#### EAM_Dynamo_BonnyPasianotCastin_2009_FeCuNi__MO_469343973171_005

Interatomic potential for Copper (Cu), Iron (Fe), Nickel (Ni).

Title A single sentence description. EAM potential (LAMMPS cubic hermite tabulation) for Fe-Cu-Ni reactor pressure vessel steels developed by Bonny et al. (2009) v005 Ternary FeCuNi EAM-type potential. The fitting was focused on solute-point defect interaction in the bcc Fe matrix. With respect to thermodynamics the following was accounted for: experimentally observed intermetallic compounds in the FeNi alloys, the Cu solubility in the FeCu binary and the CuNi miscibility gap. The potential is designed to model radiation damage in the FeCuNi model alloy which represents reactor pressure vessel steels. FeNi cross potential is taken from [Bonny et. al., Modelling Simul. Mater. Sci. Eng. 17 (2009) 025010]. FeCu cross potential is taken from [Pasianot and Malerba, J. Nucl. Mater. 360 (2007) 118]. Fe potential is taken from [Mendelev et al., Philos. Mag. 83 (2003) 3977]. Ni potential is taken from [Voter and Chen, Mater. Res. Soc. Symp. Proc. 82 (1987) 175]. Cu potential is taken from [Mishin et al., Phys. Rev. B 63 (2001) 224106]. Cu, Fe, Ni The potential is stiffened. http://www.ctcms.nist.gov/potentials/Fe.html gbonny gbonny Giovanni Bonny 2018 This Model originally published in [1] is archived in OpenKIM [2-5]. [1] Bonny G, Pasianot RC, Castin N, Malerba L. Ternary Fe–Cu–Ni many-body potential to model reactor pressure vessel steels: First validation by simulated thermal annealing. Philosophical Magazine. 2009;89(34-36):3531–46. doi:10.1080/14786430903299824 [2] Bonny G. EAM potential (LAMMPS cubic hermite tabulation) for Fe-Cu-Ni reactor pressure vessel steels developed by Bonny et al. (2009) v005. OpenKIM; 2018. doi:10.25950/23db26d9 [3] Elliott RS. EAM Model Driver for tabulated potentials with cubic Hermite spline interpolation as used in LAMMPS v005. OpenKIM; 2018. doi:10.25950/68defa36 [4] 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 [5] 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. MO_469343973171_005 EAM_Dynamo_BonnyPasianotCastin_2009_FeCuNi__MO_469343973171_005 10.25950/23db26d9 https://doi.org/10.25950/23db26d9 https://search.datacite.org/works/10.25950/23db26d9 Portable Model using Model Driver EAM_Dynamo__MD_120291908751_005 EAM_Dynamo__MD_120291908751_005 2.0 eam EAM_Dynamo_BonnyPasianotCastin_2009_FeCuNi__MO_469343973171_004

### Verification Check Dashboard

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
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
P vc-unit-conversion mandatory
The model is able to correctly convert its energy and/or forces to different unit sets; 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: Cu
Species: Fe
Species: Ni

#### 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: Fe
Species: Cu
Species: Ni

#### 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: Ni
Species: Fe
Species: Cu

#### 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: Ni
Species: Cu
Species: Fe

#### 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: Ni
Species: Cu
Species: Fe

#### 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: Ni

#### 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: Ni
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: Ni
Species: Fe

Species: Cu

Species: Fe

Species: Ni

### Tests

##### Disclaimer

The potential is stiffened.

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_Cu__TE_864632638496_003 view 3487
CohesiveEnergyVsLatticeConstant_bcc_Fe__TE_509164219708_003 view 3839
CohesiveEnergyVsLatticeConstant_bcc_Ni__TE_445944378547_003 view 3967
CohesiveEnergyVsLatticeConstant_diamond_Cu__TE_596332570306_003 view 3647
CohesiveEnergyVsLatticeConstant_diamond_Fe__TE_747158614799_003 view 3839
CohesiveEnergyVsLatticeConstant_diamond_Ni__TE_406251948779_003 view 3647
CohesiveEnergyVsLatticeConstant_fcc_Cu__TE_311348891940_003 view 3807
CohesiveEnergyVsLatticeConstant_fcc_Fe__TE_431563044903_003 view 3359
CohesiveEnergyVsLatticeConstant_fcc_Ni__TE_887529368698_003 view 3711
CohesiveEnergyVsLatticeConstant_sc_Cu__TE_767437873249_003 view 3743
CohesiveEnergyVsLatticeConstant_sc_Fe__TE_418244980127_003 view 3551
CohesiveEnergyVsLatticeConstant_sc_Ni__TE_883842739285_003 view 3519

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_Cu__TE_091603841600_006 view 1791
ElasticConstantsCubic_bcc_Fe__TE_740506315238_006 view 1983
ElasticConstantsCubic_bcc_Ni__TE_899101060802_006 view 1919
ElasticConstantsCubic_fcc_Cu__TE_188557531340_006 view 2047
ElasticConstantsCubic_fcc_Fe__TE_943136713920_006 view 2079
ElasticConstantsCubic_fcc_Ni__TE_077792808740_006 view 1919
ElasticConstantsCubic_sc_Cu__TE_319353354686_006 view 6174
ElasticConstantsCubic_sc_Fe__TE_828391579283_006 view 3807
ElasticConstantsCubic_sc_Ni__TE_667647618175_006 view 1823

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_Cu__TE_198002759922_004 view 1783
ElasticConstantsHexagonal_hcp_Fe__TE_092069407629_004 view 2388
ElasticConstantsHexagonal_hcp_Ni__TE_097694939436_004 view 2133

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_Fe__TE_175540441720_000 view 1431092
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_bcc110_Fe__TE_558145380113_000 view 4095395
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_bcc111_Fe__TE_752424681735_000 view 2002802
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_bcc112_Fe__TE_187984704771_000 view 8892582
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc100_Cu__TE_529988253259_000 view 2528425
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc100_Fe__TE_814353485766_000 view 5728534
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc100_Ni__TE_457754988992_000 view 3289869
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc110_Cu__TE_708214008908_000 view 7903400
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc110_Fe__TE_729107030375_000 view 53398225
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc110_Ni__TE_980409230161_000 view 10097252
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc111_Cu__TE_603516505525_000 view 4088220
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc111_Fe__TE_989116099275_000 view 29557286
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc111_Ni__TE_035582886963_000 view 5459942
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc112_Cu__TE_288691353820_000 view 16391543
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc112_Fe__TE_317621478872_000 view 104937548
GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle_fcc112_Ni__TE_893686795562_000 view 20889559

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_Cu__TE_873531926707_007 view 2079
LatticeConstantCubicEnergy_bcc_Fe__TE_727622321684_007 view 1919
LatticeConstantCubicEnergy_bcc_Ni__TE_942132986685_007 view 2367
LatticeConstantCubicEnergy_diamond_Cu__TE_939141232476_007 view 3423
LatticeConstantCubicEnergy_diamond_Fe__TE_099190649546_007 view 3487
LatticeConstantCubicEnergy_diamond_Ni__TE_387234303809_007 view 3423
LatticeConstantCubicEnergy_fcc_Cu__TE_387272513402_007 view 4159
LatticeConstantCubicEnergy_fcc_Fe__TE_342002765394_007 view 4606
LatticeConstantCubicEnergy_fcc_Ni__TE_155729527943_007 view 3743
LatticeConstantCubicEnergy_sc_Cu__TE_904717264736_007 view 2591
LatticeConstantCubicEnergy_sc_Fe__TE_839734634070_007 view 3135
LatticeConstantCubicEnergy_sc_Ni__TE_557502038638_007 view 2367

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_Cu__TE_344176839725_005 view 30467
LatticeConstantHexagonalEnergy_hcp_Fe__TE_035924073553_005 view 27825
LatticeConstantHexagonalEnergy_hcp_Ni__TE_708857439901_005 view 20502

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_bcc_Fe__TE_506786620750_001 view 10075191
LinearThermalExpansionCoeffCubic_fcc_Cu__TE_335019190158_001 view 7039339
LinearThermalExpansionCoeffCubic_fcc_Ni__TE_127978642829_001 view 8055342

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_Cu__TE_575177044018_004 view 52910
PhononDispersionCurve_fcc_Ni__TE_948896757313_004 view 49743

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_Cu__TE_090810770014_002 view 5708341
StackingFaultFccCrystal_0bar_Ni__TE_566405684463_002 view 6224548

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_bcc_Fe__TE_493894422725_004 view 16858
SurfaceEnergyCubicCrystalBrokenBondFit_fcc_Cu__TE_689904280697_004 view 27511
SurfaceEnergyCubicCrystalBrokenBondFit_fcc_Ni__TE_692192937218_004 view 31477

### Files

 EAM_Dynamo_BonnyPasianotCastin_2009_FeCuNi__MO_469343973171_005.txz Tar+XZ Linux and OS X archive EAM_Dynamo_BonnyPasianotCastin_2009_FeCuNi__MO_469343973171_005.zip Zip Windows archive