Furthermore these investigations might establish the prediction of conditions necessary for the simulation of the precipitation process.
To construct a spherical and topotactically aligned 3C-SiC precipitate in c-Si, the approach illustrated in the following is applied.
-A total simulation volume $V$ consisting of 21 unit cells of c-Si in each direction is used.
+A total simulation volume $V$ consisting of 21 unit cells of c-Si in each direction is created.
To obtain a minimal and stable precipitate 5500 carbon atoms are considered necessary.
+This corresponds to a spherical 3C-SiC precipitate with a radius of approximately 3 nm.
The initial precipitate configuration is constructed in two steps.
In the first step the surrounding silicon matrix is created.
This is realized by just skipping the generation of silicon atoms inside a sphere of radius $x$, which is the first unknown variable.
\hline
& C in 3C-SiC & Si in 3C-SiC & Si in c-Si surrounding & total amount of Si\\
\hline
-Expected & 5500 & 5500 & 68588 & 74088\\
Obtained & 5495 & 5486 & 68591 & 74077\\
-Difference & 5 & 14 & -3 & 11\\
+Expected & 5500 & 5500 & 68588 & 74088\\
+Difference & -5 & -14 & 3 & -11\\
\hline
\hline
\end{tabular}
After the initial configuration is constructed some of the atoms located at the 3C-SiC/c-Si interface show small distances, which results in high repulsive forces acting on the atoms.
Thus, the system is equilibrated using strong coupling to the heat bath, which is set to be $20\,^{\circ}\mathrm{C}$.
-Once the main part of th excess energy is carried out previous settings for the Berendsen thermostat are restored and the system is relaxed for another 10 ps.
+Once the main part of the excess energy is carried out previous settings for the Berendsen thermostat are restored and the system is relaxed for another 10 ps.
+
+\begin{figure}[!ht]
+\begin{center}
+\includegraphics[width=12cm]{pc_0.ps}
+\end{center}
+\caption[Radial distribution of a 3C-SiC precipitate embeeded in c-Si at $20\,^{\circ}\mathrm{C}$.]{Radial distribution of a 3C-SiC precipitate embeeded in c-Si at $20\,^{\circ}\mathrm{C}$. The Si-Si radial distribution of plain c-Si is plotted for comparison. Green arrows mark bumps in the Si-Si distribution of the precipitate configuration, which do not exist in plain c-Si.}
+\label{fig:md:pc_sic-prec}
+\end{figure}
+Figure \ref{fig:md:pc_sic-prec} shows the radial distribution of the obtained precipitate configuration.
+The Si-Si radial distribution for both, plain c-Si and the precipitate configuration show a maximum at a distance of 0.235 nm, which is the distance of next neighboured Si atoms in c-Si.
+Although no significant change of the lattice constant of the surrounding c-Si matrix was assumed, surprisingly there is no change at all within observational accuracy.
+Each side length and the total volume of the simulation box is increased by 0.4 \% and 1.2 \% respectively of the initial state.
+Indeed an increase of the total volume is expected due to the slightly lower Si density of 3C-SiC compared to c-Si.
+The expected increase in volume can be calculated by
+\begin{equation}
+I_V=\frac{N^{\text{c-Si}}_{\text{Si}}/n_{\text{Si}}^{\text{c-Si}}+
+ N^{\text{3C-SiC}}_{\text{Si}}/n_{\text{Si}}^{\text{3C-SiC}}}
+ {N^{\text{c-Si and 3C-SiC}}_{\text{Si}}/n_{\text{Si}}^{\text{c-Si}}}
+\end{equation}
+with $N_{\text{Si}}$ and $n_{\text{Si}}$ being the number of Si atoms and the Si density respectively of the corresponding material.
+Due to a slightly lower Si density of 3C-SiC compared to c-Si an increase of x \% of the total volume would be expected for precipitate with a radius of 3 nm embedded in
+
+Calc expected increase due to Si density mismatch ...
+Obviously the surrounding matrix is chosen big enough to exclude size effects ...
+Nice, since obviously matrix is big enough to exclude size effects in the system in which pbc are applied, we can consider it single precipitate in a infinite Si matrix.
+A new peak for the silicon pairs arises at 0.307 nm.
+It is identical to the peak of the C-C distribution around that value.
+It corresponds to second next neighbours in 3C-SiC, which applies for Si as well as C pairs.
+The bumps of the Si-Si distribution at higher distances, which are marked by green arrows and do not exist in plain c-Si, can be explained in the same manner.
+They correspond to the fourth and sixth next neighbour in 3C-SiC.
+Again, these peaks apply to Si and C pairs and indeed it is easily identifiale how the C-C peaks at contribute to the bumps observed in the Si-Si distribution.
+
+4.34 \AA{} compared to 4.36 \AA{}.
-PC and energy of that one.
+New lattice constant
+Surface energy
Now let's see, whether annealing will lead to some energetically more favorable configurations.
-Estimate surface energy ...
\subsection{Simulations at temperatures exceeding the silicon melting point}
LL Cool J is hot as hell!
+
+A different simulation volume and refined amount as well as shape of insertion volume for the C atoms, to stay compareable to the results gained in the latter section, is used throughout all following simulations.
+
+{\color{red}TODO: ART MD?}
+
projects / lectures / latex.git / blobdiff