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

silicon is the goal. Very thin sheet can be frozen directly from the liquid by planar flow casting, the same method used to make amorphous alloys (see Section 13.5.2). Or silicon can be added to the surface of a conventional 3% silicon steel by electrolysis, direct vapor deposition, or chemical vapor deposition, and then diffused into the sheet in a hightemperature anneal. The diffusion step is naturally easier and faster in very thin sheet material. None of these possible methods has led to commercial production of this material.

13.4.5General

We consider here several points of general importance in the application of electrical sheet steel.

Lamination Insulation The sheets that make up a core must be electrically insulated from one another to prevent large-scale eddy-current circulation in the core. The sheets may be coated with an organic varnish, but this will not withstand stress-relief annealing. More usually the insulation is simply a film of tightly adherent iron oxide, formed by means of a slightly oxidizing annealing atmosphere. Grain-oriented steel is often coated with MgO powder before the high-temperature anneal. This combines with SiO2 from the silicon in the steel to form a glassy magnesium silicate. This not only acts as an insulator but, having a smaller coefficient of thermal contraction, tends to put the steel in tension when the coated steel has cooled to room temperature. As a result, core losses decrease. The residual tensile stress is predominantly longitudinal, tending to form 1808 domain walls parallel to the rolling direction.

Cooling Both the core and copper losses show up as heat in the device. Core loss alone can lead to a temperature rise of the order of 0.2–1.58C/min, if all the generated heat remains in the core (Problem 13.4). Transformers are more difficult to cool than motors or generators. The spinning rotor of a motor or generator acts to circulate cooling air, and fan blades can be placed on the shaft to increase the air flow. Small transformers, such as are used in consumer electronics, need no forced cooling. Larger transformers, rated at 1 kW or above, are usually mounted in a tank filled with oil so that convection currents bring heat out to the tank surface. The tank may be fitted with cooling fins or tubes,

462 SOFT MAGNETIC MATERIALS

and sometimes with auxiliary fans to provide additional air flow. In some transformers, core losses are required to be low, not to increase electrical efficiency but simply to minimize heat generation. This is accomplished by using a lower-loss grade of electrical steel, or reducing the flux density, or using heavier copper windings, or some combination of these.

Noise Transformer “hum” is due to magnetostrictive vibration of the core and to the motion of the laminations as the material is alternately magnetized and demagnetized. This noise, whose basic frequency is twice the line frequency, becomes objectionable when large transformers are near residential areas, and transformer manufacturers have made considerable efforts to reduce noise. The magnetostriction of grain-oriented sheet in the rolling direction is remarkably low, sometimes positive and sometimes negative, as shown in Fig. 13.17. Since l100 is about 23 1026 for 3.2% Si–Fe, the low values indicated in Fig. 13.17 mean that magnetization occurs mainly by the motion of 1808 domain walls. This is expected from the observed domain structure in grain-oriented material. The tensile stress provided by the glassy surface coating also favors 1808 domain walls aligned in the direction of magnetization.

Stacking Factor The need to use soft magnetic material in the form of stacks of relatively thin sheets, each with an electrically insulating surface layer, means that in a magnetic device a fraction of the volume is not magnetic material, but is empty space and electrical insulation. This decrease in the effective density of magnetic material is expressed by the stacking factor (ASTM uses the term lamination factor), a number less than unity which is the fraction of the stack area that is composed of magnetic material. The stacking factor decreases for very thin sheets, for sheets of nonuniform thickness, and for heavy insulating coatings.

Fig. 13.17 Limits of static longitudinal magnetostriction as a function of induction for several grades and thicknesses of grain-oriented silicon steel sheet. Data from U.S. Steel.

Loss Reduction Improvements in the magnetic properties of grain-oriented steel have come about largely though increases in the degree of texture formation by increased purity and careful control of critical alloying additions. Improved texture is usually accompanied by larger grains, and very large grains are a cause of increased losses, because of the large domain size. Then some form of surface treatment, such as laser scribing, may be used to increase the number of domain walls. Losses have also been reduced by decreasing the thickness of the laminations. At one time, 0.014 inch or 0.36 mm was a standard thickness; now (in 2007) 0.007 inch or 0.175 mm sheet is produced and used.

13.5SPECIAL ALLOYS

These are mainly nickel–iron alloys containing either about 50 or 80% Ni, known generically as permalloys. This is a former trade name, but is now used for any Ni–Fe alloy. If a number precedes the name (79 permalloy), it denotes the Ni content. The permalloys have high permeability in low fields and low losses, and can be rolled to very small thicknesses. They are the materials of choice when excellent magnetic properties are required, and cost is not the primary consideration. The alloys were developed as commercial materials for use in the telephone system, mainly in the period 1913–1921, and are described fully in Bozorth’s book Ferromagnetism. There has been relatively little change or improvement in these materials for the last 50 years, although better manufacturing methods have increased purity and permeability to some degree. Permalloys are made and sold under a variety of trade names.

The equilibrium diagram of the iron–nickel system has been given in Fig. 10.1 and discussed in Section 10.2. In the range of 50–80% Ni the alloys are all face-centered cubic. At and near the composition FeNi3 the alloys can undergo long-range ordering below a temperature of 5038C. The ordered unit cell is shown in Fig. 10.6. The magnetic properties of the ordered alloys are inferior to those of the disordered. The disorder-to-order transformation is fortunately sluggish and can be avoided simply by fairly rapid cooling through the 500–4008C range; water quenching is unnecessary.

The variation of saturation magnetization and Curie temperature with composition is shown in Fig. 13.18. Alloys near 30% Ni contain two phases, bcc a and fcc g. The phase mixture, and the resulting magnetic and other properties, depend very strongly on the composition, impurity level, and thermal history of the sample.

Figure 13.18 also shows the variation of the magnetocrystalline anisotropy, and K1 is seen to pass through zero at about 75% Ni. The magnetostriction constants are given in Fig. 13.19. The value of l100 is zero at two compositions, near 46 and 83% Ni, while l111 is zero at about 80%. (The solid lines denote alloys given a normal furnace cool and correspond to “the more-nearly disordered state.” The dashed line denotes alloys cooled at 1.28C/h, corresponding to “the more-nearly ordered state.” The course of these two branches of the l111 curve suggest that both cooling rates have produced nearly the same state, the disordered state, because the results are in good agreement with those of Bozorth for quenched alloys.) Note also that the magnetostriction becomes isotropic (l100 ¼ l111) near 60 and 86% Ni.

We expect high permeability when K and l are small. A low value of K decreases domain-wall energy and increases domain wall thickness, so that inclusions become less effective hindrances to wall motion. A low value of l means that microstress becomes similarly less effective. Figure 13.19 shows that both K1 and l111 are near zero just

464 SOFT MAGNETIC MATERIALS

Fig. 13.18 Iron–nickel alloys. Variation with nickel content of saturation magnetization Ms, Curie temperature Tc, and magnetocrystalline anisotropy K1 (quenched alloys). [R. M. Bozorth, Ferromagnetism, reprinted by IEEE Press (1993).]

below 80% Ni, and l100 is not very large. This is the composition of 78 permalloy, and Fig. 13.20 shows the remarkable effect of heat treatment on the maximum permeability of this alloy.

The maxima in m near 50 and 80% Ni are due to near-zero values of K1 and/or l. Note that it is the value of l in the easy direction of magnetization that determines the effect of microstress on wall motion; near 50% Ni, the value of K1 is positive, k100l are easy directions, and l100 is zero; at 80% Ni the value of K1 is negative, k111l are easy directions, and l111 is zero.

Fig. 13.19 Iron–nickel alloys. Variation of saturation magnetostriction with nickel content. See text for details. The dotted line shows K1 from Fig. 13.18. [Data from R. C. Hall, J. Appl. Phys., 30 (1959) p. 816.]

Fig. 13.20 Maximum permeabilities of iron–nickel alloys.

The great sensitivity of 78 permalloy to heat treatment is due to the variation of K1, which has a value of about 22000 ergs/cm3 after quenching and 218,000 ergs/cm3 after slow cooling; the values of l100 and l111 change hardly at all with heat treatment. Slow cooling or annealing below 5008C produce partial long-range order, which has a larger effect on K1 than on l. Ordering is usually detected by X-ray diffraction, but this technique has limited utility in the case of Fe–Ni alloys because Fe and Ni are near neighbors in the periodic table and have almost the same scattering power for X-rays. Neutron diffraction, however, does not suffer from this limitation.

The soft magnetic properties of all the permalloys can be improved, in some cases dramatically, by a long high-temperature (10008C) treatment in hydrogen to remove impurities such as C and S. This is a costly process, rarely used for commercial material. The electrical resistivity is increased, and heat treatment made less critical, by small additions of nonmagnetic elements, usually Mo, Cu, and/or Cr.

The 50 permalloy alloys have higher saturation magnetization, but the 78 permalloys have higher permeability and lower coercive field. Similar but not identical materials of both families are made under various trade names. As fiber optics have replaced copper in long-distance telephony, the production of permalloy, as well as the number of manufacturers, has decreased. However, a large number of uses remain, including ground fault interrupters (which protect people from electrical shock) and magnetic shielding.

The cube texture is fairly easy to produce in 50 permalloys by primary recrystallization after heavy cold rolling. The result is a square hysteresis loop, and such materials are produced under a variety of trade names.

A constant value of permeability over some range of applied field is a requirement for some specialized applications. An alloy called Isoperm was developed in Germany by

466 SOFT MAGNETIC MATERIALS

making a cube-textured 50 Fe–50 Ni alloy and then cold rolling it to a 50% reduction in thickness. The resulting material has an easy axis in the transverse direction, as described in Section 10.5. Along the hard-axis rolling direction the permeability is low (100 or less) and constant. A range of Ni–Fe–Co ternary alloys, of which the original was 25 Co, 45 Ni, 30 Fe, develop relatively strong anisotropy when annealed in a magnetic field. When these alloys are annealed in the demagnetized state, the domain walls are strongly pinned, as described in 10.2. Over the range of H and M where the wall motion is reversible, the permeability is almost constant and reasonably high, approaching a value of 1000. These alloys are called Perminvars, for invariant permeability.

13.5.1Iron–Cobalt Alloys

Cobalt is the only alloying element that substantially increases the Curie temperature and the saturation magnetization of iron. The alloys from about 30 to 50% Co all have roomtemperature saturation magnetization about 10% higher than iron, and Curie temperatures limited by a bcc to fcc phase transformation just under 10008C. The 50–50 alloy, sold under various names, has low anisotropy and relatively high permeability, but quickly develops long-range order which makes it brittle. The addition of 2% V slows the ordering and allows the resulting alloy to be rolled into sheet form after rapid cooling from above the ordering temperature. Lower cobalt content alloys have less desirable soft magnetic properties, but cost less. The Fe–Co alloys are used where the highest saturation magnetization and/or a high Curie point is important: in the pole pieces of electromagnets, in beam-focusing lenses for electron microscopes, and in aircraft motors, generators, and transformers operating usually at 400 Hz.

13.5.2Amorphous and Nanocrystalline Alloys

In the 1960s, it was discovered that certain families of alloys, when cooled from the liquid state at very high cooling rates, solidified as noncrystalline materials. These became known as amorphous alloys or metallic glasses. The usual production method is called melt spinning: a jet of liquid metal alloy is forced through a small nozzle by gas pressure onto a rapidly rotating metal wheel, where it flattens to a thin strip, loses heat to the wheel, solidifies, and is thrown from the wheel by centrifugal force. The cooling rate is estimated to be in the range 105 –106 K/sec. The product resulting from this simple apparatus is a ribbon a few millimeters wide, 25–35 mm thick, and meters to kilometers in length. If the process is carried out in air, the wheel side of the ribbon typically contains elongated depressions attributed to air bubbles trapped between the melt and the wheel; these can be largely eliminated by casting in vacuum. With special nozzles and casting techniques, known as planar flow casting, strip widths of several inches can be attained.

The alloys of magnetic importance contain about 80 atom% Fe þ Ni þ Co and 20 atom% metalloid or glass-forming elements, mostly B and Si. The compositions generally correspond to a low melting point eutectic when the alloy is cooled at normal rates. Maximum saturation magnetization is in the range 15–19 kG (1.5–1.9 T), magnetic anisotropy is very low, and magnetostriction is 20–30 1026 except in alloys containing mostly Co, where it is low or slightly negative. Electrical resistivity is very high for metallic materials, generally over 100 mV-cm. In the as-cast state the alloys are very strong and hard, but also ductile.

The soft magnetic properties are substantially improved by a low-temperature anneal (300–4008C), and if the anneal is carried out in a magnetic field a significant anisotropy can be induced. In this condition the alloys have outstanding low-frequency soft magnetic properties, equal to or better than the best permalloys. However, the annealing treatment makes the material brittle, and needs to be the final step in processing. The losses under ac excitation are also higher than expected from the dc properties, because of the large domain size resulting from the absence of grain boundaries. Various methods have been used to refine the domain size, such as deliberately including small nonmagnetic particles as domain nuclei, and annealing to produce an array of small crystallites for the same purpose.

A related class of nanocrystalline magnetic materials is made by adding small amounts of Cu and Nb to an Fe–Si–B amorphous alloy. The most-studied composition is Fe74Si15B7Cu1Nb3. The Cu is believed to enhance nucleation of crystallites and the Nb to inhibit their growth. The amorphous alloy is annealed at about 5508C for 60 min, which results in an array of magnetic Fe3Si nanoparticles, 10–15 nm in diameter, in a magnetic amorphous matrix. The soft magnetic properties are outstanding, but the material is extremely brittle.

The largest use of amorphous alloys is in low-loss transformers up to several kilowatts in power capacity. Their use is economically justified in locations where fuel costs are high. Amorphous alloys are also used in antitheft systems, which are discussed later.

More recently, a range of alloy compositions has been found that can be made amorphous in bulk, by freezing the liquid in a mold of high thermal conductivity. Some of these alloys can be made amorphous in thicknesses up to several centimeters. Only a few of these alloy families are strongly magnetic, and their usefulness as industrial magnetic materials remains to be seen.

13.5.3Temperature Compensation Alloys

Materials with Curie temperature just above room temperature have a strong temperature dependence of saturation magnetization. This behavior can be used to correct for the temperature dependence of permanent magnet materials. The technique is to use a strip of the compensation alloy to divert or “shunt” part of the flux away from the working region of the magnet. As the temperature increases, the shunt becomes less effective, so more flux passes through the working space; this offsets the decrease in flux due to the temperature increase in the permanent magnet material. Nickel–iron alloys near 30% Ni can be used as compensator alloys, as can certain Ni–Cu alloys. The geometry of permanent magnet designs using high-coercivity ferrites and rare-earth magnets makes the use of magnetic shunts more difficult than in designs using Alnico magnets.

13.5.4Uses of Soft Magnetic Materials

The magnetically soft special alloys are used mainly in the form of cores, of varying shape and with external diameters from several inches to less than 0.25 inch (10–0.5 cm). They can be of three forms (Fig. 13.21). In stacked laminations the flux travels in all possible directions in relation to the original rolling direction of the sheet from which the laminations were cut; only the average magnetic properties in the plane of the sheet are of interest. In contrast, the flux in a tape-wound core travels only in the rolling direction of the strip (tape). To minimize core losses, the tape should be thinner the higher the frequency;

470 SOFT MAGNETIC MATERIALS

Fig. 13.24 Simple form of fluxgate magnetometer. (a) High-permeability strip or wire with drive coil and sense coil; (b) idealized hysteresis loops in zero applied field (left) and positive applied field (right); (c) upper curve is triangular current vs time in drive coil, lower curve is resulting dB/dt signal in sense coil, both on the same time axis. Solid lines correspond to zero applied field, dashed lines to small positive applied field.

exactly from its length, current, and number of turns, and is equal and opposite to the unknown applied field. The fluxgate magnetometer measures just the component of the magnetic field parallel to the axis of the device, which is sometimes an advantage, sometimes not. Various elaborations of the fluxgate magnetometer design have been proposed and built, some of which use alternate detection systems. All are limited to the measurement of low fields, typically 1 or 2 Oe (80 or 160 A/m) maximum, by heating in the drive coil or the canceling coil.