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Citation: G.J. Ackland, and R. Thetford (1987), "An improved N-body semi-empirical model for body-centred cubic transition metals", Philosophical Magazine A 56(1), 15-30. DOI: 10.1080/01418618708204464.Abstract: The recently published semi-empirical potentials of Finnis and Sinclair for the metals V, Nb, Ta, Mo and W appear to give unphysical results for properties involving small interatomic separation. This is remedied by adding to the potentials cores fitted to electron gas calculations on dimers. The adjusted potentials are shown to predict a more realistic pressure-volume relationship. Interstitial formation energies are calculated for various configurations, using quenched molecular dynamics and static relaxation. Some preliminary results on interstitial migration are presented.
Related Models: -
Equations (1987--Ackland-G-J--Mo--parameters--ipr1)Notes: The file AckThet.pdf was obtained from http://homepages.ed.ac.uk/graeme/moldy/moldy.html and posted with the permission of G.J. Ackland.
File(s): -
LAMMPS pair_style eam/fs (1987--Ackland-G-J--Mo--LAMMPS--ipr1)See Computed Properties
Notes: This implementation has been retracted as it was identified as having an incorrect functional form. It is made available solely for archival purposes.
File(s): retracted -
LAMMPS pair_style eam/alloy (1987--Ackland-G-J--Mo--LAMMPS--ipr2)See Computed Properties
Notes: This file was provided by Sergei Starikov (Ruhr-Universität Bochum, Germany) on 5 May 2019. It has been carefully tested and gives the expected property predictions. Update March 15, 2020: This version was identified to not be compatible with LAMMPS versions after 7 Aug 2019 due to more rigorous format checks.
File(s): superseded -
LAMMPS pair_style eam/alloy (1987--Ackland-G-J--Mo--LAMMPS--ipr3)See Computed Properties
Notes: This file was created by Lucas Hale and posted on 15 March 2020. It is a modification of the parameter file in the above version to be compatible with LAMMPS versions after 7 Aug 2019. It contains the same parameter tables and should behave identically to the last version, and work with any version of LAMMPS. Update Nov 18 2025: This version has been superseded as the phi(r) function was determined to differ from the source equations for small values of r.
File(s): superseded -
LAMMPS pair_style eam/fs (1987--Ackland-G-J--Mo--LAMMPS--ipr4)See Computed Properties
Notes: This file was provided by Izzy Rodger on Nov 11, 2025, and was created under the supervision of Graeme Ackland and Andreas Hermann. This version is confirmed to correctly tabulate the equations from the source papers.
File(s):
Implementation Information
Diatom Energy vs. Interatomic Spacing
Plots of the potential energy vs interatomic spacing, r, are shown below for all diatom sets associated with the interatomic potential. This calculation provides insights into the functional form of the potential's two-body interactions. A system consisting of only two atoms is created, and the potential energy is evaluated for the atoms separated by 0.02 Å <= r <= 6.0> Å in intervals of 0.02 Å. Two plots are shown: one for the "standard" interaction distance range, and one for small values of r. The small r plot is useful for determining whether the potential is suitable for radiation studies.
The calculation method used is available as the iprPy diatom_scan calculation method.
Clicking on the image of a plot will open an interactive version of it in a new tab. The underlying data for the plots can be downloaded by clicking on the links above each plot.
Notes and Disclaimers:
- These values are meant to be guidelines for comparing potentials, not the absolute values for any potential's properties. Values listed here may change if the calculation methods are updated due to improvements/corrections. Variations in the values may occur for variations in calculation methods, simulation software and implementations of the interatomic potentials.
- As this calculation only involves two atoms, it neglects any multi-body interactions that may be important in molecules, liquids and crystals.
- NIST disclaimer
Version Information:
- 2019-11-14. Maximum value range on the shortrange plots are now limited to "expected" levels as details are otherwise lost.
- 2019-08-07. Plots added.
Click on plot to load interactive version
Click on plot to load interactive version
Cohesive Energy vs. Interatomic Spacing
Plots of potential energy vs interatomic spacing, r, are shown below for a number of crystal structures. The structures are generated based on the ideal atomic positions and b/a and c/a lattice parameter ratios for a given crystal prototype. The size of the system is then uniformly scaled, and the energy calculated without relaxing the system. To obtain these plots, values of r are evaluated every 0.02 Å up to 6 Å.
The calculation method used is available as the iprPy E_vs_r_scan calculation method.
Clicking on the image of a plot will open an interactive version of it in a new tab. The underlying data for the plots can be downloaded by clicking on the links above each plot.
Notes and Disclaimers:
- These values are meant to be guidelines for comparing potentials, not the absolute values for any potential's properties. Values listed here may change if the calculation methods are updated due to improvements/corrections. Variations in the values may occur for variations in calculation methods, simulation software and implementations of the interatomic potentials.
- The minima identified by this calculation do not guarantee that the associated crystal structures will be stable since no relaxation is performed.
- NIST disclaimer
Version Information:
- 2020-12-18. Descriptions, tables and plots updated to reflect that the energy values are the measuredper atom potential energy rather than cohesive energy as some potentials have non-zero isolated atom energies.
- 2019-02-04. Values regenerated with even r spacings of 0.02 Å, and now include values less than 2 Å when possible. Updated calculation method and parameters enhance compatibility with more potential styles.
- 2019-04-26. Results for hcp, double hcp, α-As and L10 prototypes regenerated from different unit cell representations. Only α-As results show noticable (>1e-5 eV) difference due to using a different coordinate for Wykoff site c position.
- 2018-06-13. Values for MEAM potentials corrected. Dynamic versions of the plots moved to separate pages to improve page loading. Cosmetic changes to how data is shown and updates to the documentation.
- 2017-01-11. Replaced png pictures with interactive Bokeh plots. Data regenerated with 200 values of r instead of 300.
- 2016-09-28. Plots for binary structures added. Data and plots for elemental structures regenerated. Data values match the values of the previous version. Data table formatting slightly changed to increase precision and ensure spaces between large values. Composition added to plot title and structure names made longer.
- 2016-04-07. Plots for elemental structures added.
