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Two band EAM Potentials


Basic Theory

The two band EAM potentials are an extension to the regular EAM potentials. Instead of single transfer and embedding functions, different functions to model two bands are used.

$$E_\text{total}=\frac{1}{2}\sum_{i<j}^N\Phi_{ij}(r_{ij})+\sum_iF_i^d(n_i^d)+\sum_iF_i^s(n_i^s)$$ where $$n^d_i=\sum_{j\neq i}\rho^d_j(r_{ij}) \qquad \text{and} \qquad n^s_i=\sum_{j\neq i}\rho^s_j(r_{ij})$$

Number of potential functions

To describe a system with $N$ atom types you need $N(N+9)/2$ potentials.

# atom types $\Phi_{ij}$ $\rho^d_j$ $F^d_i$ $\rho^s_j$ $F^s_i$ Total # potentials
$N$ $N(N+1)/2$ $N$ $N$ $N$ $N$ $N(N+9)/2$
1 1 1 1 1 1 5
2 3 2 2 2 2 11
3 6 3 3 3 3 18
4 10 4 4 4 4 26

Order of potential functions

The potential table is assumed to be symmetric, i.e. the potential for the atom types 1-0 is the same as the potential 0-1.

The order of the TBEAM potentials in the potential file for N atom types is:

$\Phi_{00}, \ldots, \Phi_{0N}, \Phi_{11}, \ldots, \Phi_{1N}, \ldots, \Phi_{NN},$
$\rho^d_0, \ldots, \rho^d_N,$
$F^d_0, \ldots, F^d_N,$
$\rho^s_0, \ldots, \rho^s_N,$
$F^s_0, \ldots, F^s_N,$

interactions/tbeam.1515231549.txt.gz ยท Last modified: 2018/01/06 10:39 by daniel