Environmental Engineering Reference
In-Depth Information
Figure 1.15
Normalized HCACF for the
N
=
4096 atoms simulation of
12
C
diamondat300K.Thedashedlinedrawsthedoubleexponentialfit,andthe
inset zooms in for the short-time region.
A
o
τ
o
+
A
a
τ
a
k
B
T
2
V
κ
μυ
=
.
(1.57)
Thismethodremovestheambiguityontheselectionofthefitting
time interval. Although double exponential function is used for the
fitting, Che
et al.
found the high-frequency optical modes contribute
only 0.1% to thethermal conductivity of diamond[57].
About the double exponential fit approach, McGaughey
et al.
[64] found that the two-stage decaying characteristic also exists
in the mono-atomic systems, such as Lennard-Jones argon. In
a more general sense, they found that fast and slow decays
are associated with the short-wavelength and long-wavelength
phonons, respectively. Moreover, Chen
et al.
[65] found that due
to the finite time cut-off, the fitted double exponential function is
not fully relaxed to zero but to a tiny nonzero value
Y
0
, although
HCACF itself can decay to zero (Fig. 1.16). The
Y
0
term results from