OpenKIM · EAM Dynamo MendelevSrolovitzAckland 2005 AlFe MO_577453891941_005 MO_577453891941

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EAM_Dynamo_MendelevSrolovitzAckland_2005_AlFe__MO_577453891941_005

Interatomic potential for Aluminum (Al), Iron (Fe).
Use this Potential

Title A single sentence description.	Finnis-Sinclair potential (LAMMPS cubic hermite tabulation) for the Al-Fe system developed by Mendelev et al. (2005) v005
Citations This panel presents the list of papers that cite the interatomic potential whose page you are on (by its primary sources given below in "How to Cite"). Articles marked by the green star have been determined to have used the potential in computations (as opposed to only citing it as background information) by a machine learning (ML) algorithm developed by the KIM Team that analyzes the full text of the papers. Articles that do not use it are marked with a null symbol, and in cases where no information is available a question mark is shown. The full text of the articles used to train the ML algorithm is provided by the Allen Institute for AI through the Semantic Scholar project. The word cloud to the right is built from the abstracts of the primary sources and using papers to give a sense of the types of physical phenomena to which this interatomic potential is applied. IMPORTANT NOTE: Usage can only be determined for articles for which Semantic Scholar can provide OpenKIM with the full text. Where this is not the case, we ask the community for help in determining usage. If you know whether an article did or did not use a potential, let us know by clicking the cloud icon by the article and completing a one question form.	The word cloud indicates applications of this Potential. The bar chart shows citations per year of this Potential. 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.	We present an analysis, based upon atomistic simulation data, of the effect of Fe impurities on grain boundary migration in Al. The first step is the development of a new interatomic potential for Fe in Al. This potential provides an accurate description of Al–Fe liquid diffraction data and the bulk diffusivity of Fe in Al. We use this potential to determine the physical parameters in the Cahn–Lücke–Stüwe (CLS) model for the effect of impurities on grain boundary mobility. These include the heat of segregation of Fe to grain boundaries in Al and the diffusivity of Fe in Al. Using the simulation-parameterized CLS model, we predict the grain boundary mobility in Al in the presence of Fe as a function of temperature and Fe concentration. The order of magnitude and the trends in the mobility from the simulations are in agreement with existing experimental results.
Species The supported atomic species.	Al, Fe
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	The Al part of this potential leads to very low free surface energy. The potential may easily produce spontaneous cavity nucleation in MD which will be an artifact of this potential.
Content Origin	http://www.ctcms.nist.gov/potentials/Al.html

Contributor	Mikhail I. Mendelev
Maintainer	Mikhail I. Mendelev
Published on KIM	2018
How to Cite	This Model originally published in [1] is archived in OpenKIM [2-5]. [1] Mendelev MI, Srolovitz DJ, Ackland GJ, Han S. Effect of Fe Segregation on the Migration of a Non-Symmetric \Sigma5 Tilt Grain Boundary in Al. Journal of Materials Research. 2005;20(1):208–18. doi:10.1557/JMR.2005.0024 — (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] Mendelev MI. Finnis-Sinclair potential (LAMMPS cubic hermite tabulation) for the Al-Fe system developed by Mendelev et al. (2005) v005. OpenKIM; 2018. doi:10.25950/448f3c57 [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.
Funding	Not available

Short KIM ID The unique KIM identifier code.	MO_577453891941_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_MendelevSrolovitzAckland_2005_AlFe__MO_577453891941_005
DOI	10.25950/448f3c57 https://doi.org/10.25950/448f3c57 https://search.datacite.org/works/10.25950/448f3c57
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
Programming Language(s) The programming languages used in the code and the percentage of the code written in each one. "N/A" means "not applicable" and refers to model parameterizations which only include parameter tables and have no programming language.	N/A

Previous Version	EAM_Dynamo_MendelevSrolovitzAckland_2005_AlFe__MO_577453891941_004

Verification Check Dashboard

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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 3.69446e-08 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
P The model is C^1 continuous. This means that the model has continuous energy and continuous 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
P No memory leak detected.	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: Fe

Species: Al

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: Al

Diamond Lattice Constant

This bar chart plot shows the mono-atomic face-centered diamond lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: Fe

Species: Al

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: Al

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: Fe

Species: Al

FCC Stacking Fault Energies

This bar chart plot shows the intrinsic and extrinsic stacking fault energies as well as the unstable stacking and unstable twinning energies for face-centered cubic (fcc) predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: Al

FCC Surface Energies

This bar chart plot shows the mono-atomic face-centered cubic (fcc) relaxed surface energies predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: Al

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: Al

Species: Fe

Cubic Crystal Basic Properties Table

Species: Al

Species: Fe

Tests

Disclaimer From Model Developer

The Al part of this potential leads to very low free surface energy. The potential may easily produce spontaneous cavity nucleation in MD which will be an artifact of this potential.

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 Al v004	view	14183
Cohesive energy versus lattice constant curve for bcc Fe v004	view	22960
Cohesive energy versus lattice constant curve for diamond Al v004	view	19493
Cohesive energy versus lattice constant curve for diamond Fe v004	view	13914
Cohesive energy versus lattice constant curve for fcc Al v004	view	14362
Cohesive energy versus lattice constant curve for fcc Fe v004	view	14103
Cohesive energy versus lattice constant curve for sc Al v004	view	20052
Cohesive energy versus lattice constant curve for sc Fe v004	view	13546

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 Al at zero temperature v006	view	2143
Elastic constants for bcc Fe at zero temperature v006	view	2047
Elastic constants for fcc Al at zero temperature v006	view	6110
Elastic constants for fcc Fe at zero temperature v006	view	2015
Elastic constants for sc Al at zero temperature v006	view	1599
Elastic constants for sc Fe at zero temperature v006	view	1951

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	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 Al at zero temperature v004		view	1305
Elastic constants for hcp Fe at zero temperature v004		view	1846

EquilibriumCrystalStructure__TD_457028483760_000

Equilibrium structure and energy for a crystal structure at zero temperature and pressure v000

Creators:
Contributor: ilia
Publication Year: 2023
DOI: https://doi.org/10.25950/53ef2ea4

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 Al in AFLOW crystal prototype A_cF4_225_a v000	view	77890
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_cF4_225_a v000	view	135609
Equilibrium crystal structure and energy for Al in AFLOW crystal prototype A_cI2_229_a v000	view	73400
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_cI2_229_a v000	view	68909
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_hP2_194_c v000	view	75535
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_tP28_136_f2ij v000	view	91731
Equilibrium crystal structure and energy for AlFe in AFLOW crystal prototype AB_cP2_221_a_b v000	view	105249

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 AlFe in AFLOW crystal prototype A6B_oC28_63_efg_c v001	view	111388
Equilibrium crystal structure and energy for AlFe in AFLOW crystal prototype A8B5_cI52_217_cg_ce v001	view	292936
Equilibrium crystal structure and energy for AlFe in AFLOW crystal prototype A9B2_aP22_1_18a_4a v001	view	315537
Equilibrium crystal structure and energy for AlFe in AFLOW crystal prototype AB2_cF24_227_a_d v001	view	377011
Equilibrium crystal structure and energy for AlFe in AFLOW crystal prototype AB3_cF16_225_a_bc v001	view	133400

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	5356816
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in bcc Fe v001	view	16092399
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in bcc Fe v001	view	7921392
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in bcc Fe v001	view	50135052
Relaxed energy as a function of tilt angle for a 100 symmetric tilt grain boundary in fcc Al v003	view	10701909
Relaxed energy as a function of tilt angle for a 100 symmetric tilt grain boundary in fcc Fe v001	view	33413379
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in fcc Al v001	view	18942724
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in fcc Fe v001	view	201352550
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in fcc Al v001	view	16123159
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in fcc Fe v001	view	139915063
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in fcc Al v001	view	68258599
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in fcc Fe v001	view	485933439

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 Al v007	view	2207
Equilibrium zero-temperature lattice constant for bcc Fe v007	view	2111
Equilibrium zero-temperature lattice constant for diamond Al v007	view	2815
Equilibrium zero-temperature lattice constant for diamond Fe v007	view	3327
Equilibrium zero-temperature lattice constant for fcc Al v007	view	4734
Equilibrium zero-temperature lattice constant for fcc Fe v007	view	3743
Equilibrium zero-temperature lattice constant for sc Al v007	view	2335
Equilibrium zero-temperature lattice constant for sc Fe v007	view	2239

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	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 Al v005		view	21839
Equilibrium lattice constants for hcp Fe v005		view	32536

LinearThermalExpansionCoeffCubic__TD_522633393614_001

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	17775392
Linear thermal expansion coefficient of fcc Al at 293.15 K under a pressure of 0 MPa v001		view	8609839

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 Al v004		view	45904

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 Al v002		view	8365475

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	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	16218
Broken-bond fit of high-symmetry surface energies in fcc Al v004		view	26103

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	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)
Monovacancy formation energy and relaxation volume for bcc Fe		view	536767
Monovacancy formation energy and relaxation volume for fcc Al		view	384667

VacancyFormationMigration__TD_554849987965_001

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

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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	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)
Vacancy formation and migration energy for bcc Fe		view	4106404
Vacancy formation and migration energy for fcc Al		view	956183

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ElasticConstantsCubic__TD_011862047401_006

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Elastic constants for diamond Al at zero temperature v001	other	view
Elastic constants for diamond Fe at zero temperature v001	other	view

EquilibriumCrystalStructure__TD_457028483760_000

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Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_tP1_123_a v000	other	view

LatticeConstantCubicEnergy__TD_475411767977_006

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Equilibrium zero-temperature lattice constant for diamond Al	other	view
Equilibrium zero-temperature lattice constant for diamond Fe	other	view

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DimerContinuityC1__VC_303890932454_005	other	view

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Al-Fe.eam.fs
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**Notes:**

The Fe-Fe interactions in this potential are approximately identical to those of the following potentials (although seem to vary slightly due to the specific tabulation which was performed):

* [EAM_Dynamo_AcklandMendelevSrolovitz_2004_FeP__MO_884343146310_005](https://openkim.org/cite/MO_884343146310_005)
* [EAM_Dynamo_HepburnAckland_2008_FeC__MO_143977152728_005](https://openkim.org/cite/MO_143977152728_005)
* [EAM_Dynamo_MendelevHanSon_2007_VFe__MO_249706810527_005](https://openkim.org/cite/MO_249706810527_005)

**Data used in fitting:**

* Al-Al
   The following properties, summarized in Table I of Mendelev, Kramer, Becker and Asta (see citations below), were used to fit Al-Al interactions:
    * Zero-temperature
        * Lattice constant, cohesive energy, and elastic constants (C$$_{11}$$, C$$_{12}$$, C$$_{44}$$) of fcc Al
        * Unrelaxed monovacancy formation energy in fcc Al
        * <100> self-interstitial formation energy in fcc Al
        * Lattice constant of bcc Al
        * Difference between cohesive energies of bcc and fcc Al
        * Lattice constants of hcp Al
        * Difference between cohesive energies of fcc and hcp Al
        * Atomic forces (calculated using DFT) of a model liquid configuration generated using a simple pair potential
    * Finite temperature
        * Melting temperature (taken to have a value of 933 K)
        * Latent heat of fusion
        * Change in volume upon melting
        * Liquid density at melting temperature

Table I of this article also includes the predictions of this potential for surface energies and other liquid properties.  The authors specifically note that this potential predicts values for the (100), (110), and (111) fcc surface energies which are of considerably smaller magnitude than those calculated from DFT.

* Fe-Fe
The Fe-Fe interactions were fitted to a variety of properties of $$\alpha$$-iron, including cohesive energy and elastic constants, interstitial and vacancy formation energies, and surface energies.  Atomic forces present in a liquid configuration (generated using a pair potential) were also used in fitting.  Please see the wiki entry of [EAM_Dynamo_AcklandMendelevSrolovitz_2004_FeP__MO_884343146310_005](https://openkim.org/cite/MO_884343146310_005) for further details.

* Al-Fe
The Al-Fe interactions of this potential were generated iteratively.  In each step of the iteration, a liquid configuration is produced with the current parameter set.  The L1$$_{2}$$ and DO$$_{3}$$ crystal structures, both of which have composition Al$$_{3}$$Fe, are also formed (See description of these structures below.  Furthermore, note that the L1$$_{2}$$ and DO$$_{3}$$ structures were also used in the fitting of [EAM_Dynamo_AcklandMendelevSrolovitz_2004_FeP__MO_884343146310_005](https://openkim.org/cite/MO_884343146310_005).).  Computing the energies and forces of these configurations using GGA-DFT and comparing them to the predictions of the current potential, its parameters are adjusted.  Next, the interaction energy of an Al monovacancy with an Fe interstitial (sitting at a nearest-neighbor site relative to the vacancy) is computed with the potential and using DFT.  The two-body interaction of the potential, separate from the embedding density and energy, is then refitted using all of the previous properties and the entire procedure is iterated to convergence.

* L1$$_{2}$$
      This lattice is formed by replacing the corner atom in a conventional face-centered cubic (fcc) unit cell of aluminum atoms with an iron atom
    * DO$$_{3}$$
      Imagine assembling a set of eight adjacent conventional bcc unit cells of Fe atoms in a 2 x 2 x 2 configuration.  Among the top four unit cells, select two of them which are opposite one another, i.e. do not share any edges, and replace the Al atoms in the centers of these cells with Fe atoms.  Now proceed to the bottom four unit cells and do the same, but for the two unit cells opposite one another which do not lie beneath the two chosen in the top layer.  See [http://www.geocities.jp/ohba_lab_ob_page/structure2.html](http://www.geocities.jp/ohba_lab_ob_page/structure2.html) for an image.  See also "Intermetallic phases with D0$$_3$$-structure: a statistical-thermodynamic model," Ipser, Semenova, and Krachler. J. Alloys Compd. 338 (1-2), pp.20-25, 2002.

EAM_Dynamo_MendelevSrolovitzAckland_2005_AlFe__MO_577453891941_005

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