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

{{Cleanup|date=August 2006}}

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==

In [[computational chemistry]], the '''embedded atom model''', or '''EAM''' is an approximation describing the energy between two atoms. 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, the latter functions represented the electron density. 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.

In such a simulation, the potential energy due toof 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_{i\neq j} \rho_\alpha (r_{ij}) \right) + \frac{1}{2} \sum_{i\neq j} \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_\alpha</math> is the contribution to the electron charge density from atom <math>j</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.

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

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.

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_\alphabeta</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.

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 ==

{{Reflist}}

* Daw, M.S. and Baskes, MI. "Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals". ''[[Physical Review B]]'' 29:12, pp. 6443–6453, 1984, [[American Physical Society|APS]].

==External links==

* http://nickwilson.co.uk/research/bham.ac.uk/PhD/node17.html

* [http://lammps.sandia.gov/doc/pair_eam.html LAMMPS Pair EAM]

[[Category:Chemical bonding]]

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