Chemistry Reference
In-Depth Information
where
2
C
m
¼
N
A
m
ð
10
:
90
Þ
3k
is the Curie constant (referred to a mole).
Adding the diamagnetic susceptibility
d
, we have for the molar
x
magnetic susceptibility
C
T
m
d
p
x
¼ x
þx
¼
A
þ
ð
10
:
91
Þ
a result similar to that existing for electric polarizabilities.
For paramagnetic systems, where often electronic spin plays a funda-
mental role in determining susceptibilities, the first term in (10.91) is
usually negligible with respect to
p
(hence Curie's law).
A generalization of (10.89) is given by the law by Curie-Weiss:
x
C
m
T
Q
1
x
m
¼
C
m
þ
1
C
m
T
m
x
¼
)
ð
10
:
92
Þ
where
Q ð<
T
Þ
is called the Curie temperature.
Q
is a quantity character-
istic of
the different substances,
its value marking the difference
0
Þ
systems.
Equation 10.92 shows that the reciprocal of the magnetic susceptibility
is linear in the temperature T and can be used for the experimental
determination of the Curie constant (slope) and the Curie temperature
(intercept).
ðQ <
0
Þ
ðQ >
between paramagnetic
and ferromagnetic
(i) Paramagnetic susceptibilities
To investigate on the value assumed by the elementary magnetic
moment
in the case of light atoms and ions, we may resort to the
Russell-Saunders LS-coupling scheme in the so-called vector model
(Magnasco, 2007). In this scheme, the spin vectors L and S are coupled
to a resultant vector J having a component J
z
along the direction of the
magnetic field. The associated 'good' quantumnumbers J andM
J
take
the values
m
(
J
¼
L
þ
S
;
L
þ
S
1
; ...; j
L
S
j
ð
10
:
93
Þ
M
J
¼
J
; ð
J
1
Þ; ...; ð
J
1
Þ;
J
