X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Fthesis%2Fmd.tex;h=4440648ab3f1e8bd53b886ac1a7880ca80883763;hb=840f7807ab9f61a0303f3beaa11669cfe3f395b4;hp=0e695a6e63f4881b6804f5f220ae70bd44a47c86;hpb=c6aa696b5c69690f95020b041b9f8854e779b0a6;p=lectures%2Flatex.git

diff --git a/posic/thesis/md.tex b/posic/thesis/md.tex
index 0e695a6..4440648 100644
--- a/posic/thesis/md.tex
+++ b/posic/thesis/md.tex
@@ -457,6 +457,8 @@ However, by applying these values the final configuration varies only slightly f
 Obtained & 5495 & 5486 & 68591 & 74077\\
 Expected & 5500 & 5500 & 68588 & 74088\\
 Difference & -5 & -14 & 3 & -11\\
+Notation & - & $N^{\text{3C-SiC}}_{\text{Si}}$ & $N^{\text{c-Si}}_{\text{Si}}$
+         & $N^{\text{total}}_{\text{Si}}$ \\
 \hline
 \hline
 \end{tabular}
@@ -473,24 +475,40 @@ Once the main part of the excess energy is carried out previous settings for the
 \begin{center}
 \includegraphics[width=12cm]{pc_0.ps}
 \end{center}
-\caption[Radial distribution of a 3C-SiC precipitate embeeded in c-Si at $20\,^{\circ}\mathrm{C}$.]{Radial distribution of a 3C-SiC precipitate embeeded in c-Si at $20\,^{\circ}\mathrm{C}$. The Si-Si radial distribution of plain c-Si is plotted for comparison. Grey arrows mark bumps in the Si-Si distribution of the precipitate configuration, which do not exist in plain c-Si.}
+\caption[Radial distribution of a 3C-SiC precipitate embeeded in c-Si at $20\,^{\circ}\mathrm{C}$.]{Radial distribution of a 3C-SiC precipitate embeeded in c-Si at $20\,^{\circ}\mathrm{C}$. The Si-Si radial distribution of plain c-Si is plotted for comparison. Green arrows mark bumps in the Si-Si distribution of the precipitate configuration, which do not exist in plain c-Si.}
 \label{fig:md:pc_sic-prec}
 \end{figure}
-Figure \ref{fig:md:pc_sic-prec} shows the radial distribution of the obtained configuration.
-Comparing the Si-Si radial distribution of plain c-Si with the one of the precipitate configuration no difference is observed for the distances of neighboured silicon pairs.
-Although no sifnificant change of the lattice constant of the c-Si matrix was assumed, surprisingly there is no change at all within observational accuracy.
-Nice, since obviously matrix is big enough to exclude size effects in the system in which pbc are applied, we can consider it single precipitate in a infinite Si matrix.
-A new peak for the silicon pairs arises at 0.307 nm.
-It is identical to the peak of the C-C distribution around that value.
+Figure \ref{fig:md:pc_sic-prec} shows the radial distribution of the obtained precipitate configuration.
+The Si-Si radial distribution for both, plain c-Si and the precipitate configuration show a maximum at a distance of 0.235 nm, which is the distance of next neighboured Si atoms in c-Si.
+Although no significant change of the lattice constant of the surrounding c-Si matrix was assumed, surprisingly there is no change at all within observational accuracy.
+A new Si-Si peak arises at 0.307 nm, which is identical to the peak of the C-C distribution around that value.
 It corresponds to second next neighbours in 3C-SiC, which applies for Si as well as C pairs.
-The bumps of the Si-Si distribution at higher distances, which are marked by grey arrows and do not exist in plain c-Si, can be explained in the same manner.
-They correspond to the fourth and sixth next neighbour in 3C-SiC.
-Again, these peaks apply to Si and C pairs and indeed it is easily identifiale how the C-C peaks at contribute to the bumps observed in the Si-Si distribution.
+The bumps of the Si-Si distribution at higher distances marked by the green arrows can be explained in the same manner.
+They correspond to the fourth and sixth next neighbour distance in 3C-SiC.
+It is easily identifiable how these C-C peaks, which imply Si pairs at same distances inside the precipitate, contribute to the bumps observed in the Si-Si distribution.
+The Si-Si and C-C peak at 0.307 nm enables the determination of the lattic constant of the embedded 3C-SiC precipitate.
+A lattice constant of 4.34 \AA{} compared to 4.36 \AA{} for bulk 3C-SiC is obtained.
+This is in accordance with the peak of Si-C pairs at a distance of 0.188 nm.
+Thus, the precipitate structure is slightly compressed compared to the bulk phase.
+This is a quite surprising result since due to the finite size of the c-Si surrounding a non-negligible impact of the precipitate on the materializing c-Si lattice constant especially near the precipitate could be assumed.
+However, it seems that the size of the c-Si host matrix is chosen large enough to even find the precipitate in a compressed state.
+
+The fact that the lattice constant of the c-Si surrounding is unchanged is due to the possibility of the system to change its volume.
+Otherwise the increase of the lattice constant of the precipitate of roughly 4.31 \AA{} in the beginning up to 4.34 \AA{} could not take place without an accompanying reduction of the lattice constant of the c-Si surrounding.
+The expected increase in volume can be calculated by
+\begin{equation}
+ \frac{V}{V_0}=
+ \frac{\frac{N^{\text{c-Si}}_{\text{Si}}}{8/a_{\text{c-Si}}}+
+ \frac{N^{\text{3C-SiC}}_{\text{Si}}}{4/a_{\text{3C-SiC}}}}
+ {\frac{N^{\text{total}}_{\text{Si}}}{8/a_{\text{c-Si}}}}
+\end{equation}
+with the notation used in table \ref{table:md:sic_prec} and $a$ being the lattice constants at $20\,^{\circ}\mathrm{C}$ of the respective material.
 
-4.34 \AA{} compared to 4.36 \AA{}.
+Inserting the obtained amounts of atoms of table \ref{table:md:sic_prec} results in an increase of the initial volume by only 0.3 \%.
 
-New lattice constant
-Surface energy
+However, each side length and the total volume of the simulation box is increased by 0.4 \% and 1.2 \% respectively of the initial state.
+
+Surface energy ... quench to 0K!
 
 Now let's see, whether annealing will lead to some energetically more favorable configurations.
 
@@ -500,3 +518,12 @@ Now let's see, whether annealing will lead to some energetically more favorable
 LL Cool J is hot as hell!
 
 A different simulation volume and refined amount as well as shape of insertion volume for the C atoms, to stay compareable to the results gained in the latter section, is used throughout all following simulations.
+
+\subsection{Todo}
+
+{\color{red}TODO: self-guided MD!}
+
+{\color{red}TODO: other approaches!}
+
+{\color{red}TODO: ART MD?}
+