Orientational disordering

With increasing values of P the molar volume is in progressively better agreement with the experimental values. Upon heating a phase transition takes place from the a phase to an orientationally disordered fee phase at the transition temperature where we find a jump in the molar volume (Fig. 6), the molecular energy, and in the order parameter. The transition temperature of our previous classical Monte Carlo study [290,291] is T = 42.5( 0.3) K, with increasing P, T is shifted to smaller values, and in the quantum limit we obtain = 38( 0.5) K, which represents a reduction of about 11% with respect to the classical value. 

Linear N2 molecules adsorbed on graphite show a transition from a high-temperature phase with orientational disorder to a low-temperature phase with herringbone ordering of the orientational degrees of freedom (see Sec. lie and Fig. 11). 

Except for Ceo, lack of sufficient quantities of pure material has prevented more detailed structural characterization of the fullerenes by X-ray diffraction analysis, and even for Ceo problems of orientational disorder of the quasi-spherical molecules in the lattice have exacerbated the situation. At room temperature Cgo crystallizes in a face-centred cubic lattice (Fm3) but below 249 K the molecules become orientationally ordered and a simple cubic lattice (Po3) results. A neutron diffraction analysis of the ordered phase at 5K led to the structure shown in Fig. 8.7a this reveals that the ordering results from the fact that... 

Chapter 9, on entropy and molecular rotation in crystals and liquids, is concerned mostly with statistical mechanics rather than quantum mechanics, but the two appear together in SP 74. Chapter 9 contains one of Pauling s most celebrated papers, SP 73, in which he explains the experimentally measured zero-point entropy of ice as due to water-molecule orientation disorder in the tetrahedrally H-bonded ice structure with asymmetric hydrogen bonds (in which the bonding proton is not at the center of the bond). This concept has proven fully valid, and the disorder phenomenon is now known to affect greatly the physical properties of ice via the... 

Due to their demanding synthesis, diamondoids are helpful models to study structure-activity relationships in carbocations and radicals, to develop empirical computational methods for hydrocarbons, and to investigate orientational disorders in molecular crystals as well [5,32]. 

Orientational disorder and packing irregularities in terms of a modified Anderson-Hubbard Hamiltonian [63,64] will lead to a distribution of the on-site Coulomb interaction as well as of the interaction of electrons on different (at least neighboring) sites as it was explicitly pointed out by Cuevas et al. [65]. Compared to the Coulomb-gap model of Efros and Sklovskii [66], they took into account three different states of charge of the mesoscopic particles, i.e. neutral, positively and negatively charged. The VRH behavior, which dominates the electrical properties at low temperatures, can conclusively be explained with this model. 

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. 

Plastic crystals and crystals with orientational disorder still fulfill the three-dimensional translational symmetry, provided a mean partial occupation is assumed for the atomic positions of the molecules whose orientations differ from unit cell to unit cell ( split positions ). 

Metallocenes (but only with unsubstituted cyclopentadienyl rings) also form thiourea inclusion compounds. X-ray diffraction and Mdssbauer data on the ferrocene inclusion compound show that at 295 K the guest molecules are orientationally disordered at the sites of 32 symmetry. A phase change at 162 K generates a more ordered structure78). 

Orientational disordering of the carbonate groups in CaC03 above 1260 K may serve as an example of application of Landau theory. Below the transition temperature, alternate layers of planar CO3 groups point in opposite directions. In the high-temperature modification they are free to rotate and become equivalent. The sym- ... 

There are a number of possible explanations for the formation of more than one photodimer. First, due care is not always taken to ensure that the solid sample that is irradiated is crystallographically pure. Indeed, it is not at all simple to establish that all the crystals of the sample that will be exposed to light are of the same structure as the single crystal that was used for analysis of structure. A further possible cause is that there are two or more symmetry-independent molecules in the asymmetric unit then each will have a different environment and can, in principle, have contacts with neighbors that are suited to formation of different, topochemical, photodimers. This is illustrated by 61, which contrasts with monomers 62 to 65, which pack with only one molecule per asymmetric unit. Similarly, in monomers containing more than one olefinic bond there may be two or more intermolecular contacts that can lead to different, topochemical, dimers. Finally, any disorder in the crystal, for example due to defective structure or molecular-orientational disorder, can lead to formation of nontopochemical products in addition to the topochemical ones formed in the ordered phase. This would be true, too, in those cases where there is reaction in the liquid phase formed, for example, by local melting. 

The preceding observations stimulated Olander and Rice 4> to search for a substance that is simultaneously simpler" than water yet a "good model of it. They suggested that amorphous solid water [H O/as)], first reported by Burton and Oliver 5> in 1935, satisfied these two requirements. Unlike the liquid, amorphous solid water can be studied at low temperature where the effects of thermal excitation and positional and orientational disorder can be separated. Moreover, it is plausible to accept as a working hypothesis that the amorphous solid is, essentially, extensively supercooled liquid water if so, the properties of the amorphous solid should be directly related to those of the liquid. 

Experiments at high pressure have shown that the P-T phase diagram of butadiene is comparatively simple. The crystal phase I is separated from the liquid phase by an orientationally disordered phase II stable in a narrow range of pressure and temperature. The strucmre of phase I is not known, but the analyses of the infrared and Raman spectra have suggested a monoclinic structure with two molecules per unit cell as the most likely [428]. At room temperature, butadiene is stable in the liquid phase at pressures up to 0.7 GPa. At this pressure a reaction starts as revealed by the growth of new infrared bands (see the upper panel of Fig. 25). After several days a product is recovered, and the infrared spectrum identifies it as 4-vinylcyclohexene. No traces of the other dimers can be detected, and only traces of a polymer are present. If we increase the pressure to 1 GPa, the dimerization rate increases but the amount of polymer... 

McCullough, J.P., Finke, H.L., Gross, M.E., Messerly, J.F., and Waddington, G. Low temperature calorimetric studies of seven 1-olefins effect of orientational disorder in the solid state, / Phys. Chem., 61(3) 289-301, 1957. 

Pedal motion, a key process of photoreaction in crystals. Is considered to occur only in crystals that have an orientational disorder or a large void around the molecules. 

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. 

Studies on crystalline CggO [39] using calorimetry and high-resolution X-ray powder diffraction show a face centered cubic lattice (a = 14.185 A) with an orientational disorder at room temperature. An orientational ordering transition occurs at 278 K, upon which a simple cubic phase develops. At 19 K this phase, which is similar to the orientational ordered phase of Cgg itself, shows additional randomness due to a distribution of orientation of the oxygens in CggO. 

Figure 4.14. Phase diagram, coverage vs. temperature, of N2 physisorbed on graphite. Symbols used fluid without any positional or orientational order (F), reentrant fluid (RF), commensurate orientationally disordered solid (CD), commensurate herringbone ordered solid (HB), uniaxial incommensurate orientation-ally ordered (UlO) and disordered (UID) solid, triangular incommensurate orientationally ordered (lO) and disordered (ID) solid, second-layer liquid (2L), second-layer vapour (2V), second-layer fluid (2F), bilayer orientationally ordered (2SO) and disordered (2SD) solid. Solid lines are based on experimental results whereas the dashed lines are speculative. Adapted from Marx Wiechert, 1996.

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