Chemistry Reference
In-Depth Information
An external magnetic field usually changes the state of magnetisation of
a ferromagnet in a way that is nonlinear and irreversible (see fig. 7.9). A
typicalmagnetisation curve
M
is illustrated infig. 7.10(a). Starting at the
zero field (A), an initially demagnetised sample is subject to an increasing
magnetic field. The magnetisation increases with field until the sample
becomes fully magnetised, with magnetisation
M
s
(
H
)
. When the field is
removed, the magnetisation decreases to a value
M
r
, referred to as the
remanence
magnetisation. When a field
H
is now applied in the opposite
direction the magnetisation will return to zero at a finite field value,
H
c
,
referred to as the
coercivity
field. With further increase in the magnitude of
the field, the sample again approaches the saturation magnetisation value,
M
s
(
B
)
.
M
s
is an intrinsic property of the ferromagnetic phase but the
remanence
M
r
and coercivity
H
c
are not.
The
B
(
C
)
(
H
)
curve of fig. 7.10(b) is related to the
M
(
H
)
curve of fig. 7.10(a) by
eq. (6.5),
B
0
M
r
,
but the magnitude of the coercivity on the
B
-
H
plot of fig. 7.10(b),
B
H
c
,is
smaller than in fig. 7.10(a), because
B
(
H
)
=
µ
(
H
+
M
(
H
))
. The remanence
B
r
in this case is just
µ
0
=
µ
(
H
+
M
)
goes to zero when
M
0
is still
curves tend to be measured by
physicists interested in magnetisation, whereas
B
>
0. Coey (1996) remarks that
M
(
H
)
curves are of more
interest to engineers. This is because we can use the
B
(
H
)
curve of fig.
7.10(b) to determine the maximum potential energy which can be stored
in a magnet and hence design its performance for specific applications.
It can be shown that the maximum potential energy density is obtained
(at least for an ellipsoidal sample) at the point where the product
(
H
)
1
2
B
−
·
H
is
maximised. The figure of merit
max
, corresponding to the shaded area
in fig. 7.10(b), is equal to twice this maximum potential energy (Coey 1996;
Myers 1997). We can estimate the upper limits for the performance of any
magnet by noting that the figure ofmerit ismaximisedwhen the remanence
has its largest possible value,
M
r
(
BH
)
M
s
, and the magnetisation remains
independent of reverse field up to
H
c
, in which case
=
1
2
(
BH
)
=
(
µ
0
M
s
)
·
max
1
2
M
s
(
, giving the following intrinsic limitations on the performance of
permanent magnets:
)
B
r
≤
µ
0
M
s
(7.41a)
B
H
c
≤
M
s
(7.41b)
and
0
M
s
4
≤
µ
(
BH
)
(7.41c)
max
The major considerations in the design of high-performance magnets are,
therefore, to choose a ferromagnet with a large value of
M
s
and a high coer-
civity. As stated earlier, this depends both on the alloys used and also on
