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\\
+Notation & - & $N^{\text{3C-SiC}}_{\text{Si}}$ & $N^{\text{c-Si}}_{\text{Si}}$
+ & $N^{\text{total}}_{\text{Si}}$ \\
\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.
+A new Si-Si peak arises at 0.307 nm, which 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 marked by the green arrows can be explained in the same manner.
+They correspond to the fourth and sixth next neighbour distance in 3C-SiC.
+It is easily identifiable how these C-C peaks, which imply Si pairs at same distances inside the precipitate, contribute to the bumps observed in the Si-Si distribution.
+The Si-Si and C-C peak at 0.307 nm enables the determination of the lattic constant of the embedded 3C-SiC precipitate.
+A lattice constant of 4.34 \AA{} compared to 4.36 \AA{} for bulk 3C-SiC is obtained.
+This is in accordance with the peak of Si-C pairs at a distance of 0.188 nm.
+Thus, the precipitate structure is slightly compressed compared to the bulk phase.
+This is a quite surprising result since due to the finite size of the c-Si surrounding a non-negligible impact of the precipitate on the materializing c-Si lattice constant especially near the precipitate could be assumed.
+However, it seems that the size of the c-Si host matrix is chosen large enough to even find the precipitate in a compressed state.
+
+The fact that the lattice constant of the c-Si surrounding is unchanged is due to the possibility of the system to change its volume.
+Otherwise the increase of the lattice constant of the precipitate of roughly 4.31 \AA{} in the beginning up to 4.34 \AA{} could not take place without an accompanying reduction of the lattice constant of the c-Si surrounding.
+The expected increase in volume can be calculated by
+\begin{equation}
+ \frac{V}{V_0}=
+ \frac{\frac{N^{\text{c-Si}}_{\text{Si}}}{8/a_{\text{c-Si}}}+
+ \frac{N^{\text{3C-SiC}}_{\text{Si}}}{4/a_{\text{3C-SiC}}}}
+ {\frac{N^{\text{total}}_{\text{Si}}}{8/a_{\text{c-Si}}}}
+\end{equation}
+with the notation used in table \ref{table:md:sic_prec} and $a$ being the lattice constants at $20\,^{\circ}\mathrm{C}$ of the respective material.
-PC and energy of that one.
+Inserting the obtained amounts of atoms of table \ref{table:md:sic_prec} results in an increase of the initial volume by only 0.3 \%.
+
+However, each side length and the total volume of the simulation box is increased by 0.4 \% and 1.2 \% respectively of the initial state.
+
+Surface energy ... quench to 0K!
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.
+
+\subsection{Todo}
+
+{\color{red}TODO: self-guided MD!}
+
+{\color{red}TODO: other approaches!}
+
+{\color{red}TODO: ART MD?}
+
projects / lectures / latex.git / blobdiff