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2003--Zope-R-R-Mishin-Y--Ti-Al

Citation: R.R. Zope, and Y. Mishin (2003), "Interatomic potentials for atomistic simulations of the Ti-Al system", Physical Review B, 68(2), 024102. 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.

Related Models:
EAM tabulated functions (2003--Zope-R-R--Ti-Al--table--ipr1)
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)
See Computed Properties
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):
OpenKIM (MO_117656786760)
See Computed Properties
Notes: Listing found at https://openkim.org. This KIM potential is based on the files from 2003--Zope-R-R--Ti-Al--LAMMPS--ipr1.
Link(s):

Implementation Information

This page displays computed properties for the 2003--Zope-R-R--Ti-Al--LAMMPS--ipr1 implementation of the 2003--Zope-R-R-Mishin-Y--Ti-Al 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

2003--Zope-R-R--Ti-Al--LAMMPS--ipr1/diatom

Click on plot to load interactive version

2003--Zope-R-R--Ti-Al--LAMMPS--ipr1/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

2003--Zope-R-R--Ti-Al--LAMMPS--ipr1/EvsR.Al

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-134, oqmd-8100, oqmd-1214503
A15--beta-W = oqmd-1214948, oqmd-1280406
A2--W--bcc = mp-998860, oqmd-1215126
A3'--alpha-La--double-hcp = mp-1183144, oqmd-1215394
A3--Mg--hcp = oqmd-1215215, oqmd-1215304
A4--C--dc = oqmd-1215483
A5--beta-Sn = oqmd-1215572
A6--In--bct = oqmd-1215661

prototypemethodEcoh (eV/atom)Epot (eV/atom)a0 (Å)b0 (Å)c0 (Å)α (degrees)β (degrees)γ (degrees)
A1--Cu--fccdynamic-3.2988-3.364.054.054.0590.090.090.0
A3'--alpha-La--double-hcpdynamic-3.2855-3.34672.84652.84659.588590.090.0120.0
A15--beta-Wdynamic-3.2823-3.34355.07725.07725.077290.090.090.0
A3--Mg--hcpdynamic-3.2772-3.33842.83572.83574.898390.090.0120.0
A3--Mg--hcpbox-3.2772-3.33842.83582.83584.898390.090.0120.0
oqmd-1214770dynamic-3.27-3.33129.94369.94369.943690.090.090.0
oqmd-1214770box-3.2673-3.32869.9629.9629.96290.090.090.0
oqmd-1214859dynamic-3.2618-3.3236.98496.98496.984990.090.090.0
oqmd-1214859box-3.2605-3.32176.97976.97976.979790.090.090.0
mp-1244953dynamic-3.2292-3.290411.597811.873512.792584.387.980.2
mp-1245152dynamic-3.223-3.284211.660312.143112.351790.192.294.9
mp-1245129dynamic-3.2224-3.283711.648512.087512.477396.191.192.6
mp-1245307dynamic-3.2198-3.28111.61712.236412.333789.287.484.6
mp-1245067dynamic-3.2185-3.279711.875111.955712.429985.480.989.6
A2--W--bccstatic-3.2061-3.26743.23553.23553.235590.090.090.0
mp-1245129box-3.1984-3.259611.733612.166312.425793.992.695.9
mp-1244953box-3.1919-3.253112.039912.066112.335986.780.687.0
oqmd-1215037box-3.1918-3.2532.7925.015510.744190.090.090.0
mp-1245152box-3.1877-3.248911.920512.184312.250692.291.796.3
mp-1245307box-3.186-3.247211.93212.185212.193390.893.792.6
mp-1245067box-3.1752-3.236411.951912.252312.343792.797.594.1
A5--beta-Snstatic-3.0806-3.14185.37125.37122.829490.090.090.0
Ah--alpha-Po--scstatic-3.0022-3.06342.72582.72582.725890.090.090.0
oqmd-1214681box-2.9867-3.04794.33138.19064.370190.090.090.0
A7--alpha-Asbox-2.7863-2.84763.39083.390811.815590.090.0120.0
oqmd-1215928box-2.6556-2.71694.35844.35844.406790.090.0120.0
A4--C--dcstatic-2.4146-2.47585.63165.63165.631690.090.090.0

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:
116.81560.1260.120.00.00.0
60.12116.81560.120.00.00.0
60.1260.12116.8150.00.00.0
-0.0-0.00.031.660.0-0.0
-0.00.00.00.031.660.0
-0.00.0-0.00.00.031.66

Free Surface Formation Energy Predictions

Static free surface formation energies are displayed for select crystals. The values displayed here are obtained by taking a perfect periodic bulk crystal, slicing along a crystallographic plane, and using force minimization to statically relax the surfaces. The free surface formation energy is computed by comparing the energy of the defect system to the bulk system and dividing by the total surface area created by the cut.

The calculation method used is available as the iprPy surface_energy_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 calculation only performs straight cuts along crystallographic planes and static relaxations. Lower energy configurations may exist that require atomic restructuring of the surfaces.
  • Multiple values may be listed for a given plane followed by a number indicating different unique atomic planar cuts for the same theoretical plane.
  • NIST disclaimer

Version Information:

  • 2019-11-14. Calculations for the alternate #2 plane slices are now different from the #1 plane slices.
  • 2019-08-07. Data added.

Composition:
Prototype:
a0:

Download raw data

Surfaceγfs (mJ/m2)
(111)601.2
(100)607.06
(332)690.97
(322)701.16
(221)735.79
(211)755.34
(331)777.15
(311)785.89
(110)792.63
(310)798.22
(321)823.28
(320)838.8
(210)845.87

Stacking Fault Energy Predictions

Stacking fault energy plots and maps are displayed for select crystals. The values are computed by

  1. Starting with a bulk crystal system
  2. Creating a free surface along one of the system's periodic boundaries and using force minimization to relax it
  3. The system is sliced in half along a crystallographic plane parallel to the free surface. One half of the system is shifted relative to the other
  4. The atoms in the shifted system are allowed to relax only in the direction normal to the shifting plane
  5. The stacking fault energy for a given shift is computed by comparing the energy of the system before and after applying the shift, and dividing by the area of the fault plane

The calculation method used is available as the iprPy stacking_fault_map_2D 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.
  • Values between the measured points are interpolated and therefore may not perfectly capture minima and maxima.
  • Multiple values may be listed for a given plane followed by a number indicating different unique atomic planar cuts for the same theoretical plane.
  • NIST disclaimer

Version Information:

  • 2022-06-28. Table added for intrinsic and unstable energies, and ideal shear stresses. Plots (and table) now ordered by the associated planes.
  • 2019-11-14. Calculations for the alternate #2 plane slices are now different from the #1 plane slices. The 1D plotting vectors have been changed to avoid duplicates. Minor improvements to how the 2D plots are displayed.
  • 2019-08-07. Plots added.

Composition:
Prototype:
a0:
plane:

Stacking fault energies in mJ/m2 and ideal shears in GPa
E_usf a/2 [0 -1 1]281.56
τ_ideal a/2 [0 -1 1]4.65

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plot: