Jan Svoboda. Magnetic Techniques for the Treatment of Materials
Подождите немного. Документ загружается.
20 CHAPTER 1. PRINCIPLES OF MAGNETIC TREATMENT
Figure 1.9: Permeability of decarburized steel used for manufacture of magnet
yokes [B1].
Table 1.9: Magnetization and Curie temperatures of ferromagnetic materials.
Material Magnetization
0
P
v
[T] at 0 K
Curie temperature
T
f
[
0
C]
Iron 2.18 770
Nickel 0.64 358
Cobalt 1.81 1120
Armco 2.11
Si-Fe 1.97
Permalloy 45 1.6
Permendur 2.45
Mumetal 0.8
1.4. MAGNETIC PROPERTIES OF MATERIALS 21
1.4.4 Antiferromagnetism
Antiferromagnetic materials were originally thought of as a class of anomalous
paramagnets, since they have small positive susceptibilities of similar magnitude
to many materials of the latter class. However, their magnetic susceptibility does
not increase steadily as the temperature decreases all the way to absolute zero.
At high temperatures they follow the relationship
=
F
W + W
Q
(1.35)
where W
Q
is the so-called Néel temperature. At this critical temperature the
susceptibility ceases to obey eq. (1.35) and below W
Q
the susceptibility generally
decreases with decreasing temperature. The situation is depicted in Fig. 1.6.
In the original Néel’s theory, an antiferromagnetic substance was envisaged
as composed of two sublattices, one of whose spins tend to be antiparallel to
those of the other. Néel assumed the magnetic moments of the two sublattices
to be equal, so that the net moment of the material was zero, as is schematically
shown in Fig. 1.5. Since Néel’s original hypothesis the term antiferromagnetism
has been extended to include materials with more than two sublattices and those
with triangular, spiral and canted spin arrangements.
Antiferromagnetism occurs mostly in transition metal oxides, such as MnO,
CoO and NiO, as well as in other similar compounds such as sulphides and
selenides. Antiferromagnets have small (10
10
to 10
8
m
3
/kg) positive sus-
ceptibilities and hematite is one of the minerals that possess antiferromagnetic
properties.
1.4.5 Ferrimagnetism
In a ferrimagnetic material magnetic moments are ordered regularly in an an-
tiparallel sense, but the sum of the moments pointing in one direction exceeds
those pointing in the opposite direction. This situation is illustrated in Fig. 1.5.
The magnetic properties of ferromagnets and ferrimagnets are generally similar:
both exhibit saturation and their magnetization is much greater than that of
other magnetic classes. Ferrimagnetism occurs mainly in ferrites, mixed oxides
of iron and of other elements, and also in two of the oxides of iron, namely
magnetite Fe
3
O
4
and maghemite Fe
2
O
3
.
The shapes of magnetization curves of various classes of materials are shown
in Fig. 1.10 and a summary of magnetic properties of materials is given in
Table. 1.10.
1.4.6 Demagnetization
It was previously stated that the magnetic properties of ferromagnetic (v=o=)
particles also depend on the shape of the body. The magnetic field K
l
inside a
magnetized body is not equal to the field applied to it (K
0
). The magnetization
of a ferromagnetic body of a finite size will produce a magnetic field inside the
22 CHAPTER 1. PRINCIPLES OF MAGNETIC TREATMENT
Table 1.10: Classification of materials according to their magnetic properties.
Class Critical tem-
perature
Magnitude
of [SI]
Temperature
variation of
Diamagnetic None Approximately
-10
6
to
-10
5
Constant
Paramagnetic None Approximately
+10
5
to
+10
3
= F@W
Ferromagnetic Curie temper-
ature W
f
Large, e.g. A 1
(below W
f
)
Above W
f
=
F
W W
f
Antiferromag-
netic
Néel tempera-
ture W
Q
As paramag-
netic
Above W
Q
=
F
(W ±W
l
)
with
W
l
6= W
Q
below
W
Q
decreases,
anisotropic
Ferrimagnetic Curie temper-
ature W
f
As ferromag-
netic
Above W
f
F
(W ±W
l
)
with W 6=
W
l
body in a direction opposite to that of the magnetization. The induced field
is called the demagnetizing field K
g
because it always tends to oppose the
applied field K
0
. The situation is depicted in Fig. 1.11. The magnitude of K
g
is proportional to that of magnetization P:
K
g
= Q
P (1.36)
where Q is the dimensionless constant of proportionality called the demagne-
tization factor. The value of Q varies from zero to unity, depending upon the
shape of the material and the direction of magnetization. The resulting mag-
netic field inside the body is given by
K
l
=
K
0
+
K
g
=
K
0
Q
P (1.37)
In general, the calculation of Q is quite complex and numerical values for
various shapes can be found e.g. in [B2, B3, D3]. With increasing aspect ratio,
with the major axis parallel to the field, the demagnetization factor decreases.
For a sphere Q = 1/3, while for the infinitely long cylinder whose axis coincides
with the direction of the field, Q = 0. For a thin disc, perpendicular to the
field, the demagnetization factor achieves its maximum value, Q =1.
For a linear soft magnetic material, for which P = K> eq. (1.37) can be
re-written
K
l
=
1
1+Q
K
0
and
E
l
=
0
1
1+Q
K
0
(1.38)
1.4. MAGNETIC PROPERTIES OF MATERIALS 23
Figure 1.10: Shapes of the magnetization curves of various classes of materials
(not in scale).
Figure 1.11: The demagnetizing field in a short magnetic sample.
24 CHAPTER 1. PRINCIPLES OF MAGNETIC TREATMENT
In the studies of mineral magnetism it is important to distinguish extrinsic
susceptibility
h
, which is the susceptibility that is conventionally measured by
most instruments, from intrinsic susceptibility
lq
> which is the true suscepti-
bility after removal of the eects of internal demagnetizing fields [T1]. These
susceptibilities are related by the following equation:
h
=
lq
1+Q
lq
(1.39)
1.4.7 Mixtures containing ferromagnetic (s.l.) materials
In magnetic separation, many weakly magnetic materials contain ferromagnetic
(v=o=) impurities. As a result of a high magnetic permeability of most ferro-
magnetic (v=o=) materials, the bulk magnetic susceptibility of a weakly magnetic
mineral will be determined by the concentration of ferromagnetic impurities.
For such a mixture the observed magnetic susceptibility is given by
h
=
f
lq
(1 + Q
lq
)
(1.40)
where f is the volume concentration of the ferromagnetic (v=o=) material. Con-
tributions of various ferromagnetic (v=o=) and paramagnetic minerals to the total
susceptibility of a mixture is shown in Fig. 1.12 [T1].
Since the magnetic permeability and susceptibility of a ferromagnetic (v=o=)
material is a function of the magnetic field, the definition of magnetic susceptibil-
ity is determined by measuring techniques used to determine the susceptibility.
The most frequently quoted value is the initial susceptibility (or permeability)
l
as shown in Fig. 1.8. For strongly susceptible materials, such as magnetite,
h
=1@Q , and the initial susceptibility can be written:
l
=
f
Q
(1.41)
For spherical particles Q = 1/3 and thus
l
3f (1.42)
while for ovoid particles, with the ratio of long and short axes of 10, the suscep-
tibility is [L1, T1]:
l
18f (1.43)
Although the magnetic susceptibility of paramagnetic material is indepen-
dent of the magnetic field, minerals displaying various forms of magnetic order
(i.e. ferromagnets (v=o.)), or paramagnetic minerals containing the admixtures
of the magnetically ordered materials, exhibit a field-dependent magnetic sus-
ceptibility. This phenomenon can seriously alter the predictions of the results
of magnetic separation based on the field-independent magnetic susceptibility.
The measured magnetic susceptibility, in a relatively low applied magnetic
field (E? 0.6 T), can be represented by the Owen-Honda equation [O1, H1]:
1.5. MAGNETIC PROPERTIES OF MINERALS 25
Figure 1.12: Contribution of various minerals to the total susceptibility of a
mineral mixture [T1].
=
s
+
g
+
P
v
K
=
4
+
P
v
K
(1.44)
where
s
and
g
are paramagnetic and diamagnetic susceptibilities, respectively,
4
is the magnetic susceptibility extrapolated to the infinite magnetic field, and
P
v
is the saturation magnetization of the ferromagnetic (v=o=) component of the
mixture.
It has been experimentally determined ([N2, P2]) that
4
is characteristic of
a mineral, and is nearly constant for samples of the same mineral from dierent
localities. On the other hand, saturation magnetization P
v
, which indicates the
degree of weak ferromagnetism, varies widely between samples from diering
localities and between size fractions of the same sample.
1.5 Magnetic properties of minerals
1.5.1 The classification of minerals according to their mag-
netic properties
Although all matter responds to the presence of the external magnetic field,
the degree of this response varies widely. For practical reasons the technical
classification of materials, and particularly of minerals, diers from physical
26 CHAPTER 1. PRINCIPLES OF MAGNETIC TREATMENT
categorization discussed in previous sections. For the purposes of magnetic
separation, materials can be divided into three basic groups:
Strongly magnetic materials can be recovered by a magnetic separator
with the use of a relatively weak magnetic field, up to, for example, 0.15 T, with
a modest field gradient of the order of 0.5 T/m. The magnetic susceptibility
that responds to such a low magnetic field is generally greater than 10
4
m
3
/kg
and ferromagnetic and ferrimagnetic materials like mild steel, iron, magnetite,
maghemite and pyrrhotite fall under this group.
Weakly magnetic materials can be recovered by a magnetic separator
that generates magnetic induction up to 1.0 T, and the field gradient in the range
from 50 to 500 T/m. This broad group of materials includes antiferromagnetic,
paramagnetic and some ferrimagnetic minerals. The group comprises iron and
manganese oxides and carbonates, ilmenite, wolframite and other materials.
Magnetic susceptibility of these materials ranges from 10
7
m
3
/kgto5×10
6
m
3
/kg.
”Non-magnetic" materials are those materials that cannot be easily re-
covered by conventional magnetic separators. They include very weakly para-
magnetic and antiferromagnetic materials with magnetic susceptibility smaller
than, for example, 10
7
m
3
/kg. Austenitic stainless steel, aluminium, rutile,
pyrite, garnet and red blood cells belong to this group. Diamagnetic materials,
with their negative magnetic susceptibility are also included.
This classification is only conditional as it does not take into account such an
important variable as particle size, which, as we have seen in Section 1.2.2, is as
important as magnetic susceptibility in determining the e!ciency of magnetic
separation. Recent developments and innovation in magnetism extended the
range of materials that can be treated by the magnetic means to such a degree
that all classes of matter are included, down to the submicrometer or even
nanosize range.
1.5.2 Magnetite
Magnetite Fe
3
O
4
is the most fundamental and important magnetic mineral.
It has a cubic crystalline structure in which Fe
3+
and Fe
2+
cations form two
distinct lattices. Each of the lattices is magnetized in opposite directions and
magnetite behaves as a ferrimagnetic mineral .
The saturation polarization of magnetite at room temperature ranges from
0.55 T to 0.61 T and the Curie temperature is 575
0
C. The density of pure
Fe
3
O
4
is 5200 kg/m
3
, calculated from the cell dimensions [N1].
As has been mentioned earlier, magnetic properties of magnetically ordered
mineral grains depend, among other things, on the grain size. The most impor-
tant distinction is between very small particles, each of which is a single domain,
and large grains, which are multidomain. For any material there is a maximum
size for spherical simple domain, referred to as the critical size. For magnetite
this critical size is about 0.05 m [S5], while for hematite, for instance, this
value is much higher, of the order of 200 to 300 m[N1].
1.5. MAGNETIC PROPERTIES OF MINERALS 27
Figure 1.13: Magnetic susceptibility and coercive force of ferromagnetic parti-
cles, as a function of grain size.
The variation of the coercive force K
f
with particle diameter g, in granular
magnetic materials and over a wide range of grain sizes, is well represented by
the relationship
K
f
g
q
(1.45)
The value of q is usually in the range between 0.25 and 1. The eect of
transition from single domain to multidomain structure, on magnetic properties
of a ferromagnetic grain, is illustrated in Fig. 1.13. This Figure shows that, at
the transition between multidomain and single domain arrangement, magnetic
susceptibility achieves its minimum, while the coercive force is maximum. A
simplified dependence of the coercive force and mass magnetic susceptibility on
particle diameter is shown in Fig. 1.14.
Fig. 1.15 illustrates the dependence of the mass magnetic susceptibility of
magnetite on the external magnetic field, ranging from 0 to 240 kA/m (0 to 3
kOe). The data reported in [P1] were obtained with size fraction - 74 + 53 m.
1.5.3 Titanomagnetites
Titanomagnetites Fe
3{
Ti
{
O
4
are one of the most common magnetic minerals.
Magnetic susceptibility, saturation magnetization and Curie temperature vary
in a regular manner with the composition parameter { from { = 0 (magnetite)
28 CHAPTER 1. PRINCIPLES OF MAGNETIC TREATMENT
Figure 1.14: Dependence of the coercive force and magnetic susceptibility of
magnetite on the particle size (after Derkach [D4]).
Figure 1.15: The field dependence of the magnetic susceptibility of magnetite
(adapted from Derkach [D4]).
1.5. MAGNETIC PROPERTIES OF MINERALS 29
Figure 1.16: Variation of the room temperature magnetic susceptibility with
composition, for titanomagnetites (after [O1]).
to { = 1 (ulvöspinel). The variation of the initial magnetic susceptibility with
composition, for three size fractions, is shown in Fig. 1.16 [O1]. Fig. 1.17
illustrates the dependence of the initial magnetic susceptibility on particle size,
for assorted compositions of titanomagnetites.
1.5.4 Ilmenohematites
Titanium-rich ilmenohematites Fe
2|
Ti
|
O
3
are significant magnetic minerals,
as their susceptibilities are more than two to three orders of magnitude greater
than those of paramagnetic minerals. Ilmenite FeTiO
3
is antiferromagnetic
below the Néel temperature of 55 K. Above the Néel temperature ilmenite is
paramagnetic [N1] and its magnetic susceptibility (approximately 5×10
3
(SI)
or 10×10
7
m
3
/kg) is somewhat lower than for other members of the series [T1,
D2], and was found to be essentially independent of the magnetic field strength
in the range from 0.1 T to 9 T [D2].
Magnetic susceptibility measured below the Néel temperature (at 4.3 K) was
found to be equal to 150×10
7
m
3
/kg at magnetic fields smaller than 0.6 T. At
higher magnetic fields the value of the susceptibility dropped to about 100×10
7
m
3
/kg [D2]. Figure 1.18 illustrates the variation of the saturation magnetization
of ilmenohematite samples of particle size of 9.8 m, at room temperature, with
composition [O2]. It can be seen that ilmenite (| = 0) is one of the magnetically
weakest members with saturation polarization of approximately 0.012 T.