IMD

MEAM Potentials (option meam)

The Modified Embedded Atom Method was formulated by Baskes (M.I.Baskes, Phys.Rev.B 46 (1992) 2727, M.I.Baskes, Mater.Chem.Phys. 50 (1997) 152). It consists of a generalization of the EAM potentials by including angular terms.

The total energy for the MEAM potentials have a form similar to the EAM potentials:

Here F_i is the embedding energy function, rho_i is the electron density at the position of atom i, phi_ij is a pair potential, and S_ij is the screening function defined below.

For MEAM potentials, the electron density is given by

where the parameters t^(s)_i are weight factors and the quantities rho^(s)_i, s=0,...,3, are partial electron densities defined by

The functions L^(s)(z) are Legendre polynomials, L⁽⁰⁾(z) = 1, L⁽¹⁾(z) = z, L⁽²⁾(z) = z²-1/3, L⁽³⁾(z) = z³-3/5z. The atomic electron density functions from atom j at a distance r_ij from atom i are

Here, f⁰_i, r⁰_i, and beta^(s)_i are parameters, f_c is a cutoff function, and S_ij is the screening function.

The many-body screening function S_ij between atoms i and j is defined as the product of the screening factors S_ikj due to all other neighbour atoms k of i and j,

S_kij is given by

where C¹_kij and C⁰_kij are parameters and the function g_c is defined as

The cutoff function f_c used in the atomic electron density functions is given by

where r^c_ij is a cutoff length and Delta_r_ij is the width of the cutoff region.

The indices of the parameters refer to the atom types involved. The following IMD parameters correspond to the MEAM potential parameters:

`meam_cmin`	C⁰_kij
`meam_cmax`	C¹_kij
`meam_t1`	t⁽¹⁾_i
`meam_t2`	t⁽²⁾_i
`meam_t3`	t⁽³⁾_i
`meam_f0`	f⁰_i
`meam_r0`	r⁰_i
`meam_beta0`	beta⁽⁰⁾_i
`meam_beta1`	beta⁽¹⁾_i
`meam_beta2`	beta⁽²⁾_i
`meam_beta3`	beta⁽³⁾_i
`meam_deltar`	Delta_r_ij
`meam_rcut`	r^c_ij

The pair potential phi_ij has to be given as a potential table. The corresponding IMD parameter is core_potential_file.

The embedding energy function F_i can be read in as a potential table using the IMD parameter embedding_energy_file. Alternatively, IMD computes the embedding energy analytically according to

In this case, the parameters have to be specified using the following IMD parameters:

`meam_a`	A_i
`meam_e`	E_ci
`meam_rho0`	rho⁰_i

The atomic electron density functions rho^a(s)_i(r) are computed analytically. The function rho^a(0)_i(r), however, can be read in as a potential table using the IMD parameter el_density_file.

The many-body interactions of the MEAM potential are computed using neighbour tables. In constrast to the covalent potentials the IMD parameter neigh_len has the default value 12.

If more than one atom type are used, common values of the parameters meam_cmin and meam_cmax for all atom types can be chosen by specifying only one value for each parameter.

The screening function S_ij can be switched off (that is, set to unity) by choosing the parameters meam_cmin and meam_cmax to be equal.