IMD

EAM Potentials (option eam)

The energy in potentials of the Embedded Atom type consitsts of two parts, a pair potential term specifyed by the function Φ(r) representing the electrostatic core-core repulsion, and a cohesive term specifyed by the function F(ρ) 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 specifyed by the function Ρ(r).

These functions depend on the type of the embedded atom (F_i(ρ)), or on the types i and j of the two atoms involved (Ρ_ij(r), Φ_ij(r)). The corresponding tabulated functions can be given in either of two formats. Note that Ρ and Φ have to be tabulated equidistant in r².

The Embedded Atom Method (EAM) was implemented by Erik Bitzek.

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_tot = ∑_i,j^N Φ_ij(r_ij) + ∑_i^N F(ρ^h_i)
ρ^h_i = ∑_j Ρ^at_ij(r_ij)

While an identification of the pair potential term Φ_ij(r_ij) with the electrostatic core-core repulsion, and of the cohesive term F(ρ^h_i) with the energy the ion core gets when it is "embedded" in the local electron density ρ^h_i may be tempting, it is nevertheless without physical justification. Due to invariance properties of the EAM potential, a embedding energy term linear in the "electron" density can be described by pair interactions, thus shifting contributions between embedding and pair energy. So an isolated consideration of either part is not possible - physical relevance only lies in the combination of both.

The local electron density is constructed as a superposition of contributions Ρ^at_ij(r_ij) from neighboring atoms.

Also belonging to this analytical form are models like the glue model, and the Finnis-Sinclair potentials. See also the Teeseminar about EAM.

Use of eam

The eam option works on risc and mpi plattforms. It now uses actio=reactio between the atoms on the same processor. eam should work with most of the common options. See Tests for options that are guaranteed to work.

To use eam one needs tables of three functions. Therefore the parameter file should contain lines indicating these tables, e.g.:

core_potential_file     Potentials/Ni_u3/Phi_r2.Ni_u3.dat
embedding_energy_file   Potentials/Ni_u3/F_rho.Ni_u3.dat
atomic_e-density_file   Potentials/Ni_u3/Rho_r2.Ni_u3.dat

The potential file can be in either of two different formats.

It is the responsibility of the creator of the potential to make sure, that the functions of r go smoothly to zero and that the last four values are 0.0. If you're having an exotic core potential with V_ij ≠ V_ji, you have to use the option asympot.

Existing Potentials

There are a few sample EAM potentials available for download ond the potfit homepage.

Tests

The eam option was tested by

comparing the energy output for a dynamical nve simulation with those produced by an other MD program (FEAT by Peter Gumbsch)
comparing the simulated values for the cohesive energy, vacancy formation energy, surface energy, bulkmodulus, lattice constant, surface relaxation,... for different potentials with published data for the specific potentials and experimental data
checking the conservation of energy at different temperatures

Therefore one may conclude that the eam option leads to correct results at least for: one and two different atom types, with and without periodic boundary conditions, on risc and mpi plattforms, with the MIK, NVE, NVT options.

Extended EAM Potentials (option eeam)

Ouyang Yifang, Zhang Bangwei et al. (Z. Phys. B 101, 161 (1996); Physica B 262, 218, (1999)) added a modified energy term

∑_i^N M_i(P_i)

to the total energy expression E_tot of the EAM to account for the difference between the actual total energy of a system of atoms and that calculated from the original EAM using a linear superposition of spherically atomic electron densities. P_i is defined as the sum of squared "electron" densities:

P_i = ∑_j (Ρ^at_ij)²(r_ij)

Use of eeam: Compared to EAM, an additional set of embedding energy functions M_i is needed, which are read from a file specified by the parameter eeam_energy_file.
Potentials: Analytical potentials for all bcc transition metals can be found in the papers cited above.