Embedded atom model: Difference between revisions

Revision as of 05:13, 5 November 2020

Revision as of 18:14, 19 December 2021

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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.