Embedded Atom Method (EAM)

The embedded-atom method (EAM) was originally developed to model metals. [28] The basic idea of EAM is that atoms interact in a pairwise manner with the nearest neighbors but they also interact with a global field of electron density that is explicitly many-body in nature. For a system of $N$ atoms, the EAM potential is

$$\mathscr{U}({\boldsymbol r}^N) = \sum_{i=1}^{N}\left[F_i(\rho_{h,i}) + \frac{1}{2}\sum_{j\ne i} \phi_{ij}(r_{ij})\right]$$ (269)

where

$$F\left(\rho\right) = -\sqrt{\rho},$$ (270)

$$\rho_i = \sum_{j\ne i}g\left(r_{ij}\right),$$ (271)

$$g\left(r\right) = \exp{\left(-\beta r\right)},$$ (272)

$$\phi\left(r\right) = V_2\left(r\right) - 2F\left[g\left(r\right)\right],$$ (273)

$$V_2\left(r\right) = \left\{ \begin{array}{ll} V_{\rm ZBL}\left(r\right), & \mbox{$r<r... ...+\Phi_0\exp{\left(-\alpha r\right)}, & \mbox{$r\ge r_2$},\\ \end{array}\right.$$ (274)

$$V_{\rm ZBL}\left(r\right) = {{Z_1Z_2e^2}\over{4\pi\epsilon_0r}}\sum_{i=1}^{4}c_i\exp\left(-d_i{{r}\over{a}}\right)$$ (275)

The second term in Eq. 273 accounts for the fact that the electron density into which an atom is embedded does not include electrons from that atom itself. Eq. 275 is the Ziegler-Biersack-Littmark (ZBL) screened nuclear repulsion potential used for modeling high-energy collisions between atoms. The three branches that make up $V_2$ produce a spline-connection between the ZBL and a Morse-like attractive tail.

Among the many systems simulated using EAM is the sputtering of copper. [29]