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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 corecore 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 r^{2}.
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 twobody 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 corecore
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 FinnisSinclair 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_edensity_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.
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.
