Page 290 - Electrical Properties of Materials

272 Magnetic materials

But remember that the relationship between B r1 and H m is given also by the
hysteresis curve. Hence, the value of B r1 may be obtained by intersecting the
B(H) hysteresis curve by the straight line of eqn (11.32) as shown in Fig. 11.11.
B The aforegoing construction depends on the particular geometry of the per-
r
B manent magnet we assume, but similar ‘demagnetization’ will occur for other
r1
geometries as well. Hence, we may conclude in general that in order to have
a large, useful flux density, the B–H curve must be wide. We may therefore
μ l adopt, as a figure of merit, the product B r H c or, as is more usual, the product
B =– 0 H
δ (BH) max in the second quadrant.
How can one achieve a large value of H c ? It is relatively easy to give an
answer in principle. All the things which caused the quality of soft materials
H
to deteriorate are good for permanent magnets. In particular, when a domain
Fig. 11.11 gets stuck on an impurity, that is bad for a soft magnetic material but good
Construction for finding B r1 . for the hard variety. An obvious way to include impurities is to add some car-
bon. High-carbon steels were indeed the permanent magnet materials in the
nineteenth century until displaced by tungsten steels towards the end of the
century.
The simplest permanent magnet one could conceive in principle would be
a single crystal of a material that has a large anisotropy and has only one
axis of easy magnetization. The anisotropy may be characterized by an ef-
fective field H a , which attempts to keep the magnetization along the axis. If a
single-crystal material is magnetized along this axis, and a magnetic field is
applied in the opposite direction, nothing should happen in principle until the
field H a is reached, and then, suddenly, the magnetization of the whole crystal
should reverse. Going one step further in this direction, one could claim that
any collection of anisotropic particles that are too small to contain a domain
wall (having a diameter of the order of 20 nm) will have large coercivity. This
idea, due to Stoner and Wohlfarth, was the inspiration behind many attempts to
make better permanent magnets. In particular, the so-called Elongated Single
Domain (ESD) magnets owe their existence to the above concept. It is also
likely that elongated particles play a significant role in the properties of the Al-
nico series of alloys, which contain aluminium, nickel, and cobalt besides iron.
They first appeared in the early 1930s but have been steadily improving ever
since. A major early advance was the discovery that cooling in a magnetic field
produced anisotropic magnets with improved properties in the field-annealed
direction. The hysteresis curves of their best-known representatives (Alnico 5
and 9) are shown in Fig. 11.9(b).
Ferrites are also used for hard magnetic materials in the form MO·(Fe 2 O 3 ) 6
(M = Ba, Sr, or Pb). They were introduced in the 1950s. They have been stead-
ily growing in tonnage ever since, overtaking the Alnico alloys in the late 1960s
and rising in the late 1980s to 97.4% of world production (note that in value
they represent only about 60%). Their high coercivity derives from the high
anisotropy of the hexagonal phase of the materials. They have many advant-
ages: they are cheap, easily manufactured, chemically stable, and have low
densities. Their disadvantages are the relatively low remanence and declining
performance for even moderate rises in temperature.
One might be forgiven for believing that the late entry of rare-earth mag-
nets into the market place was due to their rarity. In fact, rare-earth elements
are not particularly rare, but they occur in mixtures with each other which