Magnetization comparison with experimental results

F.2.3.6. Comparison with Experimental Results. The experimental results for which the measurement parameters are controlled, which permits only the derivation of the various parameters included in the formulas and a checking of the models, were until now very limited. They concern Fe particles in Al Oj matrix and y-FCjOj particles We show an example in Figure F.2.8 for y-FCjOs particles. We can see from the figure that a weak curvature is observed for 1/x when H pp is parallel to the sample plane. It is also clear that the value of the intercept (the d p value) of the quasi-linear part of 1 ix with the temperature axis is strongly dependent of the thermal correction M ,(r)/M (0). That raises the problem of the determination of this variable. In fact, it is only directly measurable from neutron diffraction experiments (see Section F.8). It can be deduced from magnetization under high-field experiment (see Section F.3) on the condition that does not vary much with H pp. If this is not fulfilled, only approximate values are obtained, which leads to difficulties for a precise determination of the intercept. We shall discuss the A/ p(r)/A/ r(0) determination in Section F.3. 

The topics appearing in the book range from new synthesis routes to physical-chemical characterizations. They address important properties of these materials, including morphology, structure, thermal stability, superconductivity, magnetism, spectroscopic and optical behaviour. Detailed ab initio investigations and simulations provide a comparison with experimental results, and potential applications of the final products are also proposed. 

It follows from Equation 6.12 that the current depends on the surface concentrations of O and R, i.e. on the potential of the working electrode, but the current is, for obvious reasons, also dependent on the transport of O and R to and from the electrode surface. It is intuitively understood that the transport of a substrate to the electrode surface, and of intermediates and products away from the electrode surface, has to be effective in order to achieve a high rate of conversion. In this sense, an electrochemical reaction is similar to any other chemical surface process. In a typical laboratory electrolysis cell, the necessary transport is accomplished by magnetic stirring. How exactly the fluid flow achieved by stirring and the diffusion in and out of the stationary layer close to the electrode surface may be described in mathematical terms is usually of no concern the mass transport just has to be effective. The situation is quite different when an electrochemical method is to be used for kinetics and mechanism studies. Kinetics and mechanism studies are, as a rule, based on the comparison of experimental results with theoretical predictions based on a given set of rate laws and, for this reason, it is of the utmost importance that the mass transport is well defined and calculable. Since the intention here is simply to introduce the different contributions to mass transport in electrochemistry, rather than to present a full mathematical account of the transport phenomena met in various electrochemical methods, we shall consider transport in only one dimension, the x-coordinate, normal to a planar electrode surface (see also Chapter 5). 

Magnetic coupling constants determined by EPR and ENDOR techniques permit a direct comparison with experimental data. Table 28 shows that, in the particular case of the Li defect, the agreement is reasonable for the UHF result, where the hole is localized at Oi. Eor the other Hamiltonians, the disagreement increases in parallel with the delocalization of the hole. 

The characterization is based on the assumption that selected orientations for the major axes of magnetic resonance tensors exist. Another assumption is the random scattering of major axes with respect to this direction according to the Gauss law. The orientation and disordering parameters are optimised by simulation of theoretical ESR spectra and comparison with experimental spectra. The mathematical algorithm developed for the simulation program is also discussed. Results of this approach were applied to experimental data for films of copper phthalocyanine and dipivaloil methanate, obtained by sedimentation on quartz plates. 

Figure 9 Comparison between the calculated magnetic moments of Ni clusters (dark squares) and the experimental results of Apsel et al.3 and Knickelbein.4 Reproduced with permission from Ref. 48.

Ring currents cannot be directly determined by experimental methods. However, comparison of experimental values of magnetic susceptibilities and their exaltations and anisotropies as well as of H-NMR chemical shifts with the respective data calculated from the ring current model points to the adequacy of this model for the interpretation of experimental results. The magnetic susceptibility associated with the ring current / (83BCJ1853), known as the London susceptibility, is given by... 

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