Environmental Engineering Reference
In-Depth Information
discard the rest part of HCACF as noise. It is worth mentioning that
thetinybutnon-zeronoisecanaccumulateovertimeandchangethe
valueofaccumulativethermalconductivitydramaticallyasshownin
Fig. 1.18a,c.
When an obvious plateau in
κ
a
can be observed (shown in Fig.
1.18a), FD can make estimation of
τ
c
quite close to that estimated
by FA. Consequently, both two methods can give estimation of
thermal conductivity quite close to each other. In this case, the
mean value of the normalized HCACF fluctuates around zero in a
relatively short time (Fig. 1.18b). As a result, the noise does not
accumulate over time, giving rise to a plateau in
κ
a
with small
fluctuations. However, in the case without any obvious plateau in
κ
a
(Fig.1.18c),FDestimates
τ
c
(accordingtothepeakin
κ
a
)tobeabout
52 ps (marked by black arrow), while
F
(
t
) shows that HCACF has
already been contaminated by noise after about 15 ps. In this case,
FD overestimates the thermal conductivity by falsely taking into
account the contributionfrom the positive noise(see Fig. 1.18d).
1.6.4
Some Applications
Next using Silicon nanowire (SiNW) and Silicon nanotube (SiNT)
as examples [68], we show how to calculate thermal conductivity
of nanomaterials with equilibrium molecular dynamics (EMD)
simulations.TheatomicstructureofNWisinitiallyconstructedfrom
diamond-structured bulk silicon, with
N
X
,
N
Y
,and
N
Z
unit cells
in the
x
,
y
,and
z
directions, respectively. Here we set longitudinal
direction along
x
-axis, and atoms in the same layers means they
havethesame
x
-coordinate.ThestructureoftheNWsisconstructed
by selecting all the Si atoms that fall within a virtual cage placed
in bulk silicon while silicon atoms falling outside this virtual cage
are removed. For SiNT, some central atoms in SiNWs are removed
to create the SiNTs structures (Fig. 1.20). The cross-section of the
hollowregionisrectangular,itssizeiscontrolledbytwoparameters
L
y
and
L
z
, which means there are (2
L
y
+1)and(2
L
z
+ 1) layers of
silicon atoms removed away in
y
and
z
directions, respectively. With
adjustable
L
y
and
L
z
(from 1 to 6), the cross-section area of SiNTs
varies from 4.72 nm
2
to 7.30 nm
2
.
