Schottky and Wagner.75 86 The perfect lattice is thermodynamically unstable with respect to a lattice in which a certain number of atoms are removed from normal lattice sites to the surface (vacancy disorder) or in which a certain number of atoms are transferred from the surface to interstitial positions inside the crystal (interstitial disorder). These forms of disorder can occur in many elemental solids and compounds. The formation of equal numbers of vacant lattice sites in both M and X sublattices of a compound M0Xft is called Schottky disorder. In compounds in which M and X occupy different sublattices in the perfect crystal there is also the possibility of antistructure disorder in which small numbers of M and X atoms are interchanged. These three sorts of disorder can be combined to give three hybrid types of disorder in crystalline compounds. The most important of these is Frenkel disorder, in which equal numbers of vacancies and interstitials of the same kind of atom are formed in a compound. The possibility of Schottky-antistructure disorder (in which a vacancy is formed by... 

Figure 2. (a) Crystal structure ofCClfSb(OTeFs)f (b) A view of the CClf cation, with key bond lengths and bond angles, showing the two-fold positional disorder around the crystallographic inversion center.82... 

Some of the differences in solubilities are also related to different disordering of the crystal surface. As shown by Bishop et al. (1987) with Raman investigations, the biogenic phases are characterized by greater positional disorder than synthetic minerals of the same composition. 

Several steps were needed to determine the structure of the core particle to higher resolution (Fig. Id). The X-ray phases of the low-resolution models were insufficient to extend the structure to higher resolution, since the resolution of the early models of the NCP was severely limited by disorder in the crystals. The disorder was presumed to derive from both the random sequences of the DNA and from heterogeneity of the histone proteins caused by variability in post-translational modification of the native proteins. One strategy for developing an atomic position model of the NCP was to develop a high-resolution structure of the histone core. This structure could then be used with molecular replacement techniques to determine the histone core within the NCP and subsequently identify the DNA in difference Fourier electron density maps. 

Zeolite structures pose unconventional problems for crystal structure refinement. These problems arise from positional disorder pseudo-symmetry, twinning, high mobility of some atoms, and (sometimes) the inaccessibility of single-crystal data. Methods are discussed for investigating split atoms, Si-Al distribution, pseudo-symmetry, and for dealing with parameter correlation and limited data sets. Some additional techniques which have not been applied to zeolite structures are mentioned. 

Based on this simplified description of the melting and glass transitions, it is possible to propose six major types of mesophases. Figure 2 shows these mesophases in relation to the glass, crystal, and melt. First, it is possible to keep orientational order, but lose positional order. These positionally disordered crystals or orientationally ordered liquids 7) are widely known as liquid crystals 15). The name liquid crystal was given because of the obvious, liquid-like flow of these materials. By now it is too late to try to change the nomenclature, especially when the possible new names would be cumbersome 7). 

The thermotropic mesophases are well enough understood to propose a subdivision into six types. Depending on the type of disorder, they are called liquid crystals, plastic crystals or condis crystals (positional and if applicable conformational disorder, orientational disorder, and conformational disorder, respectively). For the corresponding glasses, which represent the frozen-in mesophases, the names LC-, PC-, and CD-glasses are proposed (Fig. 2). For macromolecules not only equilibrium... 

The second puzzling feature is the observation of more liquid crystal phase disorder at the 6 position than at either the 4 or 10 positions of DPPC (Table I). The results appear statistically significant and contrast vith the observed (35) NMR order parameter profile (constant from positions 2->10, diminished order from position 10 to the bilayer center). Further experiments vith DPPC derivatives deuterated at positions closer to the bilayer center may clarify the situation. 

Because of the chemical implausibility of some speculations about zeolite A, high-precision X-ray analyses were made of dehydrated crystals whose chemical composition was checked by electron microprobe analysis. Data were collected for the 24 A superstructure. All diffractions are consistent with space group Fm3c except for a few weak ones. Unpublished measurements by J.J. Pluth and G.D. Price of a hydrated Na-A (i.e. as-synthesized) showed strict obeyance of Fm3c except for a very weak (111) diffraction, and the inconsistent diffractions of the dehydrated crystals are attributed tentatively to minor positional disorder of extra-framework cations (1). 

In the crystal structure of / -cyclodextrin 11H20, the hydrogen bonding is even more complicated than in the a-cyclodextrin hydrates [454]. There are not only more hydroxyl groups and water molecules in the crystal asymmetric unit, but they also display considerable positional disorder giving rise to more complex hydrogen bonding patterns. 

Consider, for example, the case of the quasi-one-dimensional organic metal TTT2I3+5. This material often exhibits a set of disordered iodine sublattices either commensurate or incommensurate with the main lattice. Lowe-Ma et al. [85] have analyzed the intensity of the corresponding set of diffuse reciprocal layers and postulated that, in their samples, part of the It ions are substituted by I2 and I- moieties. In fact, the intensity of the zero layer is not negligible and no three-dimensional ordering of iodine chains is observed at low temperature. However, TTT2I3+8 crystals are often characterized by a varying amount of positional disorder [136] of iodine columns rather than by a chemical disorder. 

There are a number of factors that can affect the final value of the agreement factor R, such as the amount of thermal motion. Some other factors are the quality and size of the crystal used for data collection. Too small a specimen will produce weak reflections that are difficult to measure accurately. A soft crystal is readily susceptible to physical distortions that will result in attenuations in the magnitudes of the reflections. Some molecules, usually large ones, have some small variation in their conformation, such as rotations about single bonds, from cell to cell in the crystal that produce a positional disorder and have the effect of increasing the R factor. 

The structure of pumiliotoxin 25ID is shown in Fig. 14. Positional disorder in the crystal, as evidenced by the increasing size of the experimentally determined thermal parameters for each succeeding atom in the side chain, was sufficiently large that reliable values for the bond lengths and bond angle for the three terminal atoms could not be determined. However, the mass spectrum of the compound, including data recorded from the specific crystal used for the X-ray analysis, shows that the side chain does... 

Figure 21 Properties of stable trisilaallenes R2Si=Si=SiR2. The central silicon atom (Si2) in the crystal was disordered at four positions. The structural parameters shown here are those of the major part of disordered atoms...

Second harmonic generation has been used as a test for a noncentrosymmetric crystal.An example is provided by 9-methyl-lO-chloro-methylanthracene which crystallizes with disorder in the positions of the methyl and chloromethyl group and therefore it was not clear whether the space group was centrosymmetric or noncentrosymmetric. The measurement of a strong second harmonic confirmed the latter choice. 

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