Spin-line models

The objective of this review has been to provide an insight into the considerations Involved in constructing spin-line models and some of the ways in which they can be used. Like any area, the task is never complete and the development is continuing. There are many areas in which the models can be improved and made more useful. Some of the main areas that need attention ... 

The Lines approximation is expected to be quite accurate for the description of the exchange interaction between a strongly axial doublet and an arbitrary isotropic spin. For all other cases, the Lines model [84] is a reasonable approximation. Efficient implementation of the Lines model was done in the program POLY ANISO. 

Although the classical mapping formulation yields the correct quantum-mechanical level density in the special case of a one-mode spin-boson model, the classical approximation deteriorates for mulhdimensional problems, since the classical oscillators may transfer their ZPE. As a hrst example. Fig. 21a compares Nc E) as obtained for Model I in the limiting cases y = 0 and 1 (thin solid lines) to the exact quantum-mechanical density N E) (thick line). The classical level density is seen to be either much higher (for y = 1) or much lower (for y = 0) than the quantum result. Since the integral level density can be... 

Develop models that deal with spin-line crystallization. 

Representative SMS spectra of ferropericlase ((Mgo.75,Feo.25)0) as a function of pressure at room temperature (a) [23] and along with a stainless steel (SS) for CS measurements (b). Dots Experimental measurements black lines modeled spectra with the MOTIF program. The quantum bits at 0, 13, and 45 GPa are generated from the QS of the high-spin Fe " " in the sample, whereas the flat feature of the spectra at 70,79, and 92 GPa indicates disappearance of the QS and the occurrence of the low-spin Fe +. 

ET rate evaluated from different theories as a function of the coupling strength for a spin-boson model (A = 1 and 0) = 0.1) and the temperature 1. Thick solid line present approach dashed line he Zusman theory dash-dotted line FGR thin solid line interpolation thick dotted line adiabatic Kramers theory thin dotted line adiabatic limit of Zusman theory. 

Fig. 23. Spin-lattice relaxation rale (TT,) vs. temperature for various oxygen concentrations 6=0.4, 0.49, 0.78 and 0.84 in GdBa2Cu30. T, has been measured using EPR techniques (see text). The solid lines have been calculated assuming a phenomenological spin-gap model. From Atsarkin et al. (1996).

Simulations reported in this and other reviews (Singel, 1989) demonstrate that, based on the spin-Hamiltonian model, effective zero-field nuclear quadrupole interaction parameters can be obtained by invoking a condition known as exact cancellation. On the basis of observations made concerning what experimental conditions yield optimal performance in ENDOR and ESEEM experiments, it has been suggested in this review that level crossing and the associated cross-relaxation is responsible for the deep modulation and corresponding narrow lines in the ESEEM spectrum. If level crossing and the resultant cross-relaxation processes are, in fact, the requisite condition for deep ESEEM, then the techniques described here are... 

Pig. 14. A comparison between the measured neutron peak intensities (solid circles) and those calculated (lines) from the spin-slip model of Ho (a) [OOf] scan for the i = 9 structure, and (b) [lOf] scan for the h = 11 structure. 

MC path integral simulations have been performed on a spin-boson model of the RC. A phase diagram for the ET process has been compiled based on the results of many path integral simulations. This is shown in Figure 3. The solid lines show which combinations of 2 and H12 could have produced dynamics consistent with experimentally observed behaviors. There is a gap region between the sequential and the superexchange region in which no 1 -> 3 transfer consistent with experiment can be seen. 

Figure 2. Comparison of electron transfer rates k e T) shown as a function of e evaluated in the framework of the spin-boson model (solid lines) and by Marcus theory (dashed lines) at temperatures 10 K and 300 K. The functions are centered approximately around m-...

A number of well known methods are available for the determination of crystallinity in semi-crystalline polymers. However, most of these methods are not amenable for in-spin line crystallinity measurements. A vibrational spectroscopic technique like Raman offers several distinct advantages for crystallinity measurements in the spinline (1). A calibration curve for propylene cyrstallinity was developed offline, using fibers spun, under different processing conditions, from several homo-polypropylene (hPP) and propylene-ethylene copolymers (with 5-15%E). This calibration curve was subsequently used to predict the polypropylene crystallinity, in the spin line, as a function of distance from the spinneret. The calibration model correlates the normalized intensity of the 809 cm Raman band with the DSC measured crystallinity and covers a wide crystallinity range (15-67%) with an R value of 0.989. 

Figure 2. The structural energy difference (a) and the magnetic moment (b) as a function of the occupation of the canonical d-band n corresponding to the Fe-Co alloy. The same lines as in Fig. 1 are used for the different structures. In (b) the concentration dependence of the Stoner exchange integral Id used for the spin-polarized canonical d-band model calculations is shown as a thin dashed line with the solid circles. The value of Id for pure Fe and Co, calculated from LSDA and scaled to canonical units, are also shown in (b) as solid squares.

Fig. 8. X-ray reflection diagram of a thin polystyrene film on float glass [160]. The reflectivity R is plotted against the glancing angle . The film is spin coated from solution. A model fit (dashed line) to the reflectivity data is also shown where the following parameters are obtained film thickness = 59.1 0.1 nm, interface roughness glass-polymer = 0.4 0.1 nm, surface roughness polymer-air = 0.6+1 nm, mean polymer density = 1.05 + 0.01 g/cm-3. The X-ray wavelength is 0.154nm...

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