Chemistry Reference
In-Depth Information
7.00
III
6.00
II
5.00
4.00
I
3.00
1.30 K
2.00 K
3.00 K
4.21 K
Brillouin
2.00
1.00
0
10
20
H/T
×
10
-3
Gauss/Deg
30
40
Figure 6.6
Comparison of the experimentally determined variation of the magnetic
moment
m
per paramagnetic ion in several salts with the theoretically
predicted variation, using the Brillouin function (solid lines) and assuming
L
=
0, with
S
=
3
/
2
(
I, Cr
3
+
)
, 5/2
(
II, Fe
3
+
)
and 7/2
(
III, Gd
3
+
)
, respec-
tively. (Experimental data after Henry (1952), © 1952 by the American
Physical Society.)
6.8 Paramagnetism in metals
So far we have considered only electrons bound to individual atoms. Free
electrons in metals also display paramagnetic and diamagnetic behaviour,
but their susceptibility is distinguished by being virtually independent of
temperature. We saw in Chapter 5 how the density of states for a parabolic
band structurewith effectivemass
m
e
varieswith energy,
E
, above the band
edge as
2
m
e
h
2
3
/
2
E
1
/
2
g
(
E
)
=
4
π
(6.41)
In a metal at zero temperature, all states up to the Fermi energy,
E
F
,
are filled, while the states above
E
F
are empty. In zero magnetic field,
there are equal numbers of electrons with spin up and spin down, imply-
ing no net magnetisation. When a field
B
is applied, the electrons with
magnetic moment
m
along the field direction are shifted down in energy
