Magnetization model

The reversible aggregation of monomers into linear polymers exhibits critical phenomena which can be described by the 0 hmit of the -vector model of magnetism [13,14]. Unlike mean field models, the -vector model allows for fluctuations of the order parameter, the dimension n of which depends on the nature of the polymer system. (For linear chains 0, whereas for ring polymers = 1.) In order to study equilibrium polymers in solutions, one should model the system using the dilute 0 magnet model [14] however, a theoretical solution presently exists only within the mean field approximation (MFA), where it corresponds to the Flory theory of polymer solutions [16]. 

Table 1. YCo5 refined parameters for the atomic magnetic model.

Baldovi, J.J., Clemente-Juan, J.M., Coronado, E. and Gaita-Arino, A. (2013) Two pyrazolylborate dysprosium(III) and neodymium(III) single ion magnets modeled by a radial effective charge approach. Polyhedron, 66, 39—42. 

This contrasts with the assumption made in virtually all other magnetic models that the value of is independent of temperature. Several variants of the Shottky model have been developed by Miodownik (1977, 1978a) to take into account the situation where one of the two states subsequently undergoes magnetic ordering (Fig. 8.S). In such cases it may also be necessary to consider a temperature-dependent AE (Miodownik and Hillert 1980). 

Figure 8. Dependence of the reduced energy, E/J, of the ground and excited states on the Jj/J ratio for a four-spin system, with = 1/2 and 0, arranged as in the symmetric tetrameric magnetic model shown.

Fluorides are suitable 2-D and 1-D magnetic models. In the K2NiF4 series, for instance, the antiferromagnetic behavior of fluorinated compounds can perfectly be explained by means of high-temperature expansion series which is not always the case with the homologous oxides9). 

The only difference between the inverse problem formulation for gravity and magnetic fields is that now we use a complex Hilbert space of magnetization models /(C)-... 

Kodama RH (1999) Magnetic nanoparticles. J Magnet Magnetic Mater 200 359-372 Kodama RH, Berkowitz AE (1999) Atomic-scale magnetic modeling of oxide nanoparticles. Phys Rev B 59 6321-6336... 

Determination of the real magnetic topology of the crystal and of its minimal magnetic model space. 

POLYOXOMETALATES FROM MAGNETIC MODELS TO MULTIFUNCTIONAL MATERIALS... 

The electronic model is almost invariably invoked IR and UV spectra are easy to obtain and are required for proper characterization—but the information obtained is highly qualitative. Certain aspects of the magnetic model are also easy to apply, and high hopes have been held for the magnetic model as a criterion of aromaticity. Indeed, it does provide useful qualitative criteria, but chemical shifts and coupling constants are sensitive to other structural and environmental influences so as to hinder quantitative application. 

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