~~NOTOC~~ ====== Embedded Atom Method (EAM) Potentials ====== ---- The energy in potentials of the Embedded Atom type consists of two parts, a pair potential term specified by the function $\Phi(r)$ representing the electrostatic core-core repulsion, and a cohesive term specified by the function $F(n)$ representing the energy the ion core gets when it is "embedded" in the "Electron Sea". This Embedding Energy is a function of the local electron density, which in turn is constructed as a superposition of contributions from neighboring atoms. This electron transfer is specified by the function $\rho(r)$. The embedding function $F_i(n)$ depends on the type of the embedded atom, the transfer function $\rho_j(r)$ depends on the type $j$ of the donating atom, whereas the pair potential $\Phi_{ij}(r)$ depends on the types $i$ and $j$ of both atoms involved. All potential functions are given in a single file, whose format is described [[potfiles:main|here]]. The Embedded Atom Method (EAM) for [[http://imd.itap.physik.uni-stuttgart.de/|IMD]] was implemented by Erik Bitzek. It was adapted for use in //potfit// by Peter Brommer. ===== Basic Theory ===== The Embedded Atom Method was suggested by Daw and Baskes ((M. S. Daw and M. I. Baskes, //Phys. Rev. B// **29**, 6443 (1984) )) ((S. M. Foiles, M. I. Baskes, and M. S. Daw, //Phys. Rev. B// **33**, 7983 (1986) )) as a way to overcome the main problem with two-body potentials: the coordination independence of the bond strength, while still being acceptable fast (about 2 times slower than pair potentials). Ideas from the Density Functional Theory or the Tight Binding formalism may lead to the following form for the total energy: $$E_\text{total}=\frac{1}{2}\sum_{i