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Sim_LAMMPS_TersoffZBL_HenrikssonBjorkasNordlund_2013_FeC__SM_473463498269_000

Interatomic potential for Carbon (C), Iron (Fe).
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Title
A single sentence description.
LAMMPS Tersoff-ZBL potential for Fe-C developed by Henriksson, Björkas and Nordlund (2013) v000
Citations

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Description Stainless steels found in real-world applications usually have some C content in the base Fe-Cr alloy, resulting in hard and dislocation-pinning carbides - Fe3C (cementite) and Cr23C6 - being present in the finished steel product. The higher complexity of the steel microstructure has implications, for example, for the elastic properties and the evolution of defects such as Frenkel pairs and dislocations. This makes it necessary to re-evaluate the effects of basic radiation phenomena and not simply to rely on results obtained from purely metallic Fe-Cr alloys. In this report, an analytical interatomic potential parameterization in the Abell-Brenner-Tersoff form for the entire Fe-Cr-C system is presented to enable such calculations. The potential reproduces, for example, the lattice parameter(s), formation energies and elastic properties of the principal Fe and Cr carbides (Fe3C, Fe5C2, Fe7C3, Cr3C2, Cr7C3, Cr23C6), the Fe-Cr mixing energy curve, formation energies of simple C point defects in Fe and Cr, and the martensite lattice anisotropy, with fair to excellent agreement with empirical results. Tests of the predictive power of the potential show, for example, that Fe-Cr nanowires and bulk samples become elastically stiffer with increasing Cr and C concentrations. High-concentration nanowires also fracture at shorter relative elongations than wires made of pure Fe. Also, tests with Fe3C inclusions show that these act as obstacles for edge dislocations moving through otherwise pure Fe.

Notes: The Tersoff/ZBL file was contributed by Astrid Gubbels-Elzas and Peter Klaver (Delft University of Technology, Netherlands) and posted with their approval and that of Krister Henriksson (Univ. of Helsinki, Finland) on 9 Jul. 2014. Note that this file only represents the Fe-C subset of interatomic potentials developed and used in this reference.
Species
The supported atomic species.
C, Fe
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/C.html#Fe-C)
Contributor Daniel S. Karls
Maintainer Daniel S. Karls
Published on KIM 2019
How to Cite

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

[1] Henriksson KOE, Björkas C, Nordlund K. Atomistic simulations of stainless steels: a many-body potential for the Fe–Cr–C system. Journal of Physics: Condensed Matter. 2013;25(44):445401. doi:10.1088/0953-8984/25/44/445401 — (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] LAMMPS Tersoff-ZBL potential for Fe-C developed by Henriksson, Björkas and Nordlund (2013) v000. OpenKIM; 2019. doi:10.25950/ebe5cf99

[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.
Funding Not available
Short KIM ID
The unique KIM identifier code.
SM_473463498269_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_TersoffZBL_HenrikssonBjorkasNordlund_2013_FeC__SM_473463498269_000
DOI 10.25950/ebe5cf99
https://doi.org/10.25950/ebe5cf99
https://search.datacite.org/works/10.25950/ebe5cf99
KIM Item TypeSimulator Model
KIM API Version2.1
Simulator Name
The name of the simulator as defined in kimspec.edn.
LAMMPS
Potential Type tersoff
Simulator Potential tersoff/zbl

(Click here to learn more about Verification Checks)

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


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: C
Species: Fe


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: C
Species: Fe


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: C
Species: Fe


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: Fe
Species: C


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: Fe
Species: C


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.

(No matching species)

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.

(No matching species)

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: C
Species: Fe


Cubic Crystal Basic Properties Table

Species: C

Species: Fe





Cohesive energy versus lattice constant curve for monoatomic cubic lattices v002

Creators: Daniel S. Karls
Contributor: karls
Publication Year: 2018
DOI: https://doi.org/10.25950/c6746c52

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 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 Carbon view 2182
Cohesive energy versus lattice constant curve for diamond Carbon view 2535
Cohesive energy versus lattice constant curve for fcc Carbon view 2310
Cohesive energy versus lattice constant curve for sc Carbon view 2374


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 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)
Cohesive energy versus lattice constant curve for bcc Fe v004 view 1591
Cohesive energy versus lattice constant curve for diamond Fe v004 view 1591
Cohesive energy versus lattice constant curve for fcc Fe v004 view 2646
Cohesive energy versus lattice constant curve for sc Fe v004 view 1789


Elastic constants for cubic crystals at zero temperature and pressure v005

Creators: Junhao Li and Ellad Tadmor
Contributor: tadmor
Publication Year: 2019
DOI: https://doi.org/10.25950/49c5c255

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 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 C at zero temperature v005 view 3690
Elastic constants for diamond C at zero temperature v000 view 12930
Elastic constants for fcc C at zero temperature v005 view 3690
Elastic constants for sc C at zero temperature v005 view 3497


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 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)
Elastic constants for bcc Fe at zero temperature v006 view 8413
Elastic constants for diamond Fe at zero temperature v001 view 15163
Elastic constants for fcc Fe at zero temperature v006 view 5374
Elastic constants for sc Fe at zero temperature v006 view 8541


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 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)
Elastic constants for hcp Fe at zero temperature v004 view 1783


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 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)
Relaxed energy as a function of tilt angle for a 100 symmetric tilt grain boundary in bcc Fe v001 view 18112860
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in bcc Fe v001 view 89884335
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in bcc Fe v001 view 41136473
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in bcc Fe v001 view 193752044
Relaxed energy as a function of tilt angle for a 100 symmetric tilt grain boundary in fcc Fe v001 view 33302346
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in fcc Fe v001 view 99860596
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in fcc Fe v001 view 46292681
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in fcc Fe v001 view 224694103


Cohesive energy and equilibrium lattice constant of hexagonal 2D crystalline layers v002

Creators: Ilia Nikiforov
Contributor: ilia
Publication Year: 2019
DOI: https://doi.org/10.25950/dd36239b

Given atomic species and structure type (graphene-like, 2H, or 1T) of a 2D hexagonal monolayer crystal, as well as an initial guess at the lattice spacing, this Test Driver calculates the equilibrium lattice spacing and cohesive energy using Polak-Ribiere conjugate gradient minimization in LAMMPS
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)
Cohesive energy and equilibrium lattice constant of graphene v002 view 1951


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 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)
Equilibrium zero-temperature lattice constant for bcc C v007 view 6398
Equilibrium zero-temperature lattice constant for bcc Fe v007 view 4830
Equilibrium zero-temperature lattice constant for diamond C v007 view 5854
Equilibrium zero-temperature lattice constant for diamond Fe v007 view 8285
Equilibrium zero-temperature lattice constant for fcc C v007 view 6718
Equilibrium zero-temperature lattice constant for fcc Fe v007 view 8253
Equilibrium zero-temperature lattice constant for sc C v007 view 6334
Equilibrium zero-temperature lattice constant for sc Fe v007 view 6302


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 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)
Equilibrium lattice constants for hcp Fe v005 view 37917


Linear thermal expansion coefficient of cubic crystal structures v001

Creators: Mingjian Wen
Contributor: Mwen
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 bcc Fe at 293.15 K under a pressure of 0 MPa v001 view 38670574


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 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)
Broken-bond fit of high-symmetry surface energies in bcc Fe v004 view 93984


CohesiveEnergyVsLatticeConstant__TD_554653289799_002
Test Error Categories Link to Error page
Cohesive energy versus lattice constant curve for sc Carbon other view

ElasticConstantsFirstStrainGradient__TD_361847723785_000

LatticeConstantCubicEnergy__TD_475411767977_007

LatticeConstantHexagonalEnergy__TD_942334626465_005
Test Error Categories Link to Error page
Equilibrium lattice constants for hcp C v005 other view

LinearThermalExpansionCoeffCubic__TD_522633393614_000

LinearThermalExpansionCoeffCubic__TD_522633393614_001

VacancyFormationEnergyRelaxationVolume__TD_647413317626_000
Test Error Categories Link to Error page
Monovacancy formation energy and relaxation volume for bcc Fe mismatch view

VacancyFormationMigration__TD_554849987965_000
Test Error Categories Link to Error page
Vacancy formation and migration energy for bcc Fe mismatch view

No Driver
Verification Check Error Categories Link to Error page
MemoryLeak__VC_561022993723_004 other view
UnitConversion__VC_128739598203_000 mismatch view



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