embeddedatom

Embedded-atom method (EAM) is a class of semi-empirical interatomic potentials used to model metallic bonding in condensed matter simulations. It describes the energy of an N-atom system as arising from the embedding of each atom into the local electron density generated by neighboring atoms, plus a pairwise interaction term. This many-body character makes EAM more accurate for metals than simple pair potentials in reproducing properties such as cohesive energies, defect formation energies, and surface phenomena.

Mathematical form: For atom i, the local electron density rho_i is computed as a sum over neighbors j of an atomic electron-density function f_j(r_ij). The total energy is E = sum_i F_i(rho_i) + 1/2 sum_{i ≠ j} phi_{ij}(r_ij), where F_i is the embedding function and phi_{ij} is a short-range pair potential. The functions F, phi, and f are parameterized to reproduce reference data (experimental or ab initio) for properties of the target metal and its phases, enabling efficient molecular dynamics and static calculations.

History and scope: The EAM was introduced in the 1980s by Daw and Baskes to model metallic bonding and has since become a standard tool in computational materials science. Extensions such as the modified embedded-atom method (MEAM) broaden the approach to anisotropic bonding and multi-component systems. EAM potentials have been developed for a wide range of metals (e.g., Cu, Al, Ni, Fe) and are implemented in common simulation packages, enabling large-scale simulations of defects, surfaces, grain boundaries, and dislocations.

Limitations: EAM is best suited for close-packed, metallic bonding and relies on a fixed functional form and calibration data. It is less transferable to alloys with significant chemical order or non-metallic bonding, and it does not explicitly model electronic structure, magnetism, or long-range ionic interactions. Users must validate potentials for the intended applications and be mindful of their transferability and accuracy.