Chemistry Reference
In-Depth Information
where
E
is the instantaneous electric field at any point. The current density
j
=−
n
s
e
v
is therefore related to
E
by
n
s
e
2
m
e
E
d
j
d
t
=
(8.29)
and as
∇×
E
=−
∂
B
/∂
t
, we find by taking the curl of both sides of eq.
(8.29) that
n
s
e
2
m
e
B
d
d
t
(
∇×
d
d
t
j
)
=−
(8.30)
so that
m
e
B
n
s
e
2
d
d
t
∇×
j
+
=
0
(8.31)
n
s
e
2
A perfect conductor therefore requires that
is
constant
with time. From the London equation, a superconductor requires that this
constant is zero.
(
∇×
j
+
(
/
m
e
)
B
)
8.7 Application of thermodynamics
We saw earlier that the transition from the superconducting to nor-
mal state occurs at a critical field
H
c
for a Type I superconductor, and
that
H
c
decreases with increasing temperature
T
(fig. 8.4(b)). Flux is
always excluded from the superconductor no matter how we approach
the superconducting state. Because the transition from the normal to the
superconducting state is reversible, we can use thermodynamic analysis
to investigate the superconducting transition. This allows us to deduce the
energy difference between the normal and superconducting states, which
turns out to be remarkably small. We can also determine the difference
in entropy, or degree of disorder, between the two states. The results of
the thermodynamic analysis then place severe constraints on the possible
models of superconductivity.
The
Gibbs free energy
per unit volume,
G
, is the thermodynamic func-
tion which must be minimised to determine the equilibrium state of any
substance at a fixed temperature
T
, pressure
p
and applied field
H
(see,
e.g. Finn). It is defined for a magnetic material with magnetisation
M
in an
applied field
H
by
G
=
U
−
TS
+
pV
−
µ
0
H
·
M
(8.32)
where
U
is the internal energy of the substance, and
S
the entropy, which is
a measure of the degree to which the substance is disordered. (
S
increases
