Three groups of magnetic substances
Substances may be classified into three groups in accordance with
their magnetic properties: diamagnetic, paramagnetic and
ferromagnetic. The values of diamagnetic susceptibility lie in the
range of -13 x 10(-6th) (BISMUTH) TO -0.8 X 10(-6TH) for copper.
Paramagnetic bodies are characterized by positive susceptibility -
for example. 0.4 x 10 (-6th) for potassium and 320 x 10(-6th) for
Ferromagnetic bodies are characterized by large values of
permeability. These are hundreds and even thousands of times
greater than those of other bodies.
Let us examine the structural features which explain these
differences in magnetic properties for substances which otherwise do
not show great differences in properties.
Diamagnetism, it will soon be seen, is a universal property of all
bodies inasmuch as they consist of electrons. The above values show
that diamagnetic properties are weaker than paramagnetic ones and,
'a fortori', weaker than ferromagnetic properties.
Diamagnetic properties may be detected only in the absence of
properties resulting in positive magnetism.
Paramagnetic and ferromagnetic bodies have diamagnetic properties,
but they are obscured by the stronger positive paramagnetism. Thus,
diamagnetism exists for any system containing electrons. On the
other hand, positive magnetism arises only in bodies the atoms of
which possess a magnetic moment. The phenomenon of paramagnetism is
very similar to the process of electrisation of a dielectric, which
consists of rigid dipoles possessing a constant dipole movement.
The presence of a magnetic moment in atoms is also a necessary
condition for the existence of ferromagnetic properties. However,
the peculiarities of ferromagnetic substances are due to a very
specific property, viz., the formation within a body of vast regions
- domains - within which the magnetic moments of thousands of
millions of atoms are arranged parallel to one another.
Diamagnetism is a direct consequence of the tendency for an electron
to move in a circle in a magnetic field. In a magnetic field with
an induction 'B', an unbound charged particle moves in a circle with
an angular frequency (w=eB/mc).
It can be rigorously proven that the action of a magnetic field on
an electron moving in a central field - in particular, in the field
of an atomic nucleus - produces an analogous effect: the electron
will move in a circle about a line of force, but at one-half the
frequency, viz., (eB/2mc).
This motion is superimposed on other motions which may be performed
by the electron, the chaotic motion of particles of the electron gas
or the motion of the electron about an atomic nucleus.
Fundamental considerations show that such motion may be equated to a
circular electric current. When the magnetic field is switched on,
the electrons begin to rotate about the magnetic field and each
produces an elementary current. I=(ve/2(Pi)R) = (eW/2(pi)).
Multiplying this value by the area of the circle described by an
electron in its motion about a line of force, we obtain the value of
the diamagnetic moment created by one electron:
M = 1 eW e(2)
- - ----- S = - ----- mc(2) SB
c 2(pi) 4(pi)
The reason for the minus sign is clear from figure 1, (not included)
the direction of the moment is opposite to that of the field.
When a system consists of a large number of electrons, we must take
the summation of the above expression with respect to all the
M = - ---- \
4(pi)mc(2) > S B
Since by definition magnetic susceptibility is equal to the ratio of
magnetic moment per unit volume (or unit mass or mole) to induction,
X = - ----- > S
4(pi)mc(2) / i
If 'N' is Avogadro's number, 'X' represents molar diamagnetic
susceptibility. (x = x/u).
Thus, 'X' is given by the areas circumscribed by electrons in their
secondary motion in the magnetic field.
In principal, this computation can be made if we know the wave
function of the system. i.e., in the final analysis, the electron
density. Actually, since the computation is very cumbersome, the
diamagnetic susceptibility is determined experimentally.
It should be emphasized that diamagnetic susceptibility is
determined by the electron structure of the system and does not
depend (at least for atoms and molecules) on the external
conditions, including temperature.
Diamagnetic susceptibility, like molecular refraction, possesses
additivity. If the diamagnetic susceptibility is taken for a mole
of substance, the susceptibility 'X' of a molecule may be expressed
with considerable accuracy as
X = > n X
/ A A
where n is the number of atoms of type A in the molecule
and X is the increment for the given atom. For purposes
of illustration, we can use the same example as for refraction.
C,H and Cl atoms have the increments 7.4,2.0 and 18.5 (X x 10(6) ),
respectively. Thus, we obtain 15.4 for A methane, 64.9 for
chloroform, and 81.4 for carbon tetrachloride. These values are in
close agreement with experimental results.
The significance of this additivity consists probably in the
following: outer electrons weakly affect diamagnetic susceptibility.
In so far as additivity is realized, diamagnetic susceptibility is
an atomic rather than molecular property.
Diamagnetic susceptibility, as indicated in the preceding article,
is a property associated with substances, the atoms and molecules of
which do not have a constant magnetic moment. Such particles
include in the first place atoms and ions with completed shells -
the ions F-, Cl- and Na+ and atoms of the noble gasses. Atoms and
ions which in addition to a completed shell contain two more s-
electrons with anti-parallel spins, e.g., Zn, Be, Ca and Pb++, are
The group of diamagnetic molecules is incomparably larger than the
group of paramagnetic molecules. The later exists more in the
nature of exceptions. This is due to the fact that practically all
molecules have valent bonds formed by a pair of electrons with anti-
parallel spins. Usually, the total moment about a nucleus, as well
as the spin moment, equals zero in such molecules. Thus, bodies
consisting of atoms and ions such as those cited above and
practically all bodies the building blocks of which are molecules -
therefore, practically all organic substances are diamagnetic.
Diamagnetic susceptibility describes the electron cloud of a
molecule. If the distribution of electrons in a molecule is
strongly anisotropic, it's magnetic susceptibility is also
anisotropic. The anisotropy of diamagnetic susceptibility is
manifested particularly in molecules of the aromatic compounds.
For example, in benzene, X||, the molar diamagnetic susceptibility
in a direction lying in the plane of a benzene ring, equals
-37 x 10(-6) cm(3)/mole
and X1, the molar diamagnetic susceptibility in a direction
perpendicular to the plane of a ring, equals
-91 x 10(-6) cm(3)/mole;
x|| = -40 x 10(-6) cm(3)/mole and X1 = 190 x 10(-6) cm(3)/mole.
Anisotropy may be detected by measuring crystals oriented in
different directions in the field. Measurements of powders, liquids
and gasses yield a value of magnetic susceptibility for an averaged