-\documentclass[12pt,a4paper,twoside]{article}
+\documentclass[12pt,a4paper,oneside]{article}
\usepackage{verbatim}
\usepackage[english]{babel}
\newpage
\section{Model}
-A model describing the formation of nanometric selforganized ordered amorphous $SiC_x$ inclusions was introduced in \cite{1}. Figure \ref{1} shows the evolution into ordered lamellae with increasing dose.
+A model describing the formation of nanometric selforganized ordered amorphous $SiC_x$ inclusions was introduced in \cite{1}\cite{2}. Figure \ref{1} shows the evolution into ordered lamellae with increasing dose.
%\begin{figure}[!h]
%\begin{center}
\newpage
\section{Simulation}
-Before discussing the implementation some assumptions and approximations have to be done. Figure \ref{2} shows the stopping powers and carbon concentration profile calculated by TRIM. The depth region we are interested in is between $0-300 \, nm$, the region between surface of the target and start of the continuous amorphous $SiC_x$ layer (from now on called simulation window), where the nuclear stopping power and the implantation profile can be approximated by a linear function of depth. Furthermore the probability of amorphization is assumed to be proportional to the nuclear stopping power. A local probability of amorphization somewhere in the target is composed of three parts, the ballistic, carbon-induced and stress-induced amorphization. The ballistic amorphization is proportional to the nuclear stopping power, as mentioned before. the carbon-induced amorphization is a linear function of the local carbon concentration. the stress-induced amorphization is proportional to the compressive stress apllied by the amorphous neighbours. Thus the probability of a crystalline volume getting amorphous can be calculated as follows,
+Before discussing the implementation some assumptions and approximations have to be done. Figure \ref{2} shows the stopping powers and carbon concentration profile calculated by TRIM. The depth region we are interested in is between $0-300 \, nm$, the region between the surface of the target and the beginning of the continuous amorphous $SiC_x$ layer (from now on called simulation window), where the nuclear stopping power and the implantation profile can be approximated by a linear function of depth. Furthermore the probability of amorphization is assumed to be proportional to the nuclear stopping power. A local probability of amorphization somewhere in the target is composed of three parts, the ballistic, carbon-induced and stress-induced amorphization. The ballistic amorphization is proportional to the nuclear stopping power, as mentioned before. The carbon-induced amorphization is a linear function of the local carbon concentration. The stress-induced amorphization is proportional to the compressive stress apllied by the amorphous neighbours. Thus the probability of a crystalline volume getting amorphous can be calculated as follows,
\[
p_{c \rightarrow a} = b_{ap} + a_{cp} \times c^{local}_{carbon} + \sum_{amorphous \, neighbours} \frac{a_{ap} \times c_{carbon}}{distance^2}
\]
-with $b_{ap}$, $a_{cp}$ and $a_{ap}$ being parameters of the simulation to weight the three diffrent ways of amorphization. The probability of an amorphous volume turning crystalline should behave contrary to $p_{c \rightarrow a}$ and thus is assumed to $p_{a \rightarrow c} = 1 - p_{c \rightarrow a}$.
+with $b_{ap}$, $a_{cp}$ and $a_{ap}$ being parameters of the simulation to weight the three different ways of amorphization. The probability of an amorphous volume turning crystalline should behave contrary to $p_{c \rightarrow a}$ and thus is assumed to $p_{a \rightarrow c} = 1 - p_{c \rightarrow a}$.
-For the simulation, the target is devided into $50 \times 50 \times 100$ volumes with a side length of $3 \, nm$. Each of it has a state (crystalline/amorphous) and keeps the local carbon concentration. The simulation algorithm consists of three parts, the amorphization/recrystallization process, the carbon-implanting process and finaly the diffusion process.
+Figure \ref{3} shows the target devided into $64 \times 64 \times 100$ volumes with a side length of $3 \, nm$. Each of it has a state (crystalline/amorphous) and keeps the local carbon concentration. The simulation algorithm consists of three parts, the amorphization/recrystallization process, the carbon-implanting process and finaly the diffusion process.
In the first part random coordinates according to the nuclear stopping power are computed to specify the volume which is hit by an implanted carbon ion. After calculating the local probability of amorphization, another random number decides about the state of the volume. This step is looped for the average hit per ion in the simulation window, counted by TRIM collision data.
\section{Results}
+
\section{Conclusion}
\newpage
\begin{figure}[!h]
\begin{center}
-\includegraphics[width=13cm]{model1_e.eps}
+\includegraphics[width=17cm]{model1_e.eps}
\caption[Rough model explaining the selforganization of amorphous $SiC_x$ precipitates and the evolution into ordered lamellae with increasing dose]{} \label{1}
\end{center}
\end{figure}
\begin{figure}[!h]
\begin{center}
-\includegraphics[width=10cm]{2pTRIM180C.eps}
+\includegraphics[width=14cm]{2pTRIM180C.eps}
\caption[Stopping powers and concentration profile calculated by TRIM]{} \label{2}
\end{center}
\end{figure}
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=15cm]{gitter_e.eps}
+\caption[Target devided into $64 \times 64 \times 100$ volumes with a side length of $3 \, nm$ holding state and carbon concentration]{} \label{3}
+\end{center}
+\end{figure}
+
\end{document}
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