Anisotropicity axial

The four-coordinate Ni(I) complexes with saturated ligands exhibit anisotropic axial spectra with gg values being greater than g L values. The Ni(II) species of ligand-stabilized radical, which is produced from the reduction of the four-coordinate Ni(II) macrocyclic complexes with conjugated double bonds, exhibit isotropic spectra. The isotropic spectra of Ni11 (mac-) turn to anisotropic axial spectra as the complexes coordinate CO to form five-coordinate Ni(I)-CO adducts (135,137). The anisotropic axial epr spectra of four-coordinate Ni(I) complexes become rhombic as the complexes coordinate extra axial ligand such as CO or acetamide to form five-coordinate Ni(I) species (135, 136). The epr spectral data of some Ni(I) complexes are summarized in Table VII. 

A typical anisotropic axial EPR spectrum of an oxovanadium(IV) complex (inset) in frozen THF. The ligand is a Schiff base derived from vanillin and tyrosine. Diamonds indicate the eight components of A (the parallel hyperfine coupling constant parallel defined by the z direction, which is the direction of the magnetic field). Arrows indicate the five inner components of Aj. Abscissa magnetic field strength (G) ordinate, intensity (arbitrary units). 

Fig. 5.27 ESR spectra of y-ray irradiated solid (a) p-HaCpure), (b) o-D2(l mol%)/p-H2, (c) HD(1 mol%)// -H2 samples at 4.2 K. The simulated spectra of (a ) [H2(H2)H2], (b ) [H2(H2)D2], (c ) [H2(H2)HD]", and (c") [H2(HD)H2] are shown together with the assignment of the Unes. For the spectral simulations hf splittings with a small anisotropy were assumed the isotropic hf splittings used are given in Fig. 5.29. The anisotropic (axial symmetric) h/value used is, for extun-ple, (-)0.06 mT for the two equivalent H atoms of the H2 -core in [H2(H2)H2]. The spectrum below 305 mT and above 354 mT could not be measured because of the overlapping of very intense signal due to trapped H-atoms [79]. The spectra were obuiined from Dn J. Kumagai...

Abstract In this chapter, an exothermic catalytic reaction process is simulated by using computational mass transfer (CMT) models as presented in Chap. 3. The difference between the simulation in this chapter from those in Chaps. 4,5, and 6 is that chemical reaction is involved. The source term in the species conservation equation represents not only the mass transferred from one phase to the other, but also the mass created or depleted by a chemical reaction. Thus, the application of the CMT model is extended to simulating the chemical reactor. The simulation is carried out on a wall-cooled catalytic reactor for the synthesis of vinyl acetate from acetic acid and acetylene by using both c — Sc model and Reynolds mass flux model. The simulated axial concentration and temperature distributions are in agreement with the experimental measurement. As the distribution of lx shows dissimilarity with Dj and the Sci or Pri are thus varying throughout the reactor. The anisotropic axial and radial turbulent mass transfer diffusivities are predicted where the wavy shape of axial diffusivity D, along the radial direction indicates the important influence of catalysis porosity distribution on the performance of a reactor. 

Fig. 26.2. The microstructure of wood. Woods ore foams of relative densities between 0.07 and 0.5, with cell walls which ore fibre-reinforced. The properties ore very anisotropic, partly because of the cell shape and partly because the cell-wall fibres ore aligned near the axial direction.

The chemical shift of a nucleus depends in part on its spatial position in relation to a bond or a bonding system. The knowledge of such anisotropic effects is useful in structure elucidation. An example of the anisotropic effect would be the fact that axial nuclei in cyclohexane almost always show smaller H shifts than equatorial nuclei on the same C atom (illustrated in the solutions to problems 37, 47, 48, 50 and 51). The y-effect also contributes to the corresponding behaviour of C nuclei (see Section 2.3.4). 

The model of non-correlated potential fluctuations is of special interest. First, it can be solved analytically, second, the assumption that subsequent values of orienting field are non-correlated is less constrained from the physical point of view. The theory allows for consideration of a rather general orienting field. When the spherical shape of the cell is distorted and its symmetry becomes axial, the anisotropic potential is characterized by the only given axis e. However, all the spherical harmonics built on this vector contribute to its expansion, not only the term of lowest order... 

Inserting (4.65) into (4.57), we find a modified relation for the relative intensity ratio I2H1 for crystals with anisotropic (but axially symmetric) Lamb-Mossbauer factor/... 

A t)tpical feature of the Mossbauer spectra of five- or six-coordinate iron(IV) with an axial oxo group (or a OCH3, a nitrido or a imido group) is a low isomer shift (+0.1 0.15 mm s ), a large and positive quadrupole splitting (1-2 mm s ), an anisotropic hyperfine coupling tensor with moderately large values for A x/gNl N and (—16 to —23 T) and a rather small value for A Jg i (0 to —10 T)... 

Fig. 3.1.4 Anisotropic self-diffusion of water in and filled symbols, respectively). The horizon-MCM-41 as studied by PFG NMR. (a) Depen- tal lines indicate the limiting values for the axial dence of the parallel (filled rectangles) and (full lines) and radial (dotted lines) compo-perpendicular (circles) components of the axi- nents of the mean square displacements for symmetrical self-diffusion tensor on the inverse restricted diffusion in cylindrical rods of length temperature at an observation time of 10 ms. / and diameter d. The oblique lines, which are The dotted lines can be used as a visual guide, plotted for short observation times only, repre-The full line represents the self-diffusion sent the calculated time dependences of the...

When one of the Fe-coordinating Ns of the porphyrin is made inequivalent to the others, for example, by pulling on it, or by putting a protein structure around the cofactor, then the molecular x axis and y axis become inequivalent, and the axial EPR spectrum turns into the rhombic spectrum in trace d with derivative trace e (see also Table 5.4). There are now three features in the spectrum a peak, a zero crossing, and a negative peak, and their field positions closely (exactly for zero linewidth) correspond to those of the g-values, gx, gy, and gz. Finally, in trace f of Figure 5.4, which is the experimental X-band spectrum of cytochrome c, it can be seen that not only the g-value (peak position) but also the linewidth is frequently found to be anisotropic. This extra complication will be discussed extensively in Chapter 9. 

FIGURE 5.4 Anisotropy in absorption and derivative powder-type ERP spectra. (A) axial intensity pattern (B) axial EPR absorption (C) axial EPR derivative (D) rhombic EPR absorption (E) rhombic EPR derivative (F) the spectrum of horse heart cytochrome c, a rhombic EPR derivative with anisotropic broadening (Hagen 2006). (Reproduced by permission of The Royal Society of Chemistry.)... 

The first term is characterized by a scalar, 7, and it is the dominant term. Be aware of a convention disagreement in the definition of this term instead of -27, some authors write -7, or 7, or 27, and a mistake in sign definition will turn the whole scheme of spin levels upside down (see below). The second and third term are induced by anisotropic spin-orbit coupling, and their weight is predicted to be of order Ag/ge and (Ag/ge)2, respectively (Moriya 1960), when Ag is the (anisotropic) deviation from the free electron -value. The D in the second term has nothing to do with the familiar axial zero-field splitting parameter D, but it is a vector parameter, and the x means take the cross product (or vector product) an alternative way of writing is the determinant form... 

If the Ln3+ centre is a Kramers ion, the spectra can be interpreted in terms of a doublet with largely anisotropic effective -values. If one neglects the admixture of higher lying/ multiplets and considers an axial symmetry, the effective g values will be... 

An unambiguous identification of anomalous muonium with the bond-center site became possible based on pseudopotential-spin-density-functional calculations (Van de Walle, 1990). For an axially symmetric defect such as anomalous muonium the hyperfine tensor can be written in terms of an isotropic and an anisotropic hyperfine interaction. The isotropic part (labeled a) is related to the spin density at the nucleus, ip(0) [2 it is often compared to the corresponding value in vacuum, leading to the ratio i7s = a/Afee = j i (O) Hi/) / (O) vac- The anisotropic part (labeled b) describes the p-like contribution to the defect wave function. 

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