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 basic problems of analytical potential models for describing defect structures.
-However, the energy barrier is small (DAS MAL DURCHRECHNEN).
+However, the energy barrier is small.
+Todo: Check!
Hence these artifacts should have a negligent influence in finite temperature simulations.
The bond-centered configuration is unstable and the \hkl<1 0 0> dumbbell interstitial is the most unfavorable configuration for both, the Erhard/Albe and VASP calculations.
The same applies to the bonds between the interstitial and the upper two atoms in the \hkl<1 1 0> dumbbell configuration.
A more detailed description of the chemical bonding is achieved by quantum-mechanical calculations by investigating the accumulation of negative charge between the nuclei.
-Todo: Plot the electron density for these types of defect to derive conclusions of existing bonds ...
+Todo: Plot the electron density for these types of defect to derive conclusions of existing bonds?
\section{Carbon related point defects}
\end{minipage}
\end{minipage}
\end{center}
-\label{img:defects:c_mig_path}
\caption{Migration pathways of the carbon \hkl<1 0 0> interstitial dumbbell in silicon.}
+\label{img:defects:c_mig_path}
\end{figure}
-Three different migration paths are accounted in this work, which are shown in figure \ref{img:defects:c_mig_path}
+Three different migration paths are accounted in this work, which are shown in figure \ref{img:defects:c_mig_path}.
The first migration investigated is a transition of a \hkl<0 0 -1> into a \hkl<0 0 1> dumbbell interstitial configuration.
-The new silicon dumbbell partner is the one located at $\frac{a}{4}\hkl<1 1 -1>$ compared to the initial one.
-The carbon atom resides in the \hkl(1 1 0) plane along the path.
-As a last migration path, the \hkl<0 0 -1>
+During this migration the carbon atom is changing its silicon dumbbell partner.
+The new partner is the one located at $\frac{a}{4}\hkl<1 1 -1>$ relative to the initial one.
+Two of the three bonds to the next neighboured silicon atoms are preserved while the breaking of the third bond and the accompanying formation of a new bond is observed.
+The carbon atom resides in the \hkl(1 1 0) plane.
+This transition involves an intermediate bond-centerd configuration.
+Results discussed in \ref{subsection:bc} indicate, that the bond-ceneterd configuration is a real local minimum.
+Thus, the \hkl<0 0 -1> to \hkl<0 0 1> migration can be thought of a two-step mechanism in which the intermediate bond-cenetered configuration constitutes a metastable configuration.
+Due to symmetry it is enough to consider the transition from the bond-centered to the \hkl<1 0 0> configuration or vice versa.
+In the second path, the carbon atom is changing its silicon partner atom as in path one.
+However, the trajectory of the carbon atom is no longer proceeding in the \hkl(1 1 0) plane.
+The orientation of the new dumbbell configuration is transformed from \hkl<0 0 -1> to \hkl<0 -1 0>.
+Again one bond is broken while another one is formed.
+As a last migration path, the defect is only changing its orientation.
+Thus, it is not responsible for long-range migration.
+The silicon dumbbell partner remains the same.
+The bond to the face-centered silicon atom at the bottom of the unit cell breaks and a new one is formed to the face-centered atom at the forefront of the unit cell.
+Todo: \hkl<1 1 0> to \hkl<1 0 0> and bond-centerd configuration (in progress).
+Todo: \hkl<1 1 0> to \hkl<0 -1 0> (rotation of the DB, in progress).
+Todo: Comparison with classical potential simulations or explanation to only focus on ab initio calculations.
+
+Since the starting and final structure, which are both local minima of the potential energy surface, are known, the aim is to find the minimum energy path from one local minimum to the other one.
+One method to find a minimum energy path is to move the diffusing atom stepwise from the starting to the final position and only allow relaxation in the plane perpendicular to the direction of the vector connecting its starting and final position.
+No constraints are applied to the remaining atoms in order to allow relaxation of the surrounding lattice.
+To prevent the remaining lattice to migrate according to the displacement of the defect an atom far away from the defect region is fixed in all three coordinate directions.
+However, it turned out, that this method tremendously failed applying it to the present migration pathways and structures.
+Abrupt changes in structure and free energy occured among relaxed structures of two successive displacement steps.
+For some structures even the expected final configurations were never obtained.
+Thus, the method mentioned above was adjusted adding further constraints in order to obtain smooth transitions, either in energy as well as structure is concerned.
+In this new method all atoms are stepwise displaced towards their final positions.
+Relaxation of each individual atom is only allowed in the plane perpendicular to the last individual displacement vector.
+The modifications used to add this feature to the VASP code and a short instruction on how to use it can be found in appendix \ref{app:patch_vasp}.
+Due to these constraints obtained activation energies can effectively be higher.
+Todo: To refine the migration barrier one has to find the saddle point structure and recalculate the free energy of this configuration with a reduced set of constraints.
-Since the starting and final structure, which are both local minima of the potential energy surface are known, the aim is to find the minimum energy path from one local minimum to the other one.
-One method is to move the diffusing atom stepwise from the starting to the final position and only allow relaxation in the plane perpendicular to the direction of the vector connecting its starting and final position.
-No constraints are applied to the remaining atoms.
+\begin{figure}[h]
+\begin{center}
+\includegraphics[width=13cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[1.5cm]
+\begin{picture}(0,0)(150,0)
+\includegraphics[width=2.5cm]{vasp_mig/00-1.eps}
+\end{picture}
+\begin{picture}(0,0)(-10,0)
+\includegraphics[width=2.5cm]{vasp_mig/bc_00-1_sp.eps}
+\end{picture}
+\begin{picture}(0,0)(-120,0)
+\includegraphics[width=2.5cm]{vasp_mig/bc.eps}
+\end{picture}
+\begin{picture}(0,0)(25,20)
+\includegraphics[width=2.5cm]{110_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(200,0)
+\includegraphics[height=2.2cm]{001_arrow.eps}
+\end{picture}
+\end{center}
+\caption[Migration barrier and structures of the \hkl<0 0 -1> dumbbell (left) to bond-centered (right) transition.]{Migration barrier and structures of the \hkl<0 0 -1> dumbbell (left) to bond-centered (right) transition. Bonds of the carbon atoms are illustrated by blue lines.}
+\label{fig:defects:00-1_001_mig}
+\end{figure}
+In figure \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> dumbbell to the bond-ceneterd configuration is displayed.
+To reach the bond-centered configuration, which is 0.94 eV higher in energy than the \hkl<0 0 -1> dumbbell configuration, an energy barrier of approximately 1.2 eV, given by the saddle point structure at a displacement of 60 \%, has to be passed.
+This amount of energy is needed to break the bond of the carbon atom to the silicon atom at the bottom left.
+In a second process 0.25 eV of energy are needed for the system to revert into a \hkl<1 0 0> configuration.
-Different approaches were used to compute migration paths and energies.
-CRT erklaeren
-Nur C atom constrainted
-Problem, 1) relaxation of host matrix 2) abrubt changes in energy and configuration
-as can be seen in ...
-Thus, 'all atom CRT' but! relaxation perpendicular to delta step ...
+\begin{figure}[h]
+\begin{center}
+\includegraphics[width=13cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[1.6cm]
+\begin{picture}(0,0)(140,0)
+\includegraphics[width=2.5cm]{vasp_mig/00-1_a.eps}
+\end{picture}
+\begin{picture}(0,0)(20,0)
+\includegraphics[width=2.5cm]{vasp_mig/00-1_0-10_sp.eps}
+\end{picture}
+\begin{picture}(0,0)(-120,0)
+\includegraphics[width=2.5cm]{vasp_mig/0-10.eps}
+\end{picture}
+\begin{picture}(0,0)(25,20)
+\includegraphics[width=2.5cm]{100_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(200,0)
+\includegraphics[height=2.2cm]{001_arrow.eps}
+\end{picture}
+\end{center}
+\caption[Migration barrier and structures of the \hkl<0 0 -1> dumbbell (left) to the \hkl<0 -1 0> dumbbell (right) transition.]{Migration barrier and structures of the \hkl<0 0 -1> dumbbell (left) to the \hkl<0 -1 0> dumbbell (right) transition. Bonds of the carbon atoms are illustrated by blue lines.}
+\label{fig:defects:00-1_0-10_mig}
+\end{figure}
+Figure \ref{fig:defects:00-1_0-10_mig} shows the migration barrier and structures of the \hkl<0 0 -1> to \hkl<0 -1 0> dumbbell transition.
+The resulting migration barrier of approximately 0.9 eV is very close to the experimentally obtained values of 0.73 \cite{song90} and 0.87 eV \cite{tipping87}.
+
+\begin{figure}[h]
+\begin{center}
+\includegraphics[width=13cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[1.8cm]
+\begin{picture}(0,0)(140,0)
+\includegraphics[width=2.2cm]{vasp_mig/00-1_b.eps}
+\end{picture}
+\begin{picture}(0,0)(20,0)
+\includegraphics[width=2.2cm]{vasp_mig/00-1_ip0-10_sp.eps}
+\end{picture}
+\begin{picture}(0,0)(-120,0)
+\includegraphics[width=2.2cm]{vasp_mig/0-10_b.eps}
+\end{picture}
+\begin{picture}(0,0)(25,20)
+\includegraphics[width=2.5cm]{100_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(200,0)
+\includegraphics[height=2.2cm]{001_arrow.eps}
+\end{picture}
+\end{center}
+\caption[Migration barrier and structures of the \hkl<0 0 -1> dumbbell (left) to the \hkl<0 -1 0> dumbbell (right) transition in place.]{Migration barrier and structures of the \hkl<0 0 -1> dumbbell (left) to the \hkl<0 -1 0> dumbbell (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 dumbbell is changing its orientation is shown in figure \ref{fig:defects:00-1_0-10_ip_mig}.
+An energy barrier of roughly 1.2 eV is observed.
+Experimentally measured activation energies for reorientation range from 0.77 eV to 0.88 eV \cite{watkins76,song90}.
+Thus, this pathway is more likely to be composed of two consecutive steps of the second path.
-Results and comparison with diffusion experiments.
+Since the activation energy of the first and last migration path is much greater than the experimental value, the second path is identified to be responsible as a migration path for the most likely carbon interstitial in silicon explaining both, annealing and reorientation experiments.
+The activation energy of roughly 0.9 eV nicely compares to experimental values.
+The theoretical description performed in this work is improved compared to a former study \cite{capaz94}, which underestimates the experimental value by 35 \%.
+In addition the bond-ceneterd configuration, for which spin polarized calculations are necessary, is found to be a real local minimum instead of a saddle point configuration.
\section{Combination of point defects}
+The structural and energetic properties of combinations of point defects are investigated in the following.
+The focus is on combinations of the \hkl<0 0 -1> dumbbell interstitial with a second defect.
+The second defect is either another \hkl<1 0 0>-type interstitial occupying different orientations, a vacany or a substitutional carbon atom.
+Several distances of the two defects are examined.
+Investigations are restricted to quantum-mechanical calculations.
+\begin{figure}[h]
+\begin{center}
+\begin{minipage}{7.5cm}
+\includegraphics[width=7cm]{comb_pos.eps}
+% ./visualize_contcar -w 640 -h 480 -d results/.../CONTCAR -nll -0.20 -0.20 -0.6 -fur 1.2 1.2 0.6 -c 0.5 -1.5 0.3 -L 0.5 0 0 -r 0.6 -m 3.0 0.0 0.0 0.0 3.0 0.0 0.0 0.0 3.0 -A -1 2.465
+\end{minipage}
+\begin{minipage}{6.0cm}
+\underline{Positions given in $a_{\text{Si}}$}\\[0.3cm]
+Initial interstitial I: $\frac{1}{4}\hkl<1 1 1>$\\
+Relative silicon neighbour positions:
+\begin{enumerate}
+ \item $\frac{1}{4}\hkl<1 1 -1>$, $\frac{1}{4}\hkl<-1 -1 -1>$
+ \item $\frac{1}{2}\hkl<1 0 1>$, $\frac{1}{2}\hkl<0 1 -1>$,\\[0.2cm]
+ $\frac{1}{2}\hkl<0 -1 -1>$, $\frac{1}{2}\hkl<-1 0 -1>$
+ \item $\frac{1}{4}\hkl<1 -1 1>$, $\frac{1}{4}\hkl<-1 1 1>$
+ \item $\frac{1}{4}\hkl<-1 1 -3>$, $\frac{1}{4}\hkl<1 -1 -3>$
+ \item $\frac{1}{2}\hkl<-1 -1 0>$, $\frac{1}{2}\hkl<1 1 0>$
+\end{enumerate}
+\end{minipage}\\
+\begin{picture}(0,0)(190,20)
+\includegraphics[width=2.3cm]{100_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(220,0)
+\includegraphics[height=2.2cm]{001_arrow.eps}
+\end{picture}
+\end{center}
+\caption[\hkl<0 0 -1> dumbbell interstitial defect and positions of next neighboured silicon atoms used for the second defect.]{\hkl<0 0 -1> dumbbell interstitial defect and positions of next neighboured silicon atoms used for the second defect. Two possibilities exist for red numbered atoms and four possibilities exist for blue numbered atoms.}
+\label{fig:defects:pos_of_comb}
+\end{figure}
+\begin{table}[h]
+\begin{center}
+\begin{tabular}{l c c c c c c}
+\hline
+\hline
+ & 1 & 2 & 3 & 4 & 5 & R\\
+ \hline
+ \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
+ \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
+ \hkl<0 -1 0> & {\color{orange}-2.39} & -0.17 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
+ \hkl<0 1 0> & {\color{cyan}-2.25} & -1.90 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
+ \hkl<-1 0 0> & {\color{orange}-2.39} & -0.36 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
+ \hkl<1 0 0> & {\color{cyan}-2.25} & -2.16 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
+ \hline
+ C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
+ Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
+\hline
+\hline
+\end{tabular}
+\end{center}
+\caption[Energetic results of defect combinations.]{Energetic results of defect combinations. The given energies in eV are defined by equation \eqref{eq:defects:e_of_comb}. Equivalent configurations are marked by identical colors. The first column lists the types of the second defect combined with the initial \hkl<0 0 -1> dumbbell interstitial. The position index of the second defect is given in the first row according to figure \ref{fig:defects:pos_of_comb}. R is the position located at $\frac{a_{\text{Si}}}{2}\hkl<3 2 3>$ relative to the initial defect, which is the maximum realizable distance due to periodic boundary conditions.}
+\label{tab:defects:e_of_comb}
+\end{table}
+Figure \ref{fig:defects:pos_of_comb} shows the initial \hkl<0 0 -1> dumbbell interstitial defect and the positions of next neighboured silicon atoms used for the second defect.
+Table \ref{tab:defects:e_of_comb} summarizes energetic results obtained after relaxation of the defect combinations.
+The energy of interest $E_{\text{b}}$ is defined to be
+\begin{equation}
+E_{\text{b}}=
+E_{\text{f}}^{\text{defect combination}}-
+E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
+E_{\text{f}}^{\text{2nd defect}}
+\label{eq:defects:e_of_comb}
+\end{equation}
+with $E_{\text{f}}^{\text{defect combination}}$ being the formation energy of the defect combination, $E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}$ being the formation energy of the C \hkl<0 0 -1> dumbbell interstitial defect and $E_{\text{f}}^{\text{2nd defect}}$ being the formation energy of the second defect.
+For defects far away from each other the formation energy of the defect combination should approximately become the sum of the formation energies of the individual defects without an interaction resulting in $E_{\text{b}}=0$.
+Thus, $E_{\text{b}}$ can be best thought of a binding energy, which is required to bring the defects to infinite separation.
+In fact, a \hkl<0 0 -1> dumbbell interstitial created at position R with a distance of $\frac{a_{\text{Si}}}{2}\hkl<3 2 3>$ ($\approx 12.8$ \AA) from the initial one results in an energy as low as -0.19 eV.
+There is still a low interaction which is due to the equal orientation of the defects.
+By changing the orientation of the second dumbbell interstitial to the \hkl<0 -1 0>-type the interaction is even mor reduced resulting in an energy of $E_{\text{b}}=-0.05\text{ eV}$ for a distance, which is the maximum that can be realized due to periodic boundary conditions.
+The energies obtained in the R column of table \ref{eq:defects:e_of_comb} are used as a reference to identify, whether less distanced defects of the same type are favorable or unfavorable compared to the far-off located defect.
+Configurations wih energies greater than zero or the reference value are energetically unfavorable and expose a repulsive interaction.
+These configurations are unlikely to arise or to persist for non-zero temperatures.
+Energies below zero and below the reference value indicate configurations favored compared to configurations in which these point defects are separated far away from each other.
+
+Investigating the first part of table \ref{tab:defects:e_of_comb}, namely the combinations with another \hkl<1 0 0>-type interstitial, most of the combinations result in energies below zero.
+Surprisingly the most favorable configurations are the ones with the second defect created at the very next silicon neighbour and a change in orientation compared to the initial one.
+This leads to the conclusion that an agglomeration of C-Si dumbbell interstitials as proposed by the precipitation model introduced in section \ref{section:assumed_prec} is indeed an energetically favored configuration of the system.
+The reason for nearby interstitials being favored compared to isolated ones is most probably the reduction of strain energy enabled by combination in contrast to the strain energy created by two individual defects.
+\begin{figure}[h]
+\begin{center}
+\begin{minipage}[t]{7cm}
+a) \underline{$E_{\text{b}}=-2.25\text{ eV}$}
+\begin{center}
+\includegraphics[width=6cm]{00-1dc/2-25.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{7cm}
+b) \underline{$E_{\text{b}}=-2.39\text{ eV}$}
+\begin{center}
+\includegraphics[width=6cm]{00-1dc/2-39.eps}
+\end{center}
+\end{minipage}
+\end{center}
+\caption{Relaxed structures of defect complexes obtained by creating a) \hkl<1 0 0> and b) \hkl<0 -1 0> dumbbels at position 1.}
+\label{fig:defects:comb_db_01}
+\end{figure}
+Figure \ref{fig:defects:comb_db_01} shows the structure of these two configurations.
+The displayed configurations are realized by creating a \hkl<1 0 0> (a)) and \hkl<0 -1 0> (b)) dumbbell at position 1.
+Structure \ref{fig:defects:comb_db_01} b) is the energetically most favorable configuration.
+After relaxation the initial configuration is still evident.
+As expected by the initialization conditions the two carbon atoms form a bond.
+This bond has a length of 1.38 \AA{} close to the nex neighbour distance in diamond or graphite, which is approximately 1.54 \AA.
+The minimum of binding energy observed for this configuration suggests prefered C clustering as a competing mechnism to the C-Si dumbbell interstitial agglomeration inevitable for the SiC precipitation.
+Todo: Activation energy to obtain a configuration of separated C atoms again or vice versa to obtain this configuration from separated C confs?
+However, for the second most favorable configuration, presented in figure \ref{fig:defects:comb_db_01} a), the amount of possibilities for this configuration is twice as high.
+In this configuration the initial Si (I) and C (I) dumbbell atoms are displaced along \hkl<1 0 0> and \hkl<-1 0 0> in such a way that the Si atom is forming tetrahedral bonds with two silicon and two carbon atoms.
+The carbon and silicon atom constituting the second defect are as well displaced in such a way, that the carbon atom forms tetrahedral bonds with four silicon neighbours, a configuration expected in silicon carbide.
+The two carbon atoms spaced by 2.70 \AA{} do not form a bond but anyhow reside in a shorter distance as expected in silicon carbide.
+The Si atom numbered 2 is pushed towards the carbon atom, which results in the breaking of the bond to atom 4.
+The breaking of the $\sigma$ bond is indeed confirmed by investigating the charge density isosurface of this configuration.
+Todo: Is this conf really benificial for SiC prec?
+
+\begin{figure}[h]
+\begin{center}
+\begin{minipage}[t]{5cm}
+a) \underline{$E_{\text{b}}=-2.16\text{ eV}$}
+\begin{center}
+\includegraphics[width=4.8cm]{00-1dc/2-16.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{5cm}
+b) \underline{$E_{\text{b}}=-1.90\text{ eV}$}
+\begin{center}
+\includegraphics[width=4.8cm]{00-1dc/1-90.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{5cm}
+c) \underline{$E_{\text{b}}=-2.05\text{ eV}$}
+\begin{center}
+\includegraphics[width=4.8cm]{00-1dc/2-05.eps}
+\end{center}
+\end{minipage}
+\end{center}
+\caption{Relaxed structures of defect complexes obtained by creating a a) \hkl<1 0 0> and b) \hkl<0 1 0> dumbbell at position 2 and a c) \hkl<0 0 1> dumbbel at position 3.}
+\label{fig:defects:comb_db_02}
+\end{figure}
+Figure \ref{fig:defects:comb_db_02} shows the next three most energetically favorable configurations.
+The relaxed configuration obtained by creating a second \hkl<1 0 0> dumbbell at position 2 is shown in figure \ref{fig:defects:comb_db_02} a).
+A binding energy of -2.16 eV is observed.
+After relaxation the second dumbbell is aligned along \hkl<1 1 0>.
+The bond of the silicon atoms 1 and 2 does not persist.
+Instead the silicon atom forms a bond with the initial carbon interstitial and the second carbon atom forms a bond with silicon atom 1 forming four bonds in total.
+The carbon atoms are spaced by 3.14 \AA, which is very close to the expected C-C next neighbour distance of 3.08 \AA{} in silicon carbide.
+
+
+-2.05 ... both C atoms correctly coordinated, however (check C-C distance, too close?) wrong coordination of the C-Si-C bonds which reside in a plane ... all the 4 participating atoms reside in a plane ...
+
+-1.90 ... again, one C atom bound to 4 Si atoms but the second one only bond to three Si atoms. However, C-C slighlty higher.
+
+The 2.7 diatnce characteristic for configurations with one C atom bound to 4 silicon and.
+Different energies due to slightly varying constellation.
+
+the more far-off ones:
+-0.27 and -0.12 ... carbon is threefold coordinated.
+initial structures evident, seem to be independent of each other ...
+but better ...
+-1.88 and -1.38 ...
+-1.38: Si (I) moves towards 2nd Si int in 110 direction, such that both Si 4fold coordinated and C remain 3fold ...
+-1.88: threefold coordinated c atoms but all participating Si atoms fourfold coordinated ...
+
+Explanation of results of defects created along <110>.
+
+Minimum E (reorientation) per distance
+
+Todo: Si int and C sub ...
+Todo: Model of kick-out and kick-in mechnism?
+
+Todo: Jahn-Teller distortion (vacancy) $\rightarrow$ actually three possibilities! :(
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