-The bumps of the Si-Si distribution at higher distances, which are marked by grey 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{}.
+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 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 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}.
+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.