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Sim_LAMMPS_ADP_ApostolMishin_2011_AlCu__SM_667696763561_000

Interatomic potential for Aluminum (Al), Copper (Cu).
Use this Potential

Title
A single sentence description.
LAMMPS ADP potential for Al-Cu developed by Apostol and Mishin (2011) v000
Description An angular-dependent interatomic potential has been developed for the Al-Cu system based on existing embedded-atom method potentials for Al and Cu and fitting of the cross-interaction functions to experimental and first-principles data. The potential reproduces lattice parameters, formation energies, and elastic constants of the θ and θ′ phases of this system. It predicts the θ′ phase to be more stable than θ at 0 K but to become less stable at hight temperatures due to vibrational entropy. The temperate and entropy of this phase transformation are in good agreement with previous first-principles calculations [C. Wolverton and V. Ozoliņš, Phys. Rev. Lett. 86, 5518 (2001)]. The potential provides a reasonable description of the phase stability across the Al-Cu phase diagram, dilute heats of solution, and other thermodynamic properties. It has also been tested for generalized stacking fault energies in the presence of a copper layer embedded in Al. This configuration bears some resemblance to Guinier-Preston zones that strengthen Al-Cu alloys. The trends predicted by the potential for uniform shearing of this configuration are in agreement with results of first-principles density-functional calculations performed in this work. The potential is expected to be suitable for atomistic simulations of precipitation hardening of Al-Cu alloys. Notes: Prof. Mishin requested the following be noted: There was a typing error in the original ADP paper (Y. Mishin, et al., Acta Mat. 53, 4029 (2005)). More information and a correction can be found in the FAQ (https://www.ctcms.nist.gov/potentials/system/Al/faq.html#ADP).
Species
The supported atomic species.
Al, Cu
Disclaimer
A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.
None
Content Origin NIST IPRP (https://www.ctcms.nist.gov/potentials/Al.html#Al-Cu)
Contributor tadmor
Maintainer tadmor
Author Ellad Tadmor
Publication Year 2019
Item Citation

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

[1] Apostol F, Mishin Y. Interatomic potential for the Al-Cu system. Physical Review B. 2011Feb;83(5):054116. doi:10.1103/PhysRevB.83.054116

[2] Tadmor E. LAMMPS ADP potential for Al-Cu developed by Apostol and Mishin (2011) v000. OpenKIM; 2019. doi:10.25950/acf55448

[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_667696763561_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_ADP_ApostolMishin_2011_AlCu__SM_667696763561_000
DOI 10.25950/acf55448
https://doi.org/10.25950/acf55448
https://search.datacite.org/works/10.25950/acf55448
KIM Item TypeSimulator Model
KIM API Version2.1
Simulator Name
The name of the simulator as defined in kimspec.edn.
LAMMPS
Potential Type adp
Simulator Potential adp
Programming Language(s)
The programming languages used in the code and the percentage of the code written in each one.
100.00% Tcl

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
B 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: Cu


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: Cu
Species: Al


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: Cu
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: Al
Species: Cu


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: Cu
Species: Al


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: Cu
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
Species: Cu


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: Cu
Species: Al


Cubic Crystal Basic Properties Table

Species: Al

Species: Cu



Tests

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 4191
CohesiveEnergyVsLatticeConstant_bcc_Cu__TE_864632638496_003 view 4255
CohesiveEnergyVsLatticeConstant_diamond_Al__TE_024193005713_003 view 4351
CohesiveEnergyVsLatticeConstant_diamond_Cu__TE_596332570306_003 view 4127
CohesiveEnergyVsLatticeConstant_fcc_Al__TE_380539271142_003 view 4063
CohesiveEnergyVsLatticeConstant_fcc_Cu__TE_311348891940_003 view 4223
CohesiveEnergyVsLatticeConstant_sc_Al__TE_549565909158_003 view 4255
CohesiveEnergyVsLatticeConstant_sc_Cu__TE_767437873249_003 view 4223
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 3519
ElasticConstantsCubic_bcc_Cu__TE_091603841600_006 view 3295
ElasticConstantsCubic_diamond_Al__TE_677832100573_001 view 30102
ElasticConstantsCubic_diamond_Cu__TE_330878926469_001 view 50735
ElasticConstantsCubic_fcc_Al__TE_944469580177_006 view 7421
ElasticConstantsCubic_fcc_Cu__TE_188557531340_006 view 3615
ElasticConstantsCubic_sc_Al__TE_566227372929_006 view 3583
ElasticConstantsCubic_sc_Cu__TE_319353354686_006 view 3391
ElasticConstantsHexagonal__TD_612503193866_004
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_004 view 3215
ElasticConstantsHexagonal_hcp_Cu__TE_198002759922_004 view 3184
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_fcc100_Al__TE_918853243284_002 view 3049064
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc100_Cu__TE_529988253259_000 view 4614846
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc110_Al__TE_202986963854_000 view 8519974
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc110_Cu__TE_708214008908_000 view 14840864
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc111_Al__TE_117904176283_000 view 4670175
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc111_Cu__TE_603516505525_000 view 8036333
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc112_Al__TE_641102822364_000 view 20891847
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc112_Cu__TE_288691353820_000 view 34061036
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 5022
LatticeConstantCubicEnergy_bcc_Cu__TE_873531926707_007 view 5630
LatticeConstantCubicEnergy_diamond_Al__TE_586085652256_007 view 8637
LatticeConstantCubicEnergy_diamond_Cu__TE_939141232476_007 view 11420
LatticeConstantCubicEnergy_fcc_Al__TE_156715955670_007 view 20089
LatticeConstantCubicEnergy_fcc_Cu__TE_387272513402_007 view 14139
LatticeConstantCubicEnergy_sc_Al__TE_272202056996_007 view 8061
LatticeConstantCubicEnergy_sc_Cu__TE_904717264736_007 view 6686
LatticeConstantHexagonalEnergy__TD_942334626465_005
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_005 view 105409
LatticeConstantHexagonalEnergy_hcp_Cu__TE_344176839725_005 view 153768
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 59148
PhononDispersionCurve_fcc_Cu__TE_575177044018_004 view 61963
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 6996762
StackingFaultFccCrystal_0bar_Cu__TE_090810770014_002 view 9280137
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 96671
SurfaceEnergyCubicCrystalBrokenBondFit_fcc_Cu__TE_689904280697_004 view 137905


Errors

CohesiveEnergyVsLatticeConstant__TD_554653289799_002

ElasticConstantsCubic__TD_011862047401_004
Test Error Categories Link to Error page
ElasticConstantsCubic_fcc_Cu__TE_188557531340_004 other view

ElasticConstantsFirstStrainGradient__TD_361847723785_000

ElasticConstantsHexagonal__TD_612503193866_003
Test Error Categories Link to Error page
ElasticConstantsHexagonal_hcp_Al__TE_064090254718_003 other view

Grain_Boundary_Symmetric_Tilt_Relaxed_Energy_vs_Angle_Cubic_Crystal__TD_410381120771_000

LatticeInvariantShearPathCubicCrystalCBKIM__TD_083627594945_001

LinearThermalExpansionCoeffCubic__TD_522633393614_001

PhononDispersionCurve__TD_530195868545_003
Test Error Categories Link to Error page
PhononDispersionCurve_fcc_Cu__TE_575177044018_003 other view

SurfaceEnergyCubicCrystalBrokenBondFit__TD_955413365818_003

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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