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Citation: M.I. Mendelev, and G.J. Ackland (2007), "Development of an interatomic potential for the simulation of phase transformations in zirconium", Philosophical Magazine Letters, 87(5), 349-359. DOI: 10.1080/09500830701191393.
Abstract: In recent years, some 30 studies have been published on the molecular dynamics (MD) of zirconium, primarily of its twinning deformation and response to radiation damage. Its low thermal neutron absorption makes it uniquely suited for the latter application. Surprisingly, currently used interatomic potentials do not encapsulate the unique properties of Zr, namely its high stacking-fault energy, anomolous self-diffusion, melting and phase transformation under temperature and pressure (or alloying). Ab initio calculations have shown deficiencies in the description of point defects, both vacancies and interstitials, using existing interatomic potentials, deficiencies that can now be rectified by refitting. Here, we show the calculation of phase transitions self-consistently and present a potential for Zr that correctly reproduces the energetics of our extended database of ab initio configurations and high-temperature phase transitions. The potential has an analytic many-body form, making it suitable for existing large-scale MD codes. We also present a best-fit potential for the hcp structure and its defects.

Notes: This listing is for the reference's potential parameter set #1.

LAMMPS pair_style eam/alloy (2007--Mendelev-M-I--Zr-1--LAMMPS--ipr1)
Notes: This file was provided by Mikhail Mendelev.
File(s):
Citation: M.I. Mendelev, and G.J. Ackland (2007), "Development of an interatomic potential for the simulation of phase transformations in zirconium", Philosophical Magazine Letters, 87(5), 349-359. DOI: 10.1080/09500830701191393.
Abstract: In recent years, some 30 studies have been published on the molecular dynamics (MD) of zirconium, primarily of its twinning deformation and response to radiation damage. Its low thermal neutron absorption makes it uniquely suited for the latter application. Surprisingly, currently used interatomic potentials do not encapsulate the unique properties of Zr, namely its high stacking-fault energy, anomolous self-diffusion, melting and phase transformation under temperature and pressure (or alloying). Ab initio calculations have shown deficiencies in the description of point defects, both vacancies and interstitials, using existing interatomic potentials, deficiencies that can now be rectified by refitting. Here, we show the calculation of phase transitions self-consistently and present a potential for Zr that correctly reproduces the energetics of our extended database of ab initio configurations and high-temperature phase transitions. The potential has an analytic many-body form, making it suitable for existing large-scale MD codes. We also present a best-fit potential for the hcp structure and its defects.

Notes: This listing is for the reference's potential parameter set #2.

LAMMPS pair_style eam/alloy (2007--Mendelev-M-I--Zr-2--LAMMPS--ipr1)
Notes: This file was provided by Mikhail Mendelev.
File(s): superseded


LAMMPS pair_style eam/alloy (2007--Mendelev-M-I--Zr-2--LAMMPS--ipr2)
Notes: Update 09 Mar 2009: New files for Zr #2 and Zr #3 (24 Feb 2009) were sent as replacements for the previous version. They better treat radial distances smaller than 0.5 A for use in radiation damage simulations.
File(s):
Citation: M.I. Mendelev, and G.J. Ackland (2007), "Development of an interatomic potential for the simulation of phase transformations in zirconium", Philosophical Magazine Letters, 87(5), 349-359. DOI: 10.1080/09500830701191393.
Abstract: In recent years, some 30 studies have been published on the molecular dynamics (MD) of zirconium, primarily of its twinning deformation and response to radiation damage. Its low thermal neutron absorption makes it uniquely suited for the latter application. Surprisingly, currently used interatomic potentials do not encapsulate the unique properties of Zr, namely its high stacking-fault energy, anomolous self-diffusion, melting and phase transformation under temperature and pressure (or alloying). Ab initio calculations have shown deficiencies in the description of point defects, both vacancies and interstitials, using existing interatomic potentials, deficiencies that can now be rectified by refitting. Here, we show the calculation of phase transitions self-consistently and present a potential for Zr that correctly reproduces the energetics of our extended database of ab initio configurations and high-temperature phase transitions. The potential has an analytic many-body form, making it suitable for existing large-scale MD codes. We also present a best-fit potential for the hcp structure and its defects.

Notes: This listing is for the reference's potential parameter set #3.

LAMMPS pair_style eam/alloy (2007--Mendelev-M-I--Zr-3--LAMMPS--ipr1)
Notes: This file was provided by Mikhail Mendelev. Except for comments, this file is identical to "Zr_mm.eam.fs" in the August 22, 2018 LAMMPS distribution.
File(s): superseded


LAMMPS pair_style eam/alloy (2007--Mendelev-M-I--Zr-3--LAMMPS--ipr2)
Notes: Update 09 Mar 2009: New files for Zr #2 and Zr #3 (24 Feb 2009) were sent as replacements for the previous version. They better treat radial distances smaller than 0.5 A for use in radiation damage simulations.
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--Zr--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--Zr--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: G.J. Ackland, S.J. Wooding, and D.J. Bacon (1995), "Defect, surface and displacement-threshold properties of α-zirconium simulated with a many-body potential", Philosophical Magazine A, 71(3), 553-565. DOI: 10.1080/01418619508244468.
Abstract: A many-body interatomic potential has been developed for the h.c.p. metal α-zirconium using the same methodology as that used by Ackland for α-titanium. The repulsive pair part of the potential has been constructed so that the model can be employed for simulating atomic collisions. The favoured self-interstitial configurations are the 〈1120〉 crowdion and split defects, and they are highly mobile in the basal plane. The energy of surfaces is not strongly dependent on the crystallographic orientation, and the I2 stacking fault on the basal plane is not stable. The displacement threshold energy in a crystal at 0 K exhibits a similar orientation dependence to that computed recently for α-titanium by Bacon et al. and has the same minimum of 27·5 eV along the 〈1120〉 directions, but the mean value of 55 eV averaged over all orientations is higher than that of 30 eV in titanium.

Moldy FS
Notes: The parameters in zr.moldy were obtained from http://homepages.ed.ac.uk/graeme/moldy/moldy.html and posted with the permission of G.J. Ackland. From that website: "Note typoes in the journal version of zirconium."
File(s):
LAMMPS pair_style eam/fs (1995--Ackland-G-J--Zr--LAMMPS--ipr1)
Notes: A conversion to LAMMPS from MOLDY was performed by G.J. Ackland and submitted on 10 Oct. 2017. This implementation includes the short-range repulsion for radiation studies.
File(s):
 
Citation: V. Borovikov, M.I. Mendelev, and A.H. King (2016), "Effects of stable and unstable stacking fault energy on dislocation nucleation in nano-crystalline metals", Modelling and Simulation in Materials Science and Engineering, 24(8), 85017. DOI: 10.1088/0965-0393/24/8/085017.
Abstract: Dislocation nucleation from grain boundaries (GB) can control plastic deformation in nano-crystalline metals under certain conditions, but little is known about what controls dislocation nucleation, because when data from different materials are compared, the variations of many interacting properties tend to obscure the effects of any single property. In this study, we seek clarification by applying a unique capability of semi-empirical potentials in molecular dynamics simulations: the potentials can be modified such that all significant material properties but one, are kept constant. Using a set of potentials developed to isolate the effects of stacking fault energy, we show that for a given grain boundary, loading orientation and strain rate, the yield stress depends linearly on both the stable and unstable stacking fault energies. The coefficients of proportionality depend on the GB structure and the value of the yield stress is related to the density of the E structural units in the GB. While the impact of the stable stacking fault energy is easy to understand, the unstable stacking fault energy requires more elucidation and we provide a framework for understanding how it affects the nucleation and propagation process.

Notes: Dr. Mendelev noted that this potential was developed in the same manner as Cu-Zr_2.eam.fs, except that the original Cu potential was replaced by MCu31.eam.fs, which has more realistic stable and unstable stacking fault energies. This potential can be used to simulate the plastic deformation in the Cu-Zr amorphous alloys with embedded Cu particles.

LAMMPS pair_style eam/fs (2016--Borovikov-V--Cu-Zr--LAMMPS--ipr1)
Notes: These files were sent by M.I. Mendelev (Ames Laboratory) on 27 Sept. 2017 and posted with his permission.
File(s):
Citation: M.I. Mendelev, M.J. Kramer, R.T. Ott, D.J. Sordelet, D. Yagodin, and P. Popel (2009), "Development of suitable interatomic potentials for simulation of liquid and amorphous Cu-Zr alloys", Philosophical Magazine, 89(11), 967-987. DOI: 10.1080/14786430902832773.
Abstract: We present a new semi-empirical potential suitable for molecular dynamics simulations of liquid and amorphous Cu–Zr alloys. To provide input data for developing the potential, new experimental measurements of the structure factors for amorphous Cu64.5Zr35.5 alloy were performed. In this work, we propose a new method to include diffraction data in the potential development procedure, which also includes fitting to first-principles and liquid density and enthalpy of mixing data. To refine the new potential, we used first-principles and liquid enthalpy of mixing data published earlier combined with the densities of liquid Cu64.5Zr35.5 measured over a range of temperatures. We show that the potential predicts a liquid-to-glass transition temperature that agrees reasonably well with experimental data. Finally, we compare the new potential with two previously developed semi-empirical potentials for Cu–Zr alloys and examine their comparative and contrasting descriptions of structure and properties for Cu64.5Zr35.5 liquids and glasses.

LAMMPS pair_style eam/fs (2009--Mendelev-M-I--Cu-Zr--LAMMPS--ipr1)
Notes: This file was supplied by Mikhail Mendelev on 28 Nov. 2008. The reference was added on 22 Apr. 2009. Note added 14 Oct. 2010: the Cu part of this potential (M.I. Mendelev, et al., Phil. Mag. 88, 1723-1750 (2008)) has been posted separately on the Cu page to make it easier to use.
File(s):
Citation: M.I. Mendelev, D.J. Sordelet, and M.J. Kramer (2007), "Using atomistic computer simulations to analyze x-ray diffraction data from metallic glasses", Journal of Applied Physics, 102(4), 43501. DOI: 10.1063/1.2769157.
Abstract: We propose a method of using atomistic computer simulations to obtain partial pair correlation functions from wide angle diffraction experiments with metallic liquids and their glasses. In this method, a model is first created using a semiempirical interatomic potential and then an additional atomic force is added to improve the agreement with experimental diffraction data. To illustrate this approach, the structure of an amorphous Cu64.5Zr35.5 alloy is highlighted, where we present the results for the semiempirical many-body potential and fitting to x-ray diffraction data. While only x-ray diffraction data were used in the present work, the method can be easily adapted to the case when there are also data from neutron diffraction or even in combination. Moreover, this method can be employed in the case of multicomponent systems when the data of several diffraction experiments can be combined.

LAMMPS pair_style eam/fs (2007--Mendelev-M-I--Cu-Zr--LAMMPS--ipr1)
Notes: This file was supplied by Mikhail Mendelev. Note added 14 Oct. 2010: the Cu part of this potential (M.I. Mendelev, et al., Phil. Mag. 88, 1723-1750 (2008)) has been posted separately on the Cu page to make it easier to use. Except for comments, this file is equivalent to "CuZr_mm.eam.fs" in the August 22, 2018 LAMMPS distribution.
File(s):
 
Citation: D.E. Smirnova, and S.V. Starikov (2017), "An interatomic potential for simulation of Zr-Nb system", Computational Materials Science, 129, 259-272. DOI: 10.1016/j.commatsci.2016.12.016.
Abstract: We report a new attempt to study properties of Zr-Nb structural alloys. For this purpose we constructed an angular-dependent many-body interatomic potential. The potential functions were fitted towards the ab initio data computed for a large set of reference structures. The fitting procedure is described, and its accuracy is discussed. We show that the structure and properties of all Nb and Zr phases existing in the Zr-Nb binary system are reproduced with good accuracy. The interatomic potential is appropriate for study of the high-pressure hexagonal ω-phase of Zr. We also estimated characteristics of the point defects in α-Zr, β-Zr and Nb; results are proven to correlate with the existing experimental and theoretical data. In case of α-Zr the model reveals anisotropy of the vacancy diffusion, in agreement with previous calculations and experiments. The potential provides an opportunity for simulation of Zr-Nb alloys based on α-Zr and β-Zr. This conclusion is illustrated by the results obtained for the alloys with different niobium concentrations: up to 7% in case of hcp alloys and up to 50% for bcc alloys.

Notes: The reference was updated on 17 January 2017.

LAMMPS pair_style adp (2017--Smirnova-D-E--Zr-Nb--LAMMPS--ipr1)
Notes: These files were sent by D. Smirnova (Joint Institute for High Temperatures, Russian Academy of Sciences) on 15 December 2016 and posted with her permission.
File(s):
 
Citation: S.R. Wilson, and M.I. Mendelev (2015), "Anisotropy of the solid-liquid interface properties of the Ni-Zr B33 phase from molecular dynamics simulation", Philosophical Magazine, 95(2), 224-241. DOI: 10.1080/14786435.2014.995742.
Abstract: Solid–liquid interface (SLI) properties of the Ni–Zr B33 phase were determined from molecular dynamics simulations. In order to perform these measurements, a new semi-empirical potential for Ni–Zr alloy was developed that well reproduces the material properties required to model SLIs in the Ni50.0Zr50.0 alloy. In particular, the developed potential is shown to provide that the solid phase emerging from the liquid Ni50.0Zr50.0 alloy is B33 (apart from a small fraction of point defects), in agreement with the experimental phase diagram. The SLI properties obtained using the developed potential exhibit an extraordinary degree of anisotropy. It is observed that anisotropies in both the interfacial free energy and mobility are an order of magnitude larger than those measured to date in any other metallic compound. Moreover, the [0 1 0] interface is shown to play a significant role in the observed anisotropy. Our data suggest that the [0 1 0] interface simultaneously corresponds to the lowest mobility, the lowest free energy and the highest stiffness of all inclinations in B33 Ni–Zr. This finding can be understood by taking into account a rather complicated crystal structure in this crystallographic direction.

Notes: Mikhail Mendelev (Ames Laboratory) noted that the potential is an updated version of the 2012 potential, and it was designed to simulate solidification of B2, B33, and C16 phases in Ni-Zr alloys. Updated previous note on 13 Nov. 2014 to replace "NiZr2 alloy" with "Ni-Zr alloys". Updated 27 Apr 2015 to include publication information.

LAMMPS pair_style eam/fs (2015--Wilson-S-R--Ni-Zr--LAMMPS--ipr1)
Notes: This file was provided by Mikhail Mendelev (Ames Laboratory) and posted with his permission on 2 Jul. 2014.
File(s):
Citation: M.I. Mendelev, M.J. Kramer, S.G. Hao, K.M. Ho, and C.Z. Wang (2012), "Development of interatomic potentials appropriate for simulation of liquid and glass properties of NiZr2 alloy", Philosophical Magazine, 92(35), 4454-4469. DOI: 10.1080/14786435.2012.712220.
Abstract: A new interatomic potential for the Ni–Zr system is presented. This potential was developed specifically to match experimental scattering data from Ni, Zr and NiZr2 liquids. Both ab initio and published thermodynamic data were used to optimise the potential to study the liquid and amorphous structure of the NiZr2 alloy. This potential has the C16 phase, being more stable than C11b phase in the NiZr2 alloy, consistent with experiments. The potential leads to the correct glass structure in the molecular dynamics simulation and, therefore, can be used to study the liquid–glass transformation in the NiZr2 alloy.

Notes: Mikhail Mendelev (Ames Laboratory) noted that the potential is designed to simulate liquid/glass properties and solidification in the NiZr2 alloy. The potential utilizes the following interactions from other potentials: Ni = 2012--Mendelev-M-I--Ni and Zr = 2007--Mendelev-M-I--Zr-2. 31 May 2013: The reference was updated to reflect the publication status.

LAMMPS pair_style eam/fs (2012--Mendelev-M-I--Ni-Zr--LAMMPS--ipr1)
Notes: This file was provided by Mikhail Mendelev (Ames Laboratory) and posted with his permission on 26 Oct. 2010. 31 May 2013: This reference was updated to reflect the publication status. The original file is Ni-Zr_Mendelev_2010.eam.fs, where only the first line is different.
File(s):
 
Citation: A.P. Moore, B. Beeler, C. Deo, M.I. Baskes, and M.A. Okuniewski (2015), "Atomistic modeling of high temperature uranium\textendashzirconium alloy structure and thermodynamics", Journal of Nuclear Materials, 467, 802-819. DOI: 10.1016/j.jnucmat.2015.10.016.

Dynamo MEAM
Notes: These files were sent by Alexander Moore (Georgia Institute of Technology) on 13 Aug. 2015 and posted with his permission. He noted that "This is a MEAM potential for U, Zr, and U-Zr alloys. The files attached are the potential files for DYNAMO. It should be noted that use of this potential in LAMMPS requires LAMMPS to have a modified cut-off function before it is compiled." Update 27 April 2018: Publication information was added.
File(s):
Date Created: October 5, 2010 | Last updated: November 19, 2018