MEAM Potential for the Ni-H system developed by Ko et al. (2011) v002

Won-Seok Ko; Jae-Hyeok Shim; Byeong-Joo Lee

doi:10.25950/36f63a5c

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MEAM_LAMMPS_KoShimLee_2011_NiH__MO_091278480940_002

Interatomic potential for Hydrogen (H), Nickel (Ni).
Use this Potential

Title A single sentence description.	MEAM Potential for the Ni-H system developed by Ko et al. (2011) v002
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.	Second nearest-neighbor modified embedded-atom method (MEAM) interatomic potentials for the Ni–H binary system has been developed on the basis of previously developed MEAM potentials of pure Ni and H. The potential can describe various fundamental physical properties of the relevant binary alloys (structural, thermodynamic, defect, and dynamic properties of metastable hydrides or hydrogen in face-centered cubic solid solutions) in good agreement with experiments or first-principles calculations.
Species The supported atomic species.	H, Ni
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	None
Content Origin	http://cmse.postech.ac.kr/home_2nnmeam

Contributor	Jaemin Wang
Maintainer	Jaemin Wang
Developer	Won-Seok Ko Jae-Hyeok Shim Byeong-Joo Lee
Published on KIM	2023
How to Cite	This Model originally published in [1] is archived in OpenKIM [2-5]. [1] Ko W-S, Shim J-H, Lee B-J. Atomistic modeling of the Al–H and Ni–H systems. Journal of Materials Research. 2011;26(12):1552–60. doi:10.1557/jmr.2011.95 — (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] Ko W-S, Shim J-H, Lee B-J. MEAM Potential for the Ni-H system developed by Ko et al. (2011) v002. OpenKIM; 2023. doi:10.25950/36f63a5c [3] Afshar Y, Hütter S, Rudd RE, Stukowski A, Tipton WW, Trinkle DR, et al. The modified embedded atom method (MEAM) potential v002. OpenKIM; 2023. doi:10.25950/ee5eba52 [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. 13 Citations (9 used) 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 . B. Waters, D. S. Karls, I. Nikiforov, R. Elliott, E. Tadmor, and B. Runnels, “Automated determination of grain boundary energy and potential-dependence using the OpenKIM framework,” Computational Materials Science. 2022. link Times cited: 5 J. Wang and B.-J. Lee, “Second-nearest-neighbor modified embedded-atom method interatomic potential for V-M (M = Cu, Mo, Ti) binary systems,” Computational Materials Science. 2020. link Times cited: 10 B. Bal, B. Okdem, F. C. Bayram, and M. Aydin, “A detailed investigation of the effect of hydrogen on the mechanical response and microstructure of Al 7075 alloy under medium strain rate impact loading,” International Journal of Hydrogen Energy. 2020. link Times cited: 14 G. Hachet, A. Metsue, A. Oudriss, and X. Feaugas, “The influence of hydrogen on cyclic plasticity of <001> oriented nickel single crystal. Part II: Stability of edge dislocation dipoles,” International Journal of Plasticity. 2020. link Times cited: 6 P. White, S. Barter, and N. Medhekar, “Hydrogen induced amorphisation around nanocracks in aluminium,” Engineering Fracture Mechanics. 2016. link Times cited: 10 D. Ward et al., “Understanding H isotope adsorption and absorption of Al-alloys using modeling and experiments (LDRD: #165724).” 2015. link Times cited: 0 Abstract: Current austenitic stainless steel storage reservoirs for hy… read more Abstract: Current austenitic stainless steel storage reservoirs for hydrogen isotopes (e.g. deuterium and tritium) have performance and operational life-limiting interactions (e.g. embrittlement) with H-isotopes. Aluminum alloys (e.g.AA2219), alternatively, have very low H-isotope solubilities, suggesting high resistance towards aging vulnerabilities. This report summarizes the work performed during the life of the Lab Directed Research and Development in the Nuclear Weapons investment area (165724), and provides invaluable modeling and experimental insights into the interactions of H isotopes with surfaces and bulk AlCu-alloys. The modeling work establishes and builds a multi-scale framework which includes: a density functional theory informed bond-order potential for classical molecular dynamics (MD), and subsequent use of MD simulations to inform defect level dislocation dynamics models. Furthermore, low energy ion scattering and thermal desorption spectroscopy experiments are performed to validate these models and add greater physical understanding to them. read less N. Jakse and A. Pasturel, “Ab initio based understanding of diffusion mechanisms of hydrogen in liquid aluminum,” Applied Physics Letters. 2014. link Times cited: 3 Abstract: Ab initio molecular dynamics simulations are used to describ… read more Abstract: Ab initio molecular dynamics simulations are used to describe the diffusion of hydrogen in liquid aluminum at different temperatures. We show that the hydrogen motion does not follow a Brownian motion caused by a broad distribution of spatial jumps that can exceed 15 times the interatomic AlH distance. This breakdown is also evidenced in the calculation of the self-part of the van Hove distribution function that is not the Gaussian expected for a Fickian process. We show that the hydrogen motion can be described well by a generalized continuous time random walk model leading to computed self-diffusion coefficients of H in liquid aluminum in good agreement with experimental ones. Finally, the impact of impurities and alloying elements is discussed. read less J. Shim et al., “Prediction of hydrogen permeability in V–Al and V–Ni alloys,” Journal of Membrane Science. 2013. link Times cited: 21 K. Kim, J. Shim, and B.-J. Lee, “Effect of alloying elements (Al, Co, Fe, Ni) on the solubility of hydrogen in vanadium: A thermodynamic calculation,” International Journal of Hydrogen Energy. 2012. link Times cited: 24 P. Paranjape, P. Gopal, and S. G. Srinivasan, “First-principles study of diffusion and interactions of hydrogen with silicon, phosphorus, and sulfur impurities in nickel,” Journal of Applied Physics. 2019. link Times cited: 4 Abstract: Using density functional theory (DFT), we systematically stu… read more Abstract: Using density functional theory (DFT), we systematically study the effect of Si, P, and S impurities on the diffusion and binding of an H atom in a face-centered-cubic (FCC) Ni lattice. First, we quantify binding energies of an H atom to a vacancy, an impurity atom, and a vacancy-impurity atom defect pair. The energetics of H interactions show that a vacancy-impurity atom defect pair with larger binding energy traps the H atom more strongly and correlates with electronic bonding. Next, we study how the impurities influence diffusion of an H atom by using the Climbing Image Nudged Elastic band method to evaluate the Minimum Energy Path and the energy barrier for diffusion. The H atom preferentially diffuses between tetrahedral to octahedral (T-O) interstitial positions in pure Ni and when impurities are present. However, the activation energy significantly decreases from 0.95 eV in pure Ni to 0.47 eV, 0.52 eV, and 0.46 eV, respectively, in the presence of Si, P, and S impurities, which speeds up H diffusion. We rationalize this by comparing the bonding character of the saddle point configuration and changes in the electronic structure of Ni for each system. Notably, these analyses correlate the lower values of the activation energies to a local atomic strain in a Ni lattice. Our DFT study also validates the hypothesis of Berkowitz and Kane that P increases the H diffusion and, thereby, significantly increases H embrittlement susceptibility of Ni. We report a similar effect for Si and S impurities in Ni.Using density functional theory (DFT), we systematically study the effect of Si, P, and S impurities on the diffusion and binding of an H atom in a face-centered-cubic (FCC) Ni lattice. First, we quantify binding energies of an H atom to a vacancy, an impurity atom, and a vacancy-impurity atom defect pair. The energetics of H interactions show that a vacancy-impurity atom defect pair with larger binding energy traps the H atom more strongly and correlates with electronic bonding. Next, we study how the impurities influence diffusion of an H atom by using the Climbing Image Nudged Elastic band method to evaluate the Minimum Energy Path and the energy barrier for diffusion. The H atom preferentially diffuses between tetrahedral to octahedral (T-O) interstitial positions in pure Ni and when impurities are present. However, the activation energy significantly decreases from 0.95 eV in pure Ni to 0.47 eV, 0.52 eV, and 0.46 eV, respectively, in the presence of Si, P, and S impurities, which speeds up H diffusio... read less X. W. Zhou, D. Ward, and M. E. Foster, “A bond-order potential for the Al–Cu–H ternary system,” New Journal of Chemistry. 2018. link Times cited: 13 Abstract: Al-Based Al–Cu alloys have a very high strength to density r… read more Abstract: Al-Based Al–Cu alloys have a very high strength to density ratio, and are therefore important materials for transportation systems including vehicles and aircrafts. These alloys also appear to have a high resistance to hydrogen embrittlement, and as a result, are being explored for hydrogen related applications. To enable fundamental studies of mechanical behavior of Al–Cu alloys under hydrogen environments, we have developed an Al–Cu–H bond-order potential according to the formalism implemented in the molecular dynamics code LAMMPS. Our potential not only fits well to properties of a variety of elemental and compound configurations (with coordination varying from 1 to 12) including small clusters, bulk lattices, defects, and surfaces, but also passes stringent molecular dynamics simulation tests that sample chaotic configurations. Careful studies verified that this Al–Cu–H potential predicts structural property trends close to experimental results and quantum-mechanical calculations; in addition, it properly captures Al–Cu, Al–H, and Cu–H phase diagrams and enables simulations of H2 dissociation, chemisorption, and absorption on Al–Cu surfaces. read less B.-M. Lee and B.-J. Lee, “A Comparative Study on Hydrogen Diffusion in Amorphous and Crystalline Metals Using a Molecular Dynamics Simulation,” Metallurgical and Materials Transactions A. 2014. link Times cited: 35 C. Scott, S. Kenny, M. Storr, and A. Willetts, “Modelling of dissolved H in Ga stabilised δ-Pu,” Journal of Nuclear Materials. 2013. link Times cited: 5
Funding	Not available

Short KIM ID The unique KIM identifier code.	MO_091278480940_002
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.	MEAM_LAMMPS_KoShimLee_2011_NiH__MO_091278480940_002
DOI	10.25950/36f63a5c https://doi.org/10.25950/36f63a5c https://commons.datacite.org/doi.org/10.25950/36f63a5c
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 MEAM_LAMMPS__MD_249792265679_002
Driver	MEAM_LAMMPS__MD_249792265679_002
KIM API Version	2.2
Potential Type	meam

Previous Version	MEAM_LAMMPS_KoShimLee_2011_NiH__MO_091278480940_001

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 9.15723e-09 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.	vc-forces-numerical-derivative	consistency	Forces computed by the model agree with numerical derivatives of the energy; see full description.	Results	Files
F The model is C^-1 continuous. This means that the model has discontinuous energy.	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: Ni

Species: H

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: Ni

Diamond Lattice Constant

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

Species: H

Species: Ni

Dislocation Core Energies

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

(No matching species)

FCC Elastic Constants

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

Species: Ni

Species: H

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: H

Species: Ni

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: Ni

FCC Surface Energies

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

Species: Ni

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: Ni

Species: H

Cubic Crystal Basic Properties Table

Species: H

Species: Ni

Tests

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 Ni v004	view	5153
Cohesive energy versus lattice constant curve for diamond Ni v004	view	5431
Cohesive energy versus lattice constant curve for fcc Ni v004	view	5222
Cohesive energy versus lattice constant curve for sc Ni v004	view	4744

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 H at zero temperature v006	view	17813
Elastic constants for diamond H at zero temperature v001	view	33939
Elastic constants for diamond Ni at zero temperature v001	view	36589
Elastic constants for fcc H at zero temperature v006	view	16928
Elastic constants for fcc Ni at zero temperature v006	view	30184
Elastic constants for sc H at zero temperature v006	view	39902
Elastic constants for sc Ni at zero temperature v006	view	39608

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 Ni in AFLOW crystal prototype A_cF4_225_a v002	view	75093
Equilibrium crystal structure and energy for H in AFLOW crystal prototype A_cI2_229_a v002	view	85768
Equilibrium crystal structure and energy for Ni in AFLOW crystal prototype A_cI2_229_a v002	view	59180
Equilibrium crystal structure and energy for H in AFLOW crystal prototype A_hP2_194_c v002	view	181401
Equilibrium crystal structure and energy for Ni in AFLOW crystal prototype A_hP2_194_c v002	view	73400
Equilibrium crystal structure and energy for H in AFLOW crystal prototype A_hP4_194_f v002	view	99160
Equilibrium crystal structure and energy for H in AFLOW crystal prototype A_tP1_123_a v002	view	72590
Equilibrium crystal structure and energy for HNi in AFLOW crystal prototype AB_cF8_225_a_b v002	view	62826

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 fcc Ni v001	view	22098023
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in fcc Ni v001	view	72466238
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in fcc Ni v001	view	41399350

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 H v007	view	9488
Equilibrium zero-temperature lattice constant for bcc Ni v007	view	11779
Equilibrium zero-temperature lattice constant for diamond H v007	view	11597
Equilibrium zero-temperature lattice constant for diamond Ni v007	view	8393
Equilibrium zero-temperature lattice constant for fcc H v007	view	10205
Equilibrium zero-temperature lattice constant for fcc Ni v007	view	9598
Equilibrium zero-temperature lattice constant for sc H v007	view	9648
Equilibrium zero-temperature lattice constant for sc Ni v007	view	6258

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 H v005		view	83338
Equilibrium lattice constants for hcp Ni v005		view	85768

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 fcc Ni at 293.15 K under a pressure of 0 MPa v002		view	3040673

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 Ni v004		view	88224

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 Ni v002		view	37312636

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 fcc Ni v004		view	118835

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 fcc Ni		view	506951

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 fcc Ni		view	1794132

Errors

ElasticConstantsCubic__TD_011862047401_006

Test	Error Categories	Link to Error page
Elastic constants for bcc Ni at zero temperature v006	other	view

ElasticConstantsHexagonal__TD_612503193866_004

Test	Error Categories	Link to Error page
Elastic constants for hcp H at zero temperature v004	other	view
Elastic constants for hcp Ni at zero temperature v004	other	view

EquilibriumCrystalStructure__TD_457028483760_002

Test	Error Categories	Link to Error page
Equilibrium crystal structure and energy for HNi in AFLOW crystal prototype AB2_mC6_8_a_2a v002	other	view

GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle__TD_410381120771_003

Test	Error Categories	Link to Error page
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in fcc Ni v001	other	view

PhononDispersionCurve__TD_530195868545_004

Test	Error Categories	Link to Error page
Phonon dispersion relations for fcc Ni v004	other	view

SurfaceEnergyCubicCrystalBrokenBondFit__TD_955413365818_004

Test	Error Categories	Link to Error page
Broken-bond fit of high-symmetry surface energies in fcc Ni v004	other	view

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Wiki

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Parameter Choices in the SW Potential

In the original Stillinger-Weber paper (SW85: PRB 31:5262, 1985) it is stated that in order to obtain the correct “atomization energy” (cohesive energy) the following choice for epsilon must be made (see Eqn. (2.9) in [SW85]):

epsilon = 50 kcal/mol = 3.4723E-12 erg/atom

Unfortunately, there appears to be an error in the unit conversion here. (There is also an indeterminacy associated with the “kcal” unit which can mean different things.) The kcal and erg values have led to two different values for epsilon being used in articles that cite [SW85].

(a) If the kcal number is selected (assuming that S&W meant the thermochemical kcal unit), then epsilon = 2.1682 eV. This can be seen from the following conversion (which uses NIST conversion factors):

(50 kcal_th/mol)/(6.02214129 mol^-1) = 8.30269461E-23 kcal_th

8.30269461E-23 kcal_th x 4.184E+03 (J/kcal_th) = 3.47384742E-19 J

3.47384742E-19 J x 6.24150934E+18 (eV/J) = 2.168205112 eV

(b) If the erg number is selected, then epsilon = 2.1672 eV, which follows from:

3.4723E-12 erg x 6.24150934E+11 (eV/erg) = 2.16723929 eV

As noted above, both values have been used in simulations that cite the original [SW85] paper. However, it appears that S&W intended to use the 50 kcal_th/mol value since they refer to this number more than once in the paper. (See for example discussion after Eqn. (8.1) in [SW85].) Therefore we argue that the appropriate choice is

epsilon = 8.30269461E-23 kcal_th

or in eV units (reduced to 5-digit significant digits):

epsilon = 2.1682 eV

Note that in the Si.sw parameterization for this potential distributed with LAMMPS, a value of epsilon=2.1683 is used, which appears to be due to slightly different unit conversion.

Another source of confusion is that in [SW85] the potential is fitted to an incorrect value for the cohesive energy of silicon. This is corrected by Balamane in a 1992 paper. See https://openkim.org/cite/MO_113686039439_004 for more details.

SW Functions

See the Stillinger-Weber Model driver page (linked above) for the definition of the model and its functions. The graphs below are for the Stillinger-Weber parametrization for silicon.

The graph of function $f_{2}$ with the parameter values suggested by Stillinger and Weber ( $A = 7.049556277$ , $B = 0.6022245584$ , $p = 4$ , $q = 0$ , $a = 1.80$ ) is given in the following Figure:

The contour plot of the function $h$ in $f_{3}$ for $θ = \cos^{- 1} (- 0.25) = {104.48}^{\circ}$ , as a function of $r_{i j}$ and $r_{i k}$ is given below:

MEAM_LAMMPS_KoShimLee_2011_NiH__MO_091278480940_002

Verification Check Dashboard

Visualizers (in-page)

BCC Lattice Constant

Cohesive Energy Graph

Diamond Lattice Constant

Dislocation Core Energies

FCC Elastic Constants

FCC Lattice Constant

FCC Stacking Fault Energies

FCC Surface Energies

SC Lattice Constant

Cubic Crystal Basic Properties Table

Tests

Errors

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Parameter Choices in the SW Potential

SW Functions