mapp.md.atoms.ff_fs

atoms.ff_fs(A, t1, t2, k1, k2, k3, r_c_phi, r_c_rho, elems=None)

Finnis-Sinclair EAM

Assigns Finnis-Sinclair EAM force field to system. For explanation of the parameter see the Notes section.

Parameters:

A : double[nelems]

A

t1 : double[nelems][nelems]

t_1

t2 : double[nelems][nelems]

t_2

k1 : symmetric double[nelems][nelems]

k_1

k2 : symmetric double[nelems][nelems]

k_2

k3 : symmetric double[nelems][nelems]

k_3

r_c_phi : symmetric double[nelems][nelems]

r_{c,\phi}

r_c_rho : symmetric double[nelems][nelems]

r_{c,\rho}

elems : string[nelems]

mapping elements

Returns:

None

Notes

This is the analytical form of Finnis-Sinclair Embedded Atom Method (EAM) potential

U=\sum_{i}\left( -A_{\alpha}\sqrt{\sum_{j\neq i} \rho_{\beta\alpha}(r_{ij})}  + \frac{1}{2}\sum_{j\neq i} \phi_{\beta\alpha}(r_{ij}) \right),

where

\rho_{\beta\alpha}(r)=
\left\{\begin{array}{ll}
t^{\alpha\beta}_1(r-r^{\alpha\beta}_{c,\rho})^2+t^{\alpha\beta}_2(r-r^{\alpha\beta}_{c,\rho})^3, \quad & r<r^{\alpha\beta}_{c,\rho}\\
0 & r>r^{\alpha\beta}_{c,\rho}\
\end{array}\right.

and

\phi_{\beta\alpha}(r)=
\left\{\begin{array}{ll}
(r-r^{\alpha\beta}_{c,\phi})^2(k^{\alpha\beta}_1+k^{\alpha\beta}_2 r+k^{\alpha\beta}_3 r^2), \quad & r<r^{\alpha\beta}_{c,\phi}\\
0 & r>r^{\alpha\beta}_{c,\phi}\
\end{array}\right.

Examples

Iron Carbon mixture

>>> from mapp import md
>>> sim=md.cfg("configs/Cementite.cfg")
>>> sim.ff_fs(A=[1.8289905,2.9588787],
              t1=[[1.0,10.024001],[10.482408,0.0]],
              t2=[[0.504238,1.638980],[3.782595,-7.329211]],
              k1=[[1.237115],[8.972488,22.061824]],
              k2=[[-0.35921],[-4.086410,-17.468518]],
              k3=[[-0.038560],[1.483233,4.812639]],
              r_c_phi=[[3.40],[2.468801,2.875598]],
              r_c_rho=[[3.569745],[2.545937,2.892070]],
              elems=['Fe','C'])