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

Antitheft Systems One class of antitheft, or antishoplifting, system uses a short length of high-permeability ribbon or wire as the tag or target which is attached to the article to be protected. When the article, and the tag, are carried through a detection gate they are subjected to an ac field in the kilohertz frequency range, which magnetizes the tag. The ac field of the tag (or sometimes the acoustic signal due to its magnetostriction) is detected and used to activate an alarm. If the article has been paid for, the tag is deactivated, usually by causing it to be permanently magnetized by an adjacent strip of permanent magnet material. Permalloys and amorphous alloys are both used to make the tags, which must be very low in cost.

13.6SOFT FERRITES

The magnetically soft ferrites first came into commercial production in 1948. Their many applications will be briefly examined here, as well as the methods of making ferrites and the effects of such variables as porosity and grain size on their magnetic properties.

The soft ferrites have a cubic crystal structure and the general formula MO . Fe2O3, where M is a divalent metal such as Mg, Mn, or Ni. Nonmagnetic Zn ferrite is often added to increase Ms (Section 6.3) and all the commercial ferrites are mixed ferrites (solid solutions of one ferrite in another). The intrinsic properties of the pure ferrites have been given in Table 6.4. Their densities are a little over 5 g/cm3, Curie points range from about 300 to 6008C, and Ms from about 100 to 500 emu/cm3 (100–500 kA/ m). Almost all of them have k111l easy directions of magnetization, low magnetocrystalline anisotropy, and low to moderate magnetostriction.

The ferrites are distinctly inferior to magnetic metals and alloys for applications involving static or moderate-frequency (power-frequency) fields, because they have Ms values less than a third of iron and its alloys and far lower de permeabilities. But the outstanding fact about the ferrites is that they combine extremely high electrical resistivity with reasonably good magnetic properties. This means that they can operate with virtually no eddy-current loss at high frequencies, where metal cores, even those made of extremely thin tape or fine particles, would be useless. This fact accounts for virtually all the applications of soft ferrites.

Ferrites are made in the following way:

1.Starting Material. Ferric oxide Fe2O3 and whatever oxides MO are required, in powder form. Metal carbonates may also be used; during the later firing, CO2 will be given off and they will be converted to oxides.

2.Grinding. Prolonged wet grinding of the powder mixture in steel ball mills produces good mixing and a smaller particle size, which in turn decreases the porosity of the final product. After grinding, the water is removed in a filter press, and the ferrite is loosely pressed into blocks and dried.

3.Presintering. This is done in air, and the temperature goes up to about 10008C and

down to 2008C in about 20 h. In this step at least partial formation of the ferrite takes place: MO þ Fe2O3 ! MO . Fe2O3. This step produces a more uniform final product and reduces the shrinkage that occurs during final sintering.

4.Grinding. The material is ground again to promote mixing of any unreacted oxides and to reduce the particle size.

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5.Pressing or Extrusion. The dry powder is mixed with an organic binder and formed into its final shape. Most shapes, such as toroidal cores, are pressed (at 1–10 ton/in2, 14–140 MPa), but rods and tubes are extruded.

6.Sintering. This is the final and critical step. The heating and cooling cycle typically extends over 8 h or more, during which the temperature reaches 1200–14008C. Any unreacted oxides form ferrite, interdiffusion occurs between adjacent particles so that they stick (sinter) together, and porosity is reduced by the diffusion of vacancies to the surface of the part. Strict control of the furnace temperature and atmosphere is very important, because these variables have marked effects on the magnetic properties of the product. Ideally, the partial pressure of oxygen in the furnace atmosphere should equal the equilibrium oxygen pressure of the ferrite, which changes with temperature.

Iron and some other ions can exist in more than one valency state; too little oxygen, then, will change Fe3þ to Fe2þ and too much will change Mn2þ, for example, to Mn3þ.

The final product is a hard and brittle ceramic, so hard that smooth flat surfaces can only be produced by grinding. During sintering, all linear dimensions of a part shrink from 10 to 25%, and allowance for this must be made in designing the pressing mold or extrusion die.

The grain size of commercial ferrites ranges from about 5 to 40 mm, and as is true of most sintered products, metallic or nonmetallic, they are not completely dense. The percentage porosity is defined as 100(rx 2 ra)/rx, where ra is the apparent density and rx the true density in the absence of porosity. The true density is the mass of all the atoms in the unit cell divided by the volume of the unit cell. The cell volume is in turn found from the cell dimensions measured by X-ray diffraction. The density determined in this way is sometimes called the “X-ray density.” The porosity in ferrites can range from about 1 to 50%; a more typical range is 5–25%. Figure 13.25 shows how an increase in sintering temperature increases the grain size and decreases the porosity; the black areas are voids. Permeability increases as the grains become larger and as the porosity decreases. The grain-size effect is the stronger of the two. Porosity at the grain boundaries is less damaging to the permeability than porosity within the grains, because boundary porosity causes less hindrance to domain wall motion. Both kinds of porosity can be seen in Fig. 13.25.

It is not easy to perform clear-cut experiments on ferrites to isolate the effect of a single variable. A mixed ferrite like (Mn, Zn)O . Fe2O3 is a complex system; it contains, or can contain, six kinds of ions: Mn2þ, Mn3þ, Zn2þ, Fe2þ, Fe3þ, and O22. The oxygen content of the sintering atmosphere can not only change the valence of some of these ions but also alter the stoichiometry, by creating oxygen or metal-ion vacancies in the lattice. And variations in sintering temperature or time normally cause simultaneous changes in both grain size and porosity.

Commercial ferrites are sold under various trade names. Manufacturers rarely give the chemical composition of their products, preferring instead to specify the magnetic properties; these are adjustable over a rather wide range by varying the composition and the sintering conditions. Two broad classes of ferrites are produced:

1.Mn–Zn Ferrites. These have initial permeabilities of the order of 1000–2000, coercivities of less than 1 Oe, and are usable without serious losses up to frequencies of about 1 MHz. Resistivity is about 20–100 ohm-cm.

2.Ni–Zn Ferrites. These are intended for very high frequency operation, to more than 100 MHz. Initial permeabilities are about 10–1000, and coercivities are several

Fig. 13.25 Microstructure of a Mn–Zn ferrite. (a) After sintering 5 min at 13758C (10% porosity).

(b) After sintering 1 min at 14358C (5% porosity). [Figures 13.25, 13.26, and 13.27 are from J. Smit and H. P. J. Wijn, Ferrites, Wiley (1959).]

oersteds. At the highest frequencies, losses are found to be lower if domain wall motion is inhibited and the magnetization forced to change by rotation. For this reason some grades of Ni–Zn ferrites are deliberately underfired. The resulting porosity interferes with wall motion and decreases both losses and permeability. The Ni–Zn ferrites have very high resistivity, about 105 ohm-cm.

Both of these main classes of materials contain zinc ferrite. As we saw in Fig. 6.4, the addition of zinc ferrite increases the value of Ms at 0K. It also weakens the exchange interaction between ions on A and B sites, with the result that the Curie point decreases. The

474 SOFT MAGNETIC MATERIALS

Fig. 13.26 Variation with temperature of the saturation magnetization ss of Mn–Zn ferrites.

curves of Ms (or ss) vs temperature must therefore cross over, as shown in Fig. 13.26 for a series of Mn–Zn ferrites. In any magnetic material it is usual for the initial permeability m0 to increase with temperature to a maximum just below the Curie point, because the magnetocrystaline anisotropy and magnetostriction normally decrease with rising temperature. This effect is shown for the Mn–Zn ferrites in Fig. 13.27. Not only do zinc additions shift Tc and the accompanying peak in mi to lower temperatures, but they increase the height of the peak; as a result the room-temperature value of mi also increases with the zinc content. Ni–Zn ferrites behave in the same way.

Figure 13.28 shows how the initial permeability mi varies with frequency in the megahertz range for three different ferrites. The first is a Mn–Zn ferrite of unspecified

Fig. 13.27 Variation with temperature of the initial permeability mi of Mn–Zn ferrites. These specimens also contain a small ferrous (Fe2þ) ion content.

Fig. 13.28 Variation of initial permeability mi with frequency for three ferrites.

composition, the second a 50–50 mixture of Ni and Zn ferrites, and the third is pure Ni ferrite. The shape of these curves is typical. As the frequency increases, mi remains equal to its static (dc) value until a critical frequency is reached and then decreases rapidly, as may be seen more clearly if the data are plotted on linear rather than logarithmic scales. The larger the static value of mi, the lower is the frequency at which this decrease occurs. Therefore, if a particular ferrite core must have constant inductance, which requires constant permeability, at all frequencies up to several hundred megahertz, there is no option but to choose a material with low permeability.

The decrease in mi at a particular frequency is due to the onset of ferrimagnetic resonance. As mentioned in Section 12.7, electron spin resonance can occur in ferrimagnetics and is normally studied by applying a strong field to wipe out the domain structure and align the magnetization throughout the specimen with the easy axis. The spins then precess about this axis. But in a multidomain ferrite with no applied field, the spins are still precessing about the easy axis, which is the Ms direction, in each domain. The frequency of this precession depends on how strongly the magnetization is bound to the easy axis; the stronger the coupling, the higher is the natural frequency of precession. The strength of this coupling is described by the value of the magnetocrystalline anisotropy K or by the anisotropy field HK, which is proportional to K.

Suppose that the natural frequency of this spin precession is 1 MHz for a particular ferrite. Suppose also that the material is now exposed to a weak alternating field H of frequency, say, 60 Hz. Then the induction B developed in each cycle is governed by H and the initial permeability mi. (High-frequency ferrites are usually operated at low fields, which is why we are mainly interested in the initial permeability.) Let the drive frequency now be increased to, say, 1 kHz. The value of mi will remain the same, because of the great disparity between the drive frequency and the precession frequency. But when the drive frequency reaches 1 MHz, the two frequencies are matched and the precessing spins absorb power from the drive field. As a result the induction B produced in each cycle decreases, which means that mi decreases. Now the static value of mi is generally higher,

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the lower the value of K, or HK. A low value of HK means a low precession frequency. We therefore expect that mi will begin to decrease at a lower frequency if mi is large than if mi is small, in agreement with experiment (Fig. 13.28). This argument implies that spin resonance is the only loss mechanism in ferrites. This is not quite true, but the theory outlined does explain the general features of ferrite behavior.

When losses occur, B lags behind H in time, and the permeability becomes a complex number that can be written m ¼ m0 2 im00, where m0 is the real part (B in phase with H ) and m00 the imaginary part (B 908 out of phase). It is the real part m0 which is plotted in Fig. 13.28. The imaginary part m00 is very small until m0 begins to decrease. Then m00 and the losses increase.

The high-frequency applications of soft ferrites are mainly as cores for special transformers or inductors. Certain communication equipment requires broadband transformers; as the name implies, they must have cores that show the same behavior over a broad range of frequencies. Another application is in pulse transformers. Because the Fourier components of a square pulse extend over a wide range of frequencies; excessive distortion of the pulse shape occurs if the permeability of the core varies with frequency.

Built-in ferrite antennas are much used in modern radio receivers. Such an antenna is merely a ferrite rod wound with a coil. It responds to the magnetic component of the incident electromagnetic wave, and the alternating flux in the ferrite induces an emf in the coil; the ferrite core in effect multiplies the area enclosed by the coil by a factor equal to the permeability.

Finally, there are important microwave applications of ferrites, both in communications and in radar circuits. These involve frequencies of some 1010 Hz and fundamental effects not considered in this book.

PROBLEMS

13.1Verify the point at the center of the third curve from the left of Fig. 13.2 by showing that Bx=B0 ¼ 0:46 at the center of the sheet.

13.2Calculate the field penetration ratio Hx=H0 at the center of a nickel rod of 1.28 cm diameter for frequencies of 20, 50 and 60 Hz. Take mr ¼ 100 and r ¼ 0.95 1023 ohm m.

13.3Suppose a solid transformer core is divided into n laminations of equal thickness.

Show that the laminated core has a classical eddy-current loss, which is approached if the domain size is small, equal to 1/n2 times the loss of the solid core. This would

suggest the laminations should be made as thin as possible. Why are very thin laminations, say 1000 nm, not used in practice?

13.4If the core loss of plain carbon steel sheet is 11.1 W/kg at 15 kG and 60 Hz, what is the temperature rise in 8C/min if no heat is lost from the material? The specific heat is 0.113 cal/g 8C.

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14.2OPERATION OF PERMANENT MAGNETS

Before considering the materials of which magnets are made, we must examine the conditions under which a magnet operates, in order to determine what material properties are important. Because the only function of a magnet is to provide an external field, it must have free poles. A circumferentially magnetized ring, forming a closed magnetic circuit, produces no external field and so has no practical use. A permanent magnet always operates on open circuit. The resulting free poles create a demagnetizing field Hd which makes the induction lower than the remanence value Br found in a closed ring, a point that was illustrated in Fig. 2.33.

After a magnet is manufactured, a strong field H1 is applied to it and removed, causing the induction B to follow the path shown in Fig. 14.1. The operating point P of the magnet is determined by the intersection of the line OC with the second quadrant of the hysteresis loop. This quadrant is called the demagnetization curve of the material. The values of Hc and Br and the shape of this curve determine the usefulness of a material as a permanent magnet.

The line OC is called the load line. From Fig. 2.33, its slope is given by

where Nd is the demagnetizing factor of the magnet. Because Nd depends on the geometry of the magnet, it can be altered by the magnet designer, who has the freedom to choose the slope of OC and therefore put the operating point P almost anywhere on the demagnetization curve. The question then arises: What is the best operating point P?

Consider the specific case of the gapped ring of Fig. 14.2, which is similar to some actual magnetic circuits. This could be the magnet for a moving-coil meter, with the moving coil located in the air gap. The magnet must provide a field Hg of constant strength in the air gap. The induction in the magnet is Bd, which we will now call Bm, and the field is Hd, which we will now call Hm. According to Ampere’s law, Equation 2.55, the line integral of H around

Fig. 14.1 Initial magnetization and demagnetization curve of a permanent magnet. Br is the residual induction; point P is the operating point.

where lm is the length of the magnet and lg is the length of the gap. (Note that concept of magnetomotive force, as defined in Section 2.6, here loses most of its meaning, of a force that “drives” magnetic flux in a circuit. In the circuit of Fig. 14.2 the flux f is everywhere clockwise and positive, but the net magnetomotive force is zero.) The continuity of the lines of B furnishes us with a second equation:

f ¼ BgAg ¼ HgAg ¼ BmAm (cgs)

f ¼ BgAg ¼ m0HgAg ¼ BmAm (SI)

(14:3)

because B ¼ H (cgs) or m0H (SI) in the air gap. Here Ag and Am are the cross-sectional areas of the air gap and the magnet. In Fig. 14.2 these are equal, because fringing (widening) of the flux in the gap is ignored. Generally, however, Ag and Am are unequal, because of fringing flux. The problem of the magnet designer is to choose lm and Am so as to best use the material.

If Equations 14.2 and 14.3 are each solved for Hg and multiplied together, we find

where V stands for volume. This result shows that the volume Vm ¼ Amlm of magnet that is required to produce a given field in a given gap is a minimum when the product BH in the