inc temp

diff --git a/posic/publications/sic_prec.tex b/posic/publications/sic_prec.tex
index 51f2f7dfde4512cced3d12d256409ccf9eed0aa9..0524c1ab7e30831fe3502e38e8218c52db5002e1 100644 (file)
--- a/posic/publications/sic_prec.tex
+++ b/posic/publications/sic_prec.tex
@@ -194,6 +194,7 @@ This is attributed to an effective reduction in strain enabled by the respective
 Thus, a proper description with respect to the relative energies of formation is assumed for the EA potential.
 
 \subsection{Carbon mobility}
+\label{subsection:cmob}
 
 To accurately model the SiC precipitation, which involves the agglomeration of C, a proper description of the migration process of the C impurity is required.
 As shown in a previous study\cite{zirkelbach10a} quantum-mechanical results properly describe the C$_{\text{i}}$ \hkl<1 0 0> DB diffusion resulting in a migration barrier height of \unit[0.90]{eV} excellently matching experimental values of \unit[0.70-0.87]{eV}\cite{lindner06,tipping87,song90} and, for this reason, reinforcing the respective migration path as already proposed by Capaz et~al.\cite{capaz94}.
@@ -229,7 +230,7 @@ Fig.~\ref{fig:450} shows the radial distribution functions of simulations, in wh
 \includegraphics[width=\columnwidth]{../img/sic_prec_450_si-si_c-c.ps}\\
 \includegraphics[width=\columnwidth]{../img/sic_prec_450_si-c.ps}
 \end{center}
-\caption{Radial distribution function for C-C and Si-Si (top) as well as Si-C (bottom) pairs for a C insertion temperature of \unit[450]{$^{\circ}$C}. In the latter case the resulting C-Si distances for a C$_{\text{i}}$ \hkl<1 0 0> DB are given additionally.}
+\caption{Radial distribution function for C-C and Si-Si (top) as well as Si-C (bottom) pairs for C inserted at \unit[450]{$^{\circ}$C}. In the latter case the resulting C-Si distances for a C$_{\text{i}}$ \hkl<1 0 0> DB are given additionally.}
 \label{fig:450}
 \end{figure}
 There is no significant difference between C insertion into $V_2$ and $V_3$.
@@ -255,12 +256,30 @@ With respect to the precipitation model the formation of C$_{\text{i}}$ \hkl<1 0
 However, sufficient defect agglomeration is not observed.
 For high C concentrations a rearrangment of the amorphous SiC structure, which is not expected at prevailing temperatures, and a transition into 3C-SiC is not observed either.
 On closer inspection two reasons for describing this obstacle become evident.
-Inherent to MD in general ...
-Potential limitation ...
+
+First of all there is the time scale problem inherent to MD in general.
+To minimize the integration error the discretized time step must be chosen smaller than the reciprocal of the fastest vibrational mode resulting in a time step of \unit[1]{fs} for the current problem under study.
+Limitations in computer power result in a slow propgation in phase space.
+Several local minima exist, which are separated by large energy barriers.
+Due to the low probability of escaping such a local minimum a single transition event corresponds to a multiple of vibrational periods.
+Long-term evolution such as a phase transformation and defect diffusion, in turn, are made up of a multiple of these infrequent transition events.
+Thus, time scales to observe long-term evolution are not accessible by traditional MD.
+New accelerated methods have been developed to bypass the time scale problem retaining proper thermodynamic sampling\cite{voter97,voter97_2,voter98,sorensen2000,wu99}.
+
+However, the applied potential comes up with an additional limitation already mentioned in the introductory part.
+The cut-off function of the short range potential limits the interaction to next neighbors, which results in overestimated and unphysical high forces between next neighbor atoms.
+This behavior, as observed and discussed for the Tersoff potential\cite{tang95,mattoni2007}, is supported by the overestimated activation energies necessary for C diffusion as investigated in section \ref{subsection:cmob}.
+Indeed it is not only the strong C-C bond which is hard to break inhibiting C diffusion and further rearrengements in the case of the high C concentration simulations.
+This is also true for the low concentration simulations dominated by the occurrence of C$_{\text{i}}$ \hkl<1 1 0> DBs spread over the whole simulation volume, which are unable to agglomerate due to the high migration barrier.
 
 \subsection{Increased temperature simulations}
 
-Foobar ...
+Due to the potential enhanced problem of slow phase space propagation, pushing the time scale to the limits of computational ressources or applying one of the above mentioned accelerated dynamics methods exclusively might not be sufficient.
+Instead higher temperatures are utilized to compensate overestimated diffusion barriers.
+These are overestimated by a factor of 2.4 to 3.5.
+Scaling the absolute temperatures accordingly results in maximum temperatures of \unit[1460-2260]{$^{\circ}$C}.
+Since melting already occurs shortly below the melting point of the potetnial (2450 K) due to the defects, a maximum temperature of \unit[2050]{$^{\circ}$C} is used.
+Fig.~\ref{fig:tot} shows the resulting bonds for various temperatures.
 \begin{figure}
 \begin{center}
 \includegraphics[width=\columnwidth]{../img/tot_pc_thesis.ps}\\
@@ -270,6 +289,7 @@ Foobar ...
 \caption{Radial distribution function for Si-C (top), Si-Si (center) and C-C (bottom) pairs for the C insertion into $V_1$ at elevated temperatures. In the latter case dashed arrows mark C-C distances occuring from C$_{\text{i}}$ \hkl<1 0 0> DB combinations, solid arrows mark C-C distances of pure C$_{\text{s}}$ combinations and the dashed line marks C-C distances of a C$_{\text{i}}$ and C$_{\text{s}}$ combination.}
 \label{fig:tot}
 \end{figure}
+Obviously a phase transition occurs ... WEITER
 
 Barfoo ...
 \begin{figure}