Environmental Engineering Reference
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by a long tail which has a much slower decay. This two-stage
decaying characteristic of HCACF has been found in the study of
various materials. The rapid decay corresponds to the contribution
from short-wavelength phonons to thermal conductivity, while the
slowerdecaycorrespondstothecontributionfromlongwavelength
phonons. Furthermore, as shown in Fig. 1.21a, HCACF decays to
approximately zero within 100 ps (cut-off time), much shorter than
the total simulation time of 2.4 ns. Therefore, the total simulation
time of2.4 ns isadequate for the present study.
UsingthestandardEMDapproachintheintegrationofHCACFup
tothecut-offtime,thethermalconductivityofSiNWswascalculated.
Figure 1.21b shows the calculated thermal conductivity of SiNWs
with a fixed cross-section of 5
×
5 unit cells versus supercell length
N
X
at 300 K. Due to the periodic boundary condition, finite size
effect exists in the calculated thermal conductivity when simulation
domain is small. Here the thermal conductivity of SiNWs saturates
to a constant when the supercell size is 16 unit cells. Therefore, in
the following part, we set
N
X
=
16 in the longitudinal direction and
study the thermal conductivity of SiNWsand SiNTs.
Figure 1.22 shows the thermal conductivity of SiNWs and SiNTs
versus cross-section area at 300 K. Even with a very small hole, the
thermal conductivity decreases evidently, from 12.2 W/(m-K) to 8.0
W/(m-K). In this case, only a 1% reduction in cross-section area
induces the reduction of thermal conductivity of 35%.
Furthermore, with increasing of
L
y
and
L
z
, the cross-section area
decreases further, and a linear dependence of thermal conductivity
on cross-section area is observed. We also show the thermal
conductivity of SiNW with
N
Y
4. It has the same cross-
section area (4.72 nm
2
) as the SiNT with
N
Y
=
N
Z
=
=
=
5and
L
y
=
N
Z
L
z
=
6. It is clear that for SiNW, thermal conductivity increases as
cross-sectionareaincreases.However,wecanseethatwiththesame
cross-section area, thermal conductivity of SiNTs is only about 33%
of that of SiNWs. This additional reduction is due to the localization
of phonon states on the surface. Due to the inner surface in SiNTs,
which partially destroys the original periodicity of SiNWs, phonon
localization takes place on thesurface in general.
In addition to the calculation of thermal conductivity, the HCACF
can also provide more phonon information. The coherence of
