X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=blobdiff_plain;f=posic%2Fthesis%2Fmd.tex;h=8860ce2ccced889039d3bf8a39f1f356a373a9fa;hb=2d8c0065529a76ac15b8f7ac4a25408d8bf11ec8;hp=2318a656d4accf8495570c45fa518d70a088fa39;hpb=41987f78ca9b9ab7ee0f4b31fd3d5596cfa385d6;p=lectures%2Flatex.git

diff --git a/posic/thesis/md.tex b/posic/thesis/md.tex
index 2318a65..8860ce2 100644
--- a/posic/thesis/md.tex
+++ b/posic/thesis/md.tex
@@ -264,15 +264,48 @@ 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 quality value $Q$ is introduced, which is defined as
+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.
+However, the aim of the simulation on hand is to reproduce the formation of a 3C-SiC precipitate embedded in c-Si.
+The amount of Si atoms and, thus, the amount of Si atoms remaining in the silicon diamond lattice is much higher than the amount of inserted C atoms.
+Thus, counting the atoms, which exhibit proper coordination is limited to the C atoms.
+The quality value is defined to be
 \begin{equation}
 Q = \frac{\text{Amount of C atoms with 4 next neighboured Si atoms}}
          {\text{Total amount of C atoms}} \text{ .}
 \label{eq:md:qdef}
 \end{equation}
-In 3C-SiC every C atom has four next neighboured Si atoms resulting in $Q=1$.
+By this, bulk 3C-SiC will still result in $Q=1$ and precipitates will also reach values close to one.
+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 $20\,^{\circ}\mathrm{C}$. 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.
+
+Cut-off vanisches, thats a nice win ...
+
+Further explanation of PC ...
+
+100 to sub configurations ...
+
+This is 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}