Thermal motion, anisotropy

Recent improvements in the details of the CLP crystallization procedure and crystal treatment have led to even better diffracting crystals. At 1.4 A resolution, refinement, including anisotropic B factors, illustrates, the thermal motion anisotropy of the retinal and key neighbors (Fig. 4, see color insert manuscript in preparation). 

Below a critical size the particle becomes superparamagnetic in other words the thermal activation energy kTexceeds the particle anisotropy energy barrier. A typical length of such a particle is smaller than 10 nm and is of course strongly dependent on the material and its shape. The reversal of the magnetization in this type of particle is the result of thermal motion. 

Anharmonic Thermal Motion and the Bonding Anisotropy of Transition Metal Complexes... 

A determination of the structure of l,4-dibromocycl[3,2,2]azine (lp) was complicated by the considerable anisotropy of thermal motion of the bromine atoms. It was concluded that the nitrogen configuration is probably planar, but, if not, the nitrogen atom is less than 0.07 A out of the mean plane of the molecule.55... 

When micellar aggregates are formed in solutions and their aggregation numbers are not very large, they are randomly dispersed, owing to thermal motion. Weak indications of anisotropy are found at very high concentrations only. 

In sufficiently mobile, (i.e., liquid-like), systems, the anisotropy is averaged out by the isotropic thermal motions leaving only the isotropic contributions. As already stated, viscoelastic polymers represent an intermediate between the two extremes of rigid or mobile materials and the implications of this will be discussed in 14.2.3 in more detail. 

Molecules that possess magnetic anisotropy experience a slight tendency toward alignment with an imposed magnetic field, but in normal isotropic solvents random thermal motions dominate, and no effects of orientation are usually... 

The next level of approximation accounts for the anisotropy of thermal motions in a harmonic approximation and describes atoms as ellipsoids in one of the three following forms, which are, in fact, equivalent to one another ... 

The anisotropic displacement parameters can be visualized as ellipsoids Figure 2.54) that delineate the volume where atoms are located most of the time, typically at the 50 % probability level. The magnitude of the anisotropy and the orientations of the ellipsoids may be used to validate the model of the crystal structure and the quality of refinement by comparing thermal motions of atoms with their bonding states. Because of this, when new structural data are published, the ellipsoid plot is usually required when the results are based on single crystal diffraction data. 

It should be noted that more complicated forms of the temperature factor term can be employed when the crystal structure analysis is particularly precise and the resolution high. These expressions take into account the possible anisotropy of the thermal motion or statistical disorder. In the most sophisticated cases, six parameters are used to define the three-dimensional ellipsoids of thermal motion, which serve to describe anisotropic temperature factors. These should not be a source of concern to the reader at this time. 

R. J. Nelmes, (1980). Acta Cryst., A36,641-653. Anisotropy in thermal motion and in secondary extinction. 

Precision measurements of the temperature dependence of QS are not common in tin Mdssbauer spectroscopy, primarily because the splittings vary little with temperature, and most chemical structural interpretations can be based on the QS value at a single temperature, typically 77 K. The theory needed for the interpretation of the QS parameter in tin compounds has not been developed to such a point as to make precision measurements worthwhile.21-23 However, the thermal variation of the QS is commonly studied for two main reasons for monitoring structural phase transitions and for the study of the motional anisotropy... 

The intensities of the lines(Figure 4a) are in the approximate ratio 5 5 1 for a, 3. and y carbons respectively and do not reflect the true 2 2 1 ratio. This must arise from a difference in rotating frame relaxation times for the protons and/or carbons such that the Cross-polarization dynamics of the a and 3 carbons are not the same as for the y carbon(5 ). Further, sidebands introduced by the sample rotatk>n(2.8 kHz) appear to low field of the main resonances, indicating that the inherent chemical shift anisotropy of the planar molecules is not averaging by thermal motion. These data are consistent with restricted overall motion and perhaps a preferential rotation about the C 2 symmetry axis of the pyridine. 

Many experiments demonstrate that the anisotropy of nematics arises because of the tendency of the rod-like molecules in the fluid to align their long axis parallel to the director. This is shown schematically in Fig. 1(a). The director is denoted by the symbol n the rod-like molecules are represented by the short lines. Note that at finite temperatures, the thermal motion of the molecules prevents perfect alignment with n the orientations of the molecules are in fact distributed in angle, but with the director as the most probable, or the most populated, direction. 

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