X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Fthesis%2Fd_tersoff.tex;h=ca235358238d6e8b3481b245131216a1605b4aa6;hb=a3831cc8a0d5bd03cbc1b0907bd11168416fd4b2;hp=c01a65eaf34d207e955e3b23b4f2275909113b85;hpb=fdf1f976b879c9b7403c1d76c9906aa850614862;p=lectures%2Flatex.git diff --git a/posic/thesis/d_tersoff.tex b/posic/thesis/d_tersoff.tex index c01a65e..ca23535 100644 --- a/posic/thesis/d_tersoff.tex +++ b/posic/thesis/d_tersoff.tex @@ -3,7 +3,7 @@ \section{Form of the Tersoff potential and its derivative} -The Tersoff potential \cite{tersoff_m} is of the form +The Tersoff potential~\cite{tersoff_m} is of the form \begin{eqnarray} E & = & \sum_i E_i = \frac{1}{2} \sum_{i \ne j} V_{ij} \textrm{ ,} \\ V_{ij} & = & f_C(r_{ij}) [ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) ] \textrm{ .} @@ -32,7 +32,7 @@ f_C(r_{ij}) = \left\{ 0, & r_{ij} > S_{ij} \end{array} \right. \end{equation} -with $\theta_{ijk}$ being the bond angle between bonds $ij$ and $ik$ as shown in Figure \ref{img:tersoff_angle}.\\ +with $\theta_{ijk}$ being the bond angle between bonds $ij$ and $ik$ as shown in Figure~\ref{img:tersoff_angle}.\\ \\ For a three body potential, if $V_{ij}$ is not equal to $V_{ji}$, the derivative is of the form \begin{equation} @@ -185,7 +185,7 @@ Concerning $b_{ij}$, in addition to the angular term, the derivative of the cut- \subsection{Code realization} -The implementation of the force evaluation shown in the following is applied to the potential designed by Erhart and Albe \cite{albe_sic_pot}. +The implementation of the force evaluation shown in the following is applied to the potential designed by Erhart and Albe~\cite{albe_sic_pot}. There are slight differences compared to the original potential by Tersoff: \begin{itemize} \item Difference in sign of the attractive part.