From 7ad6a4b50525b0d14f94d21dcb5dd04d7dc336c8 Mon Sep 17 00:00:00 2001 From: hackbard Date: Wed, 5 May 2010 18:17:53 +0200 Subject: [PATCH] finished first prec exps, goto interface and energy + optimized/annealed structures --- posic/thesis/md.tex | 38 +++++++++++++++++++++++--------------- 1 file changed, 23 insertions(+), 15 deletions(-) diff --git a/posic/thesis/md.tex b/posic/thesis/md.tex index 4440648..bbdd448 100644 --- a/posic/thesis/md.tex +++ b/posic/thesis/md.tex @@ -457,8 +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 & - & $N^{\text{3C-SiC}}_{\text{Si}}$ & $N^{\text{c-Si}}_{\text{Si}}$ - & $N^{\text{total}}_{\text{Si}}$ \\ +Notation & $N^{\text{3C-SiC}}_{\text{C}}$ & $N^{\text{3C-SiC}}_{\text{Si}}$ + & $N^{\text{c-Si}}_{\text{Si}}$ & $N^{\text{total}}_{\text{Si}}$ \\ \hline \hline \end{tabular} @@ -481,6 +481,7 @@ 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. +Looking closer at higher order Si-Si peaks might even allow the guess of a slight increase of the lattice constant compared to the plain c-Si structure. 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. @@ -493,24 +494,31 @@ Thus, the precipitate structure is slightly compressed compared to the bulk phas 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 +The absence of a compression of the c-Si surrounding 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{} in the relaxed precipitate configuration could not take place without an accompanying reduction of the lattice constant of the c-Si surrounding. +If the total volume is assumed to be the sum of the volumes that are composed of Si atoms forming the c-Si surrounding and Si atoms involved forming the precipitate the expected increase 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}}}} + \frac{\frac{N^{\text{c-Si}}_{\text{Si}}}{8/a_{\text{c-Si of precipitate configuration}}}+ + \frac{N^{\text{3C-SiC}}_{\text{Si}}}{4/a_{\text{3C-SiC of precipitate configuration}}}} + {\frac{N^{\text{total}}_{\text{Si}}}{8/a_{\text{plain 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. - -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 \%. - -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. - +with the notation used in table \ref{table:md:sic_prec}. +The lattice constant of plain c-Si at $20\,^{\circ}\mathrm{C}$ can be determined more accurately by the side lengthes of the simulation box of an equlibrated structure instead of using the radial distribution data. +By this a value of $a_{\text{plain c-Si}}=5.439\text{ \AA}$ is obtained. +The same lattice constant is assumed for the c-Si surrounding in the precipitate configuration $a_{\text{c-Si of precipitate configuration}}$ since peaks in the radial distribution match the ones of plain c-Si. +Using $a_{\text{3C-SiC of precipitate configuration}}=4.34\text{ \AA}$ as observed from the radial distribution finally results in an increase of the initial volume by 0.12 \%. +However, each side length and the total volume of the simulation box is increased by 0.20 \% and 0.61 \% respectively compared to plain c-Si at $20\,^{\circ}\mathrm{C}$. +Since the c-Si surrounding resides in an uncompressed state the excess increase must be attributed to relaxation of strain with the strain resulting from either the compressed precipitate or the 3C-SiC/c-Si interface region. +This also explains the possibly identified slight increase of the c-Si lattice constant in the surrounding as mentioned earlier. +As the pressure is set to zero the free energy is minimized with respect to the volume enabled by the Berendsen barostat algorithm. +Apparently the minimized structure with respect to the volume is a configuration of a small compressively stressed precipitate and a large amount of slightly stretched c-Si in the surrounding. + +One way to describe interfaces is to To describe the interface Surface energy ... quench to 0K! -Now let's see, whether annealing will lead to some energetically more favorable configurations. +Since interface region is constructed and not neccesarily corresponds to the energetically most favorable layout we will now try hard to improve this ... +Let's see, whether annealing will lead to some energetically more favorable configurations. \subsection{Simulations at temperatures exceeding the silicon melting point} -- 2.20.1