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

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For this reason, the maximum energy product is considered to be the best single index of quality of a permanent magnet material, and it is always included in any list of permanent magnet properties.

When dealing with magnetic materials of high coercivity, the difference between a plot of B vs H and M vs H becomes important. Remembering that B is defined as 4pM þ H (cgs) or m0M þ m0H (SI), we can see that when the H term is small relative to M, as is the case for soft magnetic materials, the shape of a plot of B vs H is almost the same as that of a plot of M vs H. For example, the maximum field applied to measure a ring sample of Ni–Fe alloy might be 100 Oe (0.01 T), and the saturation flux density would be near 10,000 G (1 T). In this case the field H contributes no more than 1% of the flux density B.

Even in a material like alnico, with relatively low coercive field, a plot of B vs H is significantly different from a plot of M vs H. [Units cause difficulty here. In cgs units, the usual procedure is to plot B in gauss or kilogauss, and M as 4pM, which has the same units as B. The field H is plotted in oersted, which is numerically equal to gauss in air. Thus B, M, and H are all plotted in the same units. In SI, B and m0M are both plotted in tesla, and H is plotted as m0H, also in tesla. Field units of A/m are usually not used in the permanent magnet literature.] Figure 14.6 shows graphs of the demagnetizing curves of an alnico and a hard ferrite, showing both the B vs H and 4pM vs H plots; the differences are obvious, especially in the case of the hard ferrite. In particular, the coercive field required to reduce B to zero, generally labeled Hc, is significantly lower than the coercive field required to reduce M to zero. This latter quantity is called the intrinsic coercive field, and is usually written as Hci, although a variety of other notations have been used. Note that the plots coincide at Br, where H is zero. Figure 14.6 also shows the relative advantages and disadvantages of the two materials: alnico has high magnetizaton but low coercive field, hard ferrite has low magnetization and high coercive field.

Many of the newer permanent magnetic materials display a behavior previously unknown: The remanent magnetization remains almost unchanged in magnitude as

Fig. 14.6 Demagnetizing curves of alnico and hard ferrite. Solid lines are B vs H; dotted lines are 4pM vs H. Note the difference between Hc and Hci in the case of hard ferrite.

Fig. 14.7 Demagnetizing behavior of a high Hci permanent magnet. The magnetization is unchanged by negative fields less than Hc, so Hc ¼ Br (in cgs units).

increasing negative field H is applied, and remains unchanged up to a value substantially greater than Hc. Then, as seen in Fig. 14.7, the B vs H curve becomes a straight line passing through the points Br and Hc ¼ Br. The magnetization reverses fairly suddenly at a field Hci, which may be considerably larger than Hc. Under these conditions, the maximum energy product (BH)max is given by

It does not depend on Hci.

For most permanent magnet uses, there is no advantage in having Hci much larger than Hc, and there may be a disadvantage: a magnet with a high value of Hci may be difficult to magnetize, although this is not a universal rule. For the first time in the history of magnetic materials, there may be a reason to deliberately lower Hci, or to trade a lower Hci for a higher Br.

Although (BH)max is an index of material quality, it is not the only index or even the most suitable one for all applications. Magnets may operate under either static or dynamic conditions. A magnet supplying a field for a moving-coil ammeter exemplifies a static application. But the field in the gap of a holding or lifting magnet changes during operation, and the magnet “works” in a quite different way.

In Fig. 14.8a the iron armature represents the piece being lifted. When this is far away, the magnet is open-circuited and at point P on the demagnetization curve. As the iron approaches, part of the flux is diverted from the leakage gap to the useful gap. When contact is made, the demagnetizing field is reduced and the operating point moves to D. If the armature is pulled away, the point returns to P. The minor hysteresis loop thus traced out is very thin, and is often approximated by a straight line through the tips of the loop; the slope of this line, which is approximately equal to the slope of the major hysteresis loop at the Br point, is called the recoil permeability mrec. Under these dynamic conditions the best location for P does not correspond to (BH)max but to a more complex condition that depends on the details of the geometry. Of course, in a material like that in Fig. 14.7, the minor hysteresis loop is just a line coinciding with the demagnetizing curve, and the recoil permeability is zero.

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Fig. 14.8 (a) Lifting magnet. (b) Path followed on B, H curve.

In some applications, especially permanent-magnet motors, parts of the magnet may be subject to quite large demagnetizing fields from currents in the windings or from magnetized soft magnetic materials, or both. If these fields are large enough, they may cause significant permanent demagnetization of the permanent magnet material, so that it may be necessary to change the design to locate the static operating point at a lower field than that of the maximum energy product.

14.3MAGNET STEELS

We turn now to the magnet materials themselves. The earliest of these was the lodestone, sometimes “armed” by attaching soft iron at each end to concentrate the flux. This is the origin of the term “armature” for a part of a magnetic circuit. Next came high-carbon steel magnets, hardened by quenching (rapid cooling from high temperature), which were used for centuries as compass needles.

In the later 1800s, alloy steels were developed for cutting tools and for structural purposes, and the magnetic properties of alloy steels became of interest. By 1885 a steel containing about 5% tungsten was in use for magnets. This was supplanted by the cheaper chromium steel during World War I. Neither type had coercivity as much as 100 Oe (8 kA/m). The next advance was made in 1917 by the Japanese investigators Honda and Takagi, who showed that a steel containing 30–40% cobalt, plus tungsten and chromium, had a coercivity of 230 Oe. This is still the best magnet steel; it has an energy product approaching 1 MGOe or 8 kJ/m3.

Steel magnets always contain carbon, and are used in the hardened state; that is, they are quenched to produce the metastable tetragonal martensitic structure. In steels, magnetic hardness (high coercivity) accompanies physical hardness, although this is emphatically not true of magnetic materials generally. The origin of the magnetic hardness of steels, such as it is, is something of a mystery. Isolated single crystals of martensite are unobtainable, so its magnetic anisotropy is unknown. A martensitic steel is in a complex state of internal stress, and metal carbide particles may also be present; presumably both of these make domain wall motion difficult.

Magnet steels are no longer made or used, since much better materials are available. The cheapest magnet steels have very poor permanent magnetic properties, and the best ones are relatively expensive because of their high cobalt content.

14.4ALNICO

Alnico is now a generic name for a family of alloys, known by several trade names, containing substantial amounts of all three of the ferromagnetic metals, Fe, Co, and Ni, plus smaller amounts of Al, Cu, and sometimes other elements. The name comes from the chemical symbols for aluminum, nickel, and cobalt, even though all alnicos have iron as a major constituent. They were at one time the most widely used permanentmagnet materials, but have now been largely replaced by permanent magnet ferrites and rare earth-transition metal alloys. Alnicos have relatively high Curie temperatures and therefore relatively small temperature dependence of magnetic properties near room temperature, which is a major advantage in some applications.

The development of alnico dates from 1931, when Mishima in Japan discovered that an alloy of 58% Fe, 30% Ni, and 12% Al had a coercivity of over 400 Oe, nearly double that of the best magnet steel. It was soon discovered that the addition of Co and Cu improved the properties of the Mishima alloy, and many related alloys have been tested and manufactured. Producers of alnico and other permanent magnet materials do not usually specify the compositions of their alloys, but only their magnetic properties.

The alnicos are not steels. They are essentially carbon-free, do not form or contain martensite, and the mechanism of their magnetic hardness is quite different from that of steel.

All the alnicos are hard and brittle, much too brittle to be cold worked. (Hot working is possible but is not done commercially.) All production is therefore by casting of the liquid alloy or by pressing and sintering metal powders. The cast alloys have very coarse grains, of the order of 1 mm diameter. The sintered alloys are finer grained and mechanically stronger, with better surface finish but with somewhat inferior magnetic properties. They are usually limited to small magnets with cylindrical symmetry, for which the pressing operation is well suited. Surface grinding is the only finishing operation possible on either type of alnico.

The permanent magnetic properties of as-cast or as-sintered alnico are poor. A special, three-stage heat treatment is necessary to produce optimum properties:

1.Heat to 12508C for a time sufficient to produce a homogeneous solid solution.

2.Cool at a rate of the order of 18C/sec to about 5008C or lower.

3.Reheat (temper) at 6008C for a few hours.

Most alnicos are cooled (step 2 above) in a magnetic field of 1 kOe or more, or held in a magnetic field for 10–20 min at a temperature in this range. The field treatment increases the remanence measured in the direction of the applied field, and may slightly increase the coercive field. The final reheat (step 3) is not done in an applied field.

The alnicos achieve their permanent magnet properties by the precipitation of a ferromagnetic phase in a weakly magnetic matrix. Both phases are body centered cubic, and the phase separation occurs by spinodal decomposition, which results in a very regular

˚

array of ferromagnetic rods about 300 A in diameter lying along <100> directions. Applying a strong magnetic field during the precipitation process causes the rods to form preferentially along the [100] direction most nearly parallel to the field, rather than equally along all three possible <100> directions. Figure 14.9 shows the remarkable degree of alignment and uniformity that can be attained in a single crystal.

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Fig. 14.9 Electron micrograph (oxide replica) from a single crystal of field-annealed alnico. The field during annealing was directed horizontally; 50,000 [K. J. De Vos, Magnetism and Metallurgy, Volume 2, Academic Press (1969)].

A further improvement in properties can be created by producing a crystallographic texture in which all the grains are aligned with a common <001> direction. This can be done by directional solidification (see Fig. 14.10), since under these conditions all the grains grow with a <100> direction parallel to the direction of heat flow. Magnets made in this way may be identified by the letters “DG” for directional grain added to the alloy type number.

The permanent magnet properties of alnico result from the shape anisotropy of singledomain particles. The final anneal (step 3) increases the difference in magnetization between the two phases, and so increases the magnitude of the anisotropy.

Fig. 14.10 Directional solidification of alnico to produce columnar grains oriented in the ,100. direction.

Research on alnico largely ended about 1970, when the remarkable properties of rare- earth-transition metal compounds were discovered. The properties of alnico have improved only marginally since that time.

14.5BARIUM AND STRONTIUM FERRITE

Barium ferrite has the formula BaO.6Fe2O3, a hexagonal crystal structure, and a fairly large uniaxial crystal anisotropy. Its intrinsic properties were described in Section 6.5. The hexagonal c axis is the easy axis and the crystal anisotropy constant K is 3.3 106 ergs/ cm3 or 330 kJ/m3. The value of Ms is low, 380 emu/cm3 or 380 kA/m. The Curie point is 4508C. Strontium ferrite SrO.6Fe2O3 has almost identical properties except that K is somewhat larger.

Barium ferrite was developed into a commercial magnet material in 1952 in the Netherlands by the Philips Company, which called it Ferroxdure. A number of other trade names have been used, but with the expiration of patents, these materials are usually just called ceramic magnets or ferrite magnets. The composition is generally not specified, but better properties and higher prices usually mean more strontium. In the following account, the term “barium ferrite” can be understood to mean either material, or a mixture. Sometimes the general term hexaferrite is used for both materials.

Barium ferrite is made by practically the same method as the soft ferrites. Barium carbonate is mixed with Fe2O3 and fired at about 12008C to form the ferrite. This material is then ball milled to reduce the particle size, pressed dry in a die, and sintered at about 12008C. The resulting magnet has a grain size of about 1 mm and is very brittle. Anisotropic grades are made by wet pressing in a magnetic field to align the c-axes of the particles with the field, which is along the compression axis; the usual product is a cylindrical magnet with the easy axis parallel to the cylinder axis. Figure 14.11 shows the microstructure of a coarse-grained specimen with field-oriented grains. Barium ferrite has a tabular “habit,” as a mineralogist would say; i.e., it habitually crystallizes in the form of flat plates with the basal plane of the unit cell parallel to, and the c-axis at right angles to, the plate surface. In Fig. 14.11a these plates are parallel to the surface examined; in Fig. 14.11b the plates are in profile, with the c-axes more or less vertical and in the plane of the page. Even when a field is not applied during pressing, some preferred orientation will result because of the tendency for the particles to pack together with their flat surfaces parallel to one another and at right angles to the pressing direction.

Barium ferrite owes its magnetic hardness to crystal anisotropy. If it were in the form of aligned, spherical, single-domain particles, its intrinsic coercivity should be

m0Hci ¼ m0HK ¼ 1:7 T (SI):

Actually, the particles are plate-shaped, which introduces shape anisotropy. And the shape is wrong, because the easy axis due to shape is perpendicular to the easy axis due to crystal anisotropy. It is difficult to allow for this effect exactly. For an isolated particle, the shape effect reduces Hci by 4800 Oe to a value of about 12,000 Oe, as mentioned in Section 11.5; for commercial magnets with 5–10% porosity, the reduction would not be nearly as much, although the pores are the source of internal demagnetizing fields.

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Fig. 14.11 Photomicrographs of sintered barium ferrite with oriented grains. (a) Section normal to c-axes; (b) section parallel to c-axes [J. Smit and H. P. J. Wijn, Ferrites, Wiley (1959)].

The observed values of Hci are no more than one-third the lower theoretical limit. It follows that ferrite magnets are not composed of single-domain particles reversing coherently. The typical grain size of 1 mm is too large; we estimated (Problem 9.4) the critical

˚ ¼ m

size for single-domain behavior to be of the order of 1000 A ( 0.1 m). Magnetization reversal in ferrite magnets must therefore take place by wall nucleation and motion (Section 11.5). The coercivity could in principle be increased by making the particles smaller and/or smoother and with fewer crystal imperfections, in order to decrease the number of sites for wall nucleation.

The maximum value of (BH)max for commercial ferrite magnets is about 3.5 MGOe or 28 kJ/m3, and has not increased significantly for many years.

14.6RARE EARTH MAGNETS

Many of the rare-earth elements (atomic numbers 59–70) are ferromagnetic with very strong magnetic anisotropy, but all with Curie temperatures below room temperature. They form a series of intermetallic compounds with the transition metals such as Fe, Co, and Ni, and many of these compounds have Curie temperatures well above room temperature. The compounds tend to retain the strong anisotropy of the rare-earth element, which arises in the 4f electron shell and is to a large extent intrinsic to the atom rather than dependent on its surroundings. This behavior is often referred to as single-ion anisotropy.

Widespread interest in these compounds as permanent magnet materials dates from 1966, when K. J. Strnat and G. Hoffer of the U.S. Air Force Materials Laboratory reported that YCo5 has an anisotropy constant of 5.5 107 ergs/cm3 or 5.5 106 J/m3, by far the largest value for any material then known. Since then, a wide range of rare-earth/transition metal compounds have been investigated, and their crystal structures, magnetizations, anisotropies, and Curie temperatures are known. For use as a permanent magnet material, the necessary properties are a high and positive uniaxial anisotropy, giving an easy axis of magnetization rather than an easy plane; Curie temperature well above room temperature; and reasonably high saturation magnetization. Low cost, low density, good mechanical properties, and resistance to corrosion are also desirable.

Three families of useful permanent magnet materials have emerged from this extensive scientific and technological work. Each of them is greatly superior to all previously known permanent magnets, and the best of them is more than ten times better than the best alnico or ferrite, as measured by the maximum energy product. They are generally known as SmCo5, Sm2Co17, and Nd2Fe14B or NdFeB. We will consider them in the order of their historical development.

14.6.1SmCo5

This compound has a hexagonal crystal structure, and an anisotropy constant of about 7.7 107 erg/cm3 or 7.7 106 J/m3, with the easy axis along the c-axis of the unit cell. The basic production method consists of melting and casting the alloy, crushing and grinding to produce a powder with particle size near 10 mm, and with each particle consisting of a single crystal of SmCo5. The powder is aligned in a magnetic field so that the easy axes of all the particles are parallel, and then compressed in a die. Usually the alignment and compression are done sequentially in the same apparatus. The compressed powder is then sintered at a temperature above 10008C to make a final magnet.

To obtain high density and good magnetic properties, a small amount of powder made with an excess Sm content is added before compaction. This material melts at the sintering temperature, and greatly aides in attaining high density. The process is referred to as liquidphase sintering. The particle size of the powder before sintering corresponds to the grain size after sintering, and is about an order or magnitude larger than the calculated size of single-domain particles. So these are not in fact single-domain particle magnets, although they were originally developed on the basis of single-domain theory.

SmCo5 magnets have an unusual and useful property: they can be magnetized initially by a field much smaller than their intrinsic coercive field Hci. This behavior is illustrated in Fig. 14.12. The rule of thumb for permanent magnets is that the field required to satisfactorily magnetize the material is several times larger than the coercive field; this rule clearly does not apply to SmCo5. This behavior is a distinct production advantage, since reaching fields several times larger than the coercive field is difficult and expensive.

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Fig. 14.12 Magnetization and demagnetization behavior of SmCo5 (schematic).

This phenomenon of easy magnetization but difficult demagnetization is interpreted to mean that the as-prepared magnet grains contain domain walls that move relatively easily in an applied field; this allows the magnet to be magnetized to saturation in relatively low fields. Once the grains have been magnetically saturated, and the domain walls driven out, reversing the magnetization requires the nucleation of new reverse domains, and there is a strong barrier to this nucleation. When the nucleating field is reached, the field is high enough to drive the domain walls completely through the grains and into saturation in the opposite direction. A magnet that behaves in this way is said to show nucleation-controlled coercivity.

SmCo5 magnets were the first to attain an energy product of 20 MGOe ( 160 kJ/m3), and they continue to be made and used.

14.6.2Sm2Co17

The notation Sm2Co17 is shorthand for a family of complex compositions that may be expressed as Sm2(Co, Fe, Cu, Zr) 15. The microstructure is very fine-scale, and appears to consist basically of bands of SmCo5 separating regions of Sm2Co17. The high coercive field in this case results from domain wall pinning rather than domain nucleation; this is indicated by the fact that fields larger than the coercive field are required for this initial magnetization of the magnet. The production method is basically the same as SmCo5, except that a fairly complex heat treatment is needed to develop the necessary microstructure.

Some alternative production methods have evolved for producing rare-earth/transition- metal compounds. One approach combines the reduction of a rare-earth oxide such as Sm2O3 with introduction of Co, usually using Ca as the reducing agent. This is known as the reduction/diffusion process. Another variant is the use of hydrogen to produce powders. The rare-earth compounds characteristically can absorb large quantities of hydrogen at modest pressure and temperatures near room temperature, with a resulting change in crystal structure. The hydrogen can be easily removed by reducing the pressure, and the resulting reverse phase transformation converts the material to a fine powder. This is known as hydrogen decrepitation.