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Citation: M.I. Mendelev, T.L. Underwood, and G.J. Ackland (2016), "Development of an interatomic potential for the simulation of defects, plasticity, and phase transformations in titanium", The Journal of Chemical Physics, 145(15), 154102. DOI: 10.1063/1.4964654.
Abstract: New interatomic potentials describing defects, plasticity, and high temperature phase transitions for Ti are presented. Fitting the martensitic hcp-bcc phase transformation temperature requires an efficient and accurate method to determine it. We apply a molecular dynamics method based on determination of the melting temperature of competing solid phases, and Gibbs-Helmholtz integration, and a lattice-switch Monte Carlo method: these agree on the hcp-bcc transformation temperatures to within 2 K. We were able to develop embedded atom potentials which give a good fit to either low or high temperature data, but not both. The first developed potential (Ti1) reproduces the hcp-bcc transformation and melting temperatures and is suitable for the simulation of phase transitions and bcc Ti. Two other potentials (Ti2 and Ti3) correctly describe defect properties and can be used to simulate plasticity or radiation damage in hcp Ti. The fact that a single embedded atom method potential cannot describe both low and high temperature phases may be attributed to neglect of electronic degrees of freedom, notably bcc has a much higher electronic entropy. A temperature-dependent potential obtained from the combination of potentials Ti1 and Ti2 may be used to simulate Ti properties at any temperature.

Notes: This listing is for the reference's potential parameter set Ti1. Dr. Mendelev provided a short description and some basic properties which can be downloaded here.

LAMMPS pair_style eam/fs (2016--Mendelev-M-I--Ti-1--LAMMPS--ipr1)
Notes: These files were sent by M.I. Mendelev (Ames Laboratory) on 21 July 2016 and posted with his permission.
File(s):
Citation: M.I. Mendelev, T.L. Underwood, and G.J. Ackland (2016), "Development of an interatomic potential for the simulation of defects, plasticity, and phase transformations in titanium", The Journal of Chemical Physics, 145(15), 154102. DOI: 10.1063/1.4964654.
Abstract: New interatomic potentials describing defects, plasticity, and high temperature phase transitions for Ti are presented. Fitting the martensitic hcp-bcc phase transformation temperature requires an efficient and accurate method to determine it. We apply a molecular dynamics method based on determination of the melting temperature of competing solid phases, and Gibbs-Helmholtz integration, and a lattice-switch Monte Carlo method: these agree on the hcp-bcc transformation temperatures to within 2 K. We were able to develop embedded atom potentials which give a good fit to either low or high temperature data, but not both. The first developed potential (Ti1) reproduces the hcp-bcc transformation and melting temperatures and is suitable for the simulation of phase transitions and bcc Ti. Two other potentials (Ti2 and Ti3) correctly describe defect properties and can be used to simulate plasticity or radiation damage in hcp Ti. The fact that a single embedded atom method potential cannot describe both low and high temperature phases may be attributed to neglect of electronic degrees of freedom, notably bcc has a much higher electronic entropy. A temperature-dependent potential obtained from the combination of potentials Ti1 and Ti2 may be used to simulate Ti properties at any temperature.

Notes: This listing is for the reference's potential parameter set Ti2. Dr. Mendelev provided a short description and some basic properties which can be downloaded here.

LAMMPS pair_style eam/fs (2016--Mendelev-M-I--Ti-2--LAMMPS--ipr1)
Notes: These files were sent by M.I. Mendelev (Ames Laboratory) on 21 July 2016 and posted with his permission.
File(s):
Citation: M.I. Mendelev, T.L. Underwood, and G.J. Ackland (2016), "Development of an interatomic potential for the simulation of defects, plasticity, and phase transformations in titanium", The Journal of Chemical Physics, 145(15), 154102. DOI: 10.1063/1.4964654.
Abstract: New interatomic potentials describing defects, plasticity, and high temperature phase transitions for Ti are presented. Fitting the martensitic hcp-bcc phase transformation temperature requires an efficient and accurate method to determine it. We apply a molecular dynamics method based on determination of the melting temperature of competing solid phases, and Gibbs-Helmholtz integration, and a lattice-switch Monte Carlo method: these agree on the hcp-bcc transformation temperatures to within 2 K. We were able to develop embedded atom potentials which give a good fit to either low or high temperature data, but not both. The first developed potential (Ti1) reproduces the hcp-bcc transformation and melting temperatures and is suitable for the simulation of phase transitions and bcc Ti. Two other potentials (Ti2 and Ti3) correctly describe defect properties and can be used to simulate plasticity or radiation damage in hcp Ti. The fact that a single embedded atom method potential cannot describe both low and high temperature phases may be attributed to neglect of electronic degrees of freedom, notably bcc has a much higher electronic entropy. A temperature-dependent potential obtained from the combination of potentials Ti1 and Ti2 may be used to simulate Ti properties at any temperature.

Notes: This listing is for the reference's potential parameter set Ti3. Dr. Mendelev provided a short description and some basic properties which can be downloaded here.

LAMMPS pair_style eam/fs (2016--Mendelev-M-I--Ti-3--LAMMPS--ipr1)
Notes: These files were sent by M.I. Mendelev (Ames Laboratory) on 21 July 2016 and posted with his permission.
File(s):
Citation: M.I. Mendelev, T.L. Underwood, and G.J. Ackland (2016), "Development of an interatomic potential for the simulation of defects, plasticity, and phase transformations in titanium", The Journal of Chemical Physics, 145(15), 154102. DOI: 10.1063/1.4964654.
Abstract: New interatomic potentials describing defects, plasticity, and high temperature phase transitions for Ti are presented. Fitting the martensitic hcp-bcc phase transformation temperature requires an efficient and accurate method to determine it. We apply a molecular dynamics method based on determination of the melting temperature of competing solid phases, and Gibbs-Helmholtz integration, and a lattice-switch Monte Carlo method: these agree on the hcp-bcc transformation temperatures to within 2 K. We were able to develop embedded atom potentials which give a good fit to either low or high temperature data, but not both. The first developed potential (Ti1) reproduces the hcp-bcc transformation and melting temperatures and is suitable for the simulation of phase transitions and bcc Ti. Two other potentials (Ti2 and Ti3) correctly describe defect properties and can be used to simulate plasticity or radiation damage in hcp Ti. The fact that a single embedded atom method potential cannot describe both low and high temperature phases may be attributed to neglect of electronic degrees of freedom, notably bcc has a much higher electronic entropy. A temperature-dependent potential obtained from the combination of potentials Ti1 and Ti2 may be used to simulate Ti properties at any temperature.

Notes: This listing is for the reference's temperature-dependent (Tdep) potential. Dr. Mendelev provided a short description and some basic properties which can be downloaded here.

FORTRAN
Notes: This file was sent by G.J. Ackland (University of Edinburgh) on 27 Sept 2016 and posted with his permission. Dr. Ackland noted that temperature-dependent potentials are also presented in the publication. This file is a fortran program that allows a user to specify a temperature and generate a potential for that temperature. The program includes comments to aid in compiling and use.
File(s):
Citation: R.G. Hennig, T.J. Lenosky, D.R. Trinkle, S.P. Rudin, and J.W. Wilkins (2008), "Classical potential describes martensitic phase transformations between the α, β, and ω titanium phases", Physical Review B, 78(5), . DOI: 10.1103/physrevb.78.054121.
Abstract: A description of the martensitic transformations between the α, β, and ω phases of titanium that includes nucleation and growth requires an accurate classical potential. Optimization of the parameters of a modified embedded atom potential to a database of density-functional calculations yields an accurate and transferable potential as verified by comparison to experimental and density-functional data for phonons, surface and stacking fault energies, and energy barriers for homogeneous martensitic transformations. Molecular-dynamics simulations map out the pressure-temperature phase diagram of titanium. For this potential the martensitic phase transformation between α and β appears at ambient pressure and 1200 K, between α and ω at ambient conditions, between β and ω at 1200 K and pressures above 8 GPa, and the triple point occurs at 8 GPa and 1200 K. Molecular-dynamics explorations of the kinetics of the martensitic α−ω transformation show a fast moving interface with a low interfacial energy of 30 meV/Å2. The potential is applicable to the study of defects and phase transformations of Ti.

LAMMPS pair_style meam/spline (2008--Hennig-R-G--Ti--LAMMPS--ipr1)
Notes: This file was taken from the August 22, 2018 LAMMPS distribution. It is listed as being contributed by Alexander Stukowski (Technische Universität Darmstadt)
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--Ti--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--Ti--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 (1992), "Theoretical study of titanium surfaces and defects with a new many-body potential", Philosophical Magazine A, 66(6), 917-932. DOI: 10.1080/01418619208247999.
Abstract: It is shown that any force model using short-range pair-functional interactions can only have three independent h.c.p. elastic constants. Empirical data show that these elastic properties are nearly realized in a number of materials. A new parametrization of a Finnis-Sinclair-type many-body potential for titanium is presented using these relations. Particular care is taken to describe the anisotropy of the shear constants and the deviation of the c/a lattice parameter ratio from ideal, while maintaining smooth monotonic functions. Energies, stresses and reconstruction modes of various low-index surfaces are calculated and general rules for surface stability are proposed. Various stacking faults on the basal and pyramidal plane are investigated.

Moldy FS
Notes: The parameters in ti.moldy were obtained from http://homepages.ed.ac.uk/graeme/moldy/moldy.html and posted with the permission of G.J. Ackland (University of Edinburgh).
File(s):
LAMMPS pair_style eam/fs (1992--Ackland-G-J--Ti--LAMMPS--ipr1)
Notes: This conversion was performed from G.J. Ackland's parameters by M.I. Mendelev (Ames National Laboratory). The email address was changed from that of M.I. Mendelev to G.J. Ackland. C.A. Becker (NIST) tested the file to run with the 7Jul09 release of LAMMPS, but properties were not evaluated. This file was posted on 1 Dec. 2009 with the permission of G.J. Ackland and M.I. Mendelev.
File(s):
LAMMPS pair_style eam/fs (1992--Ackland-G-J--Ti--LAMMPS--ipr2)
Notes: A new conversion to LAMMPS performed by G.J. Ackland was submitted on 10 Oct. 2017. This version adds close-range repulsion for radiation studies.
File(s):
 
Citation: D. Farkas, and C. Jones (1996), "Interatomic potentials for ternary Nb - Ti - Al alloys", Modelling and Simulation in Materials Science and Engineering, 4(1), 23-32. DOI: 10.1088/0965-0393/4/1/004.
Abstract: Interatomic potentials of the embedded-atom type were developed for the Nb - Al system via an empirical fitting to the properties of A15 Nb3Al. The cohesive energy and lattice parameters are fitted by the potentials, which also give good agreement with experimental values for the same properties in the D022 NbAl3 phase. A second interatomic potential was developed for the Nb - Ti system via a fitting to the lattice parameters and thermodynamic properties of the disordered BCC phase. The Al and Ti potentials used here are the same as those used in our previous work to derive Ti - Al potentials based on TiAl. This allows the use of the present potentials in conjunction with those previously derived interactions to study ternary Nb - Ti - Al alloys. The potentials were used to calculate the heats of solution of Al and Ti in Nb, and to simulate the Ti2NbAl orthorhombic phase.

LAMMPS pair_style eam/alloy (1996--Farkas-D--Nb-Ti-Al--LAMMPS--ipr1)
Notes: This file was generated and tested by Ganga Purja Pun and Yuri Mishin (George Mason Univ.) using the files below that were supplied by Diana Farkas (Virginia Tech.). Testing information is in Test_report_AlTiNb.pdf. These files were approved by Dr. Purja Pun and Profs. Farkas and Mishin and posted on 1 Jul 2014.
File(s):
EAM tabulated functions
Notes: These files were provided by Diana Farkas and approved by her on 1 Jul 2014.
File(s):
 
Citation: R.R. Zope, and Y. Mishin (2003), "Interatomic potentials for atomistic simulations of the Ti-Al system", Physical Review B, 68(2), 24102. DOI: 10.1103/physrevb.68.024102.
Abstract: Semiempirical interatomic potentials have been developed for Al, α−Ti, and γ−TiAl within the embedded atom method (EAM) formalism by fitting to a large database of experimental as well as ab initio data. The ab initio calculations were performed by the linearized augmented plane wave (LAPW) method within the density functional theory to obtain the equations of state for a number of crystal structures of the Ti-Al system. Some of the calculated LAPW energies were used for fitting the potentials while others for examining their quality. The potentials correctly predict the equilibrium crystal structures of the phases and accurately reproduce their basic lattice properties. The potentials are applied to calculate the energies of point defects, surfaces, and planar faults in the equilibrium structures. Unlike earlier EAM potentials for the Ti-Al system, the proposed potentials provide a reasonable description of the lattice thermal expansion, demonstrating their usefulness for molecular-dynamics and Monte Carlo simulations at high temperatures. The energy along the tetragonal deformation path (Bain transformation) in γ−TiAl calculated with the EAM potential is in fairly good agreement with LAPW calculations. Equilibrium point defect concentrations in γ−TiAl are studied using the EAM potential. It is found that antisite defects strongly dominate over vacancies at all compositions around stoichiometry, indicating that γ−TiAl is an antisite disorder compound, in agreement with experimental data.

EAM tabulated functions
Notes: These files were provided by Yuri Mishin.
File(s):
Al F(ρ): F_al.plt
Ti F(ρ): F_ti.plt
Al ρ(r): fal.plt
Ti ρ(r): fti.plt
Al φ(r): pal.plt
Ti φ(r): pti.plt
Ti-Al φ(r): ptial.plt

LAMMPS pair_style eam/alloy (2003--Zope-R-R--Ti-Al--LAMMPS--ipr1)
Notes: This conversion was produced by Chandler Becker on 26 Sept. 2009 from the plt files listed above. This version is compatible with LAMMPS. Validation and usage information can be found in Zope-Ti-Al-2003_releaseNotes_1.pdf.
File(s):
 
Citation: H.-K. Kim, W.-S. Jung, and B.-J. Lee (2009), "Modified embedded-atom method interatomic potentials for the Fe-Ti-C and Fe-Ti-N ternary systems", Acta Materialia, 57(11), 3140-3147. DOI: 10.1016/j.actamat.2009.03.019.
Abstract: Modified embedded-atom method (MEAM) interatomic potentials for the Fe–Ti–C and Fe–Ti–N ternary systems have been developed based on the previously developed MEAM potentials for sub-unary and binary systems. An attempt was made to find a way to determine ternary potential parameters using the corresponding binary parameters. The calculated coherent interface properties, interfacial energy, work of separation and misfit strain energy between body-centered cubic Fe and NaCl-type TiC or TiN were reasonable when compared with relevant first-principles calculations under the same condition. The applicability of the present potentials for atomistic simulations to investigate nucleation kinetics of TiC or TiN precipitates and their effects on mechanical properties in steels is also demonstrated.

LAMMPS pair_style meam (2009--Kim-H-K--Fe-Ti-C--LAMMPS--ipr2)
Notes: This file was submitted by Sebastián ECHEVERRI RESTREPO (SKF Engineering & Research Centre) on 31 August 2015 and approved for distribution by Byeong-Joo Lee (POSTECH). This version is compatible with LAMMPS. Implementation information can be found in FeTiC_Implementation.pdf.
File(s):
 
Citation: W.-S. Ko, B. Grabowski, and J. Neugebauer (2015), "Development and application of a Ni-Ti interatomic potential with high predictive accuracy of the martensitic phase transition", Physical Review B, 92(13), 134107. DOI: 10.1103/physrevb.92.134107.
Abstract: Phase transitions in nickel-titanium shape-memory alloys are investigated by means of atomistic simulations. A second nearest-neighbor modified embedded-atom method interatomic potential for the binary nickel-titanium system is determined by improving the unary descriptions of pure nickel and pure titanium, especially regarding the physical properties at finite temperatures. The resulting potential reproduces accurately the hexagonal-close-packed to body-centered-cubic phase transition in Ti and the martensitic B2−B19′ transformation in equiatomic NiTi. Subsequent large-scale molecular-dynamics simulations validate that the developed potential can be successfully applied for studies on temperature- and stress-induced martensitic phase transitions related to core applications of shape-memory alloys. A simulation of the temperature-induced phase transition provides insights into the effect of sizes and constraints on the formation of nanotwinned martensite structures with multiple domains. A simulation of the stress-induced phase transition of a nanosized pillar indicates a full recovery of the initial structure after the loading and unloading processes, illustrating a superelastic behavior of the target system.

LAMMPS pair_style meam (2015--Ko-W-S--Ni-Ti--LAMMPS--ipr2)
Notes: These files were sent by Won-Seok Ko (University of Ulsan, South Korea) on 24 July 2016 and posted with his permission.
File(s):
 
Citation: S.B. Maisel, W.-S. Ko, J.-L. Zhang, B. Grabowski, and J. Neugebauer (2017), "Thermomechanical response of NiTi shape-memory nanoprecipitates in TiV alloys", Physical Review Materials, 1(3), 33610. DOI: 10.1103/physrevmaterials.1.033610.
Abstract: We study the properties of NiTi shape-memory nanoparticles coherently embedded in TiV matrices using three-dimensional atomistic simulations based on the modified embedded-atom method. To this end, we develop and present a suitable NiTiV potential for our simulations. Employing this potential, we identify the conditions under which the martensitic phase transformation of such a nanoparticle is triggered—specifically, how these conditions can be tuned by modifying the size of the particle, the composition of the surrounding matrix, or the temperature and strain state of the system. Using these insights, we establish how the transformation temperature of such particles can be influenced and discuss the practical implications in the context of shape-memory strengthened alloys.

LAMMPS pair_style meam (2017--Maisel-S-B--V-Ni-Ti--LAMMPS--ipr1)
Notes: These files were sent by Won-Seok Ko (School of Materials Science and Engineering, University of Ulsan) on 9 Feb. 2018 and posted with his permission.
File(s):
 
Citation: P. Zhang, and D.R. Trinkle (2016), "A modified embedded atom method potential for interstitial oxygen in titanium", Computational Materials Science, 124, 204-210. DOI: 10.1016/j.commatsci.2016.07.039.
Abstract: Modeling oxygen interstitials in titanium requires a new empirical potential. We optimize potential parameters using a fitting database of first-principle oxygen interstitial energies and forces. A new database optimization algorithm based on Bayesian sampling is applied to obtain an optimal potential for a specific testing set of density functional data. A parallel genetic algorithm minimizes the sum of logistic function evaluations of the testing set predictions. We test the transferability of the potential model against oxygen interstitials in HCP titanium, transition barriers between oxygen interstitial sites, and oxygen in the titanium prismatic stacking fault. The potential predicts that the interaction between oxygen and a screw dislocation core is weak and short-ranged.

Notes: Prof. Trinkle said that this potential is specifically intended for dilute oxygen in titanium as there's no oxygen-oxygen interaction. 9 Aug. 2016: the reference information was updated.

MEAM splines
Notes: This file was sent by Prof. Dallas Trinkle (Univ. of Illinois) on 6 Aug. 2016 and posted with his permission. Update 2018-11-06: file format changed to reflect that it does not work with LAMMPS.
File(s): superseded


MEAM splines
Notes: This file was sent by Prof. Dallas Trinkle (Univ. of Illinois) on 9 Aug. 2016 and posted with his permission. This version removes an extra comment line that was not compatible with the LAMMPS MEAM/spline code. Update 2018-11-06: file format changed to reflect that it does not work with LAMMPS (see version below).
File(s): superseded


LAMMPS pair_style meam/spline (2016--Zhang-P--Ti-O--LAMMPS--ipr1)
Notes: This file was taken from the August 22, 2018 LAMMPS distribution. It has a slightly different header section from the above versions allowing it to work in the official multi-element meam/spline implementation. This version successfully ran with the stable March 16, 2018 and August 22, 2018 LAMMPS versions.
File(s):
Date Created: October 5, 2010 | Last updated: November 19, 2018