SECTION 12.8. ALNICO MAGNETS 127
of the particles in the field direction occurs because the magnetic free energy of the parti
cles is lower when the axis with the lowest demagnetizing factor is in the direction of the
applied field. In principle, one would obtain the best properties when the magnetic field is
applied parallel to one of the three directions (for instance [001]) of an oriented sin
gle crystal. In practice, instead of expensive single crystals, so-called columnar-crystallized
Alnico alloys are applied. These alloys can be obtained by a grain-orienting process before
the thermomagnetic and tempering treatment. It is achieved by casting the alloys in heated
molds onto water-cooled steel or copper slabs. When the alloys solidify on the cold surface,
the grains tend to grow with their long axis parallel to the directions, perpendicular
to the cold surface. The result is then a semicolumnar alloy in which the columnar axis is
parallel to one of the directions, for instance, parallel to [001]. These alloys are often
referred to as Alnico directed grain (DG). The thermomagnetic treatment is subsequently
applied with the magnetic field parallel to the [001] direction of the latter alloys.
As already mentioned above, the magnetic properties in the easy magnetization direc
tion can be further improved by subsequent tempering for several hours at about 600°C. The
purpose of the 600°C tempering treatment is to enhance the difference in magnetic polar
ization between the and phases by diffusion of magnetic atoms from to and
of non-magnetic atoms from to An example of a microstructure, observed by elec
tron microscopy, of a grain-oriented alloy after thermomagnetic and tempering treatment is
shown in Fig. 12.8.3. The direction of the magnetic field applied during the thermomagnetic
treatment corresponds to the elongated direction of the columnar particles in Fig. 12.8.3a.
The relatively high coercivities and remanences in the Alnicos are principally due to
shape anisotropy of elongated Fe-rich particles in a non-ferromagnetic matrix. The Stoner-
Wohlfarth theory, already mentioned in Section 12.4, predicts that the coercivity in these
materials is proportional to the saturation polarization of the Fe-rich particles and to
a factor related to the difference in the effective demagnetization factors perpendicular
and parallel to the preferred direction of magnetization in the particles. Using
Eq. (12.5.2) and bearing in mind that in these materials is negligibly small, one finds that
Here, is an averaging factor that takes account of the various orientations of the
preferred axes of the particles with respect to the direction in which is measured. If one
assumes that the particles are magnetically non-interacting uniaxial single-domain particles
arranged at random, the factor equals about 0.5. But may approach the value
one in highly elongated particles. In the case of spheroid particles, there is a considerable
difference in the demagnetizing factor for particles magnetized perpendicular and parallel
to the flat surface of the spheroid. In the limit of an extremely flat and elongated spheroid,
thisone has Hence, the coercivity in such materials may reach an upper
limit, according to Eq. (12.8.1), equal to For
upper limit becomes and, for the coercivity becomes
Actual values found in Alnico materials are much lower, as may be seen from
the data shown in Fig. 12.8.2. This has primarily been attributed to the less perfect shape of
the thin ferromagnetic particles and also to the fact that the phase is magnetic to some
extent.