\(\renewcommand{\AA}{\text{Å}}\)
fix electron/stopping command
fix electron/stopping/fit command
Syntax
fix ID group-ID style args
ID, group-ID are documented in fix command
style = electron/stopping or electron/stopping/fit
electron/stopping args = Ecut file keyword value ... Ecut = minimum kinetic energy for electronic stopping (energy units) file = name of the file containing the electronic stopping power table electron/stopping/fit args = Ecut c1 c2 ... Ecut = minimum kinetic energy for electronic stopping (energy units) c1 c2 = linear and quadratic coefficients for the fitted quadratic polynomial
zero or more keyword/value pairs may be appended to args for style = electron/stopping
keyword = region or minneigh region value = region-ID region-ID = region whose atoms will be affected by this fix minneigh value = minneigh minneigh = minimum number of neighbors an atom to have stopping applied
Examples
fix el all electron/stopping 10.0 elstop-table.txt
fix el all electron/stopping 10.0 elstop-table.txt minneigh 3
fix el mygroup electron/stopping 1.0 elstop-table.txt region bulk
fix 1 all electron/stopping/fit 4.63 3.3e-3 4.0e-8
fix 1 all electron/stopping/fit 3.49 1.8e-3 9.0e-8 7.57 4.2e-3 5.0e-8
Description
This fix implements inelastic energy loss for fast projectiles in solids. It applies a friction force to fast moving atoms to slow them down due to electronic stopping (energy lost via electronic collisions per unit of distance). This fix should be used for simulation of irradiation damage or ion implantation, where the ions can lose noticeable amounts of energy from electron excitations. If the electronic stopping power is not considered, the simulated range of the ions can be severely overestimated (Nordlund98, Nordlund95).
The electronic stopping is implemented by applying a friction force to each atom as:
where \(\vec{F}_i\) is the resulting total force on the atom. \(\vec{F}^0_i\) is the original force applied to the atom, \(\vec{v}_i\) is its velocity and \(S_e\) is the stopping power of the ion.
Note
In addition to electronic stopping, atomic cascades and irradiation simulations require the use of an adaptive timestep (see fix dt/reset) and the repulsive ZBL potential (see ZBL potential) or similar. Without these settings the interaction between the ion and the target atoms will be faulty. It is also common to use in such simulations a thermostat (fix_nvt) in the borders of the simulation cell.
Note
This fix removes energy from fast projectiles without depositing it as a heat to the simulation cell. Such implementation might lead to the unphysical results when the amount of energy deposited to the electronic system is large, e.g. simulations of Swift Heavy Ions (energy per nucleon of 100 keV/amu or higher) or multiple projectiles. You could compensate energy loss by coupling bulk atoms with some thermostat or control heat transfer between electronic and atomic subsystems with the two-temperature model (fix_ttm).
At low velocities the electronic stopping is negligible. The electronic friction is not applied to atoms whose kinetic energy is smaller than Ecut, or smaller than the lowest energy value given in the table in file. Electronic stopping should be applied only when a projectile reaches bulk material. This fix scans neighbor list and excludes atoms with fewer than minneigh neighbors (by default one). If the pair potential cutoff is large, minneigh should be increased, though not above the number of nearest neighbors in bulk material. An alternative is to disable the check for neighbors by setting minneigh to zero and using the region keyword. This is necessary when running simulations of cluster bombardment.
If the region keyword is used, the atom must also be in the specified geometric region in order to have electronic stopping applied to it. This is useful if the position of the bulk material is fixed. By default the electronic stopping is applied everywhere in the simulation cell.
The energy ranges and stopping powers are read from the file file. Lines starting with # and empty lines are ignored. Otherwise each line must contain exactly N+1 numbers, where N is the number of atom types in the simulation.
The first column is the energy for which the stopping powers on that line apply. The energies must be sorted from the smallest to the largest. The other columns are the stopping powers \(S_e\) for each atom type, in ascending order, in force units. The stopping powers for intermediate energy values are calculated with linear interpolation between 2 nearest points.
For example:
# This is a comment
# atom-1 atom-2
# eV eV/Ang eV/Ang # units metal
10 0 0
250 60 80
750 100 150
If an atom which would have electronic stopping applied to it has a kinetic energy higher than the largest energy given in file, LAMMPS will exit with an error message.
The stopping power depends on the energy of the ion and the target material. The electronic stopping table can be obtained from scientific publications, experimental databases or by using SRIM software. Other programs such as CasP or PASS can calculate the energy deposited as a function of the impact parameter of the ion; these results can be used to derive the stopping power.
Style electron/stopping/fit calculates the electronic stopping power and cumulative energy lost to the electron gas via a quadratic functional and applies a drag force to the classical equations-of-motion for all atoms moving above some minimum cutoff velocity (i.e., kinetic energy). These coefficients can be determined by fitting a quadratic polynomial to electronic stopping data predicted by, for example, SRIM or TD-DFT. Multiple ‘Ecut c1 c2’ values can be provided for multi-species simulations in the order of the atom types. There is an examples/PACKAGES/electron_stopping/ directory, which illustrates uses of this command. Details of this implementation are further described in Stewart2018 and Lee2020.
Restart, fix_modify, output, run start/stop, minimize info
No information about this fix is written to binary restart files.
The fix_modify options are not supported.
This fix computes a global scalar, which can be accessed by various output commands. The scalar is the total energy loss from electronic stopping applied by this fix since the start of the latest run. It is considered “intensive”.
The start/stop keywords of the run command have no effect on this fix.
Restrictions
This pair style is part of the EXTRA-FIX package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info.
Default
The default is no limitation by region, and minneigh = 1.
(electronic stopping) Wikipedia - Electronic Stopping Power: https://en.wikipedia.org/wiki/Stopping_power_%28particle_radiation%29
(Nordlund98) Nordlund, Kai, et al. Physical Review B 57.13 (1998): 7556.
(Nordlund95) Nordlund, Kai. Computational materials science 3.4 (1995): 448-456.
(SRIM) SRIM webpage: http://www.srim.org/
(CasP) CasP webpage: http://www.casp-program.org/
(PASS) PASS webpage: https://www.sdu.dk/en/DPASS
(Stewart2018) J.A. Stewart, et al. (2018) Journal of Applied Physics, 123(16), 165902.
(Lee2020) C.W. Lee, et al. (2020) Physical Review B, 102(2), 024107.