Ravelo EAM¶

Description¶

The ravelo_force operator computes the EAM potential of Ravelo et al. (single species), with an analytic pair term and electron density and a tabulated embedding function.

The pair term is a Rose-type function below \(r_s\) and a polynomial tail between \(r_s\) and \(r_c\). With \(r^* = \alpha'\left(r/r_1 - 1\right)\):

\[ \phi(r) = \begin{cases} -U_0\,e^{-r^*}\left(1 + r^* + \beta_3 r^{*3} + \beta_4 r^{*4}\right) & r \le r_s \\[1ex] U_0\,(r_c - r)^{s}\left[a_1 + a_2 (r_c-r) + a_3 (r_c-r)^2 + a_4 (r_c-r)^3\right] & r_s < r \le r_c \\[1ex] 0 & r > r_c \end{cases} \]

The electron density is, with \(r_0 = \frac{\sqrt{3}}{2}a_0\) the nearest-neighbor distance of the bcc lattice,

\[ \rho(r) = \rho_0\left(\frac{r_c^{\,p} - r^{p}}{r_c^{\,p} - r_0^{\,p}}\right)^{q} \quad \text{for} \quad r \le r_c \]

The embedding function \(F(\rho)\) and its derivative are given as tables and interpolated with cubic splines.

See the EAM overview for the total energy and the available operators (ravelo_force, ravelo_emb, ravelo_force_reuse_emb, ravelo_init).

Parameter	Units	Description
`U0`	energy	Pair energy scale \(U_0\)
`r1`	distance	Reference distance \(r_1\) of the pair term
`alphap`	—	Exponent \(\alpha'\) of the pair term
`beta3`, `beta4`	—	Higher-order coefficients of the pair term
`rs`	distance	Switching distance \(r_s\) to the polynomial tail
`s`	—	Exponent of the polynomial tail
`a1` … `a4`	—	Coefficients of the polynomial tail
`rc`	distance	Cutoff \(r_c\) of the pair term and electron density
`a0`	distance	Lattice parameter \(a_0\)
`rho0`, `p`, `q`	—	Electron density parameters
`rho`, `f`, `df`	—	Tables of \(\rho\), \(F(\rho)\) and \(F'(\rho)\) (same length)
`Ec`, `alpha`, `f3`, `f4`	—	Read but not used in the force computation
`format`	—	Optional. `exastampv1`: the `f` and `df` tables are in SI units

All scalar parameters are required. Like the other parameters, the rho, f and df lists accept units on each value.

YAML syntax¶

The parameters are usually stored in a YAML file (searched in the data paths):

ravelo_force:
  rcut: VALUE UNITS
  parameters:
    file: FILENAME

The same keys can also be given directly under parameters.

VALUE = Physical value of the intended parameter.
UNITS = Units of the provided value that will be passed to the conversion helper for internal units conversion.
FILENAME = YAML file with the scalar parameters and the rho, f, df tables.

Usage example¶

Tantalum

ravelo_force:
  rcut: 5.3 ang
  parameters:
    file: ravelo_Ta1.yaml

compute_force: ravelo_force

The parameter files ravelo_Ta1.yaml and ravelo_Ta2.yaml are shipped in exaStamp/data/potentials/. Complete inputs are in exaStamp/data/regression_new/potentials/eam/eam_ravelo/. This potential runs on CPU only.