Embedded atom model: Difference between revisions

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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,<ref>{{cite journal|author1-link=Murray S. Daw|author2-link=Michael Baskes|last=Daw|first=Murray S.|author2=Mike Baskes|title=Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals|journal=[[Physical Review B]]|publisher=[[American Physical Society]]|volume=29|issue=12|pages=6443–6453|doi=10.1103/PhysRevB.29.6443|year=1984|bibcode = 1984PhRvB..29.6443D }}</ref> the latter functions represent the electron density. The EAM is related to the second moment approximation to [[tight binding (physics)|tight binding]] theory, also known as the Finnis-Sinclair model. These models are particularly appropriate for metallic systems.<ref>{{cite journal|doi=10.1016/0920-2307(93)90001-U|last=Daw|first=Murray S.|author2-link=Stephen M. Foiles|first2=Stephen M. |last2=Foiles |first3=Michael I. |last3=Baskes |title=The embedded-atom method: a review of theory and applications|journal=Mat. Sci. Eng. Rep. |volume=9|pages=251|year=1993|issue=7–8|url=https://zenodo.org/record/1258631|doi-access=free}}</ref> Embedded-atom methods are widely used in [[molecular dynamics]] simulations.

==Model simulation==

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In a simulation, the potential energy of an atom, <math>i</math>, is given by<ref>{{cite web|url=http://lammps.sandia.gov/doc/pair_eam.html|title=Pair - EAM|publisher=LAMMPS Molecular Dynamics Simulator |accessdate=2008-10-01}}</ref>

:<math>E_i = F_\alpha\left(\sum_{ij\neq ji} \rho_\beta (r_{ij}) \right) + \frac{1}{2} \sum_{ij\neq ji} \phi_{\alpha\beta}(r_{ij})</math>,

where <math>r_{ij}</math> is the distance between atoms <math>i</math> and <math>j</math>, <math>\phi_{\alpha\beta}</math> is a pair-wise potential function, <math>\rho_\beta</math> is the contribution to the electron charge density from atom <math>j</math> of type <math>\beta</math> at the ___location of atom <math>i</math>, and <math>F</math> is an embedding function that represents the energy required to place atom <math>i</math> of type <math>\alpha</math> into the electron cloud.

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