Environmental Engineering Reference
In-Depth Information
Figure 1.16
NormalizedHCACFforbulkSiat1000K.Thesolidanddashed
line draws the raw data and double exponential fit, respectively. The arrow
denotes the cut-offtime.
the contribution of long-wavelength phonons which have a longer
relaxation time than thecut-off time.
Chen
et al.
[65] proposed a nonzero correction to the double
exponentialfit method,
Cor
(
t
)
/
Cor
(0)
=
A
1
e
−
t
/τ
1
+
A
2
e
−
t
/τ
2
+
Y
0
,
(1.58)
and correspondingly thermal conductivity iscalculated as
Cor
(0)
3
k
B
T
2
V
(
A
1
τ
1
+
A
2
τ
2
+
Y
0
τ
c
),
κ
=
(1.59)
where
τ
c
isthe cut-off time.
Using bulk silicon as an example, Chen
et al.
[65] calculated the
thermal conductivity with and without this nonzero correction
Y
0
.
At 1000 K, thermal conductivity of bulk silicon is about 32W/(m-K)
[66].AsshowninFig.1.17,thesaturatedvaluefromEMDsimulation
without
Y
0
is only about 16 W/(m-K), much lower than the experi-
mentalbenchmark.Withtheimprovedcorrection,theMDpredicted
thermal conductivity agrees well with the experimental value,
demonstrates the accuracy of this improved double exponential
fitting approach.
