This preview shows pages 1–3. Sign up to view the full content.
Thermal Conductivity
I
The thermal conductivity
λ
T
is
λ
T
≡
V
k
B
T
2
Z
∞
0
d
t
h
j
ε
α
(
t
)
j
ε
α
(
0
)
i
,
(52)
with the corresponding relation
2
t
λ
T
=
V
k
B
T
2
Z
∞
0
d
t
D
(
δε
α
(
t
) 
δε
α
(
0
))
2
E
.
(53)
I
Here
j
ε
α
is a component of an energy current
(
j
ε
α
=
∂δε
α
/∂
t
), which in turn is
δε
α
=
1
V
X
i
r
i
α
(
ε
i

h
ε
i
i
)
,
ε
i
=
p
2
i
2
m
i
+
1
2
X
i
6
=
j
U
(
r
ij
)
.
(54)
Notes
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
I
Pair correlation function
(radial distribution function)
g
(
r
)
tells at which distance the atoms (on average) are from
each other in the system.
I
It is deﬁned as
g
(
r
)
≡
ρ

2
*
X
ij
δ
(
r
i
)
δ
(
r
j

r
)
+
=
V
N
2
*
X
i
X
j
δ
(
r

r
ij
)
+
,
(55)
and it basically counts the number of bonds at each
interatomic distance scaled by the corresponding atomic
density.
I
In practice, we count the number of atoms within a certain
Δ
r
, divided by the average number of atoms at the same
distance in an ideal gas.
Notes
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 02/14/2012 for the course CSE 6590 taught by Professor Kotakoski during the Winter '12 term at York University.
 Winter '12
 Kotakoski

Click to edit the document details