Environmental Engineering Reference
In-Depth Information
Figure 1.14
Normalized HCACF for perfect
β
-SiC at 760 K. The dashed line
draws the single exponential fitin the range from 10 ps to 30 ps.
where
g
and
τ
0
aretwofittingparameters,andthermalconductivity
isobtainedby analytically calculating the infiniteintegralin GKF
κ
μυ
=
g
τ
0
k
B
T
2
V
.
(1.55)
Figure 1.14 shows an example of the single exponential fit to
HCACF for
β
-SiC adapted from Ref. [56]. In the single exponential fit
method, the fitting parameters depend critically on the choice of
τ
1
and
τ
2
,whichareselectedempirically.Thismaybringcertaindegree
of ambiguity into the calculation results. Later, Che
et al.
[57] found
that due to the different relaxation time for acoustic and optical
phononsindiamond,HCACFgenerallyexhibitsatwo-stagedecaying
behavior, with a very fast decay at the beginning and followed by a
much slowerdecay in the long-timetail, asshown inFig. 1.15.
To take into account this two-stage decaying characteristic of
HCACF, Che
et al.
[57] proposed to fit HCACF based on the double
exponentialfunction,andthencalculatethermalconductivitybased
on the fitting parameters as
Cor
(
t
)
A
o
e
−
t
/τ
o
A
a
e
−
t
/τ
a
,
=
+
(1.56)
