Obtained & 5495 & 5486 & 68591 & 74077\\
Expected & 5500 & 5500 & 68588 & 74088\\
Difference & -5 & -14 & 3 & -11\\
-Notation & - & $N^{\text{3C-SiC}}_{\text{Si}}$ & $N^{\text{c-Si}}_{\text{Si}}$
- & $N^{\text{total}}_{\text{Si}}$ \\
+Notation & $N^{\text{3C-SiC}}_{\text{C}}$ & $N^{\text{3C-SiC}}_{\text{Si}}$
+ & $N^{\text{c-Si}}_{\text{Si}}$ & $N^{\text{total}}_{\text{Si}}$ \\
\hline
\hline
\end{tabular}
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.
+Looking closer at higher order Si-Si peaks might even allow the guess of a slight increase of the lattice constant compared to the plain c-Si structure.
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.
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
+The absence of a compression of the c-Si surrounding 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{} in the relaxed precipitate configuration could not take place without an accompanying reduction of the lattice constant of the c-Si surrounding.
+If the total volume is assumed to be the sum of the volumes that are composed of Si atoms forming the c-Si surrounding and Si atoms involved forming the precipitate the expected increase 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}}}}
+ \frac{\frac{N^{\text{c-Si}}_{\text{Si}}}{8/a_{\text{c-Si of precipitate configuration}}}+
+ \frac{N^{\text{3C-SiC}}_{\text{Si}}}{4/a_{\text{3C-SiC of precipitate configuration}}}}
+ {\frac{N^{\text{total}}_{\text{Si}}}{8/a_{\text{plain 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.
-
-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.
-
+with the notation used in table \ref{table:md:sic_prec}.
+The lattice constant of plain c-Si at $20\,^{\circ}\mathrm{C}$ can be determined more accurately by the side lengthes of the simulation box of an equlibrated structure instead of using the radial distribution data.
+By this a value of $a_{\text{plain c-Si}}=5.439\text{ \AA}$ is obtained.
+The same lattice constant is assumed for the c-Si surrounding in the precipitate configuration $a_{\text{c-Si of precipitate configuration}}$ since peaks in the radial distribution match the ones of plain c-Si.
+Using $a_{\text{3C-SiC of precipitate configuration}}=4.34\text{ \AA}$ as observed from the radial distribution finally results in an increase of the initial volume by 0.12 \%.
+However, each side length and the total volume of the simulation box is increased by 0.20 \% and 0.61 \% respectively compared to plain c-Si at $20\,^{\circ}\mathrm{C}$.
+Since the c-Si surrounding resides in an uncompressed state the excess increase must be attributed to relaxation of strain with the strain resulting from either the compressed precipitate or the 3C-SiC/c-Si interface region.
+This also explains the possibly identified slight increase of the c-Si lattice constant in the surrounding as mentioned earlier.
+As the pressure is set to zero the free energy is minimized with respect to the volume enabled by the Berendsen barostat algorithm.
+Apparently the minimized structure with respect to the volume is a configuration of a small compressively stressed precipitate and a large amount of slightly stretched c-Si in the surrounding.
+
+One way to describe interfaces is to To describe the interface
Surface energy ... quench to 0K!
-Now let's see, whether annealing will lead to some energetically more favorable configurations.
+Since interface region is constructed and not neccesarily corresponds to the energetically most favorable layout we will now try hard to improve this ...
+Let's see, whether annealing will lead to some energetically more favorable configurations.
\subsection{Simulations at temperatures exceeding the silicon melting point}
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