X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Fthesis%2Fbasics.tex;h=0e735ee17fe463b1147762c68966973201aa712f;hp=1dc0df93165ef9cde8a17f7b15fcac0fff91d0a1;hb=1edbeb59b2db2c95de26ce475e6cc82377da1813;hpb=dad5f6c36ea5e49ce04ca287b084843f97db6aac diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex index 1dc0df9..0e735ee 100644 --- a/posic/thesis/basics.tex +++ b/posic/thesis/basics.tex @@ -204,16 +204,22 @@ Details of the Tersoff potential derivative are presented in appendix \ref{app:d \subsubsection{Improved analytical bond order potential} Although the Tersoff potential is one of the most widely used potentials there are some shortcomings. -Describing the Si interaction Tersoff was unable to find a single parameter set to describe well both, bulk and surface properties. +Describing the Si-Si interaction Tersoff was unable to find a single parameter set to describe well both, bulk and surface properties. Due to this and since the first approach labeled T1 \cite{tersoff_si1} turned out to be unstable \cite{dodson87}, two further parametrizations exist, T2 \cite{tersoff_si2} and T3 \cite{tersoff_si3}. While T2 describes well surface properties, T3 yields improved elastic constants and should be used for describing bulk properties. However, T3, which is used in the Si/C potential, suffers from an underestimation of the dimer binding energy. -Similar behavior is found for the C interaction. +Similar behavior is found for the C-C interaction. -For this reason, Erhart and Albe provide a reparametrization of the Tersoff potential based on three independently fitted potentials for the Si-Si, C-C and Si-C interaction \cite{albe_sic_pot}. -The functional form is nearly the same like the one proposed by Tersoff. +For this reason, Erhart and Albe provide a reparametrization of the Tersoff potential based on three independently fitted parameter sets for the Si-Si, C-C and Si-C interaction \cite{albe_sic_pot}. +The functional form is similar to the one proposed by Tersoff. Differences in the energy functional and the force evaluation routine are pointed out in appendix \ref{app:d_tersoff}. -For Si ... +Concerning Si the elastic properties of the diamond phase as well as the structure and energetics of the dimer are reproduced very well. +The new parameter set for the C-C interaction yields improved dimer properties while at the same time delivers a description of the bulk phase similar to the Tersoff potential. +The potential provides succeeds in the description of the low as well as high coordinated structures is provided. +The description of elastic properties of SiC is improved with respect to the potentials available in literature. +Defect properties are only fairly reproduced but the description is comparable to previously published potentials. +It is claimed that the potential enables the modeling of widely different configurations and transitions among these and has recently been used to simulate the inert gas condensation of Si-C nanoparticles \cite{erhart04}. +Therefore the Erhart/Albe (EA) potential is considered the superior analytical bond order potential to study the SiC precipitation and associated processes in Si. \subsection{Statistical ensembles} \label{subsection:statistical_ensembles}