X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Fthesis%2Fmd.tex;h=4a7524ea5c966cc333d049d8028affef695dbcac;hb=dc8c4ad6e5ce70527a1e97f63e35ed31753fa0b5;hp=a51304e8e9312cc4d205ba2a9cb52777772f501e;hpb=742d9867fd5f4cfb04d5aba6f59bbdf3cbd00eb8;p=lectures%2Flatex.git

diff --git a/posic/thesis/md.tex b/posic/thesis/md.tex
index a51304e..4a7524e 100644
--- a/posic/thesis/md.tex
+++ b/posic/thesis/md.tex
@@ -264,6 +264,7 @@ Due to the limitations of short range potentials and conventional MD as discusse
 The simulation sequence and other parameters aside system temperature remain unchanged as in section \ref{subsection:initial_sims}.
 Since there is no significant difference among the $V_2$ and $V_3$ simulations only the $V_1$ and $V_2$ simulations are carried on and refered to as low carbon and high carbon concentration simulations.
 Temperatures ranging from $450\,^{\circ}\mathrm{C}$ up to $2050\,^{\circ}\mathrm{C}$ are used.
+
 A simple quality value $Q$ is introduced, which helps to estimate the progress of structural evolution.
 In bulk 3C-SiC every C atom has four next neighboured Si atoms and every Si atom four next neighboured C atoms.
 The quality could be determined by counting the amount of atoms which form bonds to four atoms of the other species.
@@ -280,7 +281,38 @@ By this, bulk 3C-SiC will still result in $Q=1$ and precipitates will also reach
 However, since the quality value does not account for bond lengthes, bond angles, crystallinity or the stacking sequence high values of $Q$ not necessarily correspond to structures close to 3C-SiC.
 Structures that look promising due to high quality values need to be further investigated by other means.
 
-Figure ... shows the radial distribution of Si-C bonds and the corresponding quality paragraphs.
+\begin{figure}[!ht]
+\begin{center}
+\includegraphics[width=12cm]{tot_pc_thesis.ps}\\
+\includegraphics[width=12cm]{tot_ba.ps}
+\end{center}
+\caption[Si-C radial distribution and quality evolution for the low concentration simulations at different elevated temperatures.]{Si-C radial distribution and quality evolution for the low concentration simulations at different elevated temperatures. All structures are cooled down to $20\,^{\circ}\mathrm{C}$. The grey line shows resulting Si-C bonds in a configuration if substitutional C in c-Si (C$_\text{sub}$) at zero temperature. Arrows in the quality plot mark the end of carbon insertion and the start of the cooling down step.}
+\label{fig:md:tot_si-c_q}
+\end{figure}
+Figure \ref{fig:md:tot_si-c_q} shows the radial distribution of Si-C bonds for different temperatures and the corresponding quality evolution as defined earlier for the low concentration simulaton, that is the $V_1$ simulation.
+The first noticeable and promising change in the Si-C radial distribution is the successive decline of the artificial peak at the Si-C cut-off distance with increasing temperature up to the point of disappearance at temperatures above $1650\,^{\circ}\mathrm{C}$.
+The system provides enough kinetic energy to affected atoms, which are able to escape the cut-off region.
+Another important observation in structural change is exemplified in the two shaded areas.
+In the grey shaded region a decrease of the peak at 0.186 nm and the bump at 0.175 nm and a concurrent increase of the peak at 0.197 nm with increasing temperature is visible.
+Similarly the peaks at 0.335 nm and 0.386 nm shrink in contrast to a new peak forming at 0.372 nm as can be seen in the yellow shaded region.
+Obviously the structure obtained from the $450\,^{\circ}\mathrm{C}$ simulations, which is dominated by the existence of \hkl<1 0 0> C-Si dumbbells transforms into a different structure with increasing simulation temperature.
+Investigations of the atomic data reveal substitutional carbon to be responsible for the new Si-C bonds.
+The peak at 0.197 nm corresponds to the distance of a substitutional carbon to the next neighboured silicon atoms.
+The one at 0.372 is the distance of the substitutional carbon atom to the second next silicon neighbour along the \hkl<1 1 0> direction.
+Comparing the radial distribution for the Si-C bonds at $2050\,^{\circ}\mathrm{C}$ to the resulting Si-C bonds in a configuration of a substitutional carbon atom in crystalline silicon excludes all possibility of doubt.
+The resulting bonds perfectly match and, thus, explain the peaks observe for the increased temperature simulations.
+To conclude, by increasing the simulation temperature, the \hkl<1 0 0> C-Si dumbbell characterized structure transforms into a structure dominated by substitutional C.
+
+This is also reflected in the qualities obtained for different temperatures.
+
+\begin{figure}[!ht]
+\begin{center}
+\includegraphics[width=12cm]{tot_pc2_thesis.ps}\\
+\includegraphics[width=12cm]{tot_pc3_thesis.ps}
+\end{center}
+\caption[C-C and Si-Si radial distribution for the low concentration simulations at different elevated temperatures.]{C-C and Si-Si radial distribution for the low concentration simulations at different elevated temperatures. All structures are cooled down to $20\,^{\circ}\mathrm{C}$.}
+\label{fig:md:tot_c-c_si-si}
+\end{figure}
 
 \subsection{Constructed 3C-SiC precipitate in crystalline silicon}