Environmental Engineering Reference
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1.5.2 Effects of Heat Bath
In both schemes of heat baths introduced in Section 1.4.1, there
is a free parameter, namely τ in NH heat bath and λ in Langevin
heat bath, which controls the strength of the noise in heat bath.
In this section, we take SiNWs as an example to study the impact
of heat bath on the calculated thermal properties of homogeneous
materials [32]. Moreover, we extend our study to heterogeneous
materials, such as Si/Ge NW junctions, in which a rectification of
heat current in different directions is of particular interest. Velocity
Verlet algorithm is used to numerically integrate Newton's equation
of motion. To derive the force term, SW potential is used. The
temperature of hot and cold heat baths are set as 310 K and 290 K,
respectively. Simulations are performed long enough to allow the
system to reach a non-equilibrium steady state where the heat flux
going through the system is time independent. All results given in
thissectionareobtainedbyaveragingabout5 × 10 7 timesteps,and
each time step is set as 0.8 fs. Free boundary condition is used to
atoms on the outer surface of the nanowires, and fixed boundary
condition is imposed on the boundary layers at two ends of the
nanowires.ThermalconductivityiscalculatedaccordingtoEq.1.34.
We first study thermal conductivity of [100] SiNWs with a cross-
section of 3 × 3 unit cells (lattice constant is 0.543 nm, eight atoms
in each unit cell) and 10 unit cells in the longitudinal direction. In
Fig. 1.6 we show the effect of the number of heat bath layers (NL)
on the thermal properties of SiNWs. Here τ = 0.1 and λ = 10
are used in NH heat bath and Langevin heat bath, respectively. A
linear temperature gradient is always observed in the interior, and
the main difference in temperature profile between different heat
bath types is the temperature jump between the heat bath layers
andinteriorlayers.WithonlyonelayerofNHheatbath,thereexists
a large temperature jump (TJ) between the heat bath layer and its
neighboring layer (Fig. 1.6a), while the temperature jump is much
smaller withone layerof Langevin heat bath (Fig. 1.6b).
This temperature jump can be explained by localized edge mode
(LEM) of phonons. With fixed boundary condition, there exists edge
mode localized at the neighboring layer next to the fixed boundary
[33]. This edge mode is actually a quite generic feature of materials
 
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