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![Energy loss Mechanism
1. hysteresis losses must be kept down to a minimum. When the induction is large for a
small applied field, the loop area is small and the hysteresis loss is reduced. The key factor
in the design of a soft magnet is then to have easily moving domain walls. Analogous to
grain boundaries, the domain walls tend to get pinned down by
dislocation tangles, impurity atoms, voids and nonmagnetic precipitates and
inclusions. A cold-worked material has a high dislocation density. It should be
properly annealed to reduce the dislocation density and thereby facilitate easier
motion of the domain walls. Soft magnetic materials should be free of impurities
and inclusions. Nonmetallic soft magnets such as ferrites and garnets are prone
to inherit voids during the process of manufacture by powder compacting. The
microstructure is therefore critical in sophisticated applications using ferrites and
garnets
Usually, there are easy and hard magnetization directions in a crystal. As
illustrated in Fig. 16.5, iron magnetizes more easily along the [100] direction
than along [111], which is the hard direction for iron. This property can be
exploited to reduce the area under the hysteresis loop by manufacturing
materials with a preferred orientation of grains.](https://image.slidesharecdn.com/mo201magneticmaterial-250723024125-1fcf9235/75/MO-201-magnetic-material000000000000000000000-pptx-35-2048.jpg)
MO 201 magnetic material000000000000000000000.pptx
- 1. MO 201 :Materials Science
- 2. M = Magnetisation H= Magnetic Field Strength χ = Magnetic Susceptibility magnetic flux density and magnetic field strength within the solenoid B = magnetic flux density or Magnetic induction µ = permeability
- 3.
- 7. A spinning electronhas a magnetic dipole moment, the Bohr magneton
- 11. The effect ofan applied magnetic flux density, B, on a solid: (a, b), a diamagnetic solid; (c, d) a paramagnetic solid; (e) a spin glass, similar to (c), but below a temperature Tf the orientation of the dipoles changes slowly; (f), a cluster glass with oriented dipoles in small volumes below a temperature Tf; (g) a ferromagnetic solid; (h) an antiferromagnetic solid; (i) a canted magnetic solid; (j) a ferrimagnetic solid.
- 16. The Bethe–Slater curvefor the magnitude of the exchange integral as a function of D/d. D is the separation of the atoms in a crystal and d the diameter of the 3d orbital.
- 17. Hund’s rule isa manifestation of the spin dependent electrostatic energy of the electrons in an orbital. When the electrons have the same momentum and the same spin, a certain distance must separate them from one another, in order to be consistent with the Pauli exclusion principle. This physical separation tends to increase their kinetic energy, but reduces the electrostatic repulsive energy between them. Whether the electrons will align their spins or not will depend on the sign of the net change in energy. The stable, energetically favoured order of filling of electronic orbitals in atoms is given by Hund’s rule. In the solid state, the outer electronic orbitals of neighbouring atoms overlap and produce energy bands. Consider the overlapping and the formation of energy bands in the first transition metals. At the left end of the series, the radius of the 3d orbitals in the atoms is large enough to result in good overlap between neighbours in the crystalline state. The 3d band then contains all paired up electrons and there is no net magnetic moment in the crystal. We can say that the atoms are antiferromagnetically coupled, as the magnetic moments of a pair of atoms exactly cancel out. As we go to the right in the transition series, the 3d orbitals shrink due to greater attraction from the increasing charge on the nucleus and consequently the overlap of the 3d orbitals decreases. The elements Fe, Co and Ni are in special situation. The unpaired electrons in the 3d orbitals of neighbouring atoms align their spins in a parallel fashion and thereby lower their spin dependent electrostatic energy. This lowering is partly offset by the rise in the Fermi level and the consequent increase in the average kinetic energy of the electrons. The increase in the Fermi level is directly attributable to the greater physical separation between electrons. The net gain in energy, E unmagnetized – E magnetized, called the exchange interaction energy is a sensitive function of the ratio of the atomic diameter to the 3d orbital diameter.
- 18. How does thischemical bonding viewpoint link with the band approach? The 3d band is narrow and is overlapped by broad outer bands from the 4s and 4p orbitals. Both the s and d electrons will be allocated to this composite band. As electrons are added to the band from the elements K, Ca, Sc, and so on, they occupy the broad, mainly s–p low-energy part. The number of spinup and spin-down electrons would be identical, and there is a low density of states at the Fermi level, so that relatively small numbers of electrons are promoted in a magnetic field, exchange energy is low, and Pauli paramagnetism results. As more electrons are added, moving from one transition metal to the next, (Ti, V, Cr, Mn), the electrons now occupy the narrow d portion of the band. The density of states at the Fermi level starts to rise. Large numbers of electrons can now be promoted and if energetically favourable, reverse spin, leading to greater exchange energy. The tipping point comes with iron. In this case the density of states at the Fermi level is high enough for the exchange energy to dominate and ferromagnetic ordering occurs. When the density of states at the Fermi surface is calculated with a high precision, it is found that only the three metals iron, cobalt and nickel will have sufficient exchange energy to retain a ferromagnetic state.
- 19. Magnetization = magneticmoments/volume = A m2/m3 = A m–1 The saturation magnetization of BCC iron is 1750 kA m–1. Calculate the net magnetic moment per iron atom in the crystal.
- 20. Which of thetwo solids, cobalt and gadolinium, has the higher saturation magnetization at (i) 0 K, and (ii) 300 K?
- 21. E= Eex +ED + E λ + EK + E H
- 27. Superexchange (electron coupling)between Ni2þ and O2 (schematic) leading to antiferromagnetic alignment of spins on cations.
- 30.
- 33. Double exchange (electrontransfer) between Fe2+ and Fe3+ (schematic) is possible only with parallel alignment of spins on cations and always leads to a ferromagnetic alignment of dipoles. Many crystalline structures potentially fulfil these requirements, including the ion pairs (Mn4+ , Mn3+ ) and (Co2+ , Co3+)
- 35. Energy loss Mechanism 1.hysteresis losses must be kept down to a minimum. When the induction is large for a small applied field, the loop area is small and the hysteresis loss is reduced. The key factor in the design of a soft magnet is then to have easily moving domain walls. Analogous to grain boundaries, the domain walls tend to get pinned down by dislocation tangles, impurity atoms, voids and nonmagnetic precipitates and inclusions. A cold-worked material has a high dislocation density. It should be properly annealed to reduce the dislocation density and thereby facilitate easier motion of the domain walls. Soft magnetic materials should be free of impurities and inclusions. Nonmetallic soft magnets such as ferrites and garnets are prone to inherit voids during the process of manufacture by powder compacting. The microstructure is therefore critical in sophisticated applications using ferrites and garnets Usually, there are easy and hard magnetization directions in a crystal. As illustrated in Fig. 16.5, iron magnetizes more easily along the [100] direction than along [111], which is the hard direction for iron. This property can be exploited to reduce the area under the hysteresis loop by manufacturing materials with a preferred orientation of grains.
- 37. 2. The othersource of energy loss in soft magnets is the eddy current loss. When the magnetic flux in a medium is changing, an emf is induced. As given by Lenz’s law, the induced emf is proportional to the rate of change of flux and hence to the frequency of the alternating current. The induced emf sets up eddy currents in the medium and the power loss due to the eddy currents is equal to V2/R, where V is the induced emf and R is the resistance of the medium. Eddy current losses can be minimized by increasing the resistivity of the magnetic medium. Iron which used to be the material for transformer cores is now almost entirely replaced by an Fe–Si solid solution with about 4% silicon, which has a substantially higher resistivity than pure iron
- 40. In recent years,metallic glasses produced from iron-base alloys containing 15–25% of (Si + B + C) offer substantial reduction in core losses. Such an alloy, cooled at a rate of ~104 °C s–1 from the molten state, does not crystallize but solidifies into a (ribbon-shaped) metallic glass. Owing to the larger concentrations of the impurity atoms, the electrical resistivity is higher than that for the Fe-4% Si alloy, thereby reducing eddy current losses. The absence of grain boundaries in the glassy matrix reduces hysteresis losses. The total iron losses can be reduced to 30–10% of that for the conventional Fe–Si alloy. Such a reduction can save nearly a billion dollars in distribution transformers alone in a developed country like the U.S. Soft magnets made of metallic glass are also used in phonograph cartridges and audio and computer tape heads
- 41. Fe–Si alloys aresuitable for operation at power frequencies of 50–60 Hz. They are not suitable in communications equipment, where high sensitivity and fidelity are required. Fe–Ni alloys such as Permalloy and Supermalloy are used for this purpose. These alloys have a high initial permeability which reduces considerably the area under the hysteresis loop. Hence, these alloys are suitable for higher frequencies. For frequencies exceeding MHz, metals and alloys are generally not suitable as soft magnets, as the eddy current losses are very high. The ferrimagnetic oxides, ferrites and garnets, are very suitable in the high frequency range. Being electrical insulators, they have a much higher resistivity than alloys. This reduces the eddy current losses to a negligible value. The choice depends on the application. Nickel–zinc ferrites are used for audio and TV transformers. Magnesium–manganese ferrites with a high resistivity areused as microwave isolators and gyrators in the kHz and MHz range. Garnets such as Y3Fe5O12 (yttrium–iron–garnet) have a narrow resonance line width and are widely used as microwave isolators in the very high frequency GHz range
- 43. Hard Magnetic Materials Hardmagnetic materials are used to produce permanent magnets. Hysteresis losses are of no significance here, as no repeated reversals of the magnetization is involved in a permanent magnet. The permanent magnets must have a high residual induction Br and a large coercive force Hc. The area of the hysteresis loop between Br and Hc represents the energy required to demagnetize a permanent magnet. The maximum value of this area is BrHc, called the energy product. It must be as large as possible for permanent magnets. High carbon steels and other low-alloy tungsten and chromium steels are used in the martensitic condition as permanent magnets. The same factors that improve the mechanical hardness impart better resistance to domain wall motion in permanent magnets.