Diffusivities anisotropy

Without considering radiogenic growth, effectively we are considering a non-radiogenic isotope such as Ar. Two effective shapes, plane sheet and solid sphere, are considered here. The effective shape is not necessarily the physical shape diffusive anisotropy must also be considered in determining the effective shape (Section 3.2.11 and Figure 3-13). 

Adatom diffusion, at least under the low temperature of field ion microscope measurements, almost always follows the direction of the surface channels. Thus adatoms on the W (112) and Rh (110) surfaces diffuse in one direction along the closely packed atomic rows of the surface channels. Such one-dimensional surface channel structures and random walks can be directly seen in the field ion images, and thus the diffusion anisotropy is observed directly through FIM images. Unfortunately, for smoother surfaces such as the W (110) and the fee (111), no atomic or surface channel structures can be seen in field ion images. But even in such cases, diffusion anisotropy can be established through a measurement of the two-dimensional displacement distributions, as discussed in the last section. Because of the anisotropy of a surface channel structure, the mean square displacements along any two directions will be different. In fact this is how diffusion anisotropy on the W (110) surface was initially found in an FIM observation.120... 

Diffusion anisotropy on the W (110) surface was realized when the mean square displacements of a Re adatom on a W (110) plane along the [100] and [110] directions, or x- and y-directions shown in Fig. 4.28, were... 

The factor R may be called a diffusion anisotropy factor for the surface. For diffusion of a W on the W (110), Tsong Casanova find a diffusion anisotropy factor of 1.88 from a set of data taken at 299 K, and of 2.14 from a set of data taken at 309 K. The average is 2.01, which agrees with the theoretical value, 2, to within 0.5%. A more detailed general analysis has since then been reported,137 and diffusion anisotropy on the W (110) surface has also been observed in field emission experiments.138 It should be noted, however, that the same ratio can be expected if an adatom jumps instead in the [001] and [110] directions with an equal frequency. Thus a measurement of surface diffusion anisotropy factor alone does not establish uniquely the atomic jump directions. The atomic jump directions can, of course, be established from a measurement of the displacement distribution function in two directions as discussed in the last section. Such measurements can only be done with atomic resolution field ion microscopy. 

The influence of diffusion anisotropy on the reaction rate constant k is illustrated in Figure 5-10. In accordance with the fact that lower dimensionality increases the fraction of sites that are encountered more than once by the diffusing particles, the... 

A possible modification of this expression is presented elsewhere (82). The value of t, can be related to a diffusion coefficient (e.g., tj = l2/6D, where / is the jump distance), thereby making the Ar expressions qualitatively similar for continuous and jump diffusion. A point of major contrast, however, is the inclusion of anisotropic effects in the jump diffusion model (85). That is, jumps perpendicular to the y-ray direction do not broaden the y-ray resonance. This diffusive anisotropy will be reflected in the Mossbauer effect in a manner analogous to that for the anisotropic recoil-free fraction, i.e., for single-crystal systems and for randomly oriented samples through the angular dependence of the nuclear transition probabilities (78). In this case, the various components of the Mossbauer spectrum are broadened to different extents, while for an anisotropic recoil-free fraction the relative intensities of these peaks were affected. 

In DTI, diffusion is no longer described by a single diffusion coefficient, but by an array of nine coefficients that fully characterize how diffusion in space varies according to direction (Basser 1995). With this approach, diffusion anisotropy can be exploited to provide details on tissue microstructure and fiber tracts (le Bihan 2003). To obtain sufficient information on the direction of diffusion, the full diffusion tensor needs to be sampled [for a review on theoretical foundations of DTI see Basser and Jones (2002)]. 

Axons transport materials from the cell body to the synaptic terminals (anterograde transport) and in the opposite direction (retrograde transport). Anterograde transport may occur slowly (a few millimeters/ day only) or fast (up to 400 mm/day), whereas retrograde transport is always fast. Diffusion in the perpendicular direction (not along axons) is much more limited as the membranes and the myelin sheath form obstacles. Therefore, diffusion is not isotropic (same in all directions) in the WM. This phenomenon is known as diffusion anisotropy . In contrast, diffusion is rel-... 

Gaemers, S., and A. Bax (2001) Morphology of three lyotropic liquid crystalline biological NMR media studied by translational diffusion anisotropy. J. Am. Chem. Soc. 123, 12343-11235. 

MRI study of white matter diffusion anisotropy in schizophrenia. Neuroreport 14 2025-2029. 

Ardekani BA, Nierenberg J, Hoptman MJ, Javitt DC, Lim KO. 2003. MRI study of white matter diffusion anisotropy in schizophrenia. Neuroreport 14 2025-2029. 

Buchsbaum MS, Tang CY, Peled S, Gudbjartsson H, Lu D, et al. 1998. MRI white matter diffusion anisotropy and PET metabolic rate in schizophrenia. Neuroreport 9 425-430. 

Hwang, P. M., Skrynnikov, N. R., and Kay, L. E. (2001). Domain orientation in beta-cyclodextrin-loaded maltose binding protein Diffusion anisotropy measurements confirm the results of a dipolar coupling study. J. Biomol. NMR 20, 83-88. 

The spatially distributed PGSE experiment provides a nice means of demonstrating diffusion anisotropy. The intensity of the image pixel depends on the local gradient g and the self-diffusion tensor as... 

For a diffusion tensor of axial symmetry with Dj > D., Fig. 1 shows the influence of a diffusion anisotropy on the PFG NMR spin-echo attenuation as simulated in numerical calculations 49). The quantitative analysis shows, however, that for principal tensor elements not too different from each other (i.e., for tensor elements within one order of magnitude), the ini-... 

Figure 1. A stage of diffusion in a heulandite single crystal viewed through crossed Nicols (34). The di-ferent distances moved hy the band in 2 directions show the diffusion anisotropy. The direction of more rapid penetration is normal to 201, and that of less rapid pentration is normal to 001...

It has recently become more widely appreciated that the presence of rotational diffusional anisotropy in proteins and other macromolecules can have a significant affect on the interpretation of NMR relaxation data in terms of molecular motion. Andrec et al. used a Bayesian statistical method for the detection and quantification of rotational diffusion anisotropy from NMR relaxation data. Sturz and Dolle examined the reorientational motion of toluene in neat liquid by using relaxation measurements. The relaxation rates were analyzed by rotational diffusion models. Chen et al measured self-diffusion coefficients for fluid hydrogen and fluid deuterium at pressures up to 200 MPa and in the temperature range 171-372 K by the spin echo method. The diffusion coefficients D were described by the rough sphere (RHS) model invoking the rotation translational coupling parameter A = 1. 

Most zeolites are of noncubic structure, so that generally the intracrystalline diffusivities must be expected to be orientation dependent rather than isotropic. However, except for the pioneering diffusion studies of water in heulandite by Tiselius (149-151], the phenomenon of diffusion anisotropy has so far not been... 

In principle, information about diffusion anisotropy also may be obtained from powder samples by investigating the shape of the NMR signal attenuation. In contrast to isotropic systems where the echo attenuation is found to be a simple exponential, now the echo attenuation results from a superposition of exponentials corresponding to the various orientations of the individual crystallites relative to the magnetic field gradient [72,73,154] ... 

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