The same type of interstitial may arise using random insertions.
In addition variations exist in which the displacement is only along two axes ($E_f=3.8\, eV$) or along a single axis ($E_f=3.6\, eV$) succesively approximating the tetrahedral configuration and formation energy.
-The tetrahedral and <110> dumbbel carbon interstitial configurations are stable.
+The tetrahedral and <110> dumbbell carbon interstitial configurations are stable.
The formation energies are $2.7\, eV$ and $1.8\, eV$ respectively.
Again the hexagonal one is found to be unstable.
The interstitial atom moves to the more favorable <100> dumbbell position which has a formation energy of $0.5\, eV$.
The interstitial configuration is shown in Fig. 2.
There is experimental evidence \cite{watkins76} of the existence of this configuration.
It is frequently generated and has the lowest formation energy of all the defects observed in all the simulation runs in which carbon is inserted at random positions.
+Fig. 3 schematically displays the <110> dumbbell configuration including the displacements relative to their initial positions and resulting new Si-Si and C-Si pair distances.
\begin{figure}[!h]
\begin{center}
Only bonds of the carbon interstitial atom are shown.}
\end{center}
\end{figure}
+\begin{figure}[!h]
+ \begin{center}
+ \includegraphics[width=16cm]{100-c-si-db.eps}
+ \caption{Schematic of the <100> C-Si dumbbell configuration.
+ Displacements of the atoms relative to their initial position are given.
+ The displacement of the carbon atom is relative to the initial position of atom 1.
+ New resulting Si-Si and C-Si pair distances for the atoms shown in the schematic and the distances to Si' atoms outside of the displayed region are recorded.}
+ \end{center}
+\end{figure}
%\begin{figure}[!h]
% \begin{center}
The inset shows a magnified region between 0.28 and 0.36 nm.}
\end{center}
\end{figure}
-Fig. 3 shows resulting pair correlation functions of the simulation runs targeting the observation of precipitation events.
+Fig. 4 shows resulting pair correlation functions of the simulation runs targeting the observation of precipitation events.
The contributions of Si-C and C-C pairs are presented separately each of them displaying the pair correlation for the three different volumes $V_1$, $V_2$ and $V_3$ (as explained above) exposed to carbon insertion.
Results show no signigicant difference between $V_1$ and $V_2$.
-Si-Si pairs for the case of 3000 inserted C atoms inserted into $V_2$ and a reference function for pure Si are displayed in Fig. 4.
+Si-Si pairs for the case of 3000 inserted C atoms inserted into $V_2$ and a reference function for pure Si are displayed in Fig. 5.
The amount of C-C bonds for $V_1$ are much smaller than for $V_2$ and $V_3$ since carbon atoms are spread over the total simulation volume which means that there are only 0.2 carbon atoms per silicon unit cell on average.
The first C-C peak appears at about 0.15 nm.
The peak at 0.31 nm perfectly matches the distance of two carbon atoms in the SiC lattice which in SiC is also expected for the Si-Si bonds.
After insertion of carbon atoms the Si-Si pair correlation function in fact shows non-zero values in the range of the C-C peak width while the amount of Si pairs at the regular distances at 0.24 and 0.38 nm decreases.
However no clear peak is observed and random analyses of configurations in which distances around 0.3 nm appear, i.e. visualization of such atom pairs, identify <100> C-Si dumbbells to be responsible for stretching the Si-Si next neighbour distance for low concentrations of carbon, i.e. for the $V_1$ and early stages of $V_2$ and $V_3$ simulation runs.
+This excellently agrees with the calculation for a single <100> dumbbell ($r(13)$ in Fig. 4).
For higher carbon concentrations the defect concentration is likewise increased and a considerable amount of damage is introduced into the inserted volume.
-Damage and superposition of defects generate new displacement arrangements which become hard to categorize and trace.
+Damage and superposition of defects generate new displacement arrangements which become hard to categorize and trace and obviously lead to a broader distribution of pair distances.
The slightly higher amount and intense increase of Si-Si pairs at distances smaller 0.31 nm is probably due to the Si-Si cutoff radius of 0.296 nm.
The cutoff function causes artificial forces pushing the Si atoms out of the cutoff region.
-
-Wieder durch visuelle untersuchungen -> c-c 0.31 paare durch aufeinandertreffen unterschiedlich orientierter 100 dumbbells bzw mit 110.
-C fuer sic schon besser arrangiert. Vorstellung, dass diese zuerst anordnen und spaeter dann evtl am Si ziehen ...
-Nevertheless this might indicate that carbon arranges first, then 'pulls' the Si ...
+By again visualizing the C-C atom pairs with distances of 0.31 nm concatenated, differently oriented <100> dumbbell interstitials are frequently observed.
+Since dumbbells of this type with different orientations are perpendicularly aligned the C atoms are displaced along the plane diagonal of the original lattice.
+One might now assume for the precipitation process, that C atoms are arrenged first and at a later point pull the Si atoms into the right configuration.
+In this way the hkl planes of the SiC in Si and the Si matrix would have equal orientations which is supported by experimental transmission electron microscopy data \cite{}.
+\\\\
+Ab hier weiter ...
\\\\
On the other hand the Si-C pair correlation function indicates formation of SiC bonds with an increased crystallinity for the simulation in which carbon is inserted into the whole simulation volume.
There is more carbon forming Si-C bonds than C-C bonds.
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