Ferromagnetism

Ferromagnetism may occur as the result of strong spin-spin interactions. This requires unpaired spins and high order. The ferromagnetic susceptibility t can be given as  

In this expression 0is the Curie temperature 6 0 corresponds to ferromagnetic order 6 0 means antiferromagnetic order, and is called Neel temperature. 

This has the same form as the Curie equation, and the Curie constant is given by  

The value of is proportional to the number of magnetic dipoles present. The susceptibility is thus given in several forms. In the derivation above, N is the number of dipoles per unit volume, and the susceptibility is called the volume susceptibility, Xv in m . The mass susceptibility, Xm. in which N refers to the number of magnetic dipoles per unit mass, is given by Xv/p, where p is the density in kgm . The susceptibility of one mole of the substance, the molar susceptibility, Xmoiar is given by (Xv m) where is the molar volume of the material. 

The magnetisation of a compound, M, is the dipole moment per unit volume. For ferromagnetic compounds, the saturation magnetisation, Ms, when all of the dipoles are aligned, can be measured and used to estimate the effective magnetic moment on the atoms in the stmcture when the unit cell is known. 

The first theory to account for the existence of ferromagnetic solids was proposed by Weiss. He suggested that an internal molecular field existed 

If there is significant overlap of the 3d orbitals then, by the requirements of the Pauli exclusion principle, the spins must be antiparallel (/ 0). If the separation is too large then 

Chromium dioxide (Cr02) is at present the most important ferromagnetic ceramic. It is used as magnetic media in audio and video recording tapes. In this application, the Cr02 is not in the pure form but is usually doped to improve its properties. 

For a ferromagnetic material, relationship between magnetic flux density and magnetization 

Schematic illustration of the mutual alignment of atomic dipoles for a ferromagnetic material, which will exist even in the absence of an external magnetic field. 

For nickel, computation of the number of atoms per unit volume 

Saturation Magnetization and Flux Density Computations for Nickel 

Calculate (a) the saturation magnetization and (b) the saturation flux density for nickel, which has a density of 8.90 g/cm.  

There are two basic magnetically ordered structures, which can be distinguished from each other by the presence or absence of permanent macroscopic magnetization, namely ferromagnetic and aniiferrimagnetic. 

Ferromagnetics are intensively macroscopically magnetized in an external field and are strongly drawn into it. They have the greatest application techniques. Ferromagnetic 

The presence of noncoupled d- and f-electrons in atoms does not yet completely provide the conditions necessary for ferromagnetism to occur. For example, such elements as Cr, Mn, Pt, etc., also have noncoupled electrons, but they are not ferromagnetic. In some cases they possess antiferromagnetic behavior. 

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NmI point The temperature at which magnetic susceptibility becomes normal. See anti-ferromagnetism and ferromagnetism. 

The case of thin-skin regime appears in various industrial sectors such as aerospace (with aluminium parts) and also nuclear in tubes (with ferromagnetic parts or mild steel components). The detection of deeper defects depends of course on the choice of the frequency and the dimension of the probe. Modelling can evaluate different solutions for a type of testing in order to help to choose the best NDT system. 

High selective performance of the sensor also enable to detect surface cracks in ferromagnetic and non-magnetic welded connections under rust or dirt layer without prior cleaning. 

Building and testing of probes for an optimal coating control of ferromagnetic materials. 

Remote Field Eddy Current (RFEC) technology is a variation of the conventional eddy-current method, developed for detecting flaws at any point in the walls of (particularly) ferromagnetic (Fe) tubes and pipes from the inside diameter. 

The figures show typical signals obtained from an ID inspection of non-ferromagnetic tubing with artificial flaws, Figure 1, and actual results on steel tubing. Figure 2. 

The same instrument inspects both steel and non-ferromagnetic tubing... 

P.Y. lotibert, D. Miller, D. Placko, and E. Savin. New eddy current probe and associated preprocessings for 3d image reconstruction in non ferromagnetic tubes testing. In To be published in the proceedings of the Seventh ECNDT, 1998. 

Standard Practice for Electromagnetic Examination of Ferromagnetic Steel Wire Rope, ASTM Standard E 1571-94. 

The experimental tests have validated the theoretical model for eylindrical products in non ferromagnetic material, therefore with a long solenoid ... 

The result of this study can be exploited in the industrial control practice of long conductor, non ferromagnetic product. 

New Eddy Current Probe and Associated Preprocessing for 3D Image Reconstruction in Non Ferromagnetic Tube Testing. 

D. Miller, D.Placko "Pre-processing of signals delivered by a new eddy current sensor for non ferromagnetic tubes testing" in IMTC 96... 

The eddy current method allows to evalute the state of stress in ferromagnetic material. The given method is used for determining own stress as well as that formed in effect of outside load. With regard to physical principles of own stress analysis, the dependence between the magnetic permeability and the distance between atomic surfaces is utilized. 

Fn Fig. 2. it is shown, that the stress can be evaluated by placing the probe directly on the tested surface as well as at a certain distance from it. Test results indicate to the possibility of evaluating stress in parts covered with a protective layer (vanish or non-ferromagnetic electrolytic coating). 

Magnetic particles is one of the most used nondestructive testing techniques in industry. It allows detection and localization of surfacic and subsurfacic defects of ferromagnetic pieces by making conspicuous leakage fields by a magnetic developer. 

Two such new and possibly powerful methods are described in this paper. They allow for the detection of 1. extremely small ferromagnetic inclusions in the volume of a non ferromagnetic workpiece and 2. non ferromagnetic segregations in the volume of a non ferromagnetic workpiece. 

The Ising model is isomorphic with the lattice gas and with the nearest-neighbour model for a binary alloy, enabling the solution for one to be transcribed into solutions for the others. The tlnee problems are thus essentially one and the same problem, which emphasizes the importance of the Ising model in developing our understanding not only of ferromagnets but other systems as well. 

Wlien 2 g > (Eaa BB binary alloy corresponds to an Ismg ferromagnet (J> 0) and the system splits into two phases one rich in A and the other rich in component B below the critical temperature T. On the other hand, when 2s g < (Eaa+ bb > system corresponds to an antiferromagnet the ordered phase below the critical temperature has A and B atoms occupying alternate sites. 

Iiifomiation about the behaviour of the 3D Ising ferromagnet near the critical point was first obtained from high- and low-temperatnre expansions. The expansion parameter in the high-temperatnre series is tanli K, and the corresponding parameter in the low-temperatnre expansion is exp(-2A ). A 2D square lattice is self-dual in the sense that the bisectors of the line joining the lattice points also fomi a square lattice and the coefficients of the two expansions, for the 2D square lattice system, are identical to within a factor of two. The singularity occurs when... 

Kramers H A and Wannier G H 1941 Statistics of the two-dimensional ferromagnet part I Phys. Rev. 60 252... 

Domb 0 and Sykes M F 1957 Specific heat of a ferromagnetic Substance above the Ourie point Phys. Rev. 129 567... 

Figure A2.5.16. The coexistence curve, = KI(2R) versus mole fraction v for a simple mixture. Also shown as an abscissa is the order parameter s, which makes the diagram equally applicable to order-disorder phenomena in solids and to ferromagnetism. The dotted curve is the spinodal.

The little atomic magnets are of course quantum mechanical, but Weiss s original theory of paramagnetism and ferromagnetism (1907) [7] predated even the Boln atom. He assumed that in addition to the external magnetic field Bq, there was an additional internal molecular field B. proportional to the overall magnetization M of the sample. 

Equation (A2.5.20) is the Curie-Weiss law, and the temperature at which the magnetic susceptibility becomes infinite, is the Curie temperature. Below this temperature the substance shows spontaneous magnetization and is ferromagnetic. Nonnally the Curie temperature lies between 1 and 10 K. However, typical ferromagnetic materials like iron have very much larger values for quantum-mechanical reasons that will not be pursued here. 

Smolyaninov I P, Zayats A V and Davis C C 1997 Near-field second-harmonic imaging of ferromagnetic and ferroelectric materials Opt. Lett. 22 1592-4... 

Other magnetic measurements of catalysts include electron paramagnetic resonance and magnetic susceptibility. Although those are not as common as NMR, they can be used to look at the properties of paramagnetic and ferromagnetic samples. Examples of these applications can be found in the literature [87. 

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