Magnetic particles magnetization curves

For a system of nickel particles covering a certain size range, the magnetization curve will be composed of the Langevin functions of the individual particles (see also Becker (lie)) ... 

Fig. 12. Magnetization curves for Ni/Si02 (Ni Si02 = 15 100) (fl0S fraction by weight of particles with 10a Ni atoms, etc.). Drawn curves calculated from assumed distribution.

It is easily shown that a mean value of the particle size (averaged over the weights of the particles) is given by the initial slope of the magnetization curve ... 

For a great number of catalyst samples the chemisorption yH(195° K., 100 mm. Hg) is compared with the initial slope a of the magnetization curve at 300° K. (see Fig. 13). If it is taken into account that the amounts chemisorbed are proportional to the reciprocal value of the particle radius and that the magnetic moment is proportional to the particle volume, the correlation is as good as could be expected. 

Fig. 14. Ni/Si02 (Ni Si02 = 3 1). Effect of time and temperature of reduction on particle size a Slope magnetization curve at

An extended two-particle cluster approximation involving nearest-and next-nearest neighbor exchange for para- and ferromagnets (with particular reference to EuO, EuS, EuSe, and EuTe) has been developed (22). Heat capacity curves. Curie temperatures, magnetization curves. 

The Akulov law corresponds magnetization saturation for polycrystals and nanoparticles without exchange interaction between them. In the system of exchange coupled particles the magnetization curve is described by another power low. Thus, the relation M observed in the experiment is indicative of the lack of exchange interaction between the cobalt nanoparticles. 

However, the run of the ZFC magnetization curve does not correspond to the results of TEM, EPR and IR spectroscopy results concerning particle size of y-Fe20j and the absence of its interaction with Si02 matrix. Thus, a wide maximum T ax at 145 K is typical of greater particles [1-2,4] as compared to the studied materials. A considerable distinction between T ax and Tsep (250 K) is the evidence of a wide particle size distribution. The mentioned contradictions between the particle size and magnetic behavior of the samples can be resolved considering that and T ep parameters depend not only on a particle size, but on a number of other features of materials like surface states, defectiveness of structure, cluster interaction [5]. 

It was possible to measure accurately the average metal particle size from the magnetization curve taken at 4.2 K with magnetic fields ranging from 0 up to 70 k. Oe (supra-conductive coil). 

The behavior of ferrofluid particles subject to a constant magnetizing field is adequately described by this Langevin theory of paramagnetism suitably modified to take account of a distribution of particle sizes and particle interactions. Thus ferrofluids have a magnetization curve which does not exhibit hysteresis. 

Similar magnetic behavior has been found for mPS microspheres. Figure 11a shows a typical magnetization curve for mPS particles, whose TEM is shown in Fig. 1 lb. 

Iron nanoparticles prepared by pyrolysis of poly(ferrocenylsilanes) inside periodic mesoporous sihca displayed the absence of room-temperature hysteresis in the magnetization curves which shows their superparamagnetic behavior [55]. However, magnetic properties cannot always be easily interpreted. For example, for this material data analysis of magnetization curves resulted in the ambiguous conclusion that either particle size distribution is bimodal, or iron particles have an oxide layer which behaves as small superparamagnetic nanoparticles. So magnetic measurements should be combined with other techniques (probably, in this case, EXAFS may be useful) to allow more accurate evaluation of particle structure. 

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