From 840f7807ab9f61a0303f3beaa11669cfe3f395b4 Mon Sep 17 00:00:00 2001 From: hackbard Date: Tue, 4 May 2010 18:21:31 +0200 Subject: [PATCH] sic prec findings: volume inc --- posic/thesis/md.tex | 51 +++++++++++++++++++++++++++------------------ 1 file changed, 31 insertions(+), 20 deletions(-) diff --git a/posic/thesis/md.tex b/posic/thesis/md.tex index bd6d979..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} @@ -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?} -- 2.20.1