Johnson EAM¶

Description¶

The johnson_force operator computes an analytic EAM potential in the Zhou–Johnson–Wadley form (single species). With \(x = r/r_e\), the pair term and the electron density are

\[ \phi(r) = \frac{A\,e^{-\alpha(x-1)}}{1 + (x-\kappa)^{20}} - \frac{B\,e^{-\beta(x-1)}}{1 + (x-\lambda)^{20}}, \qquad \rho(r) = \frac{f_e\,e^{-\beta(x-1)}}{1 + (x-\lambda)^{20}} \]

The embedding function is defined piecewise, with \(\rho_n = 0.85\,\rho_e\) and \(\rho_0 = 1.15\,\rho_e\):

\[ F(\rho) = \begin{cases} \displaystyle\sum_{k=0}^{3} F_{n,k}\left(\frac{\rho}{\rho_n} - 1\right)^k & \rho < \rho_n \\[2ex] \displaystyle\sum_{k=0}^{3} F_{k}\left(\frac{\rho}{\rho_e} - 1\right)^k & \rho_n \le \rho < \rho_0 \\[2ex] F_o\left[1 - \ln\left(\frac{\rho}{\rho_e}\right)^{\eta}\right]\left(\frac{\rho}{\rho_e}\right)^{\eta} & \rho \ge \rho_0 \end{cases} \]

See the EAM overview for the total energy and the available operators (johnson_force, johnson_emb, johnson_force_reuse_emb, johnson_init).

Parameter	Units	Description
`re`	distance	Equilibrium nearest-neighbor distance \(r_e\)
`fe`	—	Density scale \(f_e\)
`rhoe`	—	Equilibrium electron density \(\rho_e\)
`alpha`, `beta`	—	Decay exponents of the pair and density terms
`A`, `B`	energy	Amplitudes of the repulsive and attractive pair terms
`kappa`, `lambda`	—	Cutoff-function shifts \(\kappa\), \(\lambda\)
`Fn0` … `Fn3`	energy	Embedding coefficients for \(\rho < \rho_n\)
`F0` … `F3`	energy	Embedding coefficients for \(\rho_n \le \rho < \rho_0\)
`Fo`	energy	Embedding coefficient for \(\rho \ge \rho_0\)
`eta`	—	Embedding exponent \(\eta\)

All parameters are required. fe and rhoe only need consistent units, since only \(\rho/\rho_e\) enters the embedding function.

YAML syntax¶

johnson_force:
  rcut: VALUE UNITS
  parameters:
    re: VALUE UNITS
    fe: VALUE
    rhoe: VALUE
    alpha: VALUE
    beta: VALUE
    A: VALUE UNITS
    B: VALUE UNITS
    kappa: VALUE
    lambda: VALUE
    Fn0: VALUE UNITS
    Fn1: VALUE UNITS
    Fn2: VALUE UNITS
    Fn3: VALUE UNITS
    F0: VALUE UNITS
    F1: VALUE UNITS
    F2: VALUE UNITS
    F3: VALUE UNITS
    Fo: VALUE UNITS
    eta: VALUE

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.

Usage example¶

Tantalum

johnson_force:
  rcut: 6.1 ang
  parameters:
    re: 2.860082 ang
    fe: 3.08634 eV/ang
    rhoe: 33.787168 eV/ang
    alpha: 8.489528
    beta: 4.527748
    A: 0.611679 eV
    B: 1.032101 eV
    kappa: 0.176977
    lambda: 0.353954
    Fn0: -5.103845 eV
    Fn1: -0.405524 eV
    Fn2: 1.112997 eV
    Fn3: -3.585325 eV
    F0: -5.14 eV
    F1: 0.0 eV
    F2: 1.640098 eV
    F3: 0.221375 eV
    eta: 0.848843
    Fo: -5.141526 eV

compute_force: johnson_force

The complete input is exaStamp/data/regression_new/potentials/eam/eam_johnson/single_specy.msp.