Embedded atom model

In computational chemistry and computational physics, the embedded atom model, embedded-atom method or EAM, is an approximation describing the energy between atoms and is a type of interatomic potential. The energy is a function of a sum of functions of the separation between an atom and its neighbors. In the original model, by Murray Daw and Mike Baskes,^[1] the latter functions represent the electron density. The EAM is related to the second moment approximation to tight binding theory, also known as the Finnis-Sinclair model. These models are particularly appropriate for metallic systems.^[2] Embedded-atom methods are widely used in molecular dynamics simulations.

Model simulation

In a simulation, the potential energy of an atom, ${\displaystyle i}$, is given by^[3]

${\displaystyle E_{i}=F_{\alpha }\left(\sum _{j\neq i}\rho _{\beta }(r_{ij})\right)+{\frac {1}{2}}\sum _{j\neq i}\phi _{\alpha \beta }(r_{ij})}$,

where ${\displaystyle r_{ij}}$ is the distance between atoms ${\displaystyle i}$ and ${\displaystyle j}$, ${\displaystyle \phi _{\alpha \beta }}$ is a pair-wise potential function, ${\displaystyle \rho _{\beta }}$ is the contribution to the electron charge density from atom ${\displaystyle j}$ of type ${\displaystyle \beta }$ at the location of atom ${\displaystyle i}$, and ${\displaystyle F}$ is an embedding function that represents the energy required to place atom ${\displaystyle i}$ of type ${\displaystyle \alpha }$ into the electron cloud.

Since the electron cloud density is a summation over many atoms, usually limited by a cutoff radius, the EAM potential is a multibody potential. For a single element system of atoms, three scalar functions must be specified: the embedding function, a pair-wise interaction, and an electron cloud contribution function. For a binary alloy, the EAM potential requires seven functions: three pair-wise interactions (A-A, A-B, B-B), two embedding functions, and two electron cloud contribution functions. Generally these functions are provided in a tabularized format and interpolated by cubic splines.

See also

• Interatomic potential
• Lennard-Jones potential
• Bond order potential
• Force field (chemistry)

References

1. Daw, Murray S.; Mike Baskes (1984). "Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals". Physical Review B. 29 (12). American Physical Society: 6443–6453. Bibcode:1984PhRvB..29.6443D. doi:10.1103/PhysRevB.29.6443.
2. Daw, Murray S.; Foiles, Stephen M.; Baskes, Michael I. (1993). "The embedded-atom method: a review of theory and applications". Mat. Sci. Eng. Rep. 9 (7–8): 251. doi:10.1016/0920-2307(93)90001-U.
3. "Pair - EAM". LAMMPS Molecular Dynamics Simulator. Retrieved 2008-10-01.