About OOPSE OOPSE News Features Download CVS Mailing Lists Documentation Authors Funding Results	Embedded Atom Method OOPSE implements a potential that describes bonding in transition metal systems. [30,31,32,33,34] This potential has an attractive interaction which models ``Embedding'' a positively charged pseudo-atom core in the electron density due to the free valance ``sea'' of electrons created by the surrounding atoms in the system. A pairwise part of the potential (which is primarily repulsive) describes the interaction of the positively charged metal core ions with one another. The Embedded Atom Method (EAM) [35,36,37,38] has been widely adopted in the materials science community and has been included in OOPSE. A good review of EAM and other formulations of metallic potentials was given by Voter.[39] The EAM potential has the form: $$V = \sum_{i} F_{i}\left[\rho_{i}\right] + \sum_{i} \sum_{j \neq i} \phi_{ij}({\bf r}_{ij})$$ (3.20) where $F_{i}$ is an embedding functional that approximates the energy required to embed a positively-charged core ion $i$ into a linear superposition of spherically averaged atomic electron densities given by $\rho_{i}$ , $$\rho_{i} = \sum_{j \neq i} f_{j}({\bf r}_{ij}),$$ (3.21) Since the density at site $i$ ($\rho_i$ ) must be computed before the embedding functional can be evaluated, EAM and the related transition metal potentials require two loops through the atom pairs to compute the inter-atomic forces. The pairwise portion of the potential, $\phi_{ij}$ , is a primarily repulsive interaction between atoms $i$ and $j$ . In the original formulation of EAM[35], $\phi_{ij}$ was an entirely repulsive term; however later refinements to EAM allowed for more general forms for $\phi$ .[40] The effective cutoff distance, $r_{{\text cut}}$ is the distance at which the values of $f(r)$ and $\phi(r)$ drop to zero for all atoms present in the simulation. In practice, this distance is fairly small, limiting the summations in the EAM equation to the few dozen atoms surrounding atom $i$ for both the density $\rho$ and pairwise $\phi$ interactions. In computing forces for alloys, mixing rules as outlined by Johnson [37] are used to compute the heterogenous pair potential, $$\phi_{ab}(r)=\frac{1}{2}\left( \frac{f_{b}(r)}{f_{a}(r)}\phi_{aa}(r)+ \frac{f_{a}(r)}{f_{b}(r)}\phi_{bb}(r) \right).$$ (3.22) No mixing rule is needed for the densities, since the density at site $i$ is simply the linear sum of density contributions of all the other atoms. The EAM force field illustrates an additional feature of OOPSE. Foiles, Baskes and Daw fit EAM potentials for Cu, Ag, Au, Ni, Pd, Pt and alloys of these metals.[36] These fits are included in OOPSE as the u3 variant of the EAM force field. Voter and Chen reparamaterized a set of EAM functions which do a better job of predicting melting points.[41] These functions are included in OOPSE as the VC variant of the EAM force field. An additional set of functions (the ``Universal 6'' functions) are included in OOPSE as the u6 variant of EAM. For example, to specify the Voter-Chen variant of the EAM force field, the user would add the forceFieldVariant = "VC"; line to the meta-data file. The potential files used by the EAM force field are in the standard funcfl format, which is the format utilized by a number of other codes (e.g. ParaDyn [8], DYNAMO 86). It should be noted that the energy units in these files are in eV, not kcal mol$^{-1}$ as in the rest of the OOPSE force field files.
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	Updated on January 16, 2006