From: hackbard Date: Mon, 31 May 2010 16:55:57 +0000 (+0200) Subject: too less ... X-Git-Url: https://hackdaworld.org/gitweb/?a=commitdiff_plain;h=253e08003d7cce7a777f7355110ae0ed86e644e2;p=lectures%2Flatex.git too less ... --- diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex index 14b5514..c739087 100644 --- a/posic/thesis/defects.tex +++ b/posic/thesis/defects.tex @@ -680,11 +680,11 @@ In addition the bond-ceneterd configuration, for which spin polarized calculatio \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. -In order to find possible migration pathways that have an activation energy lower than the ones found up to now. +This is investigated in the following in order to find possible migration pathways that have an activation energy lower than the ones found up to now. The next energetically favorable defect configuration is the \hkl<1 1 0> C-Si dumbbell interstitial. Figure \ref{fig:defects:110_mig_vasp} shows the migration barrier of the \hkl<1 1 0> C-Si dumbbell to the bond-centered, \hkl<0 0 -1> and \hkl<0 -1 0> (in place) transition. Indeed less than 0.7 eV are necessary to turn a \hkl<0 -1 0>- to a \hkl<1 1 0>-type C-Si dumbbell interstitial. -This transition is carried out in place, that is the Si dumbbell pair is not changed and both, the Si and C atom share the same lattice site. +This transition is carried out in place, that is the Si dumbbell pair is not changed and both, the Si and C atom share the initial lattice site. Thus, this transition does not contribute to long-range diffusion. Once the C atom resides in the \hkl<1 1 0> interstitial configuration it can migrate into the bond-centered configuration by employing approximately 0.95 eV of activation energy, which is only slightly higher than the activation energy needed for the \hkl<0 0 -1> to \hkl<0 -1 0> pathway shown in figure \ref{fig:defects:00-1_0-10_mig}. As already known from the migration of the \hkl<0 0 -1> to the bond-centered configuration as discussed in figure \ref{fig:defects:00-1_001_mig} another 0.25 eV are needed to turn back from the bond-centered to a \hkl<1 0 0>-type interstitial. @@ -718,30 +718,54 @@ The method in which the constraints are only applied to the diffusing C atom and The same method for obtaining migration barriers and the same suggested pathways are applied to calculations employing the classical Erhard/Albe potential. Since the evaluation of the classical potential and force is less computationally intensive higher amounts of steps can be used. -The time constant $\tau$ for the Berendsen thermostat is set to 1.0 fs in order to have direct velocity scaling and with the temperature set to zero Kelvin perform a steepest descent minimazation to drive the system into a local minimum. +The time constant $\tau$ for the Berendsen thermostat is set to 1 fs in order to have direct velocity scaling and with the temperature set to zero Kelvin perform a steepest descent minimazation to drive the system into a local minimum. +However, in some cases a time constant of 100 fs resuls in lower barriers and, thus, is shown whenever appropriate. \begin{figure}[th!] \begin{center} -\includegraphics[width=13cm]{bc_00-1.ps} +\includegraphics[width=13cm]{bc_00-1.ps}\\[1.8cm] +\begin{pspicture}(0,0)(0,0) +\psframe*[linecolor=blue,fillstyle=none,fillcolor=white](-8,3)(7,0) +\end{pspicture} +\begin{picture}(0,0)(160,0) +\includegraphics[width=2.2cm]{albe_mig/bc_00-1_01.eps} +\end{picture} +\begin{picture}(0,0)(100,0) +\includegraphics[width=2.2cm]{albe_mig/bc_00-1_02.eps} +\end{picture} +\begin{picture}(0,0)(10,0) +\includegraphics[width=2.2cm]{albe_mig/bc_00-1_03.eps} +\end{picture} +\begin{picture}(0,0)(-120,0) +\includegraphics[width=2.2cm]{albe_mig/bc_00-1_04.eps} +\end{picture} +\begin{picture}(0,0)(25,20) +\includegraphics[width=2.5cm]{100_arrow.eps} +\end{picture} +\begin{picture}(0,0)(215,0) +\includegraphics[height=2.2cm]{010_arrow.eps} +\end{picture} \end{center} \caption{Migration barrier of the bond-centered to \hkl<0 0 -1> dumbbell transition using the classical Erhard/Albe potential.} \label{fig:defects:cp_bc_00-1_mig} -% ./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 +% 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} Figure \ref{fig:defects:cp_bc_00-1_mig} shows the migration barrier of the bond-centered to \hkl<0 0 -1> dumbbell transition. Since the bond-centered configuration is unstable relaxing into the \hkl<1 1 0> C-Si dumbbell interstitial configuration within this potential the low kinetic energy state is used as a starting configuration. - +Depending on the time constant activation energies of 2.4 eV and 2.2 eV respectively are obtained. +The migration path obtained by simulations with a time constant of 1 fs remains in the \hkl(1 1 0) plane. +Using 100 fs as a time constant the C atom breaks out of the \hkl(1 0 0) plane already at the beginning of the migration accompanied by a reduction in energy. +The energy barrier of this path is 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. \begin{figure}[th!] \begin{center} \includegraphics[width=13cm]{00-1_0-10.ps} \end{center} -\caption{Migration barrier of the \hkl<0 0 -1> \hkl<0 -1 0> C-Si dumbbell transition using the classical Erhard/Albe potential.} +\caption{Migration barrier of the \hkl<0 0 -1> to \hkl<0 -1 0> C-Si dumbbell transition using the classical Erhard/Albe potential.} \label{fig:defects:cp_00-1_0-10_mig} \end{figure} -Figure \ref{fig:defects:cp_00-1_0-10_mig} shows the migration barrier of the \hkl<0 0 -1> to \hkl<0 -1 0> C-Si dumbbell transition. -After the first maximum the system relaxes to a configuration similar to the \hkl<1 1 0> C-Si dumbbell configuration. - \begin{figure}[th!] \begin{center} \includegraphics[width=13cm]{00-1_ip0-10.ps} @@ -749,7 +773,18 @@ After the first maximum the system relaxes to a configuration similar to the \hk \caption{Migration barrier of the \hkl<0 0 -1> to \hkl<0 -1 0> C-Si dumbbell transition in place using the classical Erhard/Albe potential.} \label{fig:defects:cp_00-1_ip0-10_mig} \end{figure} -Figure \ref{fig:defects:cp_00-1_ip0-10_mig} shows the migration barrier of the \hkl<0 0 -1> to \hkl<0 -1 0> C-Si dumbbell transition in place. +Figure \ref{fig:defects:cp_00-1_0-10_mig} and \ref{fig:defects:cp_00-1_ip0-10_mig} show the migration barriers of \hkl<0 0 -1> to \hkl<0 -1 0> C-Si dumbbell transition, with a transition of the C atom to the neighboured lattice site in the first case and a reorientation within the same lattice site in the latter case. +Both pathways look similar. +A local minimum exists inbetween two peaks of the graph. +The corresponding configuration looks similar to the \hkl<1 1 0> configuration. +Indeed, this configuration is obtained by relaxation simulations without constraints of configurations near the minimum. +Activation energies of roughly 2.8 eV and 2.7 eV respectively are needed for migration. + +... diffusion ... +... indicate a problem that is formulated and discussed in more detail in section ... + +Since the \hkl<1 1 0> configuration einnehmen a besondere role in all migration pathways migrations mit dieser configuration are investigated further. +... \section{Combination of point defects}