# Embedded atom method¶

**GPUMD** suppports two different analytical forms of embedded atom method (EAM) potentials.
Using the form by Zhou *et al.* can simulate alloys with up to 10 atom types [Zhou2004], while using the form of Dai *et al.* the implementation only applies to systems with a single atom type [Dai2006].

## Potential form¶

### General form¶

The site potential energy is

Here, the part with \(\phi(r_{ij})\) is a pairwise potential and \(F (\rho_i)\) is the embedding potential, which depends on the electron density \(\rho_i\) at site \(i\). The many-body part of the EAM potential comes from the embedding potential.

The density \(\rho_i\) is contributed by the neighbors of \(i\):

Therefore, the form of an EAM potential is completely determined by the three functions: \(\phi\), \(f\), and \(F\).

### Version from [Zhou2004]¶

The pair potential between two atoms of the same type \(a\) is

The contribution of the electron density from an atom of type \(a\) is

The pair potential between two atoms of different types \(a\) and \(b\) is then constructed as

The embedding energy function is piecewise:

### Version from [Dai2006]¶

This is a very simple EAM-type potential, which is an extension of the Finnis-Sinclair potential. The function for the pair potential is

The function for the density is

The function for the embedding energy is

## File format¶

The potential file for the version from [Zhou2004] reads:

```
eam_zhou_2004 num_types <list of elements>
r_e f_e rho_e rho_s alpha beta A B kappa lambda F_n0 F_n1 F_n2 F_n3 F_0 F_1 F_2 F_3 eta F_e cutoff
```

There are `num_types`

rows of parameters but here we have only written a single row above.
The order of the rows should be consistent with the `<list of elements>`

in the first line.

The last parameter `cutoff`

is the cutoff distance, which is not intrinsic to the model.
The order of the parameters is the same as in Table III of [Zhou2004].
For multi-component systems, **GPUMD** will use the largest cutoff for every atom type.

The potential file for the version from [Dai2006] reads:

```
eam_dai_2006 1 Element
A d c c_0 c_1 c_2 c_3 c_4 B
```

Here, `Element`

is the chemical symbol of the element.