\begin{displaymath}E = \sum_{i} E_i = \frac{1}{2} \sum_{i\neq j} V_{ij} \end{displaymath}
\begin{displaymath}V_{ij} = f_C(r_{ij})[f_R(r_{ij})+b_{ij}f_A(r_{ij})] \end{displaymath}
\begin{displaymath}f_R(r) = Ae^{(-{\lambda_1 r})}, \makebox[0.4in]{}
f_A(r) = -Be^{(-{\lambda_2 r})} \end{displaymath}
\begin{displaymath}f_C(r) = \cases {1, \makebox[4in]{} r < R-D
\cr \frac{1}{2}-...
... \makebox[0.1in]{}
\cr 0, \makebox[4in]{} r>R+D \cr} \end{displaymath}
The strength of each bond depends upon the local environment and is expressed by $b_{ij}$. \begin{displaymath}b_{ij} = \frac{1}{(1+\beta ^n \zeta_{ij} ^n)^{1/2n}} \end{displaymath}
\begin{displaymath}\zeta_{ij} = \sum_{k\neq i,j} f_C(r_{ij})g(\theta_{ijk})
e^{[\lambda_3 ^3(r_{ij} - r_{ik})^3]} \end{displaymath}
\begin{displaymath}g(\theta) = 1+\frac{c^2}{d^2}-\frac{c^2}{[d^2+(h-\cos\theta)^2]}
where $\zeta_{ij}$ is the effective coordination number
  • The parameters were chosen to fit : the cohesive energy of several high-symmetry bulk structures, the lattice constant of diamond, the bulk modulus of diamond, the vacancy formation energy in diamond ($\approx$ 4 eV).
  • The potential was tested by calculating : the elastic constants, the phonon frequencies, and defect energies and migration barriers in diamond and graphite.