Environmental Engineering Reference
In-Depth Information
hydrocarbon systems [23], which allows for bond breaking and
creation with appropriate changes in atomic hybridization. The
Brenner potential is later improved to give a better description of
physical properties for hydrocarbon molecules [24].
1.2.3
Mixing Rule
The force field parameters are usually developed for individual
element only. In addition to single element materials, alloys offer a
continuously variable system with a wide range of crystal lattices
and band gaps, leading to various physical and chemical properties.
Forinstance,SiliconandGermaniumcanformacontinuousseriesof
substitutionalsolid.Thecontinuousvariationintheenergybandgap
in Si
1
−
x
Ge
x
provides challenging opportunities for Si optoelectronic
because it potentially allows emission and detection of the photons
in large wavelength range. Recently, single crystalline Si
1
−
x
Ge
x
NWs have been successfully grown. The experimental synthesis
offers intriguing opportunities for the development of Si
1
−
x
Ge
x
based nano thermoelectric devices. To model the interatomic
interaction in multi-component system, the force field parameters
areapproximatedbythecombinationofsingle-elementparameters.
The most frequently used mixing rules are the arithmetic average
(Lorentz rule) for lengthparameter
σ
ij
=
σ
i
+
σ
j
2
,
(1.13)
and the geometric average (Berthelot rule) for energy parameter
ε
ij
=
√
ε
i
ε
j
.
(1.14)
1.3 Integration of the Equations of Motion
Molecular dynamics simulation specifies how the positions and
velocities of the particles in the system vary with time. This can be
generatedbyintegratingNewton'slawsofmotion.Inthesimulation,
the force on each particle will change whenever the particle
and/or its neighbors change their positions. Under the influence
of a realistic potential, the motions of all the particles are coupled
