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\subsection{\label{sec:eam}Embedded Atom Method} |
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Several molecular dynamics codes\cite{dynamo86} exist which have the |
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Several other molecular dynamics packages\cite{dynamo86} exist which have the |
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capacity to simulate metallic systems, including some that have |
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parallel computational abilities\cite{plimpton93}. Potentials that |
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describe bonding transition metal |
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systems\cite{Finnis84,Ercolessi88,Chen90,Qi99,Ercolessi02} have a |
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attractive interaction which models the stabilization of ``Embedding'' |
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a positively charged metal ion in an electron density created by the |
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attractive interaction which models ``Embedding'' |
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a positively charged metal ion in the electron density due to the |
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free valance ``sea'' of electrons created by the surrounding atoms in |
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the system. A mostly repulsive pairwise part of the potential |
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describes the interaction of the positively charged metal core ions |
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with one another. A particular potential description called the |
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Embedded Atom Method\cite{Daw84,FBD86,johnson89,Lu97}(EAM) that has |
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Embedded Atom Method\cite{Daw84,FBD86,johnson89,Lu97}({\sc eam}) that has |
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particularly wide adoption has been selected for inclusion in OOPSE. A |
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good review of EAM and other metallic potential formulations was done |
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good review of {\sc eam} and other metallic potential formulations was done |
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by Voter.\cite{voter} |
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The {\sc eam} potential has the form: |
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V & = & \sum_{i} F_{i}\left[\rho_{i}\right] + \sum_{i} \sum_{j \neq i} |
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\phi_{ij}({\bf r}_{ij}) \\ |
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\rho_{i} & = & \sum_{j \neq i} f_{j}({\bf r}_{ij}) |
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\end{eqnarray} |
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\end{eqnarray}S |
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where $\phi_{ij}$ is a primarily repulsive pairwise interaction |
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between atoms $i$ and $j$.In the origional formulation of |
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EAM\cite{Daw84}, $\phi_{ij}$ was an entirely repulsive term, however |
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in later refinements to EAM have shown that nonuniqueness between $F$ |
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and $\phi$ allow for more general forms for $\phi$.\cite{Daw89} The |
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embedding function $F_{i}$ is the energy required to embedded an |
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positively-charged core ion $i$ into a linear supeposition of |
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where $F_{i} $ is the embedding function that equates the energy required to embed a |
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positively-charged core ion $i$ into a linear superposition of |
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sperically averaged atomic electron densities given by |
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$\rho_{i}$. There is a cutoff distance, $r_{cut}$, which limits the |
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$\rho_{i}$. $\phi_{ij}$ is a primarily repulsive pairwise interaction |
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between atoms $i$ and $j$. In the original formulation of |
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{\sc eam} cite{Daw84}, $\phi_{ij}$ was an entirely repulsive term, however |
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in later refinements to EAM have shown that nonuniqueness between $F$ |
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and $\phi$ allow for more general forms for $\phi$.\cite{Daw89} |
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There is a cutoff distance, $r_{cut}$, which limits the |
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summations in the {\sc eam} equation to the few dozen atoms |
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surrounding atom $i$ for both the density $\rho$ and pairwise $\phi$ |
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interactions. |
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interactions. Foiles et al. fit EAM potentials for fcc metals Cu, Ag, Au, Ni, Pd, Pt and alloys of these metals\cite{FDB86}. These potential fits are in the DYNAMO 86 format and are included with {\sc oopse}. |
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\subsection{\label{Sec:pbc}Periodic Boundary Conditions} |
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\textit{Periodic boundary conditions} are widely used to simulate truly |
