EAM potential (LAMMPS cubic hermite tabulation) for Fe-Cu-Ni reactor pressure vessel steels developed by Bonny et al. (2009) v005

Giovanni Bonny; Roberto C Pasianot; N. Castin; L. Malerba

doi:10.25950/23db26d9

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EAM_Dynamo_BonnyPasianotCastin_2009_FeCuNi__MO_469343973171_005

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

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
Citations This panel presents information regarding the papers that have cited the interatomic potential (IP) whose page you are on. The OpenKIM machine learning based Deep Citation framework is used to determine whether the citing article actually used the IP in computations (denoted by "USED") or only provides it as a background citation (denoted by "NOT USED"). For more details on Deep Citation and how to work with this panel, click the documentation link at the top of the panel. The word cloud to the right is generated from the abstracts of IP principle source(s) (given below in "How to Cite") and the citing articles that were determined to have used the IP in order to provide users with a quick sense of the types of physical phenomena to which this IP is applied. The bar chart shows the number of articles that cited the IP per year. Each bar is divided into green (articles that USED the IP) and blue (articles that did NOT USE the IP). Users are encouraged to correct Deep Citation errors in determination by clicking the speech icon next to a citing article and providing updated information. This will be integrated into the next Deep Citation learning cycle, which occurs on a regular basis. OpenKIM acknowledges the support of the Allen Institute for AI through the Semantic Scholar project for providing citation information and full text of articles when available, which are used to train the Deep Citation ML algorithm.	This panel provides information on past usage of this interatomic potential (IP) powered by the OpenKIM Deep Citation framework. The word cloud indicates typical applications of the potential. The bar chart shows citations per year of this IP (bars are divided into articles that used the IP (green) and those that did not (blue)). The complete list of articles that cited this IP is provided below along with the Deep Citation determination on usage. See the Deep Citation documentation for more information. Show Model Used Show All Help us to determine which of the papers that cite this potential actually used it to perform calculations. If you know, click the .
Description A short description of the Model describing its key features including for example: type of model (pair potential, 3-body potential, EAM, etc.), modeled species (Ac, Ag, ..., Zr), intended purpose, origin, and so on.	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].
Species The supported atomic species.	Cu, Fe, Ni
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	The potential is stiffened.
Content Origin	http://www.ctcms.nist.gov/potentials/Fe.html

Contributor	Giovanni Bonny
Maintainer	Giovanni Bonny
Developer	Giovanni Bonny Roberto C Pasianot N. Castin L. Malerba
Published on KIM	2018
How to Cite	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 — (Primary Source) A primary source is a reference directly related to the item documenting its development, as opposed to other sources that are provided as background information. [2] Bonny G, Pasianot RC, Castin N, Malerba L. 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] Foiles SM, Baskes MI, Daw MS, Plimpton SJ. 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.
Funding	Not available

Short KIM ID The unique KIM identifier code.	MO_469343973171_005
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.	EAM_Dynamo_BonnyPasianotCastin_2009_FeCuNi__MO_469343973171_005
DOI	10.25950/23db26d9 https://doi.org/10.25950/23db26d9 https://commons.datacite.org/doi.org/10.25950/23db26d9
KIM Item Type Specifies whether this is a Portable Model (software implementation of an interatomic model); Portable Model with parameter file (parameter file to be read in by a Model Driver); Model Driver (software implementation of an interatomic model that reads in parameters).	Portable Model using Model Driver EAM_Dynamo__MD_120291908751_005
Driver	EAM_Dynamo__MD_120291908751_005
KIM API Version	2.0
Potential Type	eam

Previous Version	EAM_Dynamo_BonnyPasianotCastin_2009_FeCuNi__MO_469343973171_004

Verification Check Dashboard

(Click here to learn more about Verification Checks)

Grade	Name	Category	Brief Description	Full Results	Aux File(s)
P All elements claimed by model are supported in at least one of the tested configurations.	vc-species-supported-as-stated	mandatory	The model supports all species it claims to support; see full description.	Results	Files
P Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.	vc-periodicity-support	mandatory	Periodic boundary conditions are handled correctly; see full description.	Results	Files
P Model energy has permutation symmetry for all configurations the model was able to compute.	vc-permutation-symmetry	mandatory	Total energy and forces are unchanged when swapping atoms of the same species; see full description.	Results	Files
B The letter grade B was assigned because the normalized error in the computation was 8.99312e-09 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.	vc-forces-numerical-derivative	consistency	Forces computed by the model agree with numerical derivatives of the energy; see full description.	Results	Files
F The model is C^0 continuous. This means that the model has continuous energy, but a discontinuous first derivative.	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 Model energy and forces are invariant with respect to rigid-body motion (translation and rotation) for all configurations the model was able to compute.	vc-objectivity	informational	Total energy is unchanged and forces transform correctly under rigid-body translation and rotation; see full description.	Results	Files
P Model energy has inversion symmetry for all configurations the model was able to compute.	vc-inversion-symmetry	informational	Total energy is unchanged and forces change sign when inverting a configuration through the origin; see full description.	Results	Files
N/A Unable to perform verification check due to an error.	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
P All threads give identical results for tested case. Model appears to be thread-safe.	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
P Unit conversion successful	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

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

Dislocation Core Energies

This graph shows the dislocation core energy of a cubic crystal at zero temperature and pressure for a specific set of dislocation core cutoff radii. After obtaining the total energy of the system from conjugate gradient minimizations, non-singular, isotropic and anisotropic elasticity are applied to obtain the dislocation core energy for each of these supercells with different dipole distances. Graphs are generated for each species supported by the model.

(No matching species)

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

Cubic Crystal Basic Properties Table

Species: Cu

Species: Fe

Species: Ni

Tests

Disclaimer From Model Developer

The potential is stiffened.

CohesiveEnergyVsLatticeConstant__TD_554653289799_003

Cohesive energy versus lattice constant curve for monoatomic cubic lattices v003

Creators:
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/64cb38c5

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	Link to Test Results page	Benchmark time Usertime multiplied 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)
Cohesive energy versus lattice constant curve for bcc Cu v004	view	12896
Cohesive energy versus lattice constant curve for bcc Fe v004	view	9707
Cohesive energy versus lattice constant curve for bcc Ni v004	view	9598
Cohesive energy versus lattice constant curve for diamond Cu v004	view	10324
Cohesive energy versus lattice constant curve for diamond Fe v004	view	10244
Cohesive energy versus lattice constant curve for diamond Ni v004	view	9956
Cohesive energy versus lattice constant curve for fcc Cu v004	view	10423
Cohesive energy versus lattice constant curve for fcc Fe v004	view	9528
Cohesive energy versus lattice constant curve for fcc Ni v004	view	14089
Cohesive energy versus lattice constant curve for sc Cu v004	view	10344
Cohesive energy versus lattice constant curve for sc Fe v004	view	14946
Cohesive energy versus lattice constant curve for sc Ni v004	view	9817

ElasticConstantsCubic__TD_011862047401_006

Elastic constants for cubic crystals at zero temperature and pressure v006

Creators: Junhao Li and Ellad Tadmor
Contributor: tadmor
Publication Year: 2019
DOI: https://doi.org/10.25950/5853fb8f

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	Link to Test Results page	Benchmark time Usertime multiplied 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)
Elastic constants for bcc Cu at zero temperature v006	view	1791
Elastic constants for bcc Fe at zero temperature v006	view	1983
Elastic constants for bcc Ni at zero temperature v006	view	1919
Elastic constants for fcc Cu at zero temperature v006	view	2047
Elastic constants for fcc Fe at zero temperature v006	view	2079
Elastic constants for fcc Ni at zero temperature v006	view	1919
Elastic constants for sc Cu at zero temperature v006	view	6174
Elastic constants for sc Fe at zero temperature v006	view	3807
Elastic constants for sc Ni at zero temperature v006	view	1823

ElasticConstantsHexagonal__TD_612503193866_004

Elastic constants for hexagonal crystals at zero temperature v004

Creators: Junhao Li
Contributor: jl2922
Publication Year: 2019
DOI: https://doi.org/10.25950/d794c746

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	Link to Test Results page	Benchmark time Usertime multiplied 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)
Elastic constants for hcp Cu at zero temperature v004	view	1783
Elastic constants for hcp Fe at zero temperature v004	view	2388
Elastic constants for hcp Ni at zero temperature v004	view	2133

EquilibriumCrystalStructure__TD_457028483760_001

Equilibrium structure and energy for a crystal structure at zero temperature and pressure v001

Creators:
Contributor: ilia
Publication Year: 2023
DOI: https://doi.org/10.25950/e8a7ed84

Computes the equilibrium crystal structure and energy for an arbitrary crystal at zero temperature and applied stress by performing symmetry-constrained relaxation. The crystal structure is specified using the AFLOW prototype designation. Multiple sets of free parameters corresponding to the crystal prototype may be specified as initial guesses for structure optimization. No guarantee is made regarding the stability of computed equilibria, nor that any are the ground state.

Test	Link to Test Results page	Benchmark time Usertime multiplied 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)
Equilibrium crystal structure and energy for FeNi in AFLOW crystal prototype A3B_tI8_139_ad_b v001	view	82455
Equilibrium crystal structure and energy for Cu in AFLOW crystal prototype A_cF4_225_a v001	view	61915
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_cF4_225_a v001	view	142456
Equilibrium crystal structure and energy for Ni in AFLOW crystal prototype A_cF4_225_a v001	view	73841
Equilibrium crystal structure and energy for Cu in AFLOW crystal prototype A_cI2_229_a v001	view	68393
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_cI2_229_a v001	view	71633
Equilibrium crystal structure and energy for Ni in AFLOW crystal prototype A_cI2_229_a v001	view	63534
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_hP2_194_c v001	view	63903
Equilibrium crystal structure and energy for Ni in AFLOW crystal prototype A_hP2_194_c v001	view	75019
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_tP28_136_f2ij v001	view	79510
Equilibrium crystal structure and energy for FeNi in AFLOW crystal prototype AB2_cF24_227_a_d v001	view	278727
Equilibrium crystal structure and energy for FeNi in AFLOW crystal prototype AB3_cF16_225_a_bc v001	view	122063
Equilibrium crystal structure and energy for FeNi in AFLOW crystal prototype AB3_cP4_221_a_c v001	view	85179
Equilibrium crystal structure and energy for FeNi in AFLOW crystal prototype AB3_tI8_139_a_bd v001	view	56025
Equilibrium crystal structure and energy for FeNi in AFLOW crystal prototype AB_tP2_123_a_d v001	view	74062

EquilibriumCrystalStructure__TD_457028483760_002

Equilibrium structure and energy for a crystal structure at zero temperature and pressure v002

Creators:
Contributor: ilia
Publication Year: 2024
DOI: https://doi.org/10.25950/2f2c4ad3

Computes the equilibrium crystal structure and energy for an arbitrary crystal at zero temperature and applied stress by performing symmetry-constrained relaxation. The crystal structure is specified using the AFLOW prototype designation. Multiple sets of free parameters corresponding to the crystal prototype may be specified as initial guesses for structure optimization. No guarantee is made regarding the stability of computed equilibria, nor that any are the ground state.

Test	Link to Test Results page	Benchmark time Usertime multiplied 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)
Equilibrium crystal structure and energy for FeNi in AFLOW crystal prototype A2B_cF24_227_c_b v002	view	218007
Equilibrium crystal structure and energy for FeNi in AFLOW crystal prototype A3B_cF16_225_ac_b v002	view	106755
Equilibrium crystal structure and energy for FeNi in AFLOW crystal prototype A3B_cP4_221_c_a v002	view	71412

GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle__TD_410381120771_003

Relaxed energy as a function of tilt angle for a symmetric tilt grain boundary within a cubic crystal v003

Creators:
Contributor: brunnels
Publication Year: 2022
DOI: https://doi.org/10.25950/2c59c9d6

Computes grain boundary energy for a range of tilt angles given a crystal structure, tilt axis, and material.

Test	Link to Test Results page	Benchmark time Usertime multiplied 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)
Relaxed energy as a function of tilt angle for a 100 symmetric tilt grain boundary in bcc Fe v001	view	6468146
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in bcc Fe v001	view	15072573
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in bcc Fe v001	view	8107592
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in bcc Fe v001	view	29392997
Relaxed energy as a function of tilt angle for a 100 symmetric tilt grain boundary in fcc Cu v001	view	5396043
Relaxed energy as a function of tilt angle for a 100 symmetric tilt grain boundary in fcc Fe v001	view	15234577
Relaxed energy as a function of tilt angle for a 100 symmetric tilt grain boundary in fcc Ni v001	view	11580224
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in fcc Cu v001	view	17287898
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in fcc Fe v001	view	184030947
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in fcc Ni v001	view	22840512
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in fcc Cu v001	view	16265165
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in fcc Fe v001	view	81857735
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in fcc Ni v001	view	13460439
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in fcc Cu v001	view	32718312
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in fcc Fe v001	view	313646787
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in fcc Ni v001	view	77571865

LatticeConstantCubicEnergy__TD_475411767977_007

Equilibrium lattice constant and cohesive energy of a cubic lattice at zero temperature and pressure v007

Creators: Daniel S. Karls and Junhao Li
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/2765e3bf

Equilibrium lattice constant and cohesive energy of a cubic lattice at zero temperature and pressure.

Test	Link to Test Results page	Benchmark time Usertime multiplied 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)
Equilibrium zero-temperature lattice constant for bcc Cu v007	view	2079
Equilibrium zero-temperature lattice constant for bcc Fe v007	view	1919
Equilibrium zero-temperature lattice constant for bcc Ni v007	view	2367
Equilibrium zero-temperature lattice constant for diamond Cu v007	view	3423
Equilibrium zero-temperature lattice constant for diamond Fe v007	view	3487
Equilibrium zero-temperature lattice constant for diamond Ni v007	view	3423
Equilibrium zero-temperature lattice constant for fcc Cu v007	view	4159
Equilibrium zero-temperature lattice constant for fcc Fe v007	view	4606
Equilibrium zero-temperature lattice constant for fcc Ni v007	view	3743
Equilibrium zero-temperature lattice constant for sc Cu v007	view	2591
Equilibrium zero-temperature lattice constant for sc Fe v007	view	3135
Equilibrium zero-temperature lattice constant for sc Ni v007	view	2367

LatticeConstantHexagonalEnergy__TD_942334626465_005

Equilibrium lattice constants for hexagonal bulk structures at zero temperature and pressure v005

Creators: Daniel S. Karls and Junhao Li
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/c339ca32

Calculates lattice constant of hexagonal bulk structures at zero temperature and pressure by using simplex minimization to minimize the potential energy.

Test	Link to Test Results page	Benchmark time Usertime multiplied 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)
Equilibrium lattice constants for hcp Cu v005	view	30467
Equilibrium lattice constants for hcp Fe v005	view	27825
Equilibrium lattice constants for hcp Ni v005	view	20502

LinearThermalExpansionCoeffCubic__TD_522633393614_001

Linear thermal expansion coefficient of cubic crystal structures v001

Creators: Mingjian Wen
Contributor: mjwen
Publication Year: 2019
DOI: https://doi.org/10.25950/fc69d82d

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 multiplied 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)
Linear thermal expansion coefficient of fcc Cu at 293.15 K under a pressure of 0 MPa v001		view	7039339

LinearThermalExpansionCoeffCubic__TD_522633393614_002

Linear thermal expansion coefficient of cubic crystal structures v002

Creators:
Contributor: mjwen
Publication Year: 2024
DOI: https://doi.org/10.25950/9d9822ec

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 multiplied 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)
Linear thermal expansion coefficient of bcc Fe at 293.15 K under a pressure of 0 MPa v002		view	378596
Linear thermal expansion coefficient of fcc Ni at 293.15 K under a pressure of 0 MPa v002		view	638345

PhononDispersionCurve__TD_530195868545_004

Phonon dispersion relations for an fcc lattice v004

Creators: Matt Bierbaum
Contributor: mattbierbaum
Publication Year: 2019
DOI: https://doi.org/10.25950/64f4999b

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 multiplied 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)
Phonon dispersion relations for fcc Cu v004		view	52910
Phonon dispersion relations for fcc Ni v004		view	49743

StackingFaultFccCrystal__TD_228501831190_002

Stacking and twinning fault energies of an fcc lattice at zero temperature and pressure v002

Creators:
Contributor: SubrahmanyamPattamatta
Publication Year: 2019
DOI: https://doi.org/10.25950/b4cfaf9a

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 multiplied 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)
Stacking and twinning fault energies for fcc Cu v002		view	5708341
Stacking and twinning fault energies for fcc Ni v002		view	6224548

SurfaceEnergyCubicCrystalBrokenBondFit__TD_955413365818_004

High-symmetry surface energies in cubic lattices and broken bond model v004

Creators: Matt Bierbaum
Contributor: mattbierbaum
Publication Year: 2019
DOI: https://doi.org/10.25950/6c43a4e6

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	Link to Test Results page	Benchmark time Usertime multiplied 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)
Broken-bond fit of high-symmetry surface energies in bcc Fe v004	view	16858
Broken-bond fit of high-symmetry surface energies in fcc Cu v004	view	27511
Broken-bond fit of high-symmetry surface energies in fcc Ni v004	view	31477

VacancyFormationEnergyRelaxationVolume__TD_647413317626_001

Monovacancy formation energy and relaxation volume for cubic and hcp monoatomic crystals v001

Creators:
Contributor: efuem
Publication Year: 2023
DOI: https://doi.org/10.25950/fca89cea

Computes the monovacancy formation energy and relaxation volume for cubic and hcp monoatomic crystals.

Test	Link to Test Results page	Benchmark time Usertime multiplied 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)
Monovacancy formation energy and relaxation volume for bcc Fe	view	393060
Monovacancy formation energy and relaxation volume for fcc Cu	view	328347
Monovacancy formation energy and relaxation volume for fcc Ni	view	391219

VacancyFormationMigration__TD_554849987965_001

Vacancy formation and migration energies for cubic and hcp monoatomic crystals v001

Creators:
Contributor: efuem
Publication Year: 2023
DOI: https://doi.org/10.25950/c27ba3cd

Computes the monovacancy formation and migration energies for cubic and hcp monoatomic crystals.

Test	Link to Test Results page	Benchmark time Usertime multiplied 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)
Vacancy formation and migration energy for bcc Fe	view	3371966
Vacancy formation and migration energy for fcc Cu	view	2058724
Vacancy formation and migration energy for fcc Ni	view	1972809

Errors

ElasticConstantsCubic__TD_011862047401_006

Test	Error Categories	Link to Error page
Elastic constants for diamond Cu at zero temperature v001	other	view
Elastic constants for diamond Fe at zero temperature v001	other	view
Elastic constants for diamond Ni at zero temperature v001	other	view

EquilibriumCrystalStructure__TD_457028483760_001

Test	Error Categories	Link to Error page
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_tP1_123_a v001	other	view

LatticeConstantCubicEnergy__TD_475411767977_006

Test	Error Categories	Link to Error page
Equilibrium zero-temperature lattice constant for diamond Cu	other	view
Equilibrium zero-temperature lattice constant for diamond Fe	other	view
Equilibrium zero-temperature lattice constant for diamond Ni	other	view

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Verification Check	Error Categories	Link to Error page
MemoryLeak__VC_561022993723_004	other	view

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Wiki

The Fe-Fe interactions in this potential are based upon those of  [EAM_Dynamo_MendelevHanSrolovitz_2003Potential2_Fe__MO_769582363439_005](https://openkim.org/cite/MO_769582363439_005) and are identical to those of [EAM_Dynamo_BonnyPasianotMalerba_2009_FeNi__MO_267721408934_005](https://openkim.org/cite/MO_267721408934_005).  However, as Bonny *et al.* point out, there are two transformations in the EAM paradigm that leave the total energy invariant:

$$
\begin{align}
\hat{T_1} &= \begin{cases}
                         \varphi(r) \rightarrow S \varphi(r)\\
                         F(\rho) \rightarrow F(\rho/S)
                     \end{cases}\\
\hat{T_2} &= \begin{cases}
                         F(\rho) \rightarrow F(\rho) + C \rho\\
                         V(r) \rightarrow V(r) - 2 C \varphi(r)\\
                     \end{cases}
\end{align}
$$

where $$C$$ and $$S$$ are arbitrary constants.  Therefore, the final EAM functions used by the authors is obtained by the following modifications to arrive at an "effective" set of interactions (denoted with the superscript 'eff'):

$$
\begin{align}
V^\mathrm{eff}(r) &= V(r) - 2 C \varphi(r)\\
\varphi^\mathrm{eff} &= S \varphi(r)\\
F^\mathrm{eff} &= F(\rho/S) + C/S\rho
\end{align}
$$

The values of these constants used by the authors to modify EAM_Dynamo_MendelevHanSrolovitz_2003Potential2_Fe__MO_769582363439_005 to describe interactions in pure Fe are $$C$$ = 0.116093429 and $$S$$ = 0.0380008812.  For pure Ni interactions, the authors modify the Voter--Chen potential [1] using the above transformations with $$C$$ = −24.3575774 and $$S$$ = 2.92527845.  For pure Cu interactions, the authors modify the potential of Mishin *et al.* [2] using $$C$$=-0.00195739344 and $$S$$=0.998555148.  For details on how the cross-interactions (Fe-Cu, Fe-Ni, and Cu-Ni) were fit, please see the source article.

[1] Voter A F and Chen S P, *Mater. Res. Soc. Symp. Proc.* 82 (1987), pp. 175.
[2] Y. Mishin, M.J. Mehl, D.A. Papaconstantopoulos, A.F. Voter and J.D. Kress, Phys. Rev. B 63 (2001) p.224106.

EAM_Dynamo_BonnyPasianotCastin_2009_FeCuNi__MO_469343973171_005

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