Disordered crystals

Statistically symmetric hydrogen bonds are disordered in such disordered crystals, the apparent crystalline symmetry can depend on the method of investigation. Diffraction methods give usually higher symmetry than spectroscopic methods, but even in spectroscopy the behaviour of external and internal vibrations is different. 

Fully packed conduction layer of p/f( -aluinina. For (b) and (c) the filled circles 

The distinction between cyclic dimers (M-OH)2 and infinite chains (M-OH) is based in the mutual exclusion rule for centrosymmetric cyclic dimers, i.e. infrared and Raman frequencies should not coincide. In the case of carboxylic acids R-COOH, the C=0 stretching mode is particularly sensitive and the difference between infrared and Raman frequencies can be as much as 60-70 cm .  

Penrose tiling with a fivefold symmetry axis consisting of two kinds of rhomboid tiles 

Several kinds of intermediate states exist between the state of highest order in a crystal having translational symmetry in three dimensions and the disordered distribution of particles in a liquid. Liquid crystals are closest to the liquid state. They behave macroscopically like liquids, their molecules are in constant motion, but to a certain degree there exists a crystal-like order. 

In plastic crystals all or a part of the molecules rotate about their centers of gravity. Typically, plastic crystals are formed by nearly spherical molecules, for example hexafluorides like SF6 or MoF6 or white phosphorus in a temperature range immediately below the melting point. Such crystals often are soft and can be easily deformed. 

The term plastic crystal is not used if the rotation of the particles is hindered, i.e. if the molecules or ions perform rotational vibrations (librations) about their centers of gravity with large amplitudes this may include the occurrence of several preferred orientations. Instead, such crystals are said to have orientational disorder. Such crystals are annoying during crystal structure analysis by X-ray diffraction because the atoms can hardly be located. This situation is frequent among ions like BF4, PFg or N(CH3)J. To circumvent difficulties during structure determination, experienced chemists avoid such ions and prefer heavier, less symmetrical or more bulky ions. 

Orientational disorder is also present if a molecule or part of a molecule occupies two or more different orientations in the crystal, even without performing unusual vibrations. For example, tetraethylammo-nium ions often occupy two orientations that are mutually rotated by 90°, in such a way that the positions of the C atoms of the methyl groups coincide, but the C atoms of the CH2 groups occupy the vertices of a cube around the N atom, with two occupation probabilities. 

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Reilly P D and Skinner J L 1993 Spectral diffusion of single molecule fluorescence a probe of low-frequency localized excitations in disordered crystals Phys. Rev. Lett. 71 4257-60... 

According to this model, the SEI is made of ordered or disordered crystals that are thermodynamically stable with respect to lithium. The grain boundaries (parallel to the current lines) of these crystals make a significant contribution to the conduction of ions in the SEI [1, 2], It was suggested that the equivalent circuit for the SEI consists of three parallel RC circuits in series combination (Fig. 12). Later, Thevenin and Muller [29] suggested several modifications to the SEI model ... 

We thus see that the RFOT theory provides a rather complete picture of vitrification and the microscopies of the molecular motions in glasses. The possibility of having a complete chart of allowed degrees of freedom is veiy important, because it puts strict limitations on the range of a priori scenarios of structural excitations that can take place in amorphous lattices. This will be of great help in the assessment of the family of strong interaction hypotheses mentioned in the introduction. To summarize, the present theory should apply to all amorphous materials produced by routine quenching, with quantitative deviations expected when the sample is partially crystalline. The presence and amount of crystallinity can be checked independently by X-ray. It is also likely that other classes of disordered materials, such as disordered crystals, will exhibit many similar traits, but of less universal character. 

The thiepin 13 (X = S) was found to be inert toward catalytic hydrogenation. The authors ascribe the stability of 13 (X = S) to a contribution of the charge-separated structures 13a and 13 b to the ground state of 13 (X = S) 71). An X-ray structural determination showed that 13 (X = S) is nearly planar with a disordered crystal structure similar to that of azulene 73). 

Experimental Data from Polymer Thermotropic Mesophases and Conformationally Disordered Crystals... 

Indeed, in the world of tomorrow we can expect new aspects of polymer solids to extend the conventional and successful structure ideas of this century. These, of course, were the recognition as molecular identities of the chains of repeating chemical monomers. The circumstances of those entities have resulted in interesting concepts of solubilities, viscosity, and other mechanics, and especially thermodynamic limitations m mutual solubility or comparability of polymer mixtures. But we have known for decades that even homogeneous regular chain polymers such as Carothers polyesters and polyamides formed solids with manifold imperfections and irregularities, such as order-disorder crystal configurations.(22,23)... 

Speed runs, in which precipitation was completed in 12 hours, shown in Figure 4 document that higher values of kcBa characterize rapid coprecipitation. Possible interpretations include an increase in the number of defect sites due to disorderly crystallization, and/or more efficient capture of adsorbed Ba2 ions due to enhanced probability of physical entrapment with rapid growth. 

The crystalline state of 193 was irradiated with sunlight at 5 °C (equation 93) to afford the cyclobutanes 194 and 195 in a 3 1 ratio117. Compound 195 obviously arose from the dimerization of the c/s-isomer of 193. The disordered crystal structure of 193 permits isomerization of 193 to the (. A-isomer which photolytically reacted with 193 to give 195. Interestingly, the crystalline state of compound 196 and 198 was photolysed to 197 and 198, respectively (equations 94 and 95), but /i-nitro-p-methylstyrene was photostable. 

Note 2 The term is used to describe orientationally disordered crystals, crystals with molecules in random conformations (i.e., conformationally disordered crystals), plastic crystals and liquid crystals. 

The IR bands are at 3615 cm (free surface OH groups), 3430 cm (bulk OH stretch) and at 650 cm and 450 cm (bulk OH deformations). Russell (1979) found that most OH groups were readily accessible to deuterium exchange which suggested that there is little distinction between the surface and the bulk OH groups. The large half width of the band at 3615 cm (60 cm ) is evidence for a disordered crystal structure this band is broader in 2-line than in 6-line ferrihydrite. Ferrihydrite containing a few percent Si shows a broad, intense band at 940 cm (Schwertmann Thalmann, 1976 Carlson Schwertmann, 1981 Parfitt et al., 1992 Hansen et al.. 

Fig. 6 Results from Rietveld refinement of the disordered crystal structure of the P polymorph of p-formyl-tranj--cinnamic acid. The disorder concerns two orientations of the formyl group as shown in (a). The crystal structure in (b) shows only the disorder component of higher occupancy. The results from Rietveld refinement shown at the bottom are for (c) an ordered model comprising only the major orientation of the formyl group, and (d) the final disordered model (right side). Apart from the description of the order/disorder of the formyl group, all other aspects of these refinement calculations were the same. A slight improvement in the quality of the Rietveld fit for the disordered model is evident...

The defect concentration comes from thermodynamics. While we will discuss thermodynamics of solids in more detail in Chapter 2, it is useful to introduce some of the concepts here to help us determine the defect concentrations in Eq. (1.43). The free energy of the disordered crystal, AG, can be written as the free energy of the perfect crystal, AGq, plus the free energy change necessary to create n interstitials and vacancies (n, =n-o = n), Ag, less the entropy increase in creating the interstitials ASc at a temperature T ... 

Birchall and co-workers155 found that the fluorination of SbCUF gave a product best described as a tetramer of SbCl3F2 with partial replacement of the fluorine by chlorine and corresponding to the general formula Sb4Cli2+xF8 x (x = 0-4). In the case where x = 1 (equation 49) the substitution results in a compound with a disordered crystal structure ... 

The term condis crystal , which is a contraction of the term conformationally disordered crystal , was coined to designate the most important mesophase for flexible, linear macromolecules. We are not aware of prior naming of this class of mesophases4. 

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 third group of mesophase materials represents the conformationally disordered crystals, called condis crystals. The physical properties of condis crystals, which largely maintain positional and orientational order, change in much too subtle a way from the fully ordered crystals so that a common property could be attached to their name. 

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