Chemistry: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, [math]\displaystyle{ i }[/math], is given by[3]
- [math]\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}) }[/math],
where [math]\displaystyle{ r_{ij} }[/math] is the distance between atoms [math]\displaystyle{ i }[/math] and [math]\displaystyle{ j }[/math], [math]\displaystyle{ \phi_{\alpha\beta} }[/math] is a pair-wise potential function, [math]\displaystyle{ \rho_\beta }[/math] is the contribution to the electron charge density from atom [math]\displaystyle{ j }[/math] of type [math]\displaystyle{ \beta }[/math] at the location of atom [math]\displaystyle{ i }[/math], and [math]\displaystyle{ F }[/math] is an embedding function that represents the energy required to place atom [math]\displaystyle{ i }[/math] of type [math]\displaystyle{ \alpha }[/math] 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
References
- ↑ Daw, Murray S.; Mike Baskes (1984). "Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals". Physical Review B (American Physical Society) 29 (12): 6443–6453. doi:10.1103/PhysRevB.29.6443. Bibcode: 1984PhRvB..29.6443D.
- ↑ 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. https://zenodo.org/record/1258631.
- ↑ "Pair - EAM". LAMMPS Molecular Dynamics Simulator. http://lammps.sandia.gov/doc/pair_eam.html. Retrieved 2008-10-01.
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