#### EAM_Dynamo_BonnyPasianotCastin_2009_FeCuNi__MO_469343973171_005

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 Bonny G, Pasianot RC, Castin N, Malerba L (2009) Ternary Fe–Cu–Ni many-body potential to model reactor pressure vessel steels: First validation by simulated thermal annealing. Philosophical Magazine 89(34-36):3531–3546. doi:10.1080/14786430903299824 Click here to download a 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 Parameterized Model using Model Driver EAM_Dynamo__MD_120291908751_005 EAM_Dynamo__MD_120291908751_005 2.0 EAM_Dynamo_BonnyPasianotCastin_2009_FeCuNi__MO_469343973171_004

### Verification Check Dashboard

Grade Name Category Brief Description Full Results Aux File(s)
N/A 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
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: Cu
Species: Fe
Species: Ni

Click on any thumbnail to get a full size image.

#### 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: Fe
Species: Ni

Click on any thumbnail to get a full size image.

#### 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: Fe
Species: Ni

Click on any thumbnail to get a full size image.

#### 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: Fe
Species: Ni

Click on any thumbnail to get a full size image.

#### 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: Fe
Species: Ni

Click on any thumbnail to get a full size image.

Species: Cu

Species: Fe

Species: Ni

### Tests

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_002 view 3995
CohesiveEnergyVsLatticeConstant_bcc_Fe__TE_509164219708_002 view 3299
CohesiveEnergyVsLatticeConstant_bcc_Ni__TE_445944378547_002 view 3885
CohesiveEnergyVsLatticeConstant_diamond_Cu__TE_596332570306_002 view 3702
CohesiveEnergyVsLatticeConstant_diamond_Fe__TE_747158614799_002 view 3445
CohesiveEnergyVsLatticeConstant_diamond_Ni__TE_406251948779_002 view 2859
CohesiveEnergyVsLatticeConstant_fcc_Cu__TE_311348891940_002 view 4068
CohesiveEnergyVsLatticeConstant_fcc_Fe__TE_431563044903_002 view 4252
CohesiveEnergyVsLatticeConstant_fcc_Ni__TE_887529368698_002 view 4252
CohesiveEnergyVsLatticeConstant_sc_Cu__TE_767437873249_002 view 4435
CohesiveEnergyVsLatticeConstant_sc_Fe__TE_418244980127_002 view 4215
CohesiveEnergyVsLatticeConstant_sc_Ni__TE_883842739285_002 view 4105

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_Cu__TE_091603841600_004 view 3225
ElasticConstantsCubic_bcc_Fe__TE_740506315238_004 view 3006
ElasticConstantsCubic_bcc_Ni__TE_899101060802_004 view 3262
ElasticConstantsCubic_fcc_Cu__TE_188557531340_004 view 3885
ElasticConstantsCubic_fcc_Fe__TE_943136713920_004 view 3702
ElasticConstantsCubic_fcc_Ni__TE_077792808740_004 view 3812
ElasticConstantsCubic_sc_Cu__TE_319353354686_004 view 3225
ElasticConstantsCubic_sc_Fe__TE_828391579283_004 view 3116
ElasticConstantsCubic_sc_Ni__TE_667647618175_004 view 3445

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_003 view 4215
ElasticConstantsHexagonal_hcp_Fe__TE_092069407629_003 view 3372
ElasticConstantsHexagonal_hcp_Ni__TE_097694939436_003 view 3922

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_005 view 1429
LatticeConstantCubicEnergy_bcc_Fe__TE_727622321684_005 view 1429
LatticeConstantCubicEnergy_bcc_Ni__TE_942132986685_005 view 1320
LatticeConstantCubicEnergy_diamond_Cu__TE_939141232476_005 view 1833
LatticeConstantCubicEnergy_diamond_Fe__TE_099190649546_005 view 1759
LatticeConstantCubicEnergy_diamond_Ni__TE_387234303809_005 view 1393
LatticeConstantCubicEnergy_fcc_Cu__TE_387272513402_005 view 1759
LatticeConstantCubicEnergy_fcc_Fe__TE_342002765394_005 view 1613
LatticeConstantCubicEnergy_fcc_Ni__TE_155729527943_005 view 1576
LatticeConstantCubicEnergy_sc_Cu__TE_904717264736_005 view 1393
LatticeConstantCubicEnergy_sc_Fe__TE_839734634070_005 view 1356
LatticeConstantCubicEnergy_sc_Ni__TE_557502038638_005 view 1503

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_004 view 13965
LatticeConstantHexagonalEnergy_hcp_Fe__TE_035924073553_004 view 15028
LatticeConstantHexagonalEnergy_hcp_Ni__TE_708857439901_004 view 15944

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_003 view 134003
PhononDispersionCurve_fcc_Ni__TE_948896757313_003 view 133087

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_Cu_0bar__TE_090810770014_001 view 7259896
StackingFaultFccCrystal_Ni_0bar__TE_566405684463_001 view 8040239

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_003 view 11938
SurfaceEnergyCubicCrystalBrokenBondFit_fcc_Cu__TE_689904280697_003 view 20282
SurfaceEnergyCubicCrystalBrokenBondFit_fcc_Ni__TE_692192937218_003 view 23523

### Errors

• No Errors associated with this Model

### 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 Metadata snapshot archives: https://s3.openkim.org/archives/models/MO_469343973171_005