Particles magnetization

Particles magnetic is one of the most useful testing techniques in industry. It allows the detection of surfacic and sub-surfacic defects. The main difficulty of this technique is to optimize the control conditions allowing an easiest interpretation of the results which necessite a great experience of the operator. 

The aim of the work we present in this paper is to optimize the control parameters used in particles magnetic and interpret the obtained results. Experiments are performed on samples of welds or materials containing known defects. The realized and tested defects are grooves situated at different depths with variables dimensions. Other types of defects have been studied (inclusions, lack of penetration, etc.). 

Figure 8. Relative size distribution for the MPIF Na /Pd catalyst particles before (left, 35 particles) and after catalytic tests (right, 75 particles, magnetic stirring). Arithmetic average diameters 319 and 276mm were determined for particles before and after catalytic tests, respectively. Image Pro Plus program. (Reprinted from Ref [29], 2003, with permission from Elsevier.)...

In the external field approximation the heavy particle magnetic moment factorizes and the relativistic and radiative corrections have the form... 

The Mossbauer spectra do, however, indicate that the anisotropy energy barrier for the particle magnetization flipping is quite large, 10-20 J (215), for the 1.5-nm iron particles. As discussed in Section III, A, 3, this barrier was estimated from Mossbauer spectra at various temperatures by measuring the fraction of the spectral area that appears paramagnetic. At the temperature for which this ratio is 0.5, the relaxation time can be estimated... 

Adsorb the antibody to a solid support such as the surface of a plastic tube, multiwell plate, latex particle, magnetic particle, nylon, nitrocellulose, or glass fiber filter. 

This relaxation time—which, to be specific, we have written in the Landau-Lifshitz representation—has the anticipated behavior the smaller the precession damping constant (the higher the quality factor of the oscillations), the slower does the particle magnetic moment approach its equilibrium position. For ferromagnet or ferrite nanoparticles the typical values of the material parameters are Is Is < 103G, Vm 10 18cm3, and a 0.1. Substituting them in formula (4.28) aty 2 x 108 rad/Oe s and room temperature, one obtains xD 10-9 s. 

The equilibrium distribution function of the particle magnetic moment or (if we neglect interactions) of an assembly of magnetic moments is determined by the Gibbs law... 

The rotary diffusion (Fokker-Planck) equation for the distribution function W(e,t) of the unit vector of the particle magnetic moment was derived by Brown [47]. As shown in other studies [48,54], it may be reduced to a compact form... 

Resuming the main line of our consideration, let us show how to consistently take into account the effect of the particle magnetic anisotropy by solving the Brown equation (4.90). Taking n as the polar axis of the coordinate framework, we recover the situation considered as an illustration in Section II.B. Namely, the dimensionless particle magnetization is expressed as Eq. (4.54) and the particle energy as Eq. (4.55). Then the nonstationary solution of the kinetic equation (4.90), which is equivalent to Eq. (4.27), is presented in the form of expansion (4.56) whose amplitudes satisfy Eqs. (4.60) and (4.61). 

The kinetic (rotary diffusion) equation for the particle magnetic moment may be solved with high precision, thus taking into account contributions from the intrawell motions that are essential for a correct description of SR, especially at low temperatures. 

Some estimations on the magnitude of the SR effect are given in Refs. Ill and 112. We would like also mention an extension of the framework presented for the case of the excited field nonparallel to the particle anisotropy axis. As shown in Ref. 113, despite the absence of interwell transitions for the components of the particle magnetic moment perpendicular to the anisotropy... 

Here we focus on the longitudinal situation and assume that the imposed fields are collinearly directed along the anisotropy axis n. Then the set of the angular variables reduces to the polar angle fi of e with respect to it. Setting cos ) (e n) = x, at Hp = const for the equilibrium distribution function of the particle magnetic moment, one gets... 

A consistent study of the linear and lowest nonlinear (quadratic) susceptibilities of a superparamagnetic system subjected to a constant (bias) field is presented. The particles forming the assembly are assumed to be uniaxial and identical. The method of study is mainly the numerical solution (which may be carried out with any given accuracy) of the Fokker-Planck equation for the orientational distribution function of the particle magnetic moment. Besides that, a simple heuristic expression for the quadratic response based on the effective relaxation... 

Taking thermal fluctuations into account, the motion of the particle magnetic moment is described by the orientational distribution function W(e,t) that obeys the Fokker-Planck equation (4.90). For the case considered here, the energy function is time-dependent ... 

Here, 0 is the acute angle between the orientation of the particle magnetic moment and the magnetic field vector. Before entering the magnet, the silver atoms are oriented randomly with respect to the magnetic field (i.e., cos(0) can adopt any value between -1 and 1). Classically, the interaction of... 

Due to the KV and kBT relationship in single-domain particles, magnetic properties of a self-assembled magnetic nanoparticle array are usually size and temperature dependent. A typical zero-field-cooled (ZFC) and field-cooled (FC) scans of the 11 nm Co nanoparticle assembly is shown in Fig. 11(A) [12], in which magnetization is measured as a function of temperature. 

Individual metal particles magnetically separated from lunar samples were studied intensively by Goldstein et al. 75-77 Wanke et al.6 78 and Wlotzka et al.19 80 From their trace element composition as well as from their content of Ni and Co, it was clear that the majority of the particles are of meteoritic origin. 

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