From: hackbard <hackbard@sage.physik.uni-augsburg.de>
Date: Thu, 6 May 2010 13:47:23 +0000 (+0200)
Subject: calculated interfacial energy
X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=fbf04a7729cd69c3416caa748f53453d860f165f;p=lectures%2Flatex.git

calculated interfacial energy
---

diff --git a/bibdb/bibdb.bib b/bibdb/bibdb.bib
index 40948ff..327f4c0 100644
--- a/bibdb/bibdb.bib
+++ b/bibdb/bibdb.bib
@@ -1605,3 +1605,22 @@
   notes =        "explanation of sgmd and hyper md, applied to amorphous
                  silicon",
 }
+
+@Article{taylor93,
+  author =       "W. J. Taylor and T. Y. Tan and U. G{\"{o}}sele",
+  collaboration = "",
+  title =        "Carbon precipitation in silicon: Why is it so
+                 difficult?",
+  publisher =    "AIP",
+  year =         "1993",
+  journal =      "Applied Physics Letters",
+  volume =       "62",
+  number =       "25",
+  pages =        "3336--3338",
+  keywords =     "SILICON; CARBON ADDITIONS; OXYGEN ADDITIONS; DOPED
+                 MATERIALS; PRECIPITATION; THERMODYNAMICS; SURFACE
+                 ENERGY",
+  URL =          "http://link.aip.org/link/?APL/62/3336/1",
+  doi =          "10.1063/1.109063",
+  notes =        "interfacial energy of cubic sic and si",
+}
diff --git a/posic/thesis/md.tex b/posic/thesis/md.tex
index bbdd448..fab4656 100644
--- a/posic/thesis/md.tex
+++ b/posic/thesis/md.tex
@@ -514,8 +514,23 @@ This also explains the possibly identified slight increase of the c-Si lattice c
 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!
+In the following the 3C-SiC/c-Si interface is described in further detail.
+One important size analyzing the interface is the interfacial energy.
+It is determined exactly in the same way than the formation energy as described in equation \eqref{eq:defects:ef2}.
+Using the notation of table \ref{table:md:sic_prec} and assuming that the system is composed out of $N^{\text{3C-SiC}}_{\text{C}}$ C atoms forming the SiC compound plus the remaining Si atoms, the energy is given by
+\begin{equation}
+ E_{\text{f}}=E-
+ N^{\text{3C-SiC}}_{\text{C}} \mu_{\text{SiC}}-
+ \left(N^{\text{total}}_{\text{Si}}-N^{\text{3C-SiC}}_{\text{C}}\right)
+ \mu_{\text{Si}} \text{ ,}
+\label{eq:md:ife}
+\end{equation}
+with $E$ being the free energy of the precipitate configuration at zero temperature.
+An interfacial energy of 2267.28 eV is obtained.
+The amount of C atoms together with the observed lattice constant of the precipitate leads to a precipitate radius of 29.93 \AA.
+Thus, the interface tension, given by the energy of the interface devided by the surface area of the precipitate is $20.15\,\frac{\text{eV}}{\text{nm}^2}$ or $3.23\times 10^{-4}\,\frac{\text{J}}{\text{cm}^2}$.
+This is located inside the eperimentally estimated range of $2-8\times 10^{-4}\,\frac{\text{J}}{\text{cm}^2}$ \cite{taylor93}.
+
 
 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.