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2013--Bonny-G-Castin-N-Bullens-J-et-al--Fe-Cr-W

Citation: G. Bonny, N. Castin, J. Bullens, A. Bakaev, T.C.P. Klaver, and D. Terentyev (2013), "On the mobility of vacancy clusters in reduced activation steels: an atomistic study in the Fe-Cr-W model alloy", Journal of Physics: Condensed Matter, 25(31), 315401. DOI: 10.1088/0953-8984/25/31/315401.
Abstract: Reduced activation steels are considered as structural materials for future fusion reactors. Besides iron and the main alloying element chromium, these steels contain other minor alloying elements, typically tungsten, vanadium and tantalum. In this work we study the impact of chromium and tungsten, being major alloying elements of ferritic Fe–Cr–W-based steels, on the stability and mobility of vacancy defects, typically formed under irradiation in collision cascades. For this purpose, we perform ab initio calculations, develop a many-body interatomic potential (EAM formalism) for large-scale calculations, validate the potential and apply it using an atomistic kinetic Monte Carlo method to characterize the lifetime and diffusivity of vacancy clusters. To distinguish the role of Cr and W we perform atomistic kinetic Monte Carlo simulations in Fe–Cr, Fe–W and Fe–Cr–W alloys. Within the limitation of transferability of the potentials it is found that both Cr and W enhance the diffusivity of vacancy clusters, while only W strongly reduces their lifetime. The cluster lifetime reduction increases with W concentration and saturates at about 1-2 at.%. The obtained results imply that W acts as an efficient 'breaker' of small migrating vacancy clusters and therefore the short-term annealing process of cascade debris is modified by the presence of W, even in small concentrations.

Notes: Dr. Bonny noted that the FeCr part is identical to the bcc FeCr potential by himself and posted to the NIST Repository. He further noted that since the FeCr potential is in the 2BM formalism, the ternary is in the same format.

Related Models:
LAMMPS pair_style hybrid/overlay eam/alloy eam/fs (2013--Bonny-G--Fe-Cr-W--LAMMPS--ipr1)
See Computed Properties
Notes: These files were provided by Giovanni Bonny (Nuclear Materials Science Institute of SCK-CEN, Belgium) on 7 Mar. 2018 and posted with his permission. Dr. Bonny noted that the potentials were not stiffened and cannot be used in their present form for collision cascades. 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


EAM tabulated functions (2013--Bonny-G--Fe-Cr-W--table--ipr1)
Notes: These files were provided by Giovanni Bonny (Nuclear Materials Science Institute of SCK-CEN, Belgium) on 7 Mar. 2018 and posted with his permission.
File(s):
Cr Fd(ρ): Fd_Cr.spt
Fe Fd(ρ): Fd_Fe.spt
W Fd(ρ): Fd_W.spt
Cr Fs(ρ): Fs_Cr.spt
Fe Fs(ρ): Fs_Fe.spt
Cr ρ(r): rhoCr.spt
Fe ρ(r): rhoFe.spt
Fe-Cr ρ(r): rhoFeCr.spt
W ρ(r): rhoW.spt
Cr φ(r): pCrCr.spt
Fe φ(r): pFeFe.spt
W φ(r): pWW.spt
Cr-W φ(r): pCrW.spt
Fe-Cr φ(r): pFeCr.spt
Fe-W φ(r): pFeW.spt

LAMMPS pair_style hybrid/overlay eam/alloy eam/fs (2013--Bonny-G--Fe-Cr-W--LAMMPS--ipr2)
See Computed Properties
Notes: This is a modification to the above version posted by Lucas Hale on March 15, 2020. Missing pair function tables of all zeros were added to the FeCr_s.eam.fs file to make the files compatible with LAMMPS versions after 7 Aug 2019. Update May 26 2021: This version is not compatible for LAMMPS versions starting with 29 Oct 2020 due to Infinify and NaN values no longer allowed.
File(s): superseded


LAMMPS pair_style hybrid/overlay eam/alloy eam/fs (2013--Bonny-G--Fe-Cr-W--LAMMPS--ipr3)
See Computed Properties
Notes: This is a modification to the above version posted by Lucas Hale on May 26, 2021. To make the files compatible with LAMMPS versions after 29 Oct 2020, the Infinity and NaN values associated with the Cr elemental tables at r=0 are replaced with 1e+8 and 0.0 values, respectively.
File(s):
Documentation READ_ME.txt
d_band FeCrW_d.eam.alloy
s_band FeCrW_s.eam.fs

Implementation Information

This page displays computed properties for the 2013--Bonny-G--Fe-Cr-W--LAMMPS--ipr3 implementation of the 2013--Bonny-G-Castin-N-Bullens-J-et-al--Fe-Cr-W potential. Computed values for other implementations can be seen by clicking on the links below:

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.

Download data

Click on plot to load interactive version

2013--Bonny-G--Fe-Cr-W--LAMMPS--ipr3/diatom

Click on plot to load interactive version

2013--Bonny-G--Fe-Cr-W--LAMMPS--ipr3/diatom_short

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.

Select a composition:

Download data

Click on plot to load interactive version

2013--Bonny-G--Fe-Cr-W--LAMMPS--ipr3/EvsR.Cr

Crystal Structure Predictions

Computed lattice constants and cohesive/potential energies are displayed for a variety of crystal structures. The values displayed here are obtained using the following process.

  1. Initial crystal structure guesses are taken from:
    1. The iprPy E_vs_r_scan calculation results (shown above) by identifying all energy minima along the measured curves for a given crystal prototype + composition.
    2. Structures in the Materials Project and OQMD DFT databases.
  2. All initial guesses are relaxed using three independent methods using a 10x10x10 supercell:
    1. "box": The system's lattice constants are adjusted to zero pressure without internal relaxations using the iprPy relax_box calculation with a strainrange of 1e-6.
    2. "static": The system's lattice and atomic positions are statically relaxed using the iprPy relax_static calculation with a minimization force tolerance of 1e-10 eV/Angstrom.
    3. "dynamic": The system's lattice and atomic positions are dynamically relaxed for 10000 timesteps of 0.01 ps using the iprPy relax_dynamic calculation with an nph integration plus Langevin thermostat. The final configuration is then used as input in running an iprPy relax_static calculation with a minimization force tolerance of 1e-10 eV/Angstrom.
  3. The relaxed structures obtained from #2 are then evaluated using the spglib package to identify an ideal crystal unit cell based on the results.
  4. The space group information of the ideal unit cells is compared to the space group information of the corresponding reference structures to identify which structures transformed upon relaxation. The structures that did not transform to a different structure are listed in the table(s) below. The "method" field indicates the most rigorous relaxation method where the structure did not transform. The space group information is also used to match the DFT reference structures to the used prototype, where possible.
  5. The cohesive energy, Ecoh, is calculated from the measured potential energy per atom, Epot$, by subtracting the isolated energy averaged across all atoms in the unit cell. The isolated atom energies of each species model is obtained either by evaluating a single atom atomic configuration, or by identifying the first energy plateau from the diatom scan calculations for r > 2 Å.

The calculation methods used are implemented into iprPy as the following calculation styles

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 presence of any structures in this list does not guarantee that those structures are stable. Also, the lowest energy structure may not be included in this list.
  • Multiple values for the same crystal structure but different lattice constants are possible. This is because multiple energy minima are possible for a given structure and interatomic potential. Having multiple energy minima for a structure does not necessarily make the potential "bad" as unwanted configurations may be unstable or correspond to conditions that may not be relevant to the problem of interest (eg. very high strains).
  • NIST disclaimer

Version Information:

  • 2022-05-27. The "box" method results have all been redone with an updated methodology more suited for non-orthogonal systems.
  • 2020-12-18. Cohesive energies have been corrected by making them relative to the energies of the isolated atoms. The previous cohesive energy values are now listed as the potential energies.
  • 2019-06-07. Structures with positive or near zero cohesive energies removed from the display tables. All values still present in the raw data files.
  • 2019-04-26. Calculations now computed for each implementation. Results for hcp, double hcp, α-As and L10 prototypes regenerated from different unit cell representations.
  • 2018-06-14. Methodology completely changed affecting how the information is displayed. Calculations involving MEAM potentials corrected.
  • 2016-09-28. Values for simple compounds added. All identified energy minima for each structure are listed. The existing elemental data was regenerated. Most values are consistent with before, but some differences have been noted. Specifically, variations are seen with some values for potentials where the elastic constants don't vary smoothly near the equilibrium state. Additionally, the inclusion of some high-energy structures has changed based on new criteria for identifying when structures have relaxed to another structure.
  • 2016-04-07. Values for elemental crystal structures added. Only values for the global energy minimum of each unique structure given.

Select a composition:

Download raw data (including filtered results)

Reference structure matches:
A1--Cu--fcc = mp-8633, oqmd-592135, oqmd-1214518
A15--beta-W = mp-17, oqmd-620565, oqmd-691761, oqmd-1214963, oqmd-1280318
A2--W--bcc = mp-90, oqmd-676284, oqmd-676532, oqmd-677049, oqmd-685486, oqmd-690214, oqmd-691769, oqmd-1215141
A3'--alpha-La--double-hcp = oqmd-1215409
A3--Mg--hcp = mp-89, oqmd-592444, oqmd-622452, oqmd-1215319
A4--C--dc = oqmd-1215498
A5--beta-Sn = oqmd-1215587
A6--In--bct = oqmd-1215676
A7--alpha-As = oqmd-1215765

prototypemethodEcoh (eV/atom)Epot (eV/atom)a0 (Å)b0 (Å)c0 (Å)α (degrees)β (degrees)γ (degrees)
A2--W--bccdynamic-4.1008-4.10122.8662.8662.86690.090.090.0
A15--beta-Wdynamic-4.0325-4.03294.58584.58584.585890.090.090.0
oqmd-1214785dynamic-3.9813-3.98178.90348.90348.903490.090.090.0
oqmd-1214785box-3.9749-3.97538.89478.89478.894790.090.090.0
oqmd-691775dynamic-3.9669-3.96732.55162.55166.216990.090.0120.0
oqmd-1214874static-3.9416-3.9426.25986.25986.259890.090.090.0
A3--Mg--hcpdynamic-3.9379-3.93842.59822.59824.242990.090.0120.0
A3'--alpha-La--double-hcpdynamic-3.9379-3.93842.59822.59828.485890.090.0120.0
A1--Cu--fccdynamic-3.9379-3.93843.67453.67453.674590.090.090.0
A3--Mg--hcpbox-3.9379-3.93842.59832.59834.242990.090.0120.0
oqmd-1216032box-3.9377-3.93822.59822.598219.093590.090.0120.0
oqmd-1214874box-3.9292-3.92976.26716.26716.267190.090.090.0
mp-1059289box-3.9279-3.92832.48744.62424.203690.090.090.0
mp-1192789dynamic-3.8928-3.89328.70198.70194.645190.090.090.0
mp-1192789box-3.8865-3.8878.70098.70094.646190.090.090.0
oqmd-631035box-3.8774-3.87788.63938.63934.66890.090.090.0
oqmd-1215052box-3.6546-3.65514.03698.4572.681890.090.090.0
oqmd-1214696box-3.6311-3.63152.71754.05138.550390.090.090.0
A5--beta-Snstatic-3.4695-3.46994.13984.13982.491290.090.090.0
Ah--alpha-Po--scstatic-3.1885-3.18892.19222.19222.192290.090.090.0
oqmd-1215943static-2.9517-2.95213.88823.88823.91790.090.0120.0
A7--alpha-Asbox-2.8516-2.8523.01613.01618.716290.090.0120.0
A4--C--dcdynamic-2.0728-2.07325.82245.82245.822490.090.090.0

Elastic Constants Predictions

Static elastic constants are displayed for the unique structures identified in Crystal Structure Predictions above. The values displayed here are obtained by measuring the change in virial stresses due to applying small strains to the relaxed crystals. The initial structure and the strained states are all relaxed using force minimization.

The calculation method used is available as the iprPy elastic_constants_static calculation method.

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 presence of any structures in this list does not guarantee that those structures are stable.
  • The elastic constants have been computed for a variety of strains, and in some cases for slightly different lattice constant values. The static nature of this calculation can give poor predictions if the evaluated states straddle a functional discontinuity in the potential's third derivative. Be sure to compare the elastic constants for the different strains (positive and negative).
  • NIST disclaimer

Version Information:

  • 2019-08-07. Data added.

Composition:
Prototype:
a0:
strain:

Download raw data

Cij in GPa:
132.668131.453131.453-0.0-0.0-0.0
131.453132.668131.453-0.0-0.0-0.0
131.453131.453132.668-0.0-0.0-0.0
-0.0-0.0-0.087.544-0.0-0.0
-0.0-0.0-0.0-0.087.544-0.0
-0.0-0.0-0.0-0.0-0.087.544

Phonon and Quasi-Harmonic Approximation Predictions

Phonon band structures and crystal properties estimated from quasi-harmonic approximation (QHA) calculations are displayed for select crystals. The calculations were performed using phonopy and LAMMPS. For the phonon calculations, 3x3 supercells of the potential-specific relaxed crystals were used. The QHA calculations were based on 11 strain states ranging from -0.05 to 0.05.

The calculation method used is available as the iprPy phonon calculation method.

Notes and Disclaimers:

  • The thermodynamic properties estimated from QHA are based on the assumption that only volumetric changes affect the phonon behaviors as the temperature changes. This tends to give good predictions at lower temperatures but ignores anharmonic effects such as phonon coupling and vacancy formation that can be important at higher temperatures.
  • Note that direct molecular dynamics (MD) simulations using the same potentials will disagree with the thermodynamics properties listed here for the lowest temperatures. The MD results are purely classical in nature and therefore lack a zero-point energy, whereas the phonon calculations inherently provide a zero-point energy.
  • The structures explored here are taken from the dynamically relaxed structures above. Despite the rigorous relaxation method used, some of these structures prove to be unstable once internal deformations are added. The phonon results may reflect this and give bad band gap predictions for these unstable crystals.
  • All QHA calculations performed here use the same set of strains which might not be ideal for all crystals. Be sure to check the bulk modulus and Helmholtz vs. volume plots to verify if the QHA strained states are reasonable for each crystal of interest.
  • QHA results may not be available for all crystal structures that have phonon results. Missing QHA results indicates an issue either with the strained states or with the QHA calculation itself.
  • NIST disclaimer

Version Information:

  • 2023-03-14. Phonon and QHA plots added

Band Structures, Density of States, and QHA Verification Plots

Composition:
Prototype:
a0:
plot: