The Slater–Pauling curve
The collective-electron and rigid-band models are further supported by the rather well-knownplot knownas the Slate –Pauling curve [26, 27]. In the late 1930s, Slater and Pauling independently calculated the saturation magnetization as a continuous function of the number of 3d and 4s valence electrons per atom across the first transition series. They used a rigid-band model, and obtained a linear increase in saturation magnetization from Cr to Fe, then a linear decrease, reaching zero magnetization at an electron density between Ni and Cu. They compared
their calculated values with measured magnetizations of the pure ferromagnets Fe, Co, and Ni, as well as Fe–Co, Co–Ni, and Ni–Cu alloys. The results from Pauling’s paper are shown in Fig. 6.8. The measured values agree well with the theoretical values. Although there are only three pure ferromagnetic metals, many transitionmetal alloys are ferromagnetic, and the saturation magnetic moment is more or less linearly dependent on the number of valence electrons.
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In this chapter (and in the previous chapter on paramagnetism) we have introduced and applied two complementary theories of magnetism. In the localized-moment theory, the valence electrons are attached to the atoms and cannot move about the crystal. The valence electrons contribute a magnetic moment which is localized at the atom. The localized-moment theory accounts for the variation of spontaneous magnetization with temperature in the ferromagnetic phase, and explains the Curie– Weiss behavior above the Curie temperature. In the collective-electron model, or band theory, the electrons responsible for magnetic effects are ionized from the atoms, and are able to move through the crystal. Band theory explains the noninteger values of the magnetic moment per atom that are observed in metallic Ferromagnets.
Of course in “real life” neither model is really correct, although there are some materials for which one or the other is a rather good approximation. In the rare-earth elements and their alloys, for example, magnetism comes from the tightly bound core f electrons, and so the localized-moment model works well. In materials such as Ni3Al the electrons are highly itinerant, so the band theory gives accurate results. Transition metals show some features of both localization and itinerant electrons. Permanent magnets, such as NdFe14B, are particularly hard to describe, since they combine the behavior of transition metals and rare earths.
By far the most successful method currently available for calculating the magnetic properties of solids is density functional theory (DFT). DFT is an ab initio many-body theory which includes (in principle) all the interactions between all the electrons. No assumptions are made as to whether the electrons are localized or itinerant – rather the electrons choose the arrangement which will give them the lowest possible total energy. Unfortunately, DFT calculations are both computationally intensive and difficult, in particular because the exact form of the exchange and correlation part of the inter-electronic interaction energy is not known. As an example, it has only recently been possible to obtain the correct body-centered cubic, ferromagnetic ground state for iron [28]. (Earlier studies predicted that it should be non-magnetic and face-centered cubic!) An excellent review of the use of DFT to calculate the properties of magnetic materials and beyond is given in the September 2006 issue of the Bulletin of the Materials Research Society.
We also provide neodymium magnet ceramic magnet, alnico magnet, SmCo magnet, rubber magnet and magnetic products. These products are widely used in micro-motor, motor, computer, instrument, meter, automobile, motorcycle, horologe, office equipment, toy, magnetic therapy device and daily life industries.
Xiamen Everbeen Magnet Electron Co.,Ltd. http://www.everbeenmagnet.com
Add:Unit H, 4F Rihua Mansion, No. 8 Xinfeng 2nd road, Torch Hi-Tech Zone, Xiamen, China.
Tel:0086-592-5781916
Fax:0086-592-5123653
E-mail:info@china-magnet.net
