todos, mainly short caption fixes

diff --git a/posic/thesis/ack.tex b/posic/thesis/ack.tex
index 9246d42ea7ab5f194a11e59ae445312b3cb411db..fbd816223999c0d90cb698d355c471139b5c7a20 100644 (file)
--- a/posic/thesis/ack.tex
+++ b/posic/thesis/ack.tex
@@ -22,10 +22,8 @@ The present thesis would not have been possible without her assistance and mento
 I am greatly thankful for the possibility to repeatedly visit the theory group in Paderborn.
 In this context, Dr. Simone Sanna is acknowledged for respective technical support and Michael Weinl, doctoral student of Prof. J\"org K. N. Lindner back then, for accomodation.
 
 I am greatly thankful for the possibility to repeatedly visit the theory group in Paderborn.
 In this context, Dr. Simone Sanna is acknowledged for respective technical support and Michael Weinl, doctoral student of Prof. J\"org K. N. Lindner back then, for accomodation.
 

-{\color{red}
-I am grateful to Priv.-Doz. Dr. habil. Volker Eyert for writing one of the certificates of this work.
-Furthermore, his lectures on computational physics and the electronic structure of materials, which I attented during my academic studies, influenced me to pursue scientific research in the field of computational physics.
-}
+I am grateful to Priv.-Doz. Dr. habil. Volker Eyert for {\color{red}writing one of the certificates of this work.
+Furthermore,} his lectures on computational physics and the electronic structure of materials, which I attented during my academic studies, influenced me to pursue scientific research in the field of computational physics.

 
 One more time, I would like to thank Prof. Dr. Bernd Stritzker for another two-month position as a member of his reaearch staff and various long-term employments as a reasearch assistant, which not only ensured a minimum of financial supply but also involved tutorships in the field of solid state physics that could be carried out in a more or less free and autonomous way.
 
 
 One more time, I would like to thank Prof. Dr. Bernd Stritzker for another two-month position as a member of his reaearch staff and various long-term employments as a reasearch assistant, which not only ensured a minimum of financial supply but also involved tutorships in the field of solid state physics that could be carried out in a more or less free and autonomous way.
 

diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex
index 2675ca07aa1cadbcf9258beba8f048eab2648442..ffe6942e6ebbe0a39b5801064eede01937390e58 100644 (file)
--- a/posic/thesis/defects.tex
+++ b/posic/thesis/defects.tex
@@ -18,6 +18,7 @@ Respective results allow to draw conclusions concerning the SiC precipitation in
 
 For investigating the \si{} structures a Si atom is inserted or removed according to Fig. \ref{fig:basics:ins_pos} of section \ref{section:basics:defects}.
 The formation energies of \si{} configurations are listed in Table \ref{tab:defects:si_self} for both methods used in this work as well as results obtained by other {\em ab initio} studies \cite{al-mushadani03,leung99}.
 
 For investigating the \si{} structures a Si atom is inserted or removed according to Fig. \ref{fig:basics:ins_pos} of section \ref{section:basics:defects}.
 The formation energies of \si{} configurations are listed in Table \ref{tab:defects:si_self} for both methods used in this work as well as results obtained by other {\em ab initio} studies \cite{al-mushadani03,leung99}.

+\bibpunct{}{}{,}{n}{}{}

 \begin{table}[tp]
 \begin{center}
 \begin{tabular}{l c c c c c}
 \begin{table}[tp]
 \begin{center}
 \begin{tabular}{l c c c c c}


@@ -31,7 +32,6 @@ The formation energies of \si{} configurations are listed in Table \ref{tab:defe
 \multicolumn{6}{c}{Other {\em ab initio} studies} \\
 Ref. \cite{al-mushadani03} & 3.40 & 3.45 & - & - & 3.53 \\
 Ref. \cite{leung99} & 3.31 & 3.31 & 3.43 & - & - \\
 \multicolumn{6}{c}{Other {\em ab initio} studies} \\
 Ref. \cite{al-mushadani03} & 3.40 & 3.45 & - & - & 3.53 \\
 Ref. \cite{leung99} & 3.31 & 3.31 & 3.43 & - & - \\

-% todo cite without []

 \hline
 \hline
 \end{tabular}
 \hline
 \hline
 \end{tabular}


@@ -39,6 +39,7 @@ Ref. \cite{leung99} & 3.31 & 3.31 & 3.43 & - & - \\
 \caption[Formation energies of Si self-interstitials in crystalline Si determined by classical potential MD and DFT calculations.]{Formation energies of Si self-interstitials in crystalline Si determined by classical potential MD and DFT calculations. The formation energies are given in eV. T denotes the tetrahedral and H the hexagonal interstitial configuration. V corresponds to the vacancy configuration. Dumbbell configurations are abbreviated by DB. Formation energies for unstable configurations are marked by an asterisk and determined by using the low kinetic energy configuration shortly before the relaxation into the more favorable configuration starts.}
 \label{tab:defects:si_self}
 \end{table}
 \caption[Formation energies of Si self-interstitials in crystalline Si determined by classical potential MD and DFT calculations.]{Formation energies of Si self-interstitials in crystalline Si determined by classical potential MD and DFT calculations. The formation energies are given in eV. T denotes the tetrahedral and H the hexagonal interstitial configuration. V corresponds to the vacancy configuration. Dumbbell configurations are abbreviated by DB. Formation energies for unstable configurations are marked by an asterisk and determined by using the low kinetic energy configuration shortly before the relaxation into the more favorable configuration starts.}
 \label{tab:defects:si_self}
 \end{table}

+\bibpunct{[}{]}{,}{n}{}{}

 \begin{figure}[tp]
 \begin{center}
 \begin{flushleft}
 \begin{figure}[tp]
 \begin{center}
 \begin{flushleft}


@@ -119,8 +120,7 @@ The respective relaxation energetics are likewise plotted and look similar to th
 In fact, the same type of interstitial arises using random insertions.
 In addition, variations exist, in which the displacement is only along two \hkl<1 0 0> axes ($E_\text{f}=3.8\,\text{eV}$) or along a single \hkl<1 0 0> axes ($E_\text{f}=3.6\,\text{eV}$) successively approximating the tetdrahedral configuration and formation energy.
 The existence of these local minima located near the tetrahedral configuration seems to be an artifact of the analytical potential without physical authenticity revealing fundamental problems of analytical potential models for describing defect structures.
 In fact, the same type of interstitial arises using random insertions.
 In addition, variations exist, in which the displacement is only along two \hkl<1 0 0> axes ($E_\text{f}=3.8\,\text{eV}$) or along a single \hkl<1 0 0> axes ($E_\text{f}=3.6\,\text{eV}$) successively approximating the tetdrahedral configuration and formation energy.
 The existence of these local minima located near the tetrahedral configuration seems to be an artifact of the analytical potential without physical authenticity revealing fundamental problems of analytical potential models for describing defect structures.

-% todo - energy barrier of what ?!?!
-However, the energy barrier is small.
+However, the energy barrier required for a transition into the tetrahedral configuration is small.

 \begin{figure}[tp]
 \begin{center}
 \includegraphics[width=0.7\textwidth]{nhex_tet.ps}
 \begin{figure}[tp]
 \begin{center}
 \includegraphics[width=0.7\textwidth]{nhex_tet.ps}


@@ -394,7 +394,7 @@ In the same figure the Kohn-Sham levels are shown.
 There is no magnetization density.
 An acceptor level arises at approximately $E_v+0.35\,\text{eV}$ while a band gap of about \unit[0.75]{eV} can be estimated from the Kohn-Sham level diagram for plain Si.
 However, strictly speaking, the Kohn-Sham levels and orbitals do not have a direct physical meaning and, thus, these values have to be taken with care.
 There is no magnetization density.
 An acceptor level arises at approximately $E_v+0.35\,\text{eV}$ while a band gap of about \unit[0.75]{eV} can be estimated from the Kohn-Sham level diagram for plain Si.
 However, strictly speaking, the Kohn-Sham levels and orbitals do not have a direct physical meaning and, thus, these values have to be taken with care.

-% todo band gap problem
+% todo - band gap problem, skip it?

 
 \subsection{Bond-centered interstitial configuration}
 \label{subsection:bc}
 
 \subsection{Bond-centered interstitial configuration}
 \label{subsection:bc}


@@ -589,7 +589,7 @@ The bond to the face-centered Si atom at the bottom of the unit cell breaks and
 \begin{center}
 \includegraphics[width=0.7\textwidth]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
 \end{center}
 \begin{center}
 \includegraphics[width=0.7\textwidth]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
 \end{center}

-\caption[Migration barrier and structures of the \hkl<0 0 -1> DB (left) to BC (right) transition.]{Migration barrier and structures of the \hkl<0 0 -1> DB (left) to BC (right) transition. Bonds of the C atom are illustrated by blue lines.}
+\caption[Migration barrier and structures of the {\hkl[0 0 -1]} DB to BC transition.]{Migration barrier and structures of the \hkl<0 0 -1> DB (left) to BC (right) transition. Bonds of the C atom are illustrated by blue lines.}

 \label{fig:defects:00-1_001_mig}
 \end{figure}
 In Fig. \ref{fig:defects:00-1_001_mig} results of the \hkl<0 0 -1> to \hkl<0 0 1> migration fully described by the migration of the \hkl<0 0 -1> to the BC configuration is displayed.
 \label{fig:defects:00-1_001_mig}
 \end{figure}
 In Fig. \ref{fig:defects:00-1_001_mig} results of the \hkl<0 0 -1> to \hkl<0 0 1> migration fully described by the migration of the \hkl<0 0 -1> to the BC configuration is displayed.


@@ -601,8 +601,7 @@ In a second process \unit[0.25]{eV} of energy are needed for the system to rever
 \begin{center}
 \includegraphics[width=0.7\textwidth]{00-1_0-10_vasp_s.ps}
 \end{center}
 \begin{center}
 \includegraphics[width=0.7\textwidth]{00-1_0-10_vasp_s.ps}
 \end{center}

-\caption[Migration barrier and structures of the \hkl<0 0 -1> DB (left) to the \hkl<0 -1 0> DB (right) transition.]{Migration barrier and structures of the \hkl[0 0 -1] DB (left) to the \hkl[0 -1 0] DB (right) transition. Bonds of the C atom are illustrated by blue lines.}
-% todo read above caption! enable [] hkls in short caption
+\caption[Migration barrier and structures of the {\hkl[0 0 -1]} DB to the {\hkl[0 -1 0]} DB transition.]{Migration barrier and structures of the \hkl[0 0 -1] DB (left) to the \hkl[0 -1 0] DB (right) transition. Bonds of the C atom are illustrated by blue lines.}

 \label{fig:defects:00-1_0-10_mig}
 \end{figure}
 Fig. \ref{fig:defects:00-1_0-10_mig} shows the migration barrier and structures of the \ci{} \hkl<0 0 -1> to \hkl<0 -1 0> DB transition.
 \label{fig:defects:00-1_0-10_mig}
 \end{figure}
 Fig. \ref{fig:defects:00-1_0-10_mig} shows the migration barrier and structures of the \ci{} \hkl<0 0 -1> to \hkl<0 -1 0> DB transition.


@@ -612,7 +611,7 @@ The resulting migration barrier of approximately \unit[0.9]{eV} is very close to
 \begin{center}
 \includegraphics[width=0.7\textwidth]{00-1_ip0-10_nosym_sp_fullct_vasp_s.ps}
 \end{center}
 \begin{center}
 \includegraphics[width=0.7\textwidth]{00-1_ip0-10_nosym_sp_fullct_vasp_s.ps}
 \end{center}

-\caption[Reorientation barrier and structures of the \hkl<0 0 -1> DB (left) to the \hkl<0 -1 0> DB (right) transition in place.]{Reorientation barrier and structures of the \hkl<0 0 -1> DB (left) to the \hkl<0 -1 0> DB (right) transition in place. Bonds of the carbon atoms are illustrated by blue lines.}
+\caption[Reorientation barrier and structures of the {\hkl[0 0 -1]} DB to the {\hkl[0 -1 0]} DB transition in place.]{Reorientation barrier and structures of the \hkl[0 0 -1] DB (left) to the \hkl[0 -1 0] DB (right) transition in place. Bonds of the carbon atoms are illustrated by blue lines.}

 \label{fig:defects:00-1_0-10_ip_mig}
 \end{figure}
 The third migration path, in which the DB is changing its orientation, is shown in Fig. \ref{fig:defects:00-1_0-10_ip_mig}.
 \label{fig:defects:00-1_0-10_ip_mig}
 \end{figure}
 The third migration path, in which the DB is changing its orientation, is shown in Fig. \ref{fig:defects:00-1_0-10_ip_mig}.


@@ -639,7 +638,7 @@ In addition, it is finally shown that the BC configuration, for which spin polar
 %\includegraphics[width=2.2cm]{vasp_mig/0-10_b.eps}
 %\end{picture}
 \end{center}
 %\includegraphics[width=2.2cm]{vasp_mig/0-10_b.eps}
 %\end{picture}
 \end{center}

-\caption{Migration barriers of the \hkl<1 1 0> DB to BC (blue), \hkl<0 0 -1> (green) and \hkl<0 -1 0> (in place, red) C-Si DB transition.}
+\caption[{Migration barriers of the \hkl[1 1 0] DB to BC, \hkl[0 0 -1] and \hkl[0 -1 0] (in place) C-Si DB transition.}]{Migration barriers of the \hkl[1 1 0] DB to BC (blue), \hkl[0 0 -1] (green) and \hkl[0 -1 0] (in place, red) C-Si DB transition.}

 \label{fig:defects:110_mig_vasp}
 \end{figure}
 Further migration pathways, in particular those occupying other defect configurations than the \hkl<1 0 0>-type either as a transition state or a final or starting configuration, are totally conceivable.
 \label{fig:defects:110_mig_vasp}
 \end{figure}
 Further migration pathways, in particular those occupying other defect configurations than the \hkl<1 0 0>-type either as a transition state or a final or starting configuration, are totally conceivable.


@@ -726,13 +725,13 @@ For this reason, the assumption that C diffusion and reorientation is achieved b
 %\includegraphics[height=2.2cm]{010_arrow.eps}
 %\end{picture}
 \end{center}
 %\includegraphics[height=2.2cm]{010_arrow.eps}
 %\end{picture}
 \end{center}

-\caption[Migration barrier and structures of the \ci{} BC to \hkl<0 0 -1> DB transition using the classical EA potential.]{Migration barrier and structures of the \ci{} BC to \hkl[0 0 -1] DB transition using the classical EA potential. Two migration pathways are obtained for different time constants of the Berendsen thermostat. The lowest activation energy is \unit[2.2]{eV}.}
+\caption[Migration barrier and structures of the \ci{} BC to {\hkl[0 0 -1]} DB transition using the classical EA potential.]{Migration barrier and structures of the \ci{} BC to \hkl[0 0 -1] DB transition using the classical EA potential. Two migration pathways are obtained for different time constants of the Berendsen thermostat. The lowest activation energy is \unit[2.2]{eV}.}

 \label{fig:defects:cp_bc_00-1_mig}
 % red: ./visualize -w 640 -h 480 -d saves/c_in_si_mig_bc_00-1_s20 -nll -0.56 -0.56 -0.7 -fur 0.2 0.2 0.0 -c 0.75 -1.25 -0.25 -L -0.25 -0.25 -0.25 -r 0.6 -B 0.1
 % blue: ./visualize -w 640 -h 480 -d saves/c_in_si_mig_bc_00-1_s20_tr100/ -nll -0.56 -0.56 -0.7 -fur 0.2 0.2 0.0 -c 0.0 -0.25 1.0 -L 0.0 -0.25 -0.25 -r 0.6 -B 0.1
 \end{figure}
 \label{fig:defects:cp_bc_00-1_mig}
 % red: ./visualize -w 640 -h 480 -d saves/c_in_si_mig_bc_00-1_s20 -nll -0.56 -0.56 -0.7 -fur 0.2 0.2 0.0 -c 0.75 -1.25 -0.25 -L -0.25 -0.25 -0.25 -r 0.6 -B 0.1
 % blue: ./visualize -w 640 -h 480 -d saves/c_in_si_mig_bc_00-1_s20_tr100/ -nll -0.56 -0.56 -0.7 -fur 0.2 0.2 0.0 -c 0.0 -0.25 1.0 -L 0.0 -0.25 -0.25 -r 0.6 -B 0.1
 \end{figure}

-Fig. \ref{fig:defects:cp_bc_00-1_mig} shows the evolution of structure and energy along the \ci{} BC to \hkl<0 0 -1> DB transition.
-Since the \ci{} BC configuration is unstable relaxing into the \hkl<1 1 0> DB configuration within this potential, the low kinetic energy state is used as a starting configuration.
+Fig. \ref{fig:defects:cp_bc_00-1_mig} shows the evolution of structure and energy along the \ci{} BC to \hkl[0 0 -1] DB transition.
+Since the \ci{} BC configuration is unstable relaxing into the \hkl[1 1 0] DB configuration within this potential, the low kinetic energy state is used as a starting configuration.

 Two different pathways are obtained for different time constants of the Berendse
 n thermostat.
 With a time constant of \unit[1]{fs} the C atom resides in the \hkl(1 1 0) plane
 Two different pathways are obtained for different time constants of the Berendse
 n thermostat.
 With a time constant of \unit[1]{fs} the C atom resides in the \hkl(1 1 0) plane


@@ -740,7 +739,7 @@ With a time constant of \unit[1]{fs} the C atom resides in the \hkl(1 1 0) plane
 However, weaker coupling to the heat bath realized by an increase of the time constant to \unit[100]{fs} enables the C atom to move out of the \hkl(1 1 0) plane already at the beginning, which is accompanied by a reduction in energy, approaching the final configuration on a curved path.
 The energy barrier of this path is \unit[0.2]{eV} lower in energy than the direct migration within the \hkl(1 1 0) plane.
 However, the investigated pathways cover an activation energy approximately twice as high as the one obtained by quantum-mechanical calculations.
 However, weaker coupling to the heat bath realized by an increase of the time constant to \unit[100]{fs} enables the C atom to move out of the \hkl(1 1 0) plane already at the beginning, which is accompanied by a reduction in energy, approaching the final configuration on a curved path.
 The energy barrier of this path is \unit[0.2]{eV} lower in energy than the direct migration within the \hkl(1 1 0) plane.
 However, the investigated pathways cover an activation energy approximately twice as high as the one obtained by quantum-mechanical calculations.

-If the entire transition of the \hkl<0 0 -1> into the \hkl<0 0 1> configuration is considered a two step process passing the intermediate BC configuration, an additional activation energy of \unit[0.5]{eV} is necessary to escape the BC towards the \hkl<0 0 1> configuration.
+If the entire transition of the \hkl[0 0 -1] into the \hkl[0 0 1] configuration is considered a two step process passing the intermediate BC configuration, an additional activation energy of \unit[0.5]{eV} is necessary to escape the BC towards the \hkl[0 0 1] configuration.

 Assuming equal preexponential factors for both diffusion steps, the total probability of diffusion is given by $\exp\left((2.2\,\text{eV}+0.5\,\text{eV})/k_{\text{B}}T\right)$.
 Thus, the activation energy should be located within the range of \unit[2.2-2.7]{eV}.
 
 Assuming equal preexponential factors for both diffusion steps, the total probability of diffusion is given by $\exp\left((2.2\,\text{eV}+0.5\,\text{eV})/k_{\text{B}}T\right)$.
 Thus, the activation energy should be located within the range of \unit[2.2-2.7]{eV}.
 


@@ -748,7 +747,7 @@ Thus, the activation energy should be located within the range of \unit[2.2-2.7]
 \begin{center}
 \includegraphics[width=0.7\textwidth]{00-1_0-10_albe_s.ps}
 \end{center}
 \begin{center}
 \includegraphics[width=0.7\textwidth]{00-1_0-10_albe_s.ps}
 \end{center}

-\caption{Migration barrier and structures of the \ci{} \hkl<0 0 -1> to \hkl<0 -1 0>  DB transition using the classical EA potential.}
+\caption{Migration barrier and structures of the \ci{} \hkl[0 0 -1] to \hkl[0 -1 0]  DB transition using the classical EA potential.}

 % red: ./visualize -w 640 -h 480 -d saves/c_in_si_mig_00-1_0-10_s20 -nll -0.56 -0.56 -0.8 -fur 0.3 0.2 0 -c -0.125 -1.7 0.7 -L -0.125 -0.25 -0.25 -r 0.6 -B 0.1
 \label{fig:defects:cp_00-1_0-10_mig}
 \end{figure}
 % red: ./visualize -w 640 -h 480 -d saves/c_in_si_mig_00-1_0-10_s20 -nll -0.56 -0.56 -0.8 -fur 0.3 0.2 0 -c -0.125 -1.7 0.7 -L -0.125 -0.25 -0.25 -r 0.6 -B 0.1
 \label{fig:defects:cp_00-1_0-10_mig}
 \end{figure}


@@ -756,43 +755,43 @@ Thus, the activation energy should be located within the range of \unit[2.2-2.7]
 \begin{center}
 \includegraphics[width=0.7\textwidth]{00-1_ip0-10.ps}
 \end{center}
 \begin{center}
 \includegraphics[width=0.7\textwidth]{00-1_ip0-10.ps}
 \end{center}

-\caption{Reorientation barrier of the \ci{} \hkl<0 0 -1> to \hkl<0 -1 0> DB transition in place using the classical EA potential.}
+\caption{Reorientation barrier of the \ci{} \hkl[0 0 -1] to \hkl[0 -1 0] DB transition in place using the classical EA potential.}

 \label{fig:defects:cp_00-1_ip0-10_mig}
 \end{figure}
 \label{fig:defects:cp_00-1_ip0-10_mig}
 \end{figure}

-Figures \ref{fig:defects:cp_00-1_0-10_mig} and \ref{fig:defects:cp_00-1_ip0-10_mig} show the migration barriers of the \ci{} \hkl<0 0 -1> to \hkl<0 -1 0> DB transition.
+Figures \ref{fig:defects:cp_00-1_0-10_mig} and \ref{fig:defects:cp_00-1_ip0-10_mig} show the migration barriers of the \ci{} \hkl[0 0 -1] to \hkl[0 -1 0] DB transition.

 In the first case, the transition involves a change in the lattice site of the C atom whereas in the second case, a reorientation at the same lattice site takes place.
 In the first case, the pathways for the two different time cosntants look similar.
 A local minimum exists in between two peaks of the graph.
 In the first case, the transition involves a change in the lattice site of the C atom whereas in the second case, a reorientation at the same lattice site takes place.
 In the first case, the pathways for the two different time cosntants look similar.
 A local minimum exists in between two peaks of the graph.

-The corresponding configuration, which is illustrated for the results obtained for a time constant of \unit[1]{fs}, looks similar to the \ci{} \hkl<1 1 0> configuration.
+The corresponding configuration, which is illustrated for the results obtained for a time constant of \unit[1]{fs}, looks similar to the \ci{} \hkl[1 1 0] configuration.

 Indeed, this configuration is obtained by relaxation simulations without constraints of configurations near the minimum.
 Activation energies of roughly \unit[2.8]{eV} and \unit[2.7]{eV} are needed for migration.
 
 Indeed, this configuration is obtained by relaxation simulations without constraints of configurations near the minimum.
 Activation energies of roughly \unit[2.8]{eV} and \unit[2.7]{eV} are needed for migration.
 

-The \ci{} \hkl<1 1 0> configuration seems to play a decisive role in all migration pathways in the classical potential calculations.
+The \ci{} \hkl[1 1 0] configuration seems to play a decisive role in all migration pathways in the classical potential calculations.

 As mentioned above, the starting configuration of the first migration path, i.e. the BC configuration, is fixed to be a transition point but in fact is unstable.
 As mentioned above, the starting configuration of the first migration path, i.e. the BC configuration, is fixed to be a transition point but in fact is unstable.

-Further relaxation of the BC configuration results in the \ci{} \hkl<1 1 0> configuration.
-Even the last two pathways show configurations almost identical to the \ci{} \hkl<1 1 0> configuration, which constitute local minima within the pathways.
-Thus, migration pathways involving the \ci{} \hkl<1 1 0> DB configuration as a starting or final configuration are further investigated.
+Further relaxation of the BC configuration results in the \ci{} \hkl[1 1 0] configuration.
+Even the last two pathways show configurations almost identical to the \ci{} \hkl[1 1 0] configuration, which constitute local minima within the pathways.
+Thus, migration pathways involving the \ci{} \hkl[1 1 0] DB configuration as a starting or final configuration are further investigated.

 \begin{figure}[tp]
 \begin{center}
 \includegraphics[width=0.7\textwidth]{110_mig.ps}
 \end{center}
 \begin{figure}[tp]
 \begin{center}
 \includegraphics[width=0.7\textwidth]{110_mig.ps}
 \end{center}

-\caption[Migration barriers of the \ci{} \hkl<1 1 0> DB to BC (blue), \hkl<0 0 -1> (green) and \hkl<0 -1 0> (in place, red) transition.]{Migration barriers of the \ci{} \hkl<1 1 0> DB to BC (blue), \hkl<0 0 -1> (green) and \hkl<0 -1 0> (in place, red) transition. Solid lines show results for a time constant of \unit[1]{fs} and dashed lines correspond to simulations employing a time constant of \unit[100]{fs}.}
+\caption[{Migration barriers of the \ci{} \hkl[1 1 0] DB to BC, \hkl[0 0 -1] and \hkl[0 -1 0] (in place) transition.}]{Migration barriers of the \ci{} \hkl[1 1 0] DB to BC (blue), \hkl[0 0 -1] (green) and \hkl[0 -1 0] (in place, red) transition. Solid lines show results for a time constant of \unit[1]{fs} and dashed lines correspond to simulations employing a time constant of \unit[100]{fs}.}

 \label{fig:defects:110_mig}
 \end{figure}
 \label{fig:defects:110_mig}
 \end{figure}

-Fig. \ref{fig:defects:110_mig} shows migration barriers of the \ci{} \hkl<1 1 0> DB to \hkl<0 0 -1>, \hkl<0 -1 0> (in place) and BC configuration.
+Fig. \ref{fig:defects:110_mig} shows migration barriers of the \ci{} \hkl[1 1 0] DB to \hkl[0 0 -1], \hkl[0 -1 0] (in place) and BC configuration.

 As expected there is no maximum for the transition into the BC configuration.
 As expected there is no maximum for the transition into the BC configuration.

-As mentioned earlier the BC configuration itself constitutes a saddle point configuration relaxing into the energetically more favorable \hkl<1 1 0> DB configuration.
-An activation energy of \unit[2.2]{eV} is necessary to reorientate the \hkl<0 0 -1> into the \hkl<1 1 0> DB configuration, which is \unit[1.3]{eV} higher in energy.
-Residing in this state another \unit[0.90]{eV} is enough to make the C atom form a \hkl<0 0 -1> DB configuration with the Si atom of the neighbored lattice site.
+As mentioned earlier, the BC configuration itself constitutes a saddle point configuration relaxing into the energetically more favorable \hkl[1 1 0] DB configuration.
+An activation energy of \unit[2.2]{eV} is necessary to reorientate the \hkl[0 0 -1] into the \hkl[1 1 0] DB configuration, which is \unit[1.3]{eV} higher in energy.
+Residing in this state another \unit[0.90]{eV} is enough to make the C atom form a \hkl[0 0 -1] DB configuration with the Si atom of the neighbored lattice site.

 In contrast to quantum-mechanical calculations, in which the direct transition is the energetically most favorable transition and the transition composed of the intermmediate migration steps is very unlikely to occur, the just presented pathway is much more conceivable in classical potential simulations, since the energetically most favorable transition found so far is likewise composed of two migration steps with activation energies of \unit[2.2]{eV} and \unit[0.5]{eV}, for which the intermediate state is the BC configuration, which is unstable.
 In contrast to quantum-mechanical calculations, in which the direct transition is the energetically most favorable transition and the transition composed of the intermmediate migration steps is very unlikely to occur, the just presented pathway is much more conceivable in classical potential simulations, since the energetically most favorable transition found so far is likewise composed of two migration steps with activation energies of \unit[2.2]{eV} and \unit[0.5]{eV}, for which the intermediate state is the BC configuration, which is unstable.

-Thus the just proposed migration path, which involves the \hkl<1 1 0> interstitial configuration, becomes even more probable than the initially porposed path, which involves the BC configuration that is, in fact, unstable.
+Thus the just proposed migration path, which involves the \hkl[1 1 0] interstitial configuration, becomes even more probable than the initially porposed path, which involves the BC configuration that is, in fact, unstable.

 Due to these findings, the respective path is proposed to constitute the diffusion-describing path.
 The evolution of structure and configurational energy is displayed again in Fig. \ref{fig:defects:involve110}.
 \begin{figure}[tp]
 \begin{center}
 \includegraphics[width=0.7\textwidth]{00-1_110_0-10_mig_albe.ps}
 \end{center}
 Due to these findings, the respective path is proposed to constitute the diffusion-describing path.
 The evolution of structure and configurational energy is displayed again in Fig. \ref{fig:defects:involve110}.
 \begin{figure}[tp]
 \begin{center}
 \includegraphics[width=0.7\textwidth]{00-1_110_0-10_mig_albe.ps}
 \end{center}

-\caption[Migration barrier and structures of the \ci{} \hkl<0 0 -1> (left) to the \hkl<0 -1 0> DB (right) transition involving the \hkl<1 1 0> DB (center) configuration.]{Migration barrier and structures of the \ci{} \hkl[0 0 -1] (left) to the \hkl[0 -1 0] DB (right) transition involving the \hkl[1 1 0] DB (center) configuration. Migration simulations are performed utilizing time constants of \unit[1]{fs} (solid line) and \unit[100]{fs} (dashed line) for the Berendsen thermostat.}
+\caption[Migration barrier and structures of the \ci{} {\hkl[0 0 -1]} to the {\hkl[0 -1 0]} DB transition involving the {\hkl[1 1 0]} DB configuration.]{Migration barrier and structures of the \ci{} \hkl[0 0 -1] (left) to the \hkl[0 -1 0] DB (right) transition involving the \hkl[1 1 0] DB (center) configuration. Migration simulations are performed utilizing time constants of \unit[1]{fs} (solid line) and \unit[100]{fs} (dashed line) for the Berendsen thermostat.}

 \label{fig:defects:involve110}
 \end{figure}
 Approximately \unit[2.2]{eV} are needed to turn the \ci{} \hkl[0 0 -1] into the \hkl[1 1 0] DB located at the neighbored lattice site in \hkl[1 1 -1] direction.
 \label{fig:defects:involve110}
 \end{figure}
 Approximately \unit[2.2]{eV} are needed to turn the \ci{} \hkl[0 0 -1] into the \hkl[1 1 0] DB located at the neighbored lattice site in \hkl[1 1 -1] direction.


@@ -827,7 +826,7 @@ Investigations are restricted to quantum-mechanical calculations.
 \hspace{0.5cm}
 \subfigure[]{\label{fig:defects:combos_si}\includegraphics[width=0.3\textwidth]{combos.eps}}
 \end{center}
 \hspace{0.5cm}
 \subfigure[]{\label{fig:defects:combos_si}\includegraphics[width=0.3\textwidth]{combos.eps}}
 \end{center}

-\caption{Position of the initial \ci{} \hkl[0 0 -1] DB (I) (a) and of the lattice site chosen for the initial \si{} \hkl<1 1 0> DB (\si) (b). Lattice sites for the second defect used for investigating defect pairs are numbered from 1 to 5. For black/red/blue numbers, one/two/four possible atom(s) exist for the second defect to create equivalent defect combinations.}
+\caption[Position of the initial \ci{} {\hkl[0 0 -1]} DB and of the lattice site chosen for the initial \si{} \hkl<1 1 0> DB.]{Position of the initial \ci{} \hkl[0 0 -1] DB (I) (a) and of the lattice site chosen for the initial \si{} \hkl<1 1 0> DB (\si) (b). Lattice sites for the second defect used for investigating defect pairs are numbered from 1 to 5. For black/red/blue numbers, one/two/four possible atom(s) exist for the second defect to create equivalent defect combinations.}

 \label{fig:defects:combos}
 \end{figure}
 Fig.~\ref{fig:defects:combos} schematically displays the initial \ci{} \hkl[0 0 -1] DB structure (Fig.~\ref{fig:defects:combos_ci}) as well as the lattice site chosen for the initial \si{} \hkl<1 1 0> DB (Fig.~\ref{fig:defects:combos_si}) and various positions for the second defect (1-5) that are used for investigating defect pairs.
 \label{fig:defects:combos}
 \end{figure}
 Fig.~\ref{fig:defects:combos} schematically displays the initial \ci{} \hkl[0 0 -1] DB structure (Fig.~\ref{fig:defects:combos_ci}) as well as the lattice site chosen for the initial \si{} \hkl<1 1 0> DB (Fig.~\ref{fig:defects:combos_si}) and various positions for the second defect (1-5) that are used for investigating defect pairs.


@@ -879,7 +878,7 @@ In contrast, the parallel and particularly the twisted orientations constitute e
 \hspace{0.5cm}
 \subfigure[\underline{$E_{\text{b}}=-2.39\,\text{eV}$}]{\label{fig:defects:239}\includegraphics[width=0.3\textwidth]{00-1dc/2-39.eps}}
 \end{center}
 \hspace{0.5cm}
 \subfigure[\underline{$E_{\text{b}}=-2.39\,\text{eV}$}]{\label{fig:defects:239}\includegraphics[width=0.3\textwidth]{00-1dc/2-39.eps}}
 \end{center}

-\caption{Relaxed structures of defect combinations obtained by creating \hkl[1 0 0] (a) and \hkl[0 -1 0] (b) DBs at position 1.}
+\caption[Relaxed structures of defect combinations obtained by creating {\hkl[1 0 0]} and {\hkl[0 -1 0]} DBs at position 1.]{Relaxed structures of defect combinations obtained by creating \hkl[1 0 0] (a) and \hkl[0 -1 0] (b) DBs at position 1.}

 \label{fig:defects:comb_db_01}
 \end{figure}
 Mattoni~et~al. \cite{mattoni2002} predict the ground-state configuration of \ci{} \hkl<1 0 0>-type defect pairs for a \hkl[1 0 0] or equivalently a \hkl[0 1 0] defect created at position 1 with both defects basically maintaining the as-isolated DB structure, resulting in a binding energy of \unit[-2.1]{eV}.
 \label{fig:defects:comb_db_01}
 \end{figure}
 Mattoni~et~al. \cite{mattoni2002} predict the ground-state configuration of \ci{} \hkl<1 0 0>-type defect pairs for a \hkl[1 0 0] or equivalently a \hkl[0 1 0] defect created at position 1 with both defects basically maintaining the as-isolated DB structure, resulting in a binding energy of \unit[-2.1]{eV}.


@@ -910,7 +909,7 @@ In fact, following results on migration simulations will reinforce the assumptio
 \hspace{0.2cm}
 \subfigure[\underline{$E_{\text{b}}=-2.05\,\text{eV}$}]{\label{fig:defects:205}\includegraphics[width=0.25\textwidth]{00-1dc/2-05.eps}}
 \end{center}
 \hspace{0.2cm}
 \subfigure[\underline{$E_{\text{b}}=-2.05\,\text{eV}$}]{\label{fig:defects:205}\includegraphics[width=0.25\textwidth]{00-1dc/2-05.eps}}
 \end{center}

-\caption{Relaxed structures of defect combinations obtained by creating \hkl[1 0 0] (a) and \hkl[0 1 0] (b) DBs at position 2 and a \hkl[0 0 1] (c) DB at position 3.}
+\caption[Relaxed structures of defect combinations obtained by creating {\hkl[1 0 0]} and {\hkl[0 1 0]} DBs at position 2 and a {\hkl[0 0 1]} DB at position 3.]{Relaxed structures of defect combinations obtained by creating \hkl[1 0 0] (a) and \hkl[0 1 0] (b) DBs at position 2 and a \hkl[0 0 1] (c) DB at position 3.}

 \label{fig:defects:comb_db_02}
 \end{figure}
 Fig.~\ref{fig:defects:comb_db_02} shows the next three energetically favorable configurations.
 \label{fig:defects:comb_db_02}
 \end{figure}
 Fig.~\ref{fig:defects:comb_db_02} shows the next three energetically favorable configurations.


@@ -956,7 +955,7 @@ The reduction of strain energy is higher in the second case, where the C atom of
 \hspace{0.7cm}
 \subfigure[\underline{$E_{\text{b}}=-1.38\,\text{eV}$}]{\label{fig:defects:138}\includegraphics[width=0.25\textwidth]{00-1dc/1-38.eps}}
 \end{center}
 \hspace{0.7cm}
 \subfigure[\underline{$E_{\text{b}}=-1.38\,\text{eV}$}]{\label{fig:defects:138}\includegraphics[width=0.25\textwidth]{00-1dc/1-38.eps}}
 \end{center}

-\caption{Relaxed structures of defect combinations obtained by creating \hkl[0 0 1] (a), \hkl[0 0 -1] (b), \hkl[0 -1 0] (c) and \hkl[1 0 0] (d) DBs at position 5.}
+\caption[Relaxed structures of defect combinations obtained by creating {\hkl[0 0 1]}, {\hkl[0 0 -1]}, {\hkl[0 -1 0]} and {\hkl[1 0 0]} DBs at position 5.]{Relaxed structures of defect combinations obtained by creating \hkl[0 0 1] (a), \hkl[0 0 -1] (b), \hkl[0 -1 0] (c) and \hkl[1 0 0] (d) DBs at position 5.}

 \label{fig:defects:comb_db_03}
 \end{figure}
 Energetically beneficial configurations of defect combinations are observed for interstititals of all orientations placed at position 5, a position two bonds away from the initial interstitial along the \hkl[1 1 0] direction.
 \label{fig:defects:comb_db_03}
 \end{figure}
 Energetically beneficial configurations of defect combinations are observed for interstititals of all orientations placed at position 5, a position two bonds away from the initial interstitial along the \hkl[1 1 0] direction.


@@ -999,7 +998,7 @@ Type & \hkl[-1 0 0] & \hkl[1 0 0] & \hkl[1 0 0] & \hkl[1 0 0] & \hkl[1 0 0] & \h
 \begin{center}
 \includegraphics[width=0.7\textwidth]{db_along_110_cc_n.ps}
 \end{center}
 \begin{center}
 \includegraphics[width=0.7\textwidth]{db_along_110_cc_n.ps}
 \end{center}

-\caption[Minimum binding energy of DB combinations separated along \hkl<1 1 0> with respect to the C-C distance.]{Minimum binding energy of dumbbell combinations separated along \hkl[1 1 0] with respect to the C-C distance. The blue line is a guide for the eye and the green curve corresponds to the most suitable fit function consisting of all but the first data point.}
+\caption[Minimum binding energy of DB combinations separated along {\hkl[1 1 0]} with respect to the C-C distance.]{Minimum binding energy of dumbbell combinations separated along \hkl[1 1 0] with respect to the C-C distance. The blue line is a guide for the eye and the green curve corresponds to the most suitable fit function consisting of all but the first data point.}

 \label{fig:defects:comb_db110}
 \end{figure}
 The binding energy of these configurations with respect to the C-C distance is plotted in Fig.~\ref{fig:defects:comb_db110}.
 \label{fig:defects:comb_db110}
 \end{figure}
 The binding energy of these configurations with respect to the C-C distance is plotted in Fig.~\ref{fig:defects:comb_db110}.


@@ -1025,7 +1024,7 @@ The corresponding migration energies and atomic configurations are displayed in
 \begin{center}
 \includegraphics[width=0.7\textwidth]{036-239.ps}
 \end{center}
 \begin{center}
 \includegraphics[width=0.7\textwidth]{036-239.ps}
 \end{center}

-\caption{Migration barrier and structures of the transition of a C$_{\text{i}}$ \hkl[-1 0 0] DB at position 2 (left) into a C$_{\text{i}}$ \hkl[0 -1 0] DB at position 1 (right). An activation energy of \unit[1.2]{eV} is observed.}
+\caption[Migration barrier and structures of the transition of a C$_{\text{i}}$ {\hkl[-1 0 0]} DB at position 2 into a C$_{\text{i}}$ {\hkl[0 -1 0]} DB at position 1.]{Migration barrier and structures of the transition of a C$_{\text{i}}$ \hkl[-1 0 0] DB at position 2 (left) into a C$_{\text{i}}$ \hkl[0 -1 0] DB at position 1 (right). An activation energy of \unit[1.2]{eV} is observed.}

 \label{fig:036-239}
 \end{figure}
 Since thermally activated C clustering is, thus, only possible by traversing energetically unfavored configurations, extensive C clustering is not expected.
 \label{fig:036-239}
 \end{figure}
 Since thermally activated C clustering is, thus, only possible by traversing energetically unfavored configurations, extensive C clustering is not expected.


@@ -1044,7 +1043,7 @@ The migration barrier and corresponding structures are shown in Fig.~\ref{fig:18
 \begin{center}
 \includegraphics[width=0.7\textwidth]{188-225.ps}
 \end{center}
 \begin{center}
 \includegraphics[width=0.7\textwidth]{188-225.ps}
 \end{center}

-\caption{Migration barrier and structures of the transition of a C$_{\text{i}}$ \hkl[0 -1 0] DB at position 5 (left) into a C$_{\text{i}}$ \hkl[1 0 0] DB at position 1 (right). An activation energy of \unit[0.47]{eV} is observed.}
+\caption[Migration barrier and structures of the transition of a C$_{\text{i}}$ {\hkl[0 -1 0]} DB at position 5 into a C$_{\text{i}}$ {\hkl[1 0 0]} DB at position 1.]{Migration barrier and structures of the transition of a C$_{\text{i}}$ \hkl[0 -1 0] DB at position 5 (left) into a C$_{\text{i}}$ \hkl[1 0 0] DB at position 1 (right). An activation energy of \unit[0.47]{eV} is observed.}

 \label{fig:188-225}
 \end{figure}
 Finally, as already mentioned above, this type of defect pair is represented two times more often than the ground-state configuration.
 \label{fig:188-225}
 \end{figure}
 Finally, as already mentioned above, this type of defect pair is represented two times more often than the ground-state configuration.


@@ -1067,7 +1066,7 @@ As a result, C defect agglomeration indeed is expected, but only a low probabili
 \hline
 \end{tabular}
 \end{center}
 \hline
 \end{tabular}
 \end{center}

-\caption{Binding energies of combinations of the \ci{} \hkl[0 0 -1] defect with a \cs{} atom located at positions 1 to 5 according to Fig.~\ref{fig:defects:combos_ci}. R corresponds to the position located at $\frac{a_{\text{Si}}}{2}\hkl[3 2 3]$ relative to the initial defect position, which is the maximum realizable distance due to periodic boundary conditions.}
+\caption[Binding energies of combinations of the \ci{} {\hkl[0 0 -1]} defect with a \cs{} atom located at positions 1 to 5 according to Fig.~\ref{fig:defects:combos_ci}.]{Binding energies of combinations of the \ci{} \hkl[0 0 -1] defect with a \cs{} atom located at positions 1 to 5 according to Fig.~\ref{fig:defects:combos_ci}. R corresponds to the position located at $\frac{a_{\text{Si}}}{2}\hkl[3 2 3]$ relative to the initial defect position, which is the maximum realizable distance due to periodic boundary conditions.}

 \label{tab:defects:c-s}
 \end{table}
 %\begin{figure}[tp]
 \label{tab:defects:c-s}
 \end{table}
 %\begin{figure}[tp]


@@ -1124,7 +1123,7 @@ Fig.~\ref{fig:093-095} and \ref{fig:026-128} show structures A, B and $\alpha$,
 \begin{center}
 \includegraphics[width=0.7\textwidth]{093-095.ps}
 \end{center}
 \begin{center}
 \includegraphics[width=0.7\textwidth]{093-095.ps}
 \end{center}

-\caption{Migration barrier and structures of the transition of the initial \ci{} \hkl[0 0 -1] DB and C$_{\text{s}}$ at position 3 (left) into a configuration of a twofold coordinated Si$_{\text{i}}$ located in between two C$_{\text{s}}$ atoms occupying the lattice sites of the initial DB and position 3 (right). An activation energy of \unit[0.44]{eV} is observed.}
+\caption[Migration barrier and structures of the transition of the initial \ci{} {\hkl[0 0 -1]} DB and C$_{\text{s}}$ at position 3 into a configuration of a twofold coordinated Si$_{\text{i}}$ located in between two C$_{\text{s}}$ atoms occupying the lattice sites of the initial DB and position 3.]{Migration barrier and structures of the transition of the initial \ci{} \hkl[0 0 -1] DB and C$_{\text{s}}$ at position 3 (left) into a configuration of a twofold coordinated Si$_{\text{i}}$ located in between two C$_{\text{s}}$ atoms occupying the lattice sites of the initial DB and position 3 (right). An activation energy of \unit[0.44]{eV} is observed.}

 \label{fig:093-095}
 \end{figure}
 Configuration A consists of a C$_{\text{i}}$ \hkl[0 0 -1] DB with threefold coordinated Si and C DB atoms slightly disturbed by the C$_{\text{s}}$ at position 3, facing the Si DB atom as a neighbor.
 \label{fig:093-095}
 \end{figure}
 Configuration A consists of a C$_{\text{i}}$ \hkl[0 0 -1] DB with threefold coordinated Si and C DB atoms slightly disturbed by the C$_{\text{s}}$ at position 3, facing the Si DB atom as a neighbor.


@@ -1146,7 +1145,7 @@ Obviously, either the CRT algorithm fails to seize the actual saddle point struc
 \begin{center}
 \includegraphics[width=0.7\textwidth]{comb_mig_026-128_vasp.ps}
 \end{center}
 \begin{center}
 \includegraphics[width=0.7\textwidth]{comb_mig_026-128_vasp.ps}
 \end{center}

-\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and C$_{\text{s}}$ at position 1 (left) into a C-C \hkl[1 0 0] DB occupying the lattice site at position 1 (right). An activation energy of \unit[0.1]{eV} is observed.}
+\caption[Migration barrier and structures of the transition of the initial C$_{\text{i}}$ {\hkl[0 0 -1]} DB and C$_{\text{s}}$ at position 1 into a C-C {\hkl[1 0 0]} DB occupying the lattice site at position 1.]{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and C$_{\text{s}}$ at position 1 (left) into a C-C \hkl[1 0 0] DB occupying the lattice site at position 1 (right). An activation energy of \unit[0.1]{eV} is observed.}

 \label{fig:026-128}
 \end{figure}
 Configuration $\alpha$ is similar to configuration A, except that the C$_{\text{s}}$ atom at position 1 is facing the C DB atom as a neighbor resulting in the formation of a strong C-C bond and a much more noticeable perturbation of the DB structure.
 \label{fig:026-128}
 \end{figure}
 Configuration $\alpha$ is similar to configuration A, except that the C$_{\text{s}}$ atom at position 1 is facing the C DB atom as a neighbor resulting in the formation of a strong C-C bond and a much more noticeable perturbation of the DB structure.


@@ -1190,7 +1189,7 @@ Yet less of compensation is realized if C$_{\text{s}}$ is located at position 4
 \hspace{0.2cm}
 \subfigure[\underline{$E_{\text{b}}=0.49\,\text{eV}$}]{\label{fig:defects:049}\includegraphics[width=0.25\textwidth]{00-1dc/0-49.eps}}
 \end{center}
 \hspace{0.2cm}
 \subfigure[\underline{$E_{\text{b}}=0.49\,\text{eV}$}]{\label{fig:defects:049}\includegraphics[width=0.25\textwidth]{00-1dc/0-49.eps}}
 \end{center}

-\caption{Relaxed structures of defect combinations obtained by creating \cs{} at positions 2 (a), 4 (b) and 5 (c) in the \ci{} \hkl[0 0 -1] DB configuration.}
+\caption[Relaxed structures of defect combinations obtained by creating \cs{} at positions 2, 4 and 5 in the \ci{} {\hkl[0 0 -1]} DB configuration.]{Relaxed structures of defect combinations obtained by creating \cs{} at positions 2 (a), 4 (b) and 5 (c) in the \ci{} \hkl[0 0 -1] DB configuration.}

 \label{fig_defects:245csub}
 \end{figure}
 Fig.~\ref{fig_defects:245csub} lists the remaining configurations and binding energies of the relaxed structures obtained by creating a \cs{} at positions 2, 4 and 5 in the \ci{} \hkl[0 0 -1] DB configuration.
 \label{fig_defects:245csub}
 \end{figure}
 Fig.~\ref{fig_defects:245csub} lists the remaining configurations and binding energies of the relaxed structures obtained by creating a \cs{} at positions 2, 4 and 5 in the \ci{} \hkl[0 0 -1] DB configuration.


@@ -1260,7 +1259,7 @@ Resulting binding energies of a C$_{\text{i}}$ DB and a nearby vacancy are liste
 \hline
 \end{tabular}
 \end{center}
 \hline
 \end{tabular}
 \end{center}

-\caption{Binding energies of combinations of the \ci{} \hkl[0 0 -1] defect with a vacancy located at positions 1 to 5 according to Fig.~\ref{fig:defects:combos_ci}. R corresponds to the position located at $\frac{a_{\text{Si}}}{2}\hkl[3 2 3]$ relative to the initial defect position, which is the maximum realizable distance due to periodic boundary conditions.}
+\caption[Binding energies of combinations of the \ci{} {\hkl[0 0 -1]} defect with a vacancy located at positions 1 to 5 according to Fig.~\ref{fig:defects:combos_ci}.]{Binding energies of combinations of the \ci{} \hkl[0 0 -1] defect with a vacancy located at positions 1 to 5 according to Fig.~\ref{fig:defects:combos_ci}. R corresponds to the position located at $\frac{a_{\text{Si}}}{2}\hkl[3 2 3]$ relative to the initial defect position, which is the maximum realizable distance due to periodic boundary conditions.}

 \label{tab:defects:c-v}
 \end{table}
 \begin{figure}[tp]
 \label{tab:defects:c-v}
 \end{table}
 \begin{figure}[tp]


@@ -1272,7 +1271,7 @@ Resulting binding energies of a C$_{\text{i}}$ DB and a nearby vacancy are liste
 \hspace{0.7cm}
 \subfigure[\underline{$E_{\text{b}}=-0.50\,\text{eV}$}]{\label{fig:defects:050}\includegraphics[width=0.25\textwidth]{00-1dc/0-50.eps}}
 \end{center}
 \hspace{0.7cm}
 \subfigure[\underline{$E_{\text{b}}=-0.50\,\text{eV}$}]{\label{fig:defects:050}\includegraphics[width=0.25\textwidth]{00-1dc/0-50.eps}}
 \end{center}

-\caption{Relaxed structures of defect combinations obtained by creating a vacancy at positions 2 (a), 3 (b), 4 (c) and 5 (d).}
+\caption[Relaxed structures of defect combinations obtained by creating a vacancy at positions 2, 3, 4 and 5.]{Relaxed structures of defect combinations obtained by creating a vacancy at positions 2 (a), 3 (b), 4 (c) and 5 (d).}

 \label{fig:defects:comb_db_06}
 \end{figure}
 Figure \ref{fig:defects:comb_db_06} shows the associated configurations.
 \label{fig:defects:comb_db_06}
 \end{figure}
 Figure \ref{fig:defects:comb_db_06} shows the associated configurations.


@@ -1308,14 +1307,14 @@ The migration pathways of configuration \ref{fig:defects:314} and \ref{fig:defec
 \begin{center}
 \includegraphics[width=0.7\textwidth]{314-539.ps}
 \end{center}
 \begin{center}
 \includegraphics[width=0.7\textwidth]{314-539.ps}
 \end{center}

-\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created at position 3 (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.1]{eV} is observed.}
+\caption[Migration barrier and structures of the transition of the initial C$_{\text{i}}$ {\hkl[0 0 -1]} DB and a V created at position 3 into a C$_{\text{s}}$ configuration.]{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created at position 3 (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.1]{eV} is observed.}

 \label{fig:314-539}
 \end{figure}
 \begin{figure}[tp]
 \begin{center}
 \includegraphics[width=0.7\textwidth]{059-539.ps}
 \end{center}
 \label{fig:314-539}
 \end{figure}
 \begin{figure}[tp]
 \begin{center}
 \includegraphics[width=0.7\textwidth]{059-539.ps}
 \end{center}

-\caption{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created at position 2 (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.6]{eV} is observed.}
+\caption[Migration barrier and structures of the transition of the initial C$_{\text{i}}$ {\hkl[0 0 -1]} DB and a V created at position 2 into a C$_{\text{s}}$ configuration.]{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and a V created at position 2 (left) into a C$_{\text{s}}$ configuration (right). An activation energy of \unit[0.6]{eV} is observed.}

 \label{fig:059-539}
 \end{figure}
 Activation energies as low as \unit[0.1]{eV} and \unit[0.6]{eV} are observed.
 \label{fig:059-539}
 \end{figure}
 Activation energies as low as \unit[0.1]{eV} and \unit[0.6]{eV} are observed.


@@ -1374,7 +1373,7 @@ For the follwoing study the same type of self-interstitial is assumed to provide
 \hline
 \end{tabular}
 \end{center}
 \hline
 \end{tabular}
 \end{center}

-\caption{Equivalent configurations labeled \RM{1}-\RM{10} of \hkl<1 1 0>-type Si$_{\text{i}}$ DBs created at position I and C$_{\text{s}}$ created at positions 1 to 5 according to Fig.~\ref{fig:defects:combos_si}. The respective orientation of the Si$_{\text{i}}$ DB is given in the first row.}
+\caption[Equivalent configurations labeled \RM{1}-\RM{10} of \hkl<1 1 0>-type Si$_{\text{i}}$ DBs created at position I and C$_{\text{s}}$ created at positions 1 to 5 according to Fig.~\ref{fig:defects:combos_si}.]{Equivalent configurations labeled \RM{1}-\RM{10} of \hkl<1 1 0>-type Si$_{\text{i}}$ DBs created at position I and C$_{\text{s}}$ created at positions 1 to 5 according to Fig.~\ref{fig:defects:combos_si}. The respective orientation of the Si$_{\text{i}}$ DB is given in the first row.}

 \label{tab:defects:comb_csub_si110}
 \end{table}
 \begin{table}[tp]
 \label{tab:defects:comb_csub_si110}
 \end{table}
 \begin{table}[tp]


@@ -1414,7 +1413,7 @@ The transition involving the latter two configurations is shown in Fig.~\ref{fig
 \begin{center}
 \includegraphics[width=0.7\textwidth]{162-097.ps}
 \end{center}
 \begin{center}
 \includegraphics[width=0.7\textwidth]{162-097.ps}
 \end{center}

-\caption{Migration barrier and structures of the transition of a \hkl[1 1 0] Si$_{\text{i}}$ DB next to C$_{\text{s}}$ (right) into the C$_{\text{i}}$ \hkl[0 0 -1] DB configuration (left). An activation energy of \unit[0.12]{eV} and \unit[0.77]{eV} for the reverse process is observed.}
+\caption[Migration barrier and structures of the transition of a {\hkl[1 1 0]} Si$_{\text{i}}$ DB next to C$_{\text{s}}$ into the C$_{\text{i}}$ {\hkl[0 0 -1]} DB configuration.]{Migration barrier and structures of the transition of a \hkl[1 1 0] Si$_{\text{i}}$ DB next to C$_{\text{s}}$ (right) into the C$_{\text{i}}$ \hkl[0 0 -1] DB configuration (left). An activation energy of \unit[0.12]{eV} and \unit[0.77]{eV} for the reverse process is observed.}

 \label{fig:162-097}
 \end{figure}
 An activation energy as low as \unit[0.12]{eV} is necessary for the migration into the ground-state configuration.
 \label{fig:162-097}
 \end{figure}
 An activation energy as low as \unit[0.12]{eV} is necessary for the migration into the ground-state configuration.


@@ -1426,7 +1425,7 @@ Due to the low activation energy this process must be considered to be activated
 \begin{center}
 \includegraphics[width=0.7\textwidth]{c_sub_si110.ps}
 \end{center}
 \begin{center}
 \includegraphics[width=0.7\textwidth]{c_sub_si110.ps}
 \end{center}

-\caption{Binding energies of combinations of a C$_{\text{s}}$ and a Si$_{\text{i}}$ DB with respect to the separation distance. The interaction strength of the defect pairs are well approximated by a Lennard-Jones 6-12 potential, which is used for curve fitting.}
+\caption[Binding energies of combinations of a C$_{\text{s}}$ and a Si$_{\text{i}}$ DB with respect to the separation distance.]{Binding energies of combinations of a C$_{\text{s}}$ and a Si$_{\text{i}}$ DB with respect to the separation distance. The interaction strength of the defect pairs are well approximated by a Lennard-Jones 6-12 potential, which is used for curve fitting.}

 \label{fig:dc_si-s}
 \end{figure}
 Fig.~\ref{fig:dc_si-s} shows the binding energies of pairs of C$_{\text{s}}$ and a Si$_{\text{i}}$ \hkl<1 1 0> DB with respect to the separation distance.
 \label{fig:dc_si-s}
 \end{figure}
 Fig.~\ref{fig:dc_si-s} shows the binding energies of pairs of C$_{\text{s}}$ and a Si$_{\text{i}}$ \hkl<1 1 0> DB with respect to the separation distance.


@@ -1453,11 +1452,11 @@ The atomic configurations for two different points in time are shown in Fig.~\re
 \begin{figure}[tp]
 \begin{center}
 \begin{minipage}{0.40\textwidth}
 \begin{figure}[tp]
 \begin{center}
 \begin{minipage}{0.40\textwidth}

-\includegraphics[width=\columnwidth]{md_vasp_01.eps}
+\includegraphics[width=\columnwidth]{md01_bonds.eps}

 \end{minipage}
 \hspace{1cm}
 \begin{minipage}{0.40\textwidth}
 \end{minipage}
 \hspace{1cm}
 \begin{minipage}{0.40\textwidth}

-\includegraphics[width=\columnwidth]{md_vasp_02.eps}
+\includegraphics[width=\columnwidth]{md02_bonds.eps}

 \end{minipage}\\
 \begin{minipage}{0.40\textwidth}
 \begin{center}
 \end{minipage}\\
 \begin{minipage}{0.40\textwidth}
 \begin{center}


@@ -1471,14 +1470,14 @@ $t=\unit[2900]{fs}$
 \end{center}
 \end{minipage}
 \end{center}
 \end{center}
 \end{minipage}
 \end{center}

-\caption{Atomic configurations of an ab initio molecular dynamics run at \unit[900]{$^{\circ}$C} starting from a configuration of C$_{\text{s}}$ located next to a Si$_{\text{i}}$ \hkl[1 1 0] DB (atoms 1 and 2). Equal atoms are marked by equal numbers. Bonds are drawn for substantial atoms only.}
+\caption[Atomic configurations of an ab initio molecular dynamics run at {\unit[900]{$^{\circ}$C}} starting from a configuration of C$_{\text{s}}$ located next to a Si$_{\text{i}}$ {\hkl[1 1 0]} DB.]{Atomic configurations of an ab initio molecular dynamics run at \unit[900]{$^{\circ}$C} starting from a configuration of C$_{\text{s}}$ located next to a Si$_{\text{i}}$ \hkl[1 1 0] DB (atoms 1 and 2). Equal atoms are marked by equal numbers. For substantial atoms, bonds are drawn in red color.}

 \label{fig:defects:md}
 \end{figure}
 Si atoms 1 and 2, which form the initial DB, occupy Si lattice sites in the final configuration while Si atom 3 is transferred from a regular lattice site into the interstitial lattice.
 These results support the above assumptions of an increased entropic contribution to structural formation involving C$_{\text{s}}$ to a greater extent.
 
 \label{fig:defects:md}
 \end{figure}
 Si atoms 1 and 2, which form the initial DB, occupy Si lattice sites in the final configuration while Si atom 3 is transferred from a regular lattice site into the interstitial lattice.
 These results support the above assumptions of an increased entropic contribution to structural formation involving C$_{\text{s}}$ to a greater extent.
 

-% link to migration of \si{}!
-% todo - make it a subsection
+\section{Mobility of the silicon self-interstitial}
+

 The possibility for separated configurations of \cs{} and \si{} becomes even more likely if one of the constituents exhibits a low barrier of migration.
 In this case, the \si{} is assumed to constitute the mobile defect compared to the stable \cs{} atom.
 Thus, migration paths of \si{} are investigated in the following excursus.
 The possibility for separated configurations of \cs{} and \si{} becomes even more likely if one of the constituents exhibits a low barrier of migration.
 In this case, the \si{} is assumed to constitute the mobile defect compared to the stable \cs{} atom.
 Thus, migration paths of \si{} are investigated in the following excursus.


@@ -1487,8 +1486,7 @@ Acoording to Fig.~\ref{fig:defects:si_mig1}, an activation energy of \unit[0.67]
 \begin{center}
 \includegraphics[width=0.7\textwidth]{si_110_110_mig_02_conf.ps}
 \end{center}
 \begin{center}
 \includegraphics[width=0.7\textwidth]{si_110_110_mig_02_conf.ps}
 \end{center}

-\caption[Migration barrier and structures of the \si{} \hkl<1 1 0> DB.]{Migration barrier and structures of the \si{} \hkl[0 -1 1] DB (left) to the \hkl[1 1 0] DB (right) transition. Bonds are illustrated by blue lines.}
-% todo read above caption! enable [] hkls in short caption
+\caption[Migration barrier and structures of the \si{} {\hkl[0 -1 1]} DB to the {\hkl[1 1 0]} DB transition.]{Migration barrier and structures of the \si{} \hkl[0 -1 1] DB (left) to the \hkl[1 1 0] DB (right) transition. Bonds are illustrated by blue lines.}

 \label{fig:defects:si_mig1}
 \end{figure}
 The barrier, which is even lower than the one for \ci{}, indeed indicates highly mobile \si.
 \label{fig:defects:si_mig1}
 \end{figure}
 The barrier, which is even lower than the one for \ci{}, indeed indicates highly mobile \si.


@@ -1500,8 +1498,7 @@ The respective configurational energies are shown in Fig.~\ref{fig:defects:si_mi
 \begin{center}
 \includegraphics[width=0.7\textwidth]{si_mig_rest.ps}
 \end{center}
 \begin{center}
 \includegraphics[width=0.7\textwidth]{si_mig_rest.ps}
 \end{center}

-\caption{Migration barrier of the \si{} \hkl[1 1 0] DB into the hexagonal (H) and tetrahedral (T) configuration as well as the hexagonal \si{} to tetrahedral \si{} transition.}
-% todo read above caption! enable [] hkls in short caption
+\caption[Migration barrier of the \si{} {\hkl[1 1 0]} DB into the hexagonal and tetrahedral configuration as well as the hexagonal \si{} to tetrahedral \si{} transition.]{Migration barrier of the \si{} \hkl[1 1 0] DB into the hexagonal (H) and tetrahedral (T) configuration as well as the hexagonal \si{} to tetrahedral \si{} transition.}

 \label{fig:defects:si_mig2}
 \end{figure}
 The obtained activation energies are of the same order of magnitude than values derived from other ab initio studies \cite{bloechl93,sahli05}.
 \label{fig:defects:si_mig2}
 \end{figure}
 The obtained activation energies are of the same order of magnitude than values derived from other ab initio studies \cite{bloechl93,sahli05}.

diff --git a/posic/thesis/md.tex b/posic/thesis/md.tex
index 81e94a37c29a484ad48e81306c1d722266f3871e..9d5121571b1ff5e82dfdc5d1c5bcede43a451e2b 100644 (file)
--- a/posic/thesis/md.tex
+++ b/posic/thesis/md.tex
@@ -148,7 +148,7 @@ The radial distribution function $g(r)$ for C-C and Si-Si distances is shown in
 \begin{center}
  \includegraphics[width=0.7\textwidth]{sic_prec_450_si-si_c-c.ps}
 \end{center}
 \begin{center}
  \includegraphics[width=0.7\textwidth]{sic_prec_450_si-si_c-c.ps}
 \end{center}

-\caption[Radial distribution function of the C-C and Si-Si distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of \unit\[450\]{$^{\circ}$C} and cooled down to room temperature.]{Radial distribution function of the C-C and Si-Si distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of \unit[450]{$^{\circ}$C} and cooled down to room temperature. The bright blue graph shows the Si-Si radial distribution for pure c-Si. The insets show magnified regions of the respective type of bond.}
+\caption[Radial distribution function of the C-C and Si-Si distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of {\unit[450]{$^{\circ}$C}} and cooled down to room temperature.]{Radial distribution function of the C-C and Si-Si distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of \unit[450]{$^{\circ}$C} and cooled down to room temperature. The bright blue graph shows the Si-Si radial distribution for pure c-Si. The insets show magnified regions of the respective type of bond.}

 \label{fig:md:pc_si-si_c-c}
 \end{figure}
 \begin{figure}[tp]
 \label{fig:md:pc_si-si_c-c}
 \end{figure}
 \begin{figure}[tp]


@@ -190,7 +190,7 @@ This excellently agrees with the calculated value $r(13)$ in Table~\ref{tab:defe
 \begin{center}
  \includegraphics[width=0.7\textwidth]{sic_prec_450_si-c.ps}
 \end{center}
 \begin{center}
  \includegraphics[width=0.7\textwidth]{sic_prec_450_si-c.ps}
 \end{center}

-\caption{Radial distribution function of the Si-C distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of \unit[450]{$^{\circ}$C} and cooled down to room temperature. Additionally the resulting Si-C distances of a \ci{} \hkl<1 0 0> DB configuration are given.}
+\caption[Radial distribution function of the Si-C distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of {\unit[450]{$^{\circ}$C}} and cooled down to room temperature.]{Radial distribution function of the Si-C distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of \unit[450]{$^{\circ}$C} and cooled down to room temperature. Additionally the resulting Si-C distances of a \ci{} \hkl<1 0 0> DB configuration are given.}

 \label{fig:md:pc_si-c}
 \end{figure}
 Fig.~\ref{fig:md:pc_si-c} displays the Si-C radial distribution function for all three insertion volumes together with the Si-C bonds as observed in a \ci{} \hkl<1 0 0> DB configuration.
 \label{fig:md:pc_si-c}
 \end{figure}
 Fig.~\ref{fig:md:pc_si-c} displays the Si-C radial distribution function for all three insertion volumes together with the Si-C bonds as observed in a \ci{} \hkl<1 0 0> DB configuration.


@@ -415,8 +415,12 @@ In IBS, highly energetic C atoms are able to generate vacant sites, which in tur
 This is in fact found to be favorable in the absence of the \si{}, which turned out to have a low interaction capture radius with the \cs{} atom and very likely prevents the recombination into a thermodynamically stable \ci{} DB for appropriate separations of the defect pair.
 Results gained in this chapter show preferential occupation of Si lattice sites by \cs{} enabled by increased temperatures supporting the assumptions drawn from the defect studies of the last chapter.
 
 This is in fact found to be favorable in the absence of the \si{}, which turned out to have a low interaction capture radius with the \cs{} atom and very likely prevents the recombination into a thermodynamically stable \ci{} DB for appropriate separations of the defect pair.
 Results gained in this chapter show preferential occupation of Si lattice sites by \cs{} enabled by increased temperatures supporting the assumptions drawn from the defect studies of the last chapter.
 

-Thus, it is concluded that increased temperatures is not exclusively usefull to accelerate the dynamics approximatively describing the structural evolution.
-Moreover it can be considered a necessary condition to deviate the system out of equilibrium enabling the formation of 3C-SiC, which is obviously realized by a successive agglomeration of \cs{}.
+Moreover, the cut-off effect as detailed in section~\ref{section:md:limit} is particularly significant for non-equilibrium processes.
+Thus, for instance, it is not surprising that short range potentials show overestimated melting temperatures while properties of structures that are only slightly deviated from equilibrium are well described.
+Due to this, increased temperatures are considered exceptionally necessary for modeling non-equilibrium processes and structures such as IBS and 3C-SiC.
+
+Thus, it is concluded that increased temperatures are not exclusively usefull to accelerate the dynamics approximatively describing the structural evolution.
+Moreover, it can be considered a necessary condition to deviate the system out of equilibrium enabling the formation of 3C-SiC, which is obviously realized by a successive agglomeration of \cs{}.

 
 \ifnum1=0
 
 
 \ifnum1=0
 


@@ -441,14 +445,14 @@ The return to lower temperatures is considered seperately.
 \includegraphics[width=0.7\textwidth]{c_in_si_95_v1_si-c.ps}\\
 \includegraphics[width=0.7\textwidth]{c_in_si_95_v1_c-c.ps}
 \end{center}
 \includegraphics[width=0.7\textwidth]{c_in_si_95_v1_si-c.ps}\\
 \includegraphics[width=0.7\textwidth]{c_in_si_95_v1_c-c.ps}
 \end{center}

-\caption{Si-C (top) and C-C (bottom) radial distribution for low concentration simulations at 95 \% of the potential's Si melting point at different points in time of the simulation.}
+\caption[Si-C and C-C radial distribution for low concentration simulations at {\unit[95]{\%}} of the potential's Si melting point at different points in time of the simulation.]{Si-C (top) and C-C (bottom) radial distribution for low concentration simulations at \unit[95]{\%} of the potential's Si melting point at different points in time of the simulation.}

 \label{fig:md:95_long_time_v1}
 \end{figure}
 \begin{figure}[tp]
 \begin{center}
 \includegraphics[width=0.7\textwidth]{c_in_si_95_v2.ps}
 \end{center}
 \label{fig:md:95_long_time_v1}
 \end{figure}
 \begin{figure}[tp]
 \begin{center}
 \includegraphics[width=0.7\textwidth]{c_in_si_95_v2.ps}
 \end{center}

-\caption{Si-C and C-C radial distribution for high concentration simulations at 95 \% of the potential's Si melting point at different points in time of the simulation.}
+\caption{Si-C and C-C radial distribution for high concentration simulations at \unit[95]{\%} of the potential's Si melting point at different points in time of the simulation.}

 \label{fig:md:95_long_time_v2}
 \end{figure}
 
 \label{fig:md:95_long_time_v2}
 \end{figure}
 

diff --git a/posic/thesis/sic.tex b/posic/thesis/sic.tex
index 5629f6f132be09ca6e1501b665b4e3346702dc59..1b09e3ddeea10783896a20f2f0ef327877232d94 100644 (file)
--- a/posic/thesis/sic.tex
+++ b/posic/thesis/sic.tex
@@ -35,7 +35,7 @@ Each SiC bilayer can be situated in one of three possible positions (abbreviated
 \end{minipage}
 %\includegraphics[width=10cm]{polytypes.eps}
 \end{center}
 \end{minipage}
 %\includegraphics[width=10cm]{polytypes.eps}
 \end{center}

-\caption{Stacking sequence of SiC bilayers of the most common polytypes of SiC (from left to right): 3C, 2H, 4H and 6H.}
+\caption[Stacking sequence of SiC bilayers of the most common polytypes of SiC.]{Stacking sequence of SiC bilayers of the most common polytypes of SiC (from left to right): 3C, 2H, 4H and 6H.}

 \label{fig:sic:polytypes}
 \end{figure}
 Fig.~\ref{fig:sic:polytypes} shows the stacking sequence of the most common and technologically most important SiC polytypes, which are the cubic (3C) and hexagonal (2H, 4H and 6H) polytypes.
 \label{fig:sic:polytypes}
 \end{figure}
 Fig.~\ref{fig:sic:polytypes} shows the stacking sequence of the most common and technologically most important SiC polytypes, which are the cubic (3C) and hexagonal (2H, 4H and 6H) polytypes.


@@ -103,7 +103,7 @@ Thus the cubic phase is most effective for highly efficient high-performance ele
 \begin{center}
 \includegraphics[width=0.35\columnwidth]{sic_unit_cell.eps}
 \end{center}
 \begin{center}
 \includegraphics[width=0.35\columnwidth]{sic_unit_cell.eps}
 \end{center}

-\caption{3C-SiC unit cell. Yellow and grey spheres correpsond to Si and C atoms respectively. Covalent bonds are illustrated by blue lines.}
+\caption[3C-SiC unit cell.]{3C-SiC unit cell. Yellow and grey spheres correpsond to Si and C atoms respectively. Covalent bonds are illustrated by blue lines.}

 \label{fig:sic:unit_cell}
 \end{figure}
 Its unit cell is shown in Fig.~\ref{fig:sic:unit_cell}.
 \label{fig:sic:unit_cell}
 \end{figure}
 Its unit cell is shown in Fig.~\ref{fig:sic:unit_cell}.


@@ -289,7 +289,7 @@ Fig. \ref{fig:sic:hrem_sharp} shows the respective high resolution transmission
 \begin{center}
 \includegraphics[width=0.6\columnwidth]{ibs_3c-sic.eps}
 \end{center}
 \begin{center}
 \includegraphics[width=0.6\columnwidth]{ibs_3c-sic.eps}
 \end{center}

-\caption[Bright field (a) and \hkl(1 1 1) SiC dark field (b) cross-sectional TEM micrographs of the buried SiC layer in Si created by the two-temperature implantation technique and subsequent annealing.]{Bright field (a) and \hkl(1 1 1) SiC dark field (b) cross-sectional TEM micrographs of the buried SiC layer in Si created by the two-temperature implantation technique and subsequent annealing as explained in the text \cite{lindner99_2}. The inset shows a selected area diffraction pattern of the buried layer.}
+\caption[Bright field and \hkl(1 1 1) SiC dark field cross-sectional TEM micrographs of the buried SiC layer in Si created by the two-temperature implantation technique and subsequent annealing.]{Bright field (a) and \hkl(1 1 1) SiC dark field (b) cross-sectional TEM micrographs of the buried SiC layer in Si created by the two-temperature implantation technique and subsequent annealing as explained in the text \cite{lindner99_2}. The inset shows a selected area diffraction pattern of the buried layer.}

 \label{fig:sic:hrem_sharp}
 \end{figure}
 
 \label{fig:sic:hrem_sharp}
 \end{figure}
 


@@ -375,7 +375,7 @@ The agglomerates of such dimers, which do not generate lattice strain but lead t
 \subfigure[]{\label{fig:sic:hrem:c-si}\includegraphics[width=0.25\columnwidth]{tem_c-si-db.eps}}
 \subfigure[]{\label{fig:sic:hrem:sic}\includegraphics[width=0.25\columnwidth]{tem_3c-sic.eps}}
 \end{center}
 \subfigure[]{\label{fig:sic:hrem:c-si}\includegraphics[width=0.25\columnwidth]{tem_c-si-db.eps}}
 \subfigure[]{\label{fig:sic:hrem:sic}\includegraphics[width=0.25\columnwidth]{tem_3c-sic.eps}}
 \end{center}

-\caption[High resolution transmission electron microscopy (HREM) micrographs of agglomerates of C-Si dimers showing dark contrasts and otherwise undisturbed Si lattice fringes (a) and equally sized Moir\'e patterns indicating 3C-SiC precipitates (b).]{High resolution transmission electron microscopy (HREM) micrographs \cite{lindner99_2} of agglomerates of C-Si dimers showing dark contrasts and otherwise undisturbed Si lattice fringes (a) and equally sized Moir\'e patterns indicating 3C-SiC precipitates (b).}
+\caption[High resolution transmission electron microscopy (HREM) micrographs of agglomerates of C-Si dimers showing dark contrasts and otherwise undisturbed Si lattice fringes and equally sized Moir\'e patterns indicating 3C-SiC precipitates.]{High resolution transmission electron microscopy (HREM) micrographs \cite{lindner99_2} of agglomerates of C-Si dimers showing dark contrasts and otherwise undisturbed Si lattice fringes (a) and equally sized Moir\'e patterns indicating 3C-SiC precipitates (b).}

 \label{fig:sic:hrem}
 \end{figure}
 A topotactic transformation into a 3C-SiC precipitate occurs once a critical radius of \unit[2]{nm} to \unit[4]{nm} is reached.
 \label{fig:sic:hrem}
 \end{figure}
 A topotactic transformation into a 3C-SiC precipitate occurs once a critical radius of \unit[2]{nm} to \unit[4]{nm} is reached.