Fine particles magnetic interactions

One-particle operators Hi and H3 cause relativistic corrections to the total energy. Two-particle operators H2, H3 and H s define more precisely the energy of each term, whereas H4 and H" describe their splitting (fine structure), i.e. they cause a qualitatively new effect. These operators are also often called describing magnetic interactions. 

Magnetic interactions between the Sun and the disk gave rise to powerful winds which ejected material in jets directed along open magnetic field fines out of the plane of the disk. The amount of material lost in this wind was perhaps 30-50% of the mass accreted by the Sun. Some sohd particles entrained in the wind would have fallen back into the disk, possibly many AU from the Sun (Shu et al., 1988). 

Kneller E, Puschert W (1966) Pair interaction models for fine particle assemblies. IEEE Trans Magnetics MAG-2 250... 

Spinu L, Stancu A (1998) Modelling magnetic relaxation phenomena in fine particles systems with a Preisach-Neel model. J Magnet Magnetic Mater 189 106-114 Srivastava KKP, Jones DH (1988) Toward a microscope description of superparamagnetism. Hyperfine Interactions 42 1047-1050... 

Wohlfarth EP (1964) A review of the problem of fine-particle interactions with special reference to magnetic recording. J Appl Phys 35 783-790... 

Here, h r) is a one-particle Dirac Hamiltonian for electron in a field of the finite size nucleus and y is a potential of the interelectron interaction. In order to take into account the retarding effect and magnetic interaction in the lowest order on parameter a (a is the fine structure constant), one could write [23]... 

In the world of nanoparticles and microporous materials, the interaction forces between nanosized particles and molecules from the surrounding medium, or the forces between particles themselves, may exceed the mechanical forces between bodies of the macroscopic world. This is caused by the high surface-to-volume ratio of nanoparticles and microporous materials. When familiar materials become mainly surface, they acquire new optical, magnetic, electrical, chemical, and transport properties. Thus, dispersions tend to agglomerate, fine particles show increased mechanical strength, and microporous solids develop tremendous sorption and molecular sieving properties. 

The calculation of the relaxation time t of the magnetic moment m of a particle is very important because the t value states all the experimental results. Accurate formulas are needed but difficult to establish because an actual sample of fine particles does not correspond to any simple case, due to the various anisotropies, the interparticle interactions, the surface effects, and so forth. On the other hand, experiments do not always measure the same parameters and the formulas have to be adapted. 

Figure E.l. Schematic phase diagram for fine particles with magnetic interparticle interactions. Case 1, the biocking temperature Tg increases with interactions (continuous iine). Case 2, Tg decreases with interactions (dashed line) (see text).

The calculated remanent magnetization compares favorably with some experimental results reported on spin glasses/ described in terms of a clusters-fine particles model. However, as far as we know, the Khater model has not been applied to fine particles materials. Assumed distribution function is not realistic, as well as in most cases the absence of interparticle interactions. 

The measurement of time decay of the remanent magnetization represents one of the most straightforward tools to investigate the dynamical behavior of fine particles and to study the magnetization reversal mechanisms. However, the interpretation of the experimental results is very difficult because of the complexity of actual fine particles systems (presence of size, shape, and interparticle distance distribution, random distribution of easy axes, existence of interparticle interactions, surface effects, etc.). 

In this chapter, we have tried to carry out the restatement of the magnetic properties of fine particles resulting from the relaxation of their magnetic moments from theoretical as well as experimental points of view. We discussed the models, several with some details, that allow one to calculate the relaxation time of the particle magnetic moment, to evaluate the effect of the interparticle interactions, and to interpret the experimental results. We clearly stated our objections, without use of indirect sentences understandable only by specialists, because fine-particle studies can be of interest in various fields, for example, catalysis, biology, mineralogy. Of course, this is our opinion at the present time. 

Another contribution to variations of intrinsic activity is the different number of defects and amount of disorder in the metallic Cu phase. This disorder can manifest itself in the form of lattice strain detectable, for example, by line profile analysis of X-ray diffraction (XRD) peaks [73], 63Cu nuclear magnetic resonance lines [74], or as an increased disorder parameter (Debye-Waller factor) derived from extended X-ray absorption fine structure spectroscopy [75], Strained copper has been shown theoretically [76] and experimentally [77] to have different adsorptive properties compared to unstrained surfaces. Strain (i.e. local variation in the lattice parameter) is known to shift the center of the d-band and alter the interactions of metal surface and absorbate [78]. The origin of strain and defects in Cu/ZnO is probably related to the crystallization of kinetically trapped nonideal Cu in close interfacial contact to the oxide during catalyst activation at mild conditions. A correlation of the concentration of planar defects in the Cu particles with the catalytic activity in methanol synthesis was observed in a series of industrial Cu/Zn0/Al203 catalysts by Kasatkin et al. [57]. Planar defects like stacking faults and twin boundaries can also be observed by HRTEM and are marked with arrows in Figure 5.3.8C [58],... 

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