\chapter{Silicon carbide precipitation simulations}
+\label{chapter:md}
The molecular dynamics (MD) technique is used to gain insight into the behavior of carbon existing in different concentrations in crystalline silicon on the microscopic level at finite temperatures.
Both, quantum-mechanical and classical potential molecular dynamics simulations are performed.
Molecular dynamics simulations of a single, two and ten carbon atoms in $3\times 3\times 3$ unit cells of crytsalline silicon are performed.
+{\color{red}Todo: ... in progress ...}
+
\section{Classical potential MD simulations}
In contrast to the quantum-mechanical MD simulations the developed classical potential MD code is able to do constant pressure simulations using the Berendsen barostat.
Figure \ref{fig:md:95_long_time_v1} shows the evolution in time of the radial distribution for Si-C and C-C pairs for a low C concentration simulation.
Differences are observed for both types of atom pairs indeed indicating proceeding structural changes even well beyond 100 ps of simulation time.
Peaks attributed to the existence of substitutional C increase and become more distinct.
+This finding complies with the predicted increase of quality evolution as explained earlier.
+More and more C forms tetrahedral bonds to four Si neighbours occupying vacant Si sites.
However, no increase of the amount of total C-C pairs within the observed region can be identified.
-Carbon, whether substitutional or as a dumbbell does not agglomerate within the simulated period of time.
+Carbon, whether substitutional or as a dumbbell does not agglomerate within the simulated period of time visible by the unchanging area beneath the graphs.
Figure \ref{fig:md:95_long_time_v2} shows the evolution in time of the radial distribution for Si-C and C-C pairs for a high C concentration simulation.
There are only small changes identifiable.
-Explain more ...
+A slight increase of the Si-C peak at approximately 0.36 nm attributed to the distance of substitutional C and the next but one Si atom along \hkl<1 1 0> is observed.
+In the same time the C-C peak at approximately 0.32 nm corresponding to the distance of two C atoms interconnected by a Si atom along \hkl<1 1 0> slightly decreases.
+Obviously the system preferes a slight increase of isolated substitutional C at the expense of incoherent C-Si-C precipitate configurations, which at a first glance actually appear as promising configurations in the precipitation event.
+On second thoughts however, this process of splitting a C atom out of this structure is considered necessary in order to allow for the rearrangement of C atoms on substitutional lattice sites on the one hand and for C diffusion otherwise, which is needed to end up in a structure, in which one of the two fcc sublattices is composed out of carbon only.
-For both, high and low concentration simulations the radial distribution converges as can be seen by the nearly identical graphs for the last two points in time.
+For both, high and low concentration simulations the radial distribution converges as can be seen by the nearly identical graphs of the two most advanced configurations.
Changes exist ... bridge to results after cooling down to 20 degree C.
-{\color{red}Todo: Cooling down to 20 degree C and compare.}
+{\color{red}Todo: Cooling down to $20\,^{\circ}\mathrm{C}$ by $1\,^{\circ}\mathrm{C/s}$ in progress.}
{\color{red}Todo: Remember NVE simulations (prevent melting).}
{\color{red}Todo: other approaches?}
{\color{red}Todo: ART MD?\\
-How about forcing a migration of a $V_2$ configuration to a constructed prec configuration, detrmine the maximum saddle point and let the simulation run?
+How about forcing a migration of a $V_2$ configuration to a constructed prec configuration, determine the saddle point configuration and continue the simulation from this configuration?
}
\section{Conclusions concerning the SiC conversion mechanism}
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