Environmental Engineering Reference
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Figure 5.4 Basic algorithm of Green-Kubo MDsimulations.
B ij is a function of the number of neighboring atoms, bond angles,
and bond lengths. The detailed expressions of Tersoff potential
functions and the parameters for silicon, nitrogen, and hydrogen
atomsarereportedbyDeBritoMota et al. [48].Tersoffpotentialhas
beensuccessfullyappliedtocalculatethermalconductivityofSiNWs
[13, 17] and SiGe NWs[28].
Figure 5.4 shows the basic algorithm of the EMD method. After
a NVT (constant particle number N , volume V , and temperature
T ) equilibration, NVE (constant N , V , and total energy E )MD
simulationsarecarriedouttoobtainheatcurrent J ( t )whichisgiven
by
d
dt
J ( t ) =
( r i E i ),
(5.2)
i
where r i and E i are the time-dependent atomic position vector and
the microscopic total energy of atom i , respectively. The thermal
conductivity along the z -axial direction is then calculated with the
Green-Kubo formula [49],
Vk B T 2
1
0
κ z =
J z (0) J z ( t )
dt ,
(5.3)
 
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