Environmental Engineering Reference
In-Depth Information
attempt to numerically solve the Schrodinger equation for a system
ofmanynucleiandelectronsistooformidableandnotatallfeasible
in practice. Thus, onehas to resort to approximations.
Molecular dynamics (MD) simulation is an extremely powerful
tool to handle many-body problems at atomic level based on
classical mechanics, which numerically solves Newton's equation of
motion for a many-body system. It has the advantage of simulating
realistic material with accurate many-body interatomic interaction
obtained from first-principles calculations, which was not available
butsimplifiedbythetwo-bodypotentialswithanalyticalforminthe
earlier theoretical model. The applications of MD simulation have
covered a wide range of research topics, such as liquids [1], defects
[2], fatigue [3], surface [4, 5], clusters [6, 7], and biomolecules
[8]. Therefore, MD simulation has become indispensable in today's
research ofphysical and material science.
The typical feature size that current first-principle calculations,
such as density-functional theory (DFT), can be used to explore the
thermal properties of nanostructures is on the order of several nm
[9-11]. With MD simulations, the system size under study can be
enlarged a lot. For instance, MD simulations of silicon nanowires
with length up to
μ
m [12] and cross-sectional area up to 806 nm
2
[13] have been reported. Moreover, Markussen
et al.
[9] studied
thermal properties of thin silicon nanowires with both DFT and
classicalcalculationsbasedonTersoffpotential.Theyfoundthatthe
calculation results of thermal conductance obtained from DFT and
Tersoff calculations agree within10% [9].
The validity of the classical approximation can be evaluated
based on the de Broglie thermal wavelength [14] defined as
2
π
2
mk
B
T
,
=
(1.1)
where
is Planck's constant,
m
is the atom mass,
k
B
is Boltzmann's
constant, and
T
is the temperature. The classical approximation
is valid if
<<
a
,where
a
is the nearest neighbor separation.
Under this condition, the entire system can be treated as dilute gas
model based on which the classical kinetic gas theory is formulated
[15]. In this case, each molecule can be considered as a classical
particle with a well-defined position and momentum. Moreover,