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Citation: M.-C. Marinica, L. Ventelon, M.R. Gilbert, L. Proville, S.L. Dudarev, J. Marian, G. Bencteux, and F. Willaime (2013), "Interatomic potentials for modelling radiation defects and dislocations in tungsten", Journal of Physics: Condensed Matter, 25(39), 395502. DOI: 10.1088/0953-8984/25/39/395502.
Abstract: We have developed empirical interatomic potentials for studying radiation defects and dislocations in tungsten. The potentials use the embedded atom method formalism and are fitted to a mixed database, containing various experimentally measured properties of tungsten and ab initio formation energies of defects, as well as ab initio interatomic forces computed for random liquid configurations. The availability of data on atomic force fields proves critical for the development of the new potentials. Several point and extended defect configurations were used to test the transferability of the potentials. The trends predicted for the Peierls barrier of the 1/2<111> screw dislocation are in qualitative agreement with ab initio calculations, enabling quantitative comparison of the predicted kink-pair formation energies with experimental data.

Notes: This listing is for potential the reference's potential parameter set EAM2.

LAMMPS pair_style eam/fs (2013--Marinica-M-C--W-2--LAMMPS--ipr1)
Notes: This file was sent by M.-C. Marinica (CEA, France) on 9 January 2017 and posted with his permission.
File(s):
Citation: M.-C. Marinica, L. Ventelon, M.R. Gilbert, L. Proville, S.L. Dudarev, J. Marian, G. Bencteux, and F. Willaime (2013), "Interatomic potentials for modelling radiation defects and dislocations in tungsten", Journal of Physics: Condensed Matter, 25(39), 395502. DOI: 10.1088/0953-8984/25/39/395502.
Abstract: We have developed empirical interatomic potentials for studying radiation defects and dislocations in tungsten. The potentials use the embedded atom method formalism and are fitted to a mixed database, containing various experimentally measured properties of tungsten and ab initio formation energies of defects, as well as ab initio interatomic forces computed for random liquid configurations. The availability of data on atomic force fields proves critical for the development of the new potentials. Several point and extended defect configurations were used to test the transferability of the potentials. The trends predicted for the Peierls barrier of the 1/2<111> screw dislocation are in qualitative agreement with ab initio calculations, enabling quantitative comparison of the predicted kink-pair formation energies with experimental data.

Notes: This listing is for potential the reference's potential parameter set EAM3.

LAMMPS pair_style eam/fs (2013--Marinica-M-C--W-3--LAMMPS--ipr1)
Notes: This file was sent by M.-C. Marinica (CEA, France) on 9 January 2017 and posted with his permission.
File(s):
Citation: M.-C. Marinica, L. Ventelon, M.R. Gilbert, L. Proville, S.L. Dudarev, J. Marian, G. Bencteux, and F. Willaime (2013), "Interatomic potentials for modelling radiation defects and dislocations in tungsten", Journal of Physics: Condensed Matter, 25(39), 395502. DOI: 10.1088/0953-8984/25/39/395502.
Abstract: We have developed empirical interatomic potentials for studying radiation defects and dislocations in tungsten. The potentials use the embedded atom method formalism and are fitted to a mixed database, containing various experimentally measured properties of tungsten and ab initio formation energies of defects, as well as ab initio interatomic forces computed for random liquid configurations. The availability of data on atomic force fields proves critical for the development of the new potentials. Several point and extended defect configurations were used to test the transferability of the potentials. The trends predicted for the Peierls barrier of the 1/2<111> screw dislocation are in qualitative agreement with ab initio calculations, enabling quantitative comparison of the predicted kink-pair formation energies with experimental data.

Notes: This listing is for potential the reference's potential parameter set EAM4.

LAMMPS pair_style eam/fs (2013--Marinica-M-C--W-4--LAMMPS--ipr1)
Notes: This file was sent by M.-C. Marinica (CEA, France) on 9 January 2017 and posted with his permission.
File(s):
Citation: J. Wang, Y.L. Zhou, M. Li, and Q. Hou (2013), "A modified W-W interatomic potential based on ab initio calculations", Modelling and Simulation in Materials Science and Engineering, 22(1), 15004. DOI: 10.1088/0965-0393/22/1/015004.
Abstract: In this paper we have developed a Finnis–Sinclair-type interatomic potential for W-W interactions that is based on ab initio calculations. The modified potential is able to reproduce the correct formation energies of self-interstitial atom (SIA) defects in tungsten, offering a significant improvement over the Ackland–Thetford tungsten potential. Using the modified potential, the thermal expansion is calculated in a temperature range from 0 to 3500 K. The results are in reasonable agreement with the experimental data, thus overcoming the shortcomings of the negative thermal expansion using the Derlet–Nguyen–Manh–Dudarev tungsten potential. The W–W potential presented here is also applied to study in detail the diffusion of SIAs in tungsten. We reveal that the initial SIA initiates a sequence of tungsten atom displacements and replacements in the 〈111〉 direction. An Arrhenius fit to the diffusion data at temperatures below 550 K indicates a migration energy of 0.022 eV, which is in reasonable agreement with the experimental data.

Finnis-Sinclair tables
Notes: These files were sent by Dr. Jun Wang and Prof. Qing Hou (Sichuan Univ.) and approved on 24 Jan. 2014. Additional information is found in Wang_W_2014_information.pdf, including a correction to equations 4 and 5 in the publication. Specifically, according to Dr. Wang, "'f(r)' should be 'V(r)' in equation (4) and in equation (5) 'V(r)' should be 'f(r)'."
File(s):
Citation: P.A.T. Olsson (2009), "Semi-empirical atomistic study of point defect properties in BCC transition metals", Computational Materials Science, 47(1), 135-145. DOI: 10.1016/j.commatsci.2009.06.025.
Abstract: We have constructed a set of embedded atom method (EAM) potentials for Fe, Ta, W and V and used them in order to study point defect properties. The parametrizations of the potentials ensure that the third order elastic constants are continuous and they have been fitted to the cohesive energies, the lattice constants, the unrelaxed vacancy formation energies and the second order elastic constants. Formation energies for different self-interstitials reveal that the <1 1 0> split dumbbell is the most stable configuration for Fe while for Ta, W and V we find that the <1 1 1> split dumbbell is preferred. Self-interstitial migration energies are simulated using the nudged elastic band method and for Fe and W the migration energies are found to be in good agreement with experimental and ab initio data. Migration energies for Ta and V self-interstitials are found to be quite low. The calculated formation, activation and migration energies for monovacancies are in good agreement with experimental data. Formation energies for divacancies reveal that the second nearest neighbor divacancy is more energetically favorable than nearest neighbor divacancies and the migration energies indicate that nearest neighbor migration paths are more likely to occur than second nearest neighbor migration jumps. For Fe, we have also studied the influence of the pair potential behavior between the second and third nearest neighbor on the stability of the <1 1 0> split dumbbell, which revealed that the higher the energy level of the pair potential is in that region, the more stable the <1 1 0> split dumbbell becomes.

EAM tabulated functions
Notes: These files were provided by Pär Olsson (Malmoe University, Sweden) on 11 November 2018 and posted with his permission.
File(s):
F(ρ): F_w.plt
ρ(r): rho_w.plt
φ(r): phi_w.plt

LAMMPS pair_style eam/alloy (2009--Olsson-P-A-T--W--LAMMPS--ipr1)
Notes: This file was provided by Pär Olsson (Malmoe University, Sweden) on 11 November 2018 and posted with his permission.
File(s):
Citation: X.W. Zhou, R.A. Johnson, and H.N.G. Wadley (2004), "Misfit-energy-increasing dislocations in vapor-deposited CoFe/NiFe multilayers", Physical Review B, 69(14), 144113. DOI: 10.1103/physrevb.69.144113.
Abstract: Recent molecular dynamics simulations of the growth of [Ni0.8Fe0.2/Au] multilayers have revealed the formation of misfit-strain-reducing dislocation structures very similar to those observed experimentally. Here we report similar simulations showing the formation of edge dislocations near the interfaces of vapor-deposited (111) [NiFe/CoFe/Cu] multilayers. Unlike misfit dislocations that accommodate lattice mismatch, the dislocation structures observed here increase the mismatch strain energy. Stop-action observations of the dynamically evolving atomic structures indicate that during deposition on the (111) surface of a fcc lattice, adatoms may occupy either fcc sites or hcp sites. This results in the random formation of fcc and hcp domains, with dislocations at the domain boundaries. These dislocations enable atoms to undergo a shift from fcc to hcp sites, or vice versa. These shifts lead to missing atoms, and therefore a later deposited layer can have missing planes compared to a previously deposited layer. This dislocation formation mechanism can create tensile stress in fcc films. The probability that such dislocations are formed was found to quickly diminish under energetic deposition conditions.

FORTRAN
Notes: These are the original files sent by X.W. Zhou (Sandia National Laboratory) and posted with his permission. C.A. Becker (NIST) modified create.f to include the reference in the generated potential files and the EAM.input file for this composition. These files can be used to generate alloy potentials for Cu, Ag, Au, Ni, Pd, Pt, Al, Pb, Fe, Mo, Ta, W, Mg, Co, Ti, and Zr by editing EAM.input. However, as addressed in the reference, these potentials were not designed for use with metal compounds.
File(s): superseded


LAMMPS pair_style eam/alloy (2004--Zhou-X-W--W--LAMMPS--ipr1)
Notes: This file was generated by C.A. Becker (NIST) from create.f and posted with X.W. Zhou's (Sandia National Laboratory) permission.
File(s): superseded


FORTRAN
Notes: The file Zhou04_create_v2.f is an updated version of create.f modified by L.M. Hale (NIST) following advice from X.W. Zhou (Sandia National Laboratory). This version removes spurious fluctuations in the tabulated functions of the original potential files caused by single/double precision floating point number conflicts.
File(s):
LAMMPS pair_style eam/alloy (2004--Zhou-X-W--W--LAMMPS--ipr2)
Notes: This file was generated by L.M. Hale from Zhou04_create_v2.f on 13 April 2018 and posted with X.W. Zhou's (Sandia National Laboratory) permission. This version corrects an issue with spurious fluctuations in the tabulated functions.
File(s):
Citation: S. Han, L.A. Zepeda-Ruiz, G.J. Ackland, R. Car, and D.J. Srolovitz (2003), "Interatomic potential for vanadium suitable for radiation damage simulations", Journal of Applied Physics, 93(6), 3328-3335. DOI: 10.1063/1.1555275.
Abstract: The ability to predict the behavior of point defects in metals, particularly interstitial defects, is central to accurate modeling of the microstructural evolution in environments with high radiation fluxes. Existing interatomic potentials of embedded atom method type predict disparate stable interstitial defect configurations in vanadium. This is not surprising since accurate first-principles interstitial data were not available when these potentials were fitted. In order to provide the input information required to fit a vanadium potential appropriate for radiation damage studies, we perform a series of first-principles calculations on six different interstitial geometries and vacancies. These calculations identify the 〈111〉 dumbbell as the most stable interstitial with a formation energy of approximately 3.1 eV, at variance with predictions based upon existing potentials. Our potential is of Finnis–Sinclair type and is fitted exactly to the experimental equilibrium lattice parameter, cohesive energy, elastic constants and a calculated unrelaxed vacancy formation energy. Two additional potential parameters were used to obtain the best fit to the set of interstitial formation energies determined from the first-principles calculations. The resulting potential was found to accurately predict both the magnitude and ordering of the formation energies of six interstitial configurations and the unrelaxed vacancy ground state, in addition to accurately describing the migration characteristics of the stable interstitial and vacancy. This vanadium potential is capable of describing the point defect properties appropriate for radiation damage simulations as well as for simulations of more common crystal and simple defect properties.

Moldy FS
Notes: The parameters in W.moldy were 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 (2003--Han-S--W--LAMMPS--ipr1)
Notes: This conversion was performed from G.J. Ackland's parameters by M.I. Mendelev. Conversion checks from M.I. Mendelev can be found in conversion_check.pdf. These files were posted on 2 July 2009 with the permission of G.J. Ackland and M.I. Mendelev.
File(s):
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.

Equations
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):
 
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.

LAMMPS pair_style hybrid/overlay eam/alloy eam/fs (2013--Bonny-G--Fe-Cr-W-LAMMPS--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. Dr. Bonny noted that the potentials were not stiffened and cannot be used in their present form for collision cascades.
File(s):
EAM tabulated functions
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

 
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.

LAMMPS pair_style eam/alloy (2013--Bonny-G--Fe-W--LAMMPS--ipr1)
Notes: This file was 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 this potential was not stiffened and cannot be used in its present form for collision cascades.
File(s):
 
Citation: G. Bonny, P. Grigorev, and D. Terentyev (2014), "On the binding of nanometric hydrogen-helium clusters in tungsten", Journal of Physics: Condensed Matter, 26(48), 485001. DOI: 10.1088/0953-8984/26/48/485001.
Abstract: In this work we developed an embedded atom method potential for large scale atomistic simulations in the ternary tungsten–hydrogen–helium (W–H–He) system, focusing on applications in the fusion research domain. Following available ab initio data, the potential reproduces key interactions between H, He and point defects in W and utilizes the most recent potential for matrix W. The potential is applied to assess the thermal stability of various H–He complexes of sizes too large for ab initio techniques. The results show that the dissociation of H–He clusters stabilized by vacancies will occur primarily by emission of hydrogen atoms and then by break-up of V–He complexes, indicating that H–He interaction does influence the release of hydrogen.

Notes: This listing is for the reference's potential parameter set EAM1.

LAMMPS pair_style eam/alloy (2014--Bonny-G--W-H-He-1--LAMMPS--ipr1)
Notes: These files were sent by Giovanni Bonny (Nuclear Materials Science Institute of SCK-CEN, Belgium) on 18 Mar. 2016 and posted with his permission. Giovanni Bonny also noted that only W has electron density function and embedding function. The embedding contributions to the energy from H and He are zero.
File(s):
EAM tabulated functions
Notes: Same functions in separate EAM tables.
File(s):
Citation: G. Bonny, P. Grigorev, and D. Terentyev (2014), "On the binding of nanometric hydrogen-helium clusters in tungsten", Journal of Physics: Condensed Matter, 26(48), 485001. DOI: 10.1088/0953-8984/26/48/485001.
Abstract: In this work we developed an embedded atom method potential for large scale atomistic simulations in the ternary tungsten–hydrogen–helium (W–H–He) system, focusing on applications in the fusion research domain. Following available ab initio data, the potential reproduces key interactions between H, He and point defects in W and utilizes the most recent potential for matrix W. The potential is applied to assess the thermal stability of various H–He complexes of sizes too large for ab initio techniques. The results show that the dissociation of H–He clusters stabilized by vacancies will occur primarily by emission of hydrogen atoms and then by break-up of V–He complexes, indicating that H–He interaction does influence the release of hydrogen.

Notes: This listing is for the reference's potential parameter set EAM2.

LAMMPS pair_style eam/alloy (2014--Bonny-G--W-H-He-2--LAMMPS--ipr1)
Notes: These files were sent by Giovanni Bonny (Nuclear Materials Science Institute of SCK-CEN, Belgium) on 18 Mar. 2016 and posted with his permission. Giovanni Bonny also noted that only W has electron density function. Both W and H have embedding functions that take the electron density from W as an argument. The embedding contributions to the energy from He are zero.
File(s):
EAM tabulated functions
Notes: Same functions in separate EAM tables.
File(s):
 
Citation: G. Bonny, A. Bakaev, D. Terentyev, and Y.A. Mastrikov (2017), "Interatomic potential to study plastic deformation in tungsten-rhenium alloys", Journal of Applied Physics, 121(16), 165107. DOI: 10.1063/1.4982361.
Abstract: In this work, an interatomic potential for the W-Re system is fitted and benchmarked against experimental and density functional theory (DFT) data, of which part are generated in this work. Having in mind studies related to the plasticity of W-Re alloys under irradiation, emphasis is put on fitting point-defect properties, elastic constants, and dislocation properties. The developed potential can reproduce the mechanisms responsible for the experimentally observed softening, i.e., decreasing shear moduli, decreasing Peierls barrier, and asymmetric screw dislocation core structure with increasing Re content in W-Re solid solutions. In addition, the potential predicts elastic constants in reasonable agreement with DFT data for the phases forming non-coherent precipitates (σ- and χ-phases) in W-Re alloys. In addition, the mechanical stability of the different experimentally observed phases is verified in the temperature range of interest (700–1500 K). As a conclusion, the presented potential provides an excellent tool to study plasticity in W-Re alloys at the atomic level.

EAM tabulated functions
Notes: These files were sent by Dr. Giovanni Bonny (Nuclear Materials Science Institute of SCK-CEN, Belgium) on 2 November 2017 and posted with his permission.
File(s):
W F(ρ): F_W.spt
Re F(ρ): F_Re.spt
W ρ(r): rhoW.spt
Re ρ(r): rhoRe.spt
W-W φ(r): pWW.spt
Re-Re φ(r): pReRe.spt
W-Re φ(r): pWRe.spt

LAMMPS pair_style eam/alloy (2017--Bonny-G--W-Re--LAMMPS--ipr1)
Notes: LAMMPS-compatible file sent by Dr. Giovanni Bonny (Nuclear Materials Science Institute of SCK-CEN, Belgium) on 2 November 2017 and posted with his permission.
File(s):
Date Created: October 5, 2010 | Last updated: November 19, 2018