Finnis-Sinclair potential (LAMMPS cubic hermite tabulation) for the Fe-P system developed by Ackland et al. (2004) v000

Mikhail I. Mendelev; Graeme J. Ackland; David J. Srolovitz; Seungwu Han; Alexander V Barashev

doi:10.25950/cf64bcf2

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EAM_Dynamo_AcklandMendelevSrolovitz_2004_FeP__MO_884343146310_005

Interatomic potential for Iron (Fe), Phosphorus (P).
Use this Potential

Title A single sentence description.	Finnis-Sinclair potential (LAMMPS cubic hermite tabulation) for the Fe-P system developed by Ackland et al. (2004) v000
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.	Finnis-Sinclair potential for the Fe-P system developed by Ackland et al. (2004) in EAM format based primarily on ab initio data. Transferability in this system is extremely problematic, and the potential is intended specifically to address the problem of radiation damage and point defects in iron containing low concentrations of phosphorus atoms. Some preliminary molecular dynamics calculations show that P strongly affects point defect migration.
Species The supported atomic species.	Fe, P
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	This potential is intended specifically to address the problem of radiation damage and point defects in iron containing low concentrations of phosphorus atoms. Note that the Fe part is not the same as 2003 Fe potential by Mendelev from [M.I. Mendelev, S. Han, D.J. Srolovitz, G.J. Ackland, D.Y. Sun and M. Asta, Phil. Mag. 83, 3977-3994 (2003).], which is available as https://openkim.org/cite/MO_769582363439_004.
Content Origin	NIST IPRP (https://www.ctcms.nist.gov/potentials/Fe.html#Fe-P)
Content Other Locations	http://homepages.ed.ac.uk/graeme/moldy/moldy.html

Contributor	Mikhail I. Mendelev
Maintainer	Mikhail I. Mendelev
Developer	Mikhail I. Mendelev Graeme J. Ackland David J. Srolovitz Seungwu Han Alexander V Barashev
Published on KIM	2018
How to Cite	This Model originally published in [1] is archived in OpenKIM [2-5]. [1] Ackland GJ, Mendelev MI, Srolovitz DJ, Han S, Barashev AV. Development of an interatomic potential for phosphorus impurities in α-iron. Journal of Physics: Condensed Matter. 2004;16(27):S2629. doi:10.1088/0953-8984/16/27/003 — (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, Ackland GJ, Srolovitz DJ, Han S, Barashev AV. Finnis-Sinclair potential (LAMMPS cubic hermite tabulation) for the Fe-P system developed by Ackland et al. (2004) v000. OpenKIM; 2018. doi:10.25950/cf64bcf2 [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.
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 .
Funding	Not available

Short KIM ID The unique KIM identifier code.	MO_884343146310_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_AcklandMendelevSrolovitz_2004_FeP__MO_884343146310_005
DOI	10.25950/cf64bcf2 https://doi.org/10.25950/cf64bcf2 https://commons.datacite.org/doi.org/10.25950/cf64bcf2
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_AcklandMendelevSrolovitz_2004_FeP__MO_884343146310_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 2.81640e-07 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: P

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: P

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: Fe

Species: P

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: P

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: P

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.

(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: Fe

Species: P

Cubic Crystal Basic Properties Table

Species: Fe

Species: P

Tests

Disclaimer From Model Developer

This potential is intended specifically to address the problem of radiation damage and point defects in iron containing low concentrations of phosphorus atoms. Note that the Fe part is not the same as 2003 Fe potential by Mendelev from [M.I. Mendelev, S. Han, D.J. Srolovitz, G.J. Ackland, D.Y. Sun and M. Asta, Phil. Mag. 83, 3977-3994 (2003).], which is available as https://openkim.org/cite/MO_769582363439_004.

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 Fe v004	view	13964
Cohesive energy versus lattice constant curve for bcc P v004	view	14452
Cohesive energy versus lattice constant curve for diamond Fe v004	view	14481
Cohesive energy versus lattice constant curve for diamond P v004	view	16712
Cohesive energy versus lattice constant curve for fcc Fe v004	view	14312
Cohesive energy versus lattice constant curve for fcc P v004	view	16638
Cohesive energy versus lattice constant curve for sc Fe v004	view	14044
Cohesive energy versus lattice constant curve for sc P v004	view	16417

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 Fe at zero temperature v006	view	1791
Elastic constants for bcc P at zero temperature v006	view	1695
Elastic constants for diamond P at zero temperature v001	view	1663
Elastic constants for fcc Fe at zero temperature v006	view	6782
Elastic constants for fcc P at zero temperature v006	view	3487
Elastic constants for sc Fe at zero temperature v006	view	4319
Elastic constants for sc P at zero temperature v006	view	6366

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 Fe at zero temperature v004		view	1528
Elastic constants for hcp P at zero temperature v004		view	1624

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 FeP in AFLOW crystal prototype A2B_hP9_189_fg_ad v002	view	47757
Equilibrium crystal structure and energy for FeP in AFLOW crystal prototype A2B_oC18_38_abde_ae v002	view	142750
Equilibrium crystal structure and energy for FeP in AFLOW crystal prototype A3B_tI32_82_3g_g v002	view	289329
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_cF4_225_a v002	view	155266
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_cI2_229_a v002	view	50127
Equilibrium crystal structure and energy for P in AFLOW crystal prototype A_cP1_221_a v002	view	82823
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_hP2_194_c v002	view	70381
Equilibrium crystal structure and energy for P in AFLOW crystal prototype A_tI4_139_e v002	view	75903
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_tP28_136_f2ij v002	view	110431
Equilibrium crystal structure and energy for FeP in AFLOW crystal prototype AB2_oP6_58_a_g v002	view	86430
Equilibrium crystal structure and energy for FeP in AFLOW crystal prototype AB4_mC40_15_ae_4f v002	view	257076
Equilibrium crystal structure and energy for FeP in AFLOW crystal prototype AB4_mP30_14_ae_6e v002	view	162351
Equilibrium crystal structure and energy for FeP in AFLOW crystal prototype AB_oP8_62_c_c v002	view	79596

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	3398429
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in bcc Fe v001	view	9976236
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in bcc Fe v001	view	7615117
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in bcc Fe v001	view	29001940
Relaxed energy as a function of tilt angle for a 100 symmetric tilt grain boundary in fcc Fe v001	view	21974714
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in fcc Fe v001	view	178772166
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in fcc Fe v001	view	98046978
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in fcc Fe v001	view	294747535

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 Fe v007	view	2367
Equilibrium zero-temperature lattice constant for bcc P v007	view	2559
Equilibrium zero-temperature lattice constant for diamond Fe v007	view	3615
Equilibrium zero-temperature lattice constant for diamond P v007	view	3071
Equilibrium zero-temperature lattice constant for fcc Fe v007	view	4414
Equilibrium zero-temperature lattice constant for fcc P v007	view	2815
Equilibrium zero-temperature lattice constant for sc Fe v007	view	3263
Equilibrium zero-temperature lattice constant for sc P v007	view	2207

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 Fe v005		view	34669
Equilibrium lattice constants for hcp P v005		view	20471

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	488840

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	16538

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	359342

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	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	3124012

Errors

ElasticConstantsCubic__TD_011862047401_006

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

EquilibriumCrystalStructure__TD_457028483760_002

Test	Error Categories	Link to Error page
Equilibrium crystal structure and energy for FeP in AFLOW crystal prototype A4B_tP5_123_ace_b v002	other	view
Equilibrium crystal structure and energy for P in AFLOW crystal prototype A_aP24_2_12i v002	other	view
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**Notes:**

Parameters of this potential are given in Table 5 of the article cited below.  Note that the authors warn that this potential is specifically intended for studying radiation damage and point defects in Fe-rich compounds of FeP, and should not necessarily be expected to be transferable to other scenarios.  Specifically, they note that no properties of pure phosphorus or phosphorus-rich FeP were used in the fitting process.

It is also stated in the article that the Fe-Fe interactions of this potential are taken directly from [M.I. Mendelev, S. Han, D.J. Srolovitz, G.J. Ackland, D.Y. Sun and M. Asta, Phil. Mag. 83, 3977-3994 (2003)](http://dx.doi.org/10.1080/14786430310001613264).  However, the predictions of this potential for properties of pure Fe do not appear to match those of any of the five parametrizations found in this reference.  Therefore, it is not completely clear which properties were used to fit the Fe-Fe interactions.

The following potentials feature identical (or approximately identical) Fe-Fe interactions to this potential:

* [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)
* [EAM_Dynamo_MendelevSrolovitzAckland_2005_AlFe__MO_577453891941_005](https://openkim.org/cite/MO_577453891941_005)

**Data used in fitting:**

This potential was fitted to point defects in iron, their interactions with phosphorus atoms, and hypothetical Fe-rich structures of FeP.  Unless stated explicitly, all results below were computed using GGA DFT.

* Perfect crystals
  * Experimental values of the cohesive energy and elastic constants (C$$_{11}$$, C$$_{12}$$, C$$_{44}$$) of body-centered cubic (bcc) Fe ($$\alpha$$-Fe)
  * A bcc Fe lattice where every fourth (001) plane of atoms is replaced with phosphorus atoms.  The authors refer to this as a "stripe" structure.
  * The Fe$$_2$$P crystal lattice.  Although the authors state has been observed experimentally, they compute its equilibrium geometry, energy, and magnetic moment using GGA DFT.
  * Hypothetical crystal lattices with composition Fe$$_{3}$$P
    * L1$$_{2}$$
      This lattice is formed by replacing the corner atom in a conventional face-centered cubic (fcc) unit cell of iron atoms with a phosphorus 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 Fe atoms in the centers of these cells with phosphorus 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.
    * DO$$_{32}$$
      Imagine the same set of eight bcc unit cells as in the case of the DO$$_{3}$$ lattice above, this time leaving all of the atoms in the centers of the indivudal conventional unit cells to be Fe.  Instead, replace Fe atoms in the remaining layers of atoms with phosphorus so that when one proceeds along any two edges of the individual conventional bcc unit cells, the species of the atoms encountered alternates between Fe and P.  See [http://www.geocities.jp/ohba_lab_ob_page/structure2.html](http://www.geocities.jp/ohba_lab_ob_page/structure2.html) for an image.

* Vacancies
  * Monovacancy in 16-atom and 32-atom $$\alpha$$-Fe supercells
  * Divacancy in a 16-atom $$\alpha$$-Fe cell where the vacancies are at nearest-neighbor sites of one another
  * Divacancy in a 16-atom $$\alpha$$-Fe cell where the vacancies are at second-nearest-neighbor sites relative to one another

* Substitutional impurities (relaxed under constant-volume constraints)
  * Single substitution of Fe$$\rightarrow$$P in a 16-atom and 54-atom supercells of $$\alpha$$-Fe
  * Pairs of P substitutions on neighboring sites in 16-atom and 54-atom supercells of $$\alpha$$-Fe.  These pairs are located
  The authors indicate that because of the small unit cells used, these quantities are *not* to be interpreted as the energies of isolated defects.

* Combinations of vacancies and substitutional impurities
  * Monovacancy in a 16-atom $$\alpha$$-Fe supercell with a substitutional Fe$$\rightarrow$$P defect placed at the nearest-neighbor site
  * Monovacancy in a 16-atom $$\alpha$$-Fe supercell with a substitutional Fe$$\rightarrow$$P defect placed at the second-nearest-neighbor site
  * Nearest-neighbor divacancy in a 16-atom $$\alpha$$-Fe supercell with a P atom placed midway between one of the vacancy sites and a <111> interstitial site
  * Monovacancy in a 32-atom $$\alpha$$-Fe supercell with a substitutional Fe$$\rightarrow$$P defect placed at the nearest-neighbor site
  * Monovacancy in a 32-atom $$\alpha$$-Fe supercell with a substitutional Fe$$\rightarrow$$P defect placed at the second-nearest-neighbor site
  * Nearest-neighbor divacancy in a 32-atom $$\alpha$$-Fe supercell with a P atom placed midway between one of the vacancy sites and a <100> interstitial site
  * Nearest-neighbor divacancy in a 32-atom $$\alpha$$-Fe supercell with a P atom placed midway between one of the vacancy sites and a <111> interstitial site

* Interstitials
  * Tetrahedral and octahedral self-interstitials in a 16-atom $$\alpha$$-Fe supercell
  * [001], [011], [111] dumbbell self-interstitials in a 16-atom $$\alpha$$-Fe supercell
  * [100], [011], and [111] dumbbell interstitials of P atoms in 16-atom $$\alpha$$-Fe supercell
  * Mixed [001], [011], and [111] dumbbell interstitials in 16-atom $$\alpha$$-Fe supercell
  * Tetrahedral and octahedral P interstitials in a 16-atom $$\alpha$$-Fe supercell

* Surfaces and monolayers
  * The (100) surface energy of $$\alpha$$-iron.  This was computed using a slab containing a total of eight layers of Fe atoms.
  * Seven layers of Fe atoms (in the $$\alpha$$-iron bcc configuration) with one layer of P atoms on top
  * Six layers of Fe atoms followed by one layer of P atoms and another layer of Fe atoms
  Energies of these configurations were recorded at a number of different strains.

* Liquid configurations generated using a simple pair potential

**Cutoffs:**
The pair potentials of this Model (for Fe-Fe, P-P, and Fe-P) all have a cutoff of 5.3 Angstroms.  The three density functions (Fe-Fe, P-P, Fe-P) all have a cutoff of 4.2 Angstroms.  The effective cutoff for all *atomic forces* is thus 9.5 Angstroms.

For the case of pure Fe, the pair potential decays to an absolute value of less than 0.01 eV at approximately 4.5 Angstroms and the electron density decays to a value of 0.01 at approximately 4.0 Angstroms, yielding an effective force range of 8.5 Angstroms.

**Source citation DOI:**

* G.J. Ackland, M.I. Mendelev, D.J. Srolovitz, S. Han and A.V. Barashev, J. Phys.: Condens. Matter 16, S2629-S2642 (2004).
    - http://dx.doi.org/10.1088/0953-8984/16/27/003

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