sic prec findings: volume inc

diff --git a/posic/thesis/md.tex b/posic/thesis/md.tex
index bd6d979b58f1a86bb3b6dc9a5d64823e08fba3ed..4440648ab3f1e8bd53b886ac1a7880ca80883763 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\\
+Notation & - & $N^{\text{3C-SiC}}_{\text{Si}}$ & $N^{\text{c-Si}}_{\text{Si}}$
+         & $N^{\text{total}}_{\text{Si}}$ \\
 \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.
-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}
-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}
-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.
 
@@ -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.
 
+\subsection{Todo}
+
+{\color{red}TODO: self-guided MD!}
+
+{\color{red}TODO: other approaches!}
+
 {\color{red}TODO: ART MD?}