From be08a476ec89ceb6c2937c935d607260e97532e6 Mon Sep 17 00:00:00 2001 From: hackbard Date: Thu, 4 Mar 2010 18:04:34 +0100 Subject: [PATCH] next complex structure --- posic/thesis/defects.tex | 50 ++++++++++++++++++++++++++++++++-------- 1 file changed, 40 insertions(+), 10 deletions(-) diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex index 0f09f03..9d6d236 100644 --- a/posic/thesis/defects.tex +++ b/posic/thesis/defects.tex @@ -661,6 +661,7 @@ Investigations are restricted to quantum-mechanical calculations. \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] @@ -694,13 +695,13 @@ Relative silicon neighbour positions: \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} & -2.16 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{magenta}-1.88} & -0.09\\ - \hkl<0 1 0> & {\color{cyan}-2.25} & -0.36 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{violet}-1.38} & -\\ - \hkl<-1 0 0> & {\color{orange}-2.39} & -1.90 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{magenta}-1.88} & -\\ - \hkl<1 0 0> & {\color{cyan}-2.25} & -0.17 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{violet}-1.38} & -\\ + \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 & -\\ - Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -\\ + 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} @@ -723,7 +724,7 @@ For defects far away from each other the formation energy of the defect combinat 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 ...-type the interaction is even mor reduced resulting in an energy of $E_{\text{b}}=...\text{ eV}$ for a distance, which is the maximum that can be realized due to periodic boundary conditions. +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. @@ -767,9 +768,38 @@ The Si atom numbered 2 is pushed towards the carbon atom, which results in the b 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? -Figure \ref{} shows the next three configurations energetically favored. --2.16 ... next to correct C-Si also a nicely C-C distance observed! -sth similar to C-Si 110 db without delta h due to the involevment of initial c int atom. +\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 ... -- 2.20.1