sic prec findings: volume inc

diff --git a/posic/thesis/md.tex b/posic/thesis/md.tex
index bd6d979..4440648 100644 (file)
--- 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\\
 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}
 \hline
 \hline
 \end{tabular}


@@ -479,31 +481,34 @@ Once the main part of the excess energy is carried out previous settings for the
 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.
 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.

-Each side length and the total volume of the simulation box is increased by 0.4 \% and 1.2 \% respectively of the initial state.
-Indeed an increase of the total volume is expected due to the slightly lower Si density of 3C-SiC compared to c-Si.
+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 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}
 The expected increase in volume can be calculated by
 \begin{equation}

-I_V=\frac{N^{\text{c-Si}}_{\text{Si}}/n_{\text{Si}}^{\text{c-Si}}+
-           N^{\text{3C-SiC}}_{\text{Si}}/n_{\text{Si}}^{\text{3C-SiC}}}
-          {N^{\text{c-Si and 3C-SiC}}_{\text{Si}}/n_{\text{Si}}^{\text{c-Si}}}
+ \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}
 \end{equation}

-with $N_{\text{Si}}$ and $n_{\text{Si}}$ being the number of Si atoms and the Si density respectively of the corresponding material.
-Due to a slightly lower Si density of 3C-SiC compared to c-Si an increase of x \% of the total volume would be expected for precipitate with a radius of 3 nm embedded in 
-
-Calc expected increase due to Si density mismatch ...
-Obviously the surrounding matrix is chosen big enough to exclude size effects ...
-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.
-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 green 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.
+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.
+
+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 \%.

 
 

-4.34 \AA{} compared to 4.36 \AA{}.
+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.

 
 

-New lattice constant
-Surface energy
+Surface energy ... quench to 0K!

 
 Now let's see, whether annealing will lead to some energetically more favorable configurations.
 
 
 Now let's see, whether annealing will lead to some energetically more favorable configurations.
 


@@ -514,5 +519,11 @@ 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.
 
 
 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?}
 
 {\color{red}TODO: ART MD?}