Cullity B.D. Introduction to Magnetic Materials. Second Edition (2008)

14.14.2Mechanical-to-Electrical

If the flux through a winding is changed, an emf will be induced in that winding. The flux change can be effected by any mechanically produced relative motion of a magnet and the winding. This principle is the basis for devices like the magneto and the microphone. The magneto consists of a magnet rotating within an iron core carrying a winding. It is used to produce the sparks for ignition in small gasoline engines, such as those used in power lawn mowers and outboard motors.

The magnetic microphone is simply the inverse of the loudspeaker. It is rarely used, except in some simple communication systems where the loudspeaker also serves as the microphone.

14.14.3Microwave Equipment

Included here is equipment both for communications and radar. The devices involved bear such names as magnetron and traveling wave tube, and the details of their operation are matters for a specialist. In some traveling wave tubes for military and radar applications, the requirements are so severe that only materials of very high coercivity, like PtCo and SmCo5, are suitable.

14.14.4Wigglers and Undulators

The electron current in a synchrotron emits radiation when it is accelerated into a curved path. This synchrotron radiation is an unwanted power loss and radiation hazard to the people using the electrons, but a valuable source of high-intensity X-radiation of adjustable frequency to the solid-state physicist and similar scientific workers. The intensity and characteristics of the synchrotron radiation can be enhanced by passing the electron beam through an array of permanent magnets that force the electron beam to accelerate up and down or side to side. Such arrays are known as wigglers and undulators.

14.14.5Force Applications

If either pole of a permanent magnet is brought near a piece of iron, the field of the magnet will magnetize the iron in such a direction that an opposite pole will be, to use the ancient term, “induced” in the iron, and attraction will occur. On the other hand, if like poles of two permanent magnets are brought together, repulsion will result. The calculation of these forces is not easy.

Attraction. If the flat end of a magnet makes good contact with a material of high permeability or with the flat end of a magnet of opposite polarity, the force of attraction between the two is

where in SI units the force F is in newtons, A is the area of contact in m2, B is the flux density in tesla, and C4 ¼ 1. In cgs units, F is in dynes, A in cm2, B in gauss, and C4 ¼ 4p. This equation can be derived by summing the Coulomb forces between all the poles

502 HARD MAGNETIC MATERIALS

Fig. 14.20 Permanent magnet chuck.

assumed to lie on the two surfaces. But it can be understood more simply in another way. Suppose the two pieces are pulled apart to a small distance d, creating a very thin gap. If there is no fringing, the field in this gap is B, and the energy density of the field is B2/8p (cgs units), from Equation 7.43. The work done is Fd and the field energy is (B2/8p)(Ad). If the two are equated, Equation 14.11 follows. This equation holds only when the two pieces are very close together; the attractive force falls off very rapidly as the two are separated.

Attractive forces are exploited in permanent-magnet chucks, which are gripping devices that can be used, for example, to hold steel objects in place for a machining or grinding operation. Naturally, there must be some means of turning off the holding force, and many ingenious ways of doing so have been contrived. The simplest is shown in Fig. 14.20. When the magnet is rotated into the vertical position, the flux is short-circuited by the pole pieces, which have a lower reluctance than the path through the load. Another holding application is the magnetic latch, widely used on kitchen cupboard doors. These are made in large volume at low cost, using ferrite magnets.

Magnets are used as separators. The most common application is the removal of scrap iron and steel from liquids and powdered or granular materials, such as grain or sugar. Loose nuts, bolts, nails, and wire are ubiquitous in any environment inhabited by modern man. Other uses are in the separation of ferromagnetic items from trash, and the separation of mineral ores on the basis of their magnetic permeabilities. A related use is the protection of cattle from ingested iron. Cattle can pick up along with their food bits of baling wire, nails, and other pieces of iron. This sharp-edged material lodges in the cow’s second stomach, which it can irritate or puncture, leading to infection and other complications, a malady known as “hardware disease.” The remedy is a cylindrical magnet of alnico or ferrite, 2–3 inches (5–7.5 cm) long and 12 inch (1.25 cm) in diameter, with rounded ends, and protected with a thin plastic coating. It is simply dropped down the cow’s throat; it lodges in the second stomach and remains there for the life of the cow, attracting and holding any iron that enters.

Magnets can be used as large-scale positioners to transmit linear or rotary motion across a solid barrier. This is useful for positioning equipment inside a sealed space, such as a vacuum or controlled atmosphere chamber. Many designs have been proposed and constructed.

Fig. 14.21 Floating globe using magnetic suspension with feedback.

14.14.6Magnetic Levitation

For centuries there had been dreams of magnetic levitation, i.e., the stable suspension in the air of a body made of iron or other magnetic material, without physical contact, by an artful arrangement of magnets exerting the proper attraction and repulsion. But such hopes were dashed in 1839 when S. Earnshaw [Trans. Cambridge Phil. Soc., 7 (1837–1842) p. 97] proved that it could not be done. His theorem relates to both electrostatic and magnetostatic forces, or to any system of particles which exert forces on one another varying inversely as the square of the distance. For magnetic systems, Earnshaw’s theorem may be stated as follows: Stable levitation of one body by one or more other bodies is impossible, if all bodies in the system have a permeability greater than 1.

Stable levitation can be achieved for a positive permeability material if a position detector and feedback system are employed so that the force acting on the floating object is continuously adjusted, usually by varying the current through an electromagnet. This is the basis for various floating novelty items (see Fig. 14.21) as well as for nearly zero-friction suspensions for various kinds of rotating instruments and machines.

If diamagnetic materials are included in the system, stable levitation becomes possible without power input. Levitation of this kind is easiest with a perfect diamagnet, namely, a superconductor (Chapter 16). Figure 14.22 shows a bar magnet floating over the slightly concave surface of superconducting lead at 4K. The magnet is in effect supported by its own field, which cannot penetrate into the lead.

The permeability of a superconductor is zero, and there are many diamagnetic materials with permeabilities slightly less than unity. But there are no diamagnetic materials with intermediate values of m, like 20.5. This means that only very light bodies, a few grams

504 HARD MAGNETIC MATERIALS

Fig. 14.22 Bar magnet suspended over a superconducting plate.

in weight, can be stably levitated at room temperature with the help of ordinary diamagnetic materials, like graphite or bismuth, because their flux-repelling powers are so feeble.

Quite large weights can be supported by the repulsion between permanent magnets, the lower one fixed to a base and the upper one to the underside of the load. Some lateral constraint is needed to make the load stable, but it need not be strong. The magnets must have high coercivity. Barium ferrite and rare-earth magnets are well suited to this application since they can be made in flat pieces of fairly large area, magnetized in the thickness direction. G. R. Polgreen has written a book mainly devoted to this subject [New Applications of Permanent Magnets, MacDonald (1966)].

PROBLEMS

14.1 Show that the slope of the load line of a permanent magnet circuit is given by

Bm ¼ 1 Nd (SI):

Hm Nd

14.2Given two iron rods, identical except that one is magnetized lengthwise and the other is demagnetized, how could you tell them apart without using any experimental apparatus?

14.3A cobalt steel magnet with (BH)max ¼ 1.0 MGOe is 12 cm3 in volume. If the steel is replaced by an alnico magnet with (BH)max ¼ 7.5 MGOe, what volume of alnico will be required to produce the same field in the same air gap? What volume of material is required if the alnico is replaced by FeNdB, with (BH)max ¼ 40 MGOe? (This is actually not a very useful comparison, because the very high coercive

fields of rare-earth magnets permit geometries not possible with steel or alnico.)

head generates a signal voltage in the head winding. This voltage contains the recorded information, and can be amplified to recreate the recorded sound or video. Note that since the read head coil voltage is proportional to the time derivative of the flux change in the head, the amplification must include an integration step.

15.3.1Materials Considerations

The write and read heads must be high-permeability, low-coercivity magnetic materials capable of operating at reasonably high frequencies. Originally, very thin permalloy laminations were used, and amorphous alloys have been tried. The usual choice for analog recording, however, is a magnetically soft ferrite.

The recording medium must have low enough coercivity to be written on, high enough coercivity to resist local demagnetizing fields and retain a recorded pattern indefinitely, and high enough magnetization to provide a readable signal to the read head. The usual choice for audio recording is g-Fe2O3 (maghemite) particles in a flexible matrix. The packing fraction of the particles in the coating is about 0.4. The crystal and spin structure of g-Fe2O3 have already been described (Section 6.6); it is a ferrimagnetic spinel with ss ¼ 76 emu/g or A m2/kg. (Ms ¼ 390 emu/cm3 or 3.9 104 A/m). The oxide is in the form of elongated single-domain particles, about 0.1 mm in diameter and with a length/ diameter ratio near 6. They owe their coercivity, 250–300 Oe, to shape anisotropy. Since this value is only about a tenth of that expected for coherent rotation (2p Ms ¼ 2450 Oe), the magnetization of these particles must reverse incoherently. The particles in the tape coating are aligned by a field during the coating process so that their long axes are aligned parallel with the length of the tape; this is done in order to make the remanence, after magnetization in that direction, as large as possible.

The elongated oxide particles are made from hydrated ferric oxide (a-FeO . OH) particles, which are already elongated, in the following steps: (1) dehydration to hematite (a-Fe2O3); (2) reduction by hydrogen at 4008C to magnetite (Fe3O4); and (3) careful oxidation at about 2508C to g-Fe2O3. The addition of cobalt, either in solid solution or as an adsorbed surface layer, has beneficial effects on the magnetic properties.

Chromium dioxide (CrO2) is commonly used for video recording tape, and also for higher grades of audio recording tape. This material is one of nature’s rarities, a ferromagnetic oxide (Section 4.5). It has ss equal to 90–100 emu/g or A m2/kg, depending on how it is made, and fine particles can be prepared with greater elongations and smoother surfaces than g-Fe2O3. Its coercivity is therefore higher, about 400 Oe.

Audio tape has been made using Fe or FeCo particles instead of oxide particles, and also using a continuous magnetic metal alloy layer, usually based on Co.

15.3.2ac Bias

To minimize distortion due to the nonlinear and irreversible nature of the hysteresis loop of the recording medium, a sinusoidal current at about 100 kHz is superimposed on the recording signal current, and the combined signal is fed to the recording head. Figure 15.2 illustrates this combined signal. The ac bias field is at a higher frequency than the highest frequency to be recorded, and of sufficient magnitude to drive the material of the tape near magnetic saturation. Under these conditions, a section of tape passing under the write head sees a strong ac field superimposed on an almost constant dc field, which is the signal to be recorded. The resulting remanent magnetization in the tape, after the