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Sim_LAMMPS_MEAM_AlmyrasSangiovanniSarakinos_2019_NAlTi__SM_871795249052_000

Title
A single sentence description.
LAMMPS MEAM potential for the Ti-Al-N system developed by Almyras et al. v000
Description Semi-Empirical Force-Field Model for the Ti1-xAlxN (0 ≤ x ≤ 1) System

G. A. Almyras, D. G. Sangiovanni, K. Sarakinos

We present a modified embedded atom method (MEAM) semi-empirical force-field model for the Ti1-xAlxN (0 ≤ x ≤ 1) alloy system. The MEAM parameters, determined via an adaptive simulated-annealing (ASA) minimization scheme, optimize the model’s predictions with respect to 0 K equilibrium volumes, elastic constants, cohesive energies, enthalpies of mixing, and point-defect formation energies, for a set of 40 elemental, binary, and ternary Ti-Al-N structures and configurations. Subsequently, the reliability of the model is thoroughly verified against known finite-temperature thermodynamic and kinetic properties of key binary Ti-N and Al-N phases, as well as properties of Ti1-xAlxN (0 < x < 1) alloys. The successful outcome of the validation underscores the transferability of our model, opening the way for large-scale molecular dynamics simulations of, e.g., phase evolution, interfacial processes, and mechanical response in Ti-Al-N-based alloys, superlattices, and nanostructures.
Species
The supported atomic species.
Al, N, Ti
Disclaimer
A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.
None
Content Origin https://www.mdpi.com/journal/materials/special_issues/Computational_alloys
Contributor dgsan
Maintainer dgsan
Author Almyras, G. A. and Sangiovanni, D. G. and Sarakinos, K.
Publication Year 2019
Item Citation

This Simulator Model originally published in [1] is archived in OpenKIM [2-4].

[1] Almyras GA, Sangiovanni DG, Sarakinos K. Semi-Empirical Force-Field Model for the Ti1−xAlxN (0 ≤ x ≤ 1) System. Materials [Internet]. 2019;12(2). Available from: http://www.mdpi.com/1996-1944/12/2/215 doi:10.3390/ma12020215

[2] Almyras GA, Sangiovanni DG, Sarakinos K. LAMMPS MEAM potential for the Ti-Al-N system developed by Almyras et al. v000. OpenKIM; 2019. doi:10.25950/fcde776e

[3] Tadmor EB, Elliott RS, Sethna JP, Miller RE, Becker CA. The potential of atomistic simulations and the Knowledgebase of Interatomic Models. JOM. 2011;63(7):17. doi:10.1007/s11837-011-0102-6

[4] Elliott RS, Tadmor EB. Knowledgebase of Interatomic Models (KIM) Application Programming Interface (API). OpenKIM; 2011. doi:10.25950/ff8f563a

Click here to download the above citation in BibTeX format.
Short KIM ID
The unique KIM identifier code.
SM_871795249052_000
Extended KIM ID
The long form of the KIM ID including a human readable prefix (100 characters max), two underscores, and the Short KIM ID. Extended KIM IDs can only contain alpha-numeric characters (letters and digits) and underscores and must begin with a letter.
Sim_LAMMPS_MEAM_AlmyrasSangiovanniSarakinos_2019_NAlTi__SM_871795249052_000
DOI 10.25950/fcde776e
https://doi.org/10.25950/fcde776e
https://search.datacite.org/works/10.25950/fcde776e
KIM Item TypeSimulator Model
KIM API Version2.1
Simulator Name
The name of the simulator as defined in kimspec.edn.
LAMMPS
Potential Type meam
Simulator Potential meam/c

Verification Check Dashboard

(Click here to learn more about Verification Checks)

Grade Name Category Brief Description Full Results Aux File(s)
P vc-species-supported-as-stated mandatory
The model supports all species it claims to support; see full description.
Results Files
P vc-periodicity-support mandatory
Periodic boundary conditions are handled correctly; see full description.
Results Files
P vc-permutation-symmetry mandatory
Total energy and forces are unchanged when swapping atoms of the same species; see full description.
Results Files
A vc-forces-numerical-derivative consistency
Forces computed by the model agree with numerical derivatives of the energy; see full description.
Results Files
F vc-dimer-continuity-c1 informational
The energy versus separation relation of a pair of atoms is C1 continuous (i.e. the function and its first derivative are continuous); see full description.
Results Files
P vc-objectivity informational
Total energy is unchanged and forces transform correctly under rigid-body translation and rotation; see full description.
Results Files
P vc-inversion-symmetry informational
Total energy is unchanged and forces change sign when inverting a configuration through the origin; see full description.
Results Files
P vc-memory-leak informational
The model code does not have memory leaks (i.e. it releases all allocated memory at the end); see full description.
Results Files
N/A vc-thread-safe mandatory
The model returns the same energy and forces when computed in serial and when using parallel threads for a set of configurations. Note that this is not a guarantee of thread safety; see full description.
Results Files

Visualizers (in-page)


BCC Lattice Constant

This bar chart plot shows the mono-atomic body-centered cubic (bcc) lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: Al
Species: Ti


Cohesive Energy Graph

This graph shows the cohesive energy versus volume-per-atom for the current mode for four mono-atomic cubic phases (body-centered cubic (bcc), face-centered cubic (fcc), simple cubic (sc), and diamond). The curve with the lowest minimum is the ground state of the crystal if stable. (The crystal structure is enforced in these calculations, so the phase may not be stable.) Graphs are generated for each species supported by the model.

Species: Ti
Species: Al
Species: N


Diamond Lattice Constant

This bar chart plot shows the mono-atomic face-centered diamond lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: Ti
Species: Al


FCC Elastic Constants

This bar chart plot shows the mono-atomic face-centered cubic (fcc) elastic constants predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: Ti
Species: Al
Species: N


FCC Lattice Constant

This bar chart plot shows the mono-atomic face-centered cubic (fcc) lattice constant predicted by the current model (shown in red) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: Al
Species: Ti


FCC Stacking Fault Energies

This bar chart plot shows the intrinsic and extrinsic stacking fault energies as well as the unstable stacking and unstable twinning energies for face-centered cubic (fcc) predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: Al


FCC Surface Energies

This bar chart plot shows the mono-atomic face-centered cubic (fcc) relaxed surface energies predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: Al


SC Lattice Constant

This bar chart plot shows the mono-atomic simple cubic (sc) lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: Ti
Species: Al


Cubic Crystal Basic Properties Table

Species: Al

Species: N

Species: Ti



Tests

CohesiveEnergyVsLatticeConstant__TD_554653289799_002
This Test Driver uses LAMMPS to compute the cohesive energy of a given monoatomic cubic lattice (fcc, bcc, sc, or diamond) at a variety of lattice spacings. The lattice spacings range from a_min (=a_min_frac*a_0) to a_max (=a_max_frac*a_0) where a_0, a_min_frac, and a_max_frac are read from stdin (a_0 is typically approximately equal to the equilibrium lattice constant). The precise scaling and number of lattice spacings sampled between a_min and a_0 (a_0 and a_max) is specified by two additional parameters passed from stdin: N_lower and samplespacing_lower (N_upper and samplespacing_upper). Please see README.txt for further details.
Test Test Results Link to Test Results page Benchmark time
Usertime muliplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.

Measured in Millions of Whetstone Instructions (MWI)
CohesiveEnergyVsLatticeConstant_bcc_N__TE_898324402903_002 view 3386
CohesiveEnergyVsLatticeConstant_diamond_N__TE_456700639184_002 view 4837
CohesiveEnergyVsLatticeConstant_fcc_N__TE_545694115193_002 view 4772
CohesiveEnergyVsLatticeConstant_sc_N__TE_283273116367_002 view 4837
CohesiveEnergyVsLatticeConstant__TD_554653289799_003
This Test Driver uses LAMMPS to compute the cohesive energy of a given monoatomic cubic lattice (fcc, bcc, sc, or diamond) at a variety of lattice spacings. The lattice spacings range from a_min (=a_min_frac*a_0) to a_max (=a_max_frac*a_0) where a_0, a_min_frac, and a_max_frac are read from stdin (a_0 is typically approximately equal to the equilibrium lattice constant). The precise scaling and number of lattice spacings sampled between a_min and a_0 (a_0 and a_max) is specified by two additional parameters passed from stdin: N_lower and samplespacing_lower (N_upper and samplespacing_upper). Please see README.txt for further details.
Test Test Results Link to Test Results page Benchmark time
Usertime muliplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.

Measured in Millions of Whetstone Instructions (MWI)
CohesiveEnergyVsLatticeConstant_bcc_Al__TE_320860761056_003 view 4830
CohesiveEnergyVsLatticeConstant_bcc_Ti__TE_269215961393_003 view 4798
CohesiveEnergyVsLatticeConstant_diamond_Al__TE_024193005713_003 view 4798
CohesiveEnergyVsLatticeConstant_diamond_Ti__TE_804305295553_003 view 4670
CohesiveEnergyVsLatticeConstant_fcc_Al__TE_380539271142_003 view 4702
CohesiveEnergyVsLatticeConstant_fcc_Ti__TE_406056102498_003 view 4702
CohesiveEnergyVsLatticeConstant_sc_Al__TE_549565909158_003 view 4670
CohesiveEnergyVsLatticeConstant_sc_Ti__TE_376517511478_003 view 4798
ElasticConstantsCubic__TD_011862047401_004
Computes the cubic elastic constants for some common crystal types (fcc, bcc, sc) by calculating the hessian of the energy density with respect to strain. An estimate of the error associated with the numerical differentiation performed is reported.
Test Test Results Link to Test Results page Benchmark time
Usertime muliplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.

Measured in Millions of Whetstone Instructions (MWI)
ElasticConstantsCubic_bcc_N__TE_793923119557_004 view 2289
ElasticConstantsCubic_fcc_N__TE_320719669104_004 view 2160
ElasticConstantsCubic_sc_N__TE_205493877097_004 view 2966
ElasticConstantsCubic__TD_011862047401_006
Computes the cubic elastic constants for some common crystal types (fcc, bcc, sc, diamond) by calculating the hessian of the energy density with respect to strain. An estimate of the error associated with the numerical differentiation performed is reported.
Test Test Results Link to Test Results page Benchmark time
Usertime muliplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.

Measured in Millions of Whetstone Instructions (MWI)
ElasticConstantsCubic_bcc_Al__TE_143620255826_006 view 2975
ElasticConstantsCubic_bcc_Ti__TE_530002460811_006 view 3103
ElasticConstantsCubic_diamond_Al__TE_677832100573_001 view 14363
ElasticConstantsCubic_diamond_Ti__TE_528940095865_001 view 18905
ElasticConstantsCubic_fcc_Al__TE_944469580177_006 view 8797
ElasticConstantsCubic_fcc_Ti__TE_944384516355_006 view 8445
ElasticConstantsCubic_sc_Al__TE_566227372929_006 view 2943
ElasticConstantsCubic_sc_Ti__TE_457585945605_006 view 2463
ElasticConstantsHexagonal__TD_612503193866_003
Computes the elastic constants for hcp crystals by calculating the hessian of the energy density with respect to strain. An estimate of the error associated with the numerical differentiation performed is reported.
Test Test Results Link to Test Results page Benchmark time
Usertime muliplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.

Measured in Millions of Whetstone Instructions (MWI)
ElasticConstantsHexagonal_hcp_Al__TE_064090254718_003 view 2837
ElasticConstantsHexagonal_hcp_Ti__TE_148372627069_003 view 2451
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle__TD_410381120771_002
Computes grain boundary energy for a range of tilt angles given a crystal structure, tilt axis, and material.
Test Test Results Link to Test Results page Benchmark time
Usertime muliplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.

Measured in Millions of Whetstone Instructions (MWI)
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_bcc100_Al__TE_328628786494_000 view 19095071
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_bcc110_Al__TE_522288021788_000 view 42824977
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_bcc111_Al__TE_740790901265_000 view 19110015
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc100_Al__TE_918853243284_002 view 8809245
LatticeConstantCubicEnergy__TD_475411767977_005
Equilibrium lattice constant and cohesive energy of a cubic lattice at zero temperature and pressure.
Test Test Results Link to Test Results page Benchmark time
Usertime muliplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.

Measured in Millions of Whetstone Instructions (MWI)
LatticeConstantCubicEnergy_bcc_N__TE_613577614022_005 view 1225
LatticeConstantCubicEnergy_diamond_N__TE_248372489650_005 view 1386
LatticeConstantCubicEnergy_fcc_N__TE_022839468009_005 view 1032
LatticeConstantCubicEnergy_sc_N__TE_268219140650_005 view 1064
LatticeConstantCubicEnergy__TD_475411767977_007
Equilibrium lattice constant and cohesive energy of a cubic lattice at zero temperature and pressure.
Test Test Results Link to Test Results page Benchmark time
Usertime muliplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.

Measured in Millions of Whetstone Instructions (MWI)
LatticeConstantCubicEnergy_bcc_Al__TE_201065028814_007 view 2847
LatticeConstantCubicEnergy_bcc_Ti__TE_679433293274_007 view 7070
LatticeConstantCubicEnergy_diamond_Al__TE_586085652256_007 view 8381
LatticeConstantCubicEnergy_diamond_Ti__TE_302148205183_007 view 10236
LatticeConstantCubicEnergy_fcc_Al__TE_156715955670_007 view 12476
LatticeConstantCubicEnergy_fcc_Ti__TE_652085158810_007 view 8349
LatticeConstantCubicEnergy_sc_Al__TE_272202056996_007 view 7549
LatticeConstantCubicEnergy_sc_Ti__TE_129979632673_007 view 7901
LatticeConstantHexagonalEnergy__TD_942334626465_004
Calculates lattice constant of hexagonal bulk structures at zero temperature and pressure by using simplex minimization to minimize the potential energy.
Test Test Results Link to Test Results page Benchmark time
Usertime muliplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.

Measured in Millions of Whetstone Instructions (MWI)
LatticeConstantHexagonalEnergy_hcp_Al__TE_248740869817_004 view 7126
LatticeConstantHexagonalEnergy_hcp_Ti__TE_433102354515_004 view 8738
LinearThermalExpansionCoeffCubic__TD_522633393614_001
This Test Driver uses LAMMPS to compute the linear thermal expansion coefficient at a finite temperature under a given pressure for a cubic lattice (fcc, bcc, sc, diamond) of a single given species.
Test Test Results Link to Test Results page Benchmark time
Usertime muliplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.

Measured in Millions of Whetstone Instructions (MWI)
LinearThermalExpansionCoeffCubic_fcc_Al__TE_957040092249_001 view 34057057
PhononDispersionCurve__TD_530195868545_004
Calculates the phonon dispersion relations for fcc lattices and records the results as curves.
Test Test Results Link to Test Results page Benchmark time
Usertime muliplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.

Measured in Millions of Whetstone Instructions (MWI)
PhononDispersionCurve_fcc_Al__TE_363050395011_004 view 62794
StackingFaultFccCrystal__TD_228501831190_002
Intrinsic and extrinsic stacking fault energies, unstable stacking fault energy, unstable twinning energy, stacking fault energy as a function of fractional displacement, and gamma surface for a monoatomic FCC lattice at zero temperature and pressure.
Test Test Results Link to Test Results page Benchmark time
Usertime muliplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.

Measured in Millions of Whetstone Instructions (MWI)
StackingFaultFccCrystal_0bar_Al__TE_104913236993_002 view 19997316
SurfaceEnergyCubicCrystalBrokenBondFit__TD_955413365818_004
Calculates the surface energy of several high symmetry surfaces and produces a broken-bond model fit. In latex form, the fit equations are given by:

E_{FCC} (\vec{n}) = p_1 (4 \left( |x+y| + |x-y| + |x+z| + |x-z| + |z+y| +|z-y|\right)) + p_2 (8 \left( |x| + |y| + |z|\right)) + p_3 (2 ( |x+ 2y + z| + |x+2y-z| + |x-2y + z| + |x-2y-z| + |2x+y+z| + |2x+y-z| +|2x-y+z| +|2x-y-z| +|x+y+2z| +|x+y-2z| +|x-y+2z| +|x-y-2z| ) + c

E_{BCC} (\vec{n}) = p_1 (6 \left( | x+y+z| + |x+y-z| + |-x+y-z| + |x-y+z| \right)) + p_2 (8 \left( |x| + |y| + |z|\right)) + p_3 (4 \left( |x+y| + |x-y| + |x+z| + |x-z| + |z+y| +|z-y|\right)) +c.

In Python, these two fits take the following form:

def BrokenBondFCC(params, index):

import numpy
x, y, z = index
x = x / numpy.sqrt(x**2.+y**2.+z**2.)
y = y / numpy.sqrt(x**2.+y**2.+z**2.)
z = z / numpy.sqrt(x**2.+y**2.+z**2.)

return params[0]*4* (abs(x+y) + abs(x-y) + abs(x+z) + abs(x-z) + abs(z+y) + abs(z-y)) + params[1]*8*(abs(x) + abs(y) + abs(z)) + params[2]*(abs(x+2*y+z) + abs(x+2*y-z) +abs(x-2*y+z) +abs(x-2*y-z) + abs(2*x+y+z) +abs(2*x+y-z) +abs(2*x-y+z) +abs(2*x-y-z) + abs(x+y+2*z) +abs(x+y-2*z) +abs(x-y+2*z) +abs(x-y-2*z))+params[3]

def BrokenBondBCC(params, x, y, z):


import numpy
x, y, z = index
x = x / numpy.sqrt(x**2.+y**2.+z**2.)
y = y / numpy.sqrt(x**2.+y**2.+z**2.)
z = z / numpy.sqrt(x**2.+y**2.+z**2.)

return params[0]*6*(abs(x+y+z) + abs(x-y-z) + abs(x-y+z) + abs(x+y-z)) + params[1]*8*(abs(x) + abs(y) + abs(z)) + params[2]*4* (abs(x+y) + abs(x-y) + abs(x+z) + abs(x-z) + abs(z+y) + abs(z-y)) + params[3]
Test Test Results Link to Test Results page Benchmark time
Usertime muliplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.

Measured in Millions of Whetstone Instructions (MWI)
SurfaceEnergyCubicCrystalBrokenBondFit_fcc_Al__TE_761372278666_004 view 216917


Errors

ElasticConstantsFirstStrainGradient__TD_361847723785_000
Test Error Categories Link to Error page
ElasticConstantsFirstStrainGradientNumerical_fcc_Al__TE_531821030293_000 mismatch view

Grain_Boundary_Symmetric_Tilt_Relaxed_Energy_vs_Angle_Cubic_Crystal__TD_410381120771_000

LatticeConstantCubicEnergy__TD_475411767977_007

LatticeConstantHexagonalEnergy__TD_942334626465_005

LinearThermalExpansionCoeffCubic__TD_522633393614_000
Test Error Categories Link to Error page
LinearThermalExpansionCoeff_fcc_Al__TE_957040092249_000 mismatch view

StackingFaultFccCrystal__TD_228501831190_001
Test Error Categories Link to Error page
StackingFaultFccCrystal_Al_0bar__TE_104913236993_001 other view

VacancyFormationEnergyRelaxationVolume__TD_647413317626_000

VacancyFormationMigration__TD_554849987965_000

No Driver
Verification Check Error Categories Link to Error page
UnitConversion__VC_128739598203_000 mismatch view



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