Embedded-Atom Model (EAM)¶

In the Embedded-Atom Model, the energy of atom \(i\) is the energy needed to embed it in the electron density created by its neighbors, plus a pair term:

\[ E_i = F\left(\rho_i\right) + \frac{1}{2}\sum_{j \neq i} \phi\left(r_{ij}\right), \qquad \rho_i = \sum_{j \neq i} \rho\left(r_{ij}\right) \]

where \(F\) is the embedding function, \(\rho(r)\) the electron density contributed by a neighbor at distance \(r\), and \(\phi(r)\) the pair interaction. EAM models differ by the choice of \(F\), \(\rho\) and \(\phi\):

Model	Operator prefix	Species	GPU	Parameters
EAM alloy (tabulated, setfl file)	`eam_alloy`	several	yes	file
Johnson (Zhou–Johnson–Wadley form)	`johnson`	one	yes	analytic
Ravelo	`ravelo`	one	no	analytic + tabulated \(F\)
Sutton–Chen	`sutton_chen`	one	no	analytic
VNIITF	`vniitf`	one	yes	analytic
Tabulated EAM	`tabeam`	one	no	tabulated

Single-species models¶

Analytic and tabulated single-species models (johnson, ravelo, sutton_chen, vniitf, tabeam) all provide the same four operators. Below, X stands for the model prefix.

Operator	Description
`X_force`	Complete EAM computation: embedding term on owned and ghost atoms, then forces and energies.
`X_emb`	First pass only: embedding term on owned atoms.
`X_force_reuse_emb`	Second pass only: forces and energies, using an embedding term computed before.
`X_init`	Reads the `parameters` once (typically in `init_parameters`), without computing anything.

Syntax

X_force:
  rcut: <float>
  parameters: <model parameters>

Parameters

rcut:        float, required      # Cutoff radius of the potential.
parameters:  map, required        # Model parameters, see each model page.

X_force computes the embedding term on ghost atoms too, so that no communication is needed between the two passes. It therefore raises ghost_dist_max to twice the cutoff. To keep a ghost layer of one cutoff only, split the computation and exchange the embedding term (field rho_dEmb) between the two passes:

compute_force:
  - johnson_emb
  - ghost_update_opt: { opt_fields: [ "rho_dEmb" ] }
  - johnson_force_reuse_emb

with the same rcut and parameters given to johnson_emb and johnson_force_reuse_emb (for instance with a YAML anchor).

Multi-species model¶

eam_alloy handles several species and splits the computation into passes that can be called separately. Its options are described on its page.