EAM potential (LAMMPS cubic hermite tabulation) for the Co-Al system developed by Vailhé and Farkas (1997) v005

Christophe Vailhé; Diana Farkas

doi:10.25950/32f48dd4

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EAM_Dynamo_VailheFarkas_1997_CoAl__MO_284963179498_005

Interatomic potential for Aluminum (Al), Cobalt (Co).
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Title A single sentence description.	EAM potential (LAMMPS cubic hermite tabulation) for the Co-Al system developed by Vailhé and Farkas (1997) v005
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.	Interatomic potentials of the embedded atom and embedded defect type were derived for the Co–Al system by empirical fitting to the properties of the B2 CoAl phase. The embedded atom potentials reproduced most of the properties needed, except that, in using this method, the elastic constants cannot be fitted exactly because CoAl has a negative Cauchy pressure. In order to overcome this limitation and fit the elastic constants correctly, angular forces were added using the embedded defect technique. The effects of angular forces to the embedded atom potentials were seen in the elastic constants, particularly C44. Planar fault energies changed up to 30% in the {110} and {112} γ surfaces and the vacancy formation energies were also very sensitive to the non-central forces. Dislocation core structures and Peierls stress values were computed for the 〈100〉 and 〈111〉 dislocations without angular forces. As a general result, the dislocations with a planar core moved for critical stress values below 250 MPa in contrast with the nonplanar cores for which the critical stress values were above 1500 MPa. The easiest dislocations to move were the 1/2〈111〉 edge superpartials, and the overall preferred slip plane was {110}. These results were compared with experimental observations in CoAl and previously simulated dislocations in NiAl.
Species The supported atomic species.	Al, Co
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	None

Contributor	Diana Farkas
Maintainer	Diana Farkas
Developer	Christophe Vailhé Diana Farkas
Published on KIM	2018
How to Cite	This Model originally published in [1] is archived in OpenKIM [2-5]. [1] Vailhé C, Farkas D. Shear faults and dislocation core structures in B2 CoAl. Journal of Materials Research. 1997;12(10):2559–70. doi:10.1557/JMR.1997.0340 — (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] Vailhé C, Farkas D. EAM potential (LAMMPS cubic hermite tabulation) for the Co-Al system developed by Vailhé and Farkas (1997) v005. OpenKIM; 2018. doi:10.25950/32f48dd4 [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. 32 Citations (23 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 . G. P. P. Pun, V. Yamakov, and Y. Mishin, “Interatomic potential for the ternary Ni–Al–Co system and application to atomistic modeling of the B2–L10 martensitic transformation,” Modelling and Simulation in Materials Science and Engineering. 2015. link Times cited: 80 Abstract: Ni–Al–Co is a promising system for ferromagnetic shape memor… read more Abstract: Ni–Al–Co is a promising system for ferromagnetic shape memory applications. This paper reports on the development of a ternary embedded-atom potential for this system by fitting to experimental and first-principles data. Reasonably good agreement is achieved for physical properties between values predicted by the potential and values known from experiment and/or first-principles calculations. The potential reproduces basic features of the martensitic phase transformation from the B2-ordered high-temperature phase to a tetragonal CuAu-ordered low-temperature phase. The compositional and temperature ranges of this transformation and the martensite microstructure predicted by the potential compare well with existing experimental data. These results indicate that the proposed potential can be used for simulations of the shape memory effect in the Ni–Al–Co system. read less C. Zhang, S. Huang, J. Shen, and N. Chen, “Atomistic modeling of Co–Al compounds,” Journal of Materials Research. 2013. link Times cited: 2 Abstract: The structural properties, the formation enthalpies, and the… read more Abstract: The structural properties, the formation enthalpies, and the mechanical properties of Co–Al compounds (CoAl, CoAl_3, Co_3Al, Co_2Al_5, Co_2Al_9, and Co_4Al_13) are studied by using Chen’s lattice inversion embedded-atom method. The potential is transferable and therefore does well for studying different Co–Al compounds. The calculated lattice parameters and cohesive energies are consistent with the experimental and theoretical results. The formation enthalpies of all the Co–Al compounds are negative; therefore, the chemical bonding between Co and Al atoms increases the stability of compounds. According to elastic constant restrictions, all the six Co–Al compounds are mechanically stable. CoAl alloy with the larger moduli and lower Poisson’s ratio is the hard or brittle phase. Moreover, CoAl_3, Co_3Al, Co_2Al_5, and Co_2Al_9 alloys are considered to be ductile materials, which have lower ratio of shear modulus to bulk modulus. read less C. Liu et al., “Glass-forming ability of Al-Co alloy under rapid annealing,” Journal of Applied Physics. 2013. link Times cited: 5 Abstract: By using molecular dynamics method, transition of Al-Co allo… read more Abstract: By using molecular dynamics method, transition of Al-Co alloy from liquid to amorphous structure has been investigated theoretically. The structure parameters, pair distribution functions (PDF), bond-angle distribution functions, and Voronoi polyhedra analysis are adopted as indicators of the evolution of clusters in Al-Co alloy during the rapid cooling processes. We found that below transition temperature, the second peak of PDF curves splits into two pronounced subpeaks, while at all temperature the PDF curves gradually converge to unity at large distance. This indicates that the amorphous alloy exhibits local ordering structure and has no long-range ordering. Besides, the bond-angle distribution function predicts that the degrees in the vicinity of 63.4 and 113.4 are dominated in the system during the processes of rapid annealing, which represent that the icosahedral structures are dominant. Together with the cluster structures observed in simulation, Voronoi polyhedra analysis shows that the most popu... read less M. Nó, Á. Ibarra, D. Caillard, and J. Juan, “Stress-induced phase transformations studied by in-situ transmission electron microscopy.” 2010. link Times cited: 6 Abstract: In this work, we carry out a detailed study, by in-situ Tran… read more Abstract: In this work, we carry out a detailed study, by in-situ Transmission Electron Microscopy (in-situ TEM), focused on two single-crystals of Cu-Al-Ni shape memory alloys with different transformation temperatures. The first single crystal is in beta phase at Room Temperature (RT) and has been cycled under stress, by super-elastic effect, inside the TEM. Two different mechanisms for the nucleation of β'3 and γ'3 martensite phases were observed: a) Martensite can nucleate on dislocations during super-elastic tests and when withdrawing the stress, the reverse transformation takes place by the disappearance of the martensite plate on the dislocation. b) During mechanical cycling martensite plates nucleate in other plates. The second single crystal is in martensite phase at RT, and when the stress is applied different mechanisms are observed: a) Reorientation and interface motion of the plates under the external applied stress, b) nucleation of mobile dislocations inside the martensite. A quantitative analysis of the experimental results, having into account the images and the diffraction patterns, has been realized and different mechanisms have been proposed to explain the experimental results. read less S.-G. Lee and Y.-C. Chung, “Molecular dynamics investigation of interfacial mixing behavior in transition metals (Fe, Co, Ni)-Al multilayer system,” Journal of Applied Physics. 2009. link Times cited: 15 Abstract: The interface and surface structure of transition metal (TM)… read more Abstract: The interface and surface structure of transition metal (TM) (Fe, Co, and Ni) thin film deposited on Al(001) substrate at atomic level were investigated by molecular dynamics simulation. In spite of the low adatom incident energy of 0.1 eV, TM-Al intermixing occurred actively at the surface of Al(001) at room temperature. At the interface region of TM/Al(001), an intermetallic compound was formed and found to be of B2 structure. The Co/Al system showed different layer coverage and pair correlation function characteristics, in comparison with Fe/Al and Ni/Al systems. The different structural and intermixing characteristics at the interface were successfully explained in terms of lattice matching, cohesive energy, and local acceleration effect. read less S. P. Kim, S.-C. Lee, K.-R. Lee, and Y.-C. Chung, “Asymmetric surface intermixing during thin-film growth in the Co–Al system: Role of local acceleration of the deposited atoms,” Acta Materialia. 2008. link Times cited: 15 Á. Ibarra, D. Caillard, J. Juan, and M. Nó, “Martensite nucleation on dislocations in Cu–Al–Ni shape memory alloys,” Applied Physics Letters. 2007. link Times cited: 64 Abstract: In the present work, the martensite nucleation on dislocatio… read more Abstract: In the present work, the martensite nucleation on dislocations has been observed. Cu–Al–Ni shape memory alloys have been superelastic cycled inside the transmission electron microscope. The in situ experiences show that the dislocations in β phase can be a nucleation site for γ3′ and β3′ martensites, which at the same time have been characterized by electron diffraction. The martensite plates can nucleate on the dislocations when the stress is applied and retransform to the βL21 phase when the sample is unloaded. The results are discussed in terms of the atomic configuration of the dislocation core, which facilitates the martensite nucleation.In the present work, the martensite nucleation on dislocations has been observed. Cu–Al–Ni shape memory alloys have been superelastic cycled inside the transmission electron microscope. The in situ experiences show that the dislocations in β phase can be a nucleation site for γ3′ and β3′ martensites, which at the same time have been characterized by electron diffraction. The martensite plates can nucleate on the dislocations when the stress is applied and retransform to the βL21 phase when the sample is unloaded. The results are discussed in terms of the atomic configuration of the dislocation core, which facilitates the martensite nucleation. read less S.-P. Kim, S.-C. Lee, K.-R. Lee, and Y.-C. Chung, “Molecular Dynamics Simulation at the Early Stage of Thin-Film Deposition: Al or Co on Co(111),” Japanese Journal of Applied Physics. 2003. link Times cited: 3 Abstract: The growth mechanisms at the early stage of thin-film deposi… read more Abstract: The growth mechanisms at the early stage of thin-film deposition were quantitatively investigated using the molecular dynamics method, focusing on the cases of Al and Co on an fcc-Co(111) system. In the case of Al on Co(111), Al adatoms were grown basically in the layer-by-layer growth mode. Moreover, this growth behavior became more obvious with increasing substrate temperature from 80 K to 300 K. In the case of Co on Co(111), Co adatoms apparently favored the island growth mode at a low incident energy. By increasing the energy, however, the tendency towards the layer-by-layer growth mode highly increased. These could be explained by the difference in surface diffusion barrier between the two cases. read less M. Muralles, J. T. Oh, and Z. Chen, “Modified embedded atom method interatomic potentials for the Fe-Al, Fe-Cu, Fe-Nb, Fe-W, and Co-Nb binary alloys,” Computational Materials Science. 2023. link Times cited: 0 Y. Li and W. Qiang, “Compositional effects on the antiphase boundary energies in B2-type NiTi and NiTi-based high-entropy intermetallics,” Materials Chemistry and Physics. 2023. link Times cited: 0 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 B.-H. Kim, S. Kim, J. Kang, Y.-C. Chung, K.-S. Kim, and K.-R. Lee, “Ion irradiation induced surface composition modulation in equiatomic binary alloys,” Applied Surface Science. 2021. link Times cited: 0 S. Zhang, S. Ukai, S. M. S. Aghamiri, N. Oono, and S. Hayashi, “Tensile properties of Co-added FeCrAl oxide dispersion strengthened alloy,” Journal of Alloys and Compounds. 2021. link Times cited: 4 H. N. Pishkenari, F. S. Yousefi, and A. Taghibakhshi, “Determination of surface properties and elastic constants of FCC metals: a comparison among different EAM potentials in thin film and bulk scale,” Materials Research Express. 2018. link Times cited: 22 Abstract: Three independent elastic constants C11, C12, and C44 were c… read more Abstract: Three independent elastic constants C11, C12, and C44 were calculated and compared using available potentials of eight different metals with FCC crystal structure; Gold, Silver, Copper, Nickel, Platinum, Palladium, Aluminum and Lead. In order to calculate the elastic constants, the second derivative of the energy density of each system was calculated with respect to different directions of strains. Each set of the elastic constants of the metals in bulk scale was compared with experimental results, and the average relative error was for each was calculated and compared with other available potentials. Then, using the Voigt-Reuss-Hill method, approximated values for Young and shear moduli and Poisson’s ratio of the FCC metals in the bulk scale were found for each potential. Furthermore, to observe the surface effects on the metals in nanoscale, surface elastic constants of the thin films of the metals have been calculated. In the study of the thin films of materials in nanoscale, the number of surface atoms is considerable compared to all atoms of the object. This leads to an increase in the surface effects, which influence the elastic properties. By considering this fact and employing related definitions and equations, the properties of the thin films of the metals were calculated, and the surface effects for different crystallographic directions were compared. Subsequently, in some cases, comparisons among characteristics of the metals in the thin film and bulk material were made. read less H. Yasuda, Y. Odawara, K. Soma, T. Yoshimoto, and K. Cho, “Effects of CoAl precipitates on deformation behavior of Fe-Al-Co single crystals,” Intermetallics. 2017. link Times cited: 5 V. Paidar and M. Cak, “Three types of dislocation core structure in B2 alloys,” Intermetallics. 2016. link Times cited: 6 W. Dong, H.-K. Kim, W. Ko, B.-M. Lee, and B.-J. Lee, “Atomistic modeling of pure Co and Co–Al system,” Calphad-computer Coupling of Phase Diagrams and Thermochemistry. 2012. link Times cited: 42 C. Chung and Y.-C. Chung, “Interfacial mixing behavior of Fe/Al magnetic thin films: molecular dynamics simulation,” INTERMAG Asia 2005. Digests of the IEEE International Magnetics Conference, 2005. 2005. link Times cited: 3 Abstract: The deposition behavior of Fe adatoms on Al [001] substrates… read more Abstract: The deposition behavior of Fe adatoms on Al [001] substrates was qualitatively investigated using molecular dynamics simulation to elucidate interface properties. The mixing phenomena originated from atomistic penetration and mutual diffusion. It was inferred that interfacial mixing was insensitive of the change in the initial kinetic energy of adatoms but strongly dependent on substrate temperature. read less S.-P. Kim, Y.-C. Chung, S.-C. Lee, K.-R. Lee, and K. Lee, “Surface alloy formation of Co on Al surface: Molecular dynamics simulation,” Journal of Applied Physics. 2003. link Times cited: 44 Abstract: Control of the interface structure of atomic scale multilaye… read more Abstract: Control of the interface structure of atomic scale multilayers is a fundamental issue to improve the performance of spin electronic devices. Deposition behavior of Co on Al surface at 300 K was investigated by molecular dynamics simulation. The deposited Co resulted in the formation of CoAl surface alloy regardless of the Al surface orientation. Structure of the surface alloy was dependent on the substrate orientation. Crystalline B2 structure was formed on Al (001) surface. On the contrary, amorphous mixed layers were evolved on Al (011) and (111) surfaces. In the case of Al (001) surface, 4 ML of the surface alloy were observed, which is consistent with the previous experimental observation. The present work shows that the formation of CoAl surface alloy should be considered even at the low substrate temperature and the low incident energy of deposited atoms. read less D. Farkas, “Atomistic simulations of fracture in the B2 phase of the Nb–Ti–Al system,” Materials Science and Engineering A-structural Materials Properties Microstructure and Processing. 1998. link Times cited: 15 C. Vailhé and D. Farkas, “Shear faults and dislocation core structure simulations in B2 FeAl,” Acta Materialia. 1997. link Times cited: 51 C. Jones and D. Farkas, “Embedded atom simulation of the B2 phase in Nb-Ti-Al,” Computational Materials Science. 1996. link Times cited: 6 V. Shastry and D. Farkas, “Atomistic simulation of fracture in CoAl and FeAl,” Intermetallics. 1998. link Times cited: 11 Y.-S. Lin, M. Cak, V. Paidar, and V. Vítek, “Why is the slip direction different in different B2 alloys,” Acta Materialia. 2012. link Times cited: 29 D. Farkas, C. Vailhé, and J. Panova, “Empirical angular-dependent potentials for intermetallics,” Journal of Phase Equilibria. 1997. link Times cited: 3 V. Vítek and V. Paidar, “Chapter 87 - Non-planar Dislocation Cores: A Ubiquitous Phenomenon Affecting Mechanical Properties of Crystalline Materials.” 2008. link Times cited: 104 O. Bindech, C. Goyhenex, and É. Gaudry, “A tight-binding atomistic approach for point defects and surfaces applied to the o-Al13Co4 quasicrystalline approximant,” Computational Materials Science. 2021. link Times cited: 0 D. Farkas and A. Caro, “Model interatomic potentials for Fe–Ni–Cr–Co–Al high-entropy alloys,” Journal of Materials Research. 2020. link Times cited: 76 Abstract: A set of embedded atom model (EAM) interatomic potentials wa… read more Abstract: A set of embedded atom model (EAM) interatomic potentials was developed to represent highly idealized face-centered cubic (FCC) mixtures of Fe–Ni–Cr–Co–Al at near-equiatomic compositions. Potential functions for the transition metals and their crossed interactions are taken from our previous work for Fe–Ni–Cr–Co–Cu [D. Farkas and A. Caro: J. Mater. Res. 33 (19), 3218–3225, 2018], while cross-pair interactions involving Al were developed using a mix of the component pair functions fitted to known intermetallic properties. The resulting heats of mixing of all binary equiatomic random FCC mixtures not containing Al is low, but significant short-range ordering appears in those containing Al, driven by a large atomic size difference. The potentials are utilized to predict the relative stability of FCC quinary mixtures, as well as ordered L1_2 and B2 phases as a function of Al content. These predictions are in qualitative agreement with experiments. This interatomic potential set is developed to resemble but not model precisely the properties of this complex system, aiming at providing a tool to explore the consequences of the addition of a large size-misfit component into a high entropy mixture that develops multiphase microstructures. read less S.-P. Kim, Y.-C. Chung, S.-C. Lee, K.-R. Lee, and D.-S. Kim, “Co/CoAl/Co trilayer fabrication using spontaneous intermixing of Co and Al: Molecular dynamics simulation,” Materials Science and Engineering B-advanced Functional Solid-state Materials. 2006. link Times cited: 4 S. C. Lee, S. P. Kim, K. Lee, and Y.-C. Chung, “Local Acceleration Effects of Adatom at the Vicinity on the Surface: Case of Co Nano Thin-Films on Al Surface,” Key Engineering Materials. 2006. link Times cited: 0 Abstract: The local acceleration effects, which are peculiar phenomena… read more Abstract: The local acceleration effects, which are peculiar phenomena during atomic scale deposition process, were investigated byMolecular Dynamics (MD) simulation. The values of local acceleration were distributed widely for various surface orientations. Deposited atoms were accelerated along the potential energy surface, and accelerated values were evidently dependent on the local configuration of the surface. In contrast, the local acceleration became negligibly small for clusters consisting of many atoms. read less S.-P. Kim, S.-C. Lee, K.-R. Lee, and Y.-C. Chung, “Atomic Mixing Behavior of Co/Al(001) vs. Al/fcc-Co(001): Molecular Dynamics Simulation,” Journal of Electroceramics. 2004. link Times cited: 10 C.-Y. Chung and Y.-C. Chung, “Interfacial mixing behavior of Fe-Al magnetic thin films: molecular dynamics Simulation,” IEEE Transactions on Magnetics. 2005. link Times cited: 0 Abstract: The interfacial mixing phenomenon for Fe-Al magnetic thin-fi… read more Abstract: The interfacial mixing phenomenon for Fe-Al magnetic thin-film system was quantitatively investigated using molecular dynamics simulation. The Fe-Al system has shown different characteristics such as layer coverage function and mixing length, compared with other ferromagnetic/nonferromagnetic metallic bilayer systems. The different intermixing behavior could be successfully explained in terms of cohesive energy and local acceleration effect. In addition, it can be clearly seen that intermixing was rather insensitive to changes in the adatom kinetic energy but dependent on the substrate temperature. read less
Funding	Not available

Short KIM ID The unique KIM identifier code.	MO_284963179498_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_VailheFarkas_1997_CoAl__MO_284963179498_005
DOI	10.25950/32f48dd4 https://doi.org/10.25950/32f48dd4 https://commons.datacite.org/doi.org/10.25950/32f48dd4
KIM Item Type Specifies whether this is a Portable Model (software implementation of an interatomic model); Portable Model with parameter file (parameter file to be read in by a Model Driver); Model Driver (software implementation of an interatomic model that reads in parameters).	Portable Model using Model Driver EAM_Dynamo__MD_120291908751_005
Driver	EAM_Dynamo__MD_120291908751_005
KIM API Version	2.0
Potential Type	eam

Previous Version	EAM_Dynamo_VailheFarkas_1997_CoAl__MO_284963179498_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 9.84423e-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
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
N/A Unable to perform verification check due to an error.	vc-memory-leak	informational	The model code does not have memory leaks (i.e. it releases all allocated memory at the end); see full description.	Results	Files
P All threads give identical results for tested case. Model appears to be thread-safe.	vc-thread-safe	mandatory	The model returns the same energy and forces when computed in serial and when using parallel threads for a set of configurations. Note that this is not a guarantee of thread safety; see full description.	Results	Files
P Unit conversion successful	vc-unit-conversion	mandatory	The model is able to correctly convert its energy and/or forces to different unit sets; see full description.	Results	Files

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

Species: Al

Species: Co

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: Co

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: Al

Species: Co

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: Co

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: Co

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: Co

Species: Al

Cubic Crystal Basic Properties Table

Species: Al

Species: Co

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 Al v004	view	4814
Cohesive energy versus lattice constant curve for bcc Co v004	view	4883
Cohesive energy versus lattice constant curve for diamond Al v004	view	5162
Cohesive energy versus lattice constant curve for diamond Co v004	view	5321
Cohesive energy versus lattice constant curve for fcc Al v004	view	4874
Cohesive energy versus lattice constant curve for fcc Co v004	view	5669
Cohesive energy versus lattice constant curve for sc Al v004	view	7193
Cohesive energy versus lattice constant curve for sc Co v004	view	5374

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	3039
Elastic constants for bcc Co at zero temperature v006	view	1759
Elastic constants for diamond Co at zero temperature v001	view	12796
Elastic constants for fcc Al at zero temperature v006	view	6398
Elastic constants for fcc Co at zero temperature v006	view	2111
Elastic constants for sc Al at zero temperature v006	view	1919
Elastic constants for sc Co at zero temperature v006	view	2047

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	1464
Elastic constants for hcp Co at zero temperature v004		view	1751

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 AlCo in AFLOW crystal prototype A5B2_hP28_194_ahk_ch v002	view	72790
Equilibrium crystal structure and energy for AlCo in AFLOW crystal prototype A9B2_mP22_14_a4e_e v002	view	75525
Equilibrium crystal structure and energy for Al in AFLOW crystal prototype A_cF4_225_a v002	view	58694
Equilibrium crystal structure and energy for Co in AFLOW crystal prototype A_cF4_225_a v002	view	61246
Equilibrium crystal structure and energy for Al in AFLOW crystal prototype A_cI2_229_a v002	view	56021
Equilibrium crystal structure and energy for Co in AFLOW crystal prototype A_hP2_194_c v002	view	55413
Equilibrium crystal structure and energy for Co in AFLOW crystal prototype A_tI2_139_a v002	view	71633
Equilibrium crystal structure and energy for Co in AFLOW crystal prototype A_tP28_136_f2ij v002	view	58816
Equilibrium crystal structure and energy for AlCo in AFLOW crystal prototype AB3_cP4_221_a_c v002	view	85547
Equilibrium crystal structure and energy for AlCo in AFLOW crystal prototype AB3_hP8_194_c_h v002	view	52071
Equilibrium crystal structure and energy for AlCo in AFLOW crystal prototype AB_cP2_221_a_b v002	view	120222

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 Al v003	view	7280191
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in fcc Al v001	view	13355449
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in fcc Al v001	view	7282043
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in fcc Al v001	view	25309387

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	1599
Equilibrium zero-temperature lattice constant for bcc Co v007	view	1663
Equilibrium zero-temperature lattice constant for diamond Al v007	view	2111
Equilibrium zero-temperature lattice constant for diamond Co v007	view	3711
Equilibrium zero-temperature lattice constant for fcc Al v007	view	3935
Equilibrium zero-temperature lattice constant for fcc Co v007	view	3359
Equilibrium zero-temperature lattice constant for sc Al v007	view	2015
Equilibrium zero-temperature lattice constant for sc Co v007	view	1919

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	12703
Equilibrium lattice constants for hcp Co v005		view	20821

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 Al at 293.15 K under a pressure of 0 MPa v002		view	483771

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	53933

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	6594660

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 Al v004		view	25143

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 Al		view	340863
Monovacancy formation energy and relaxation volume for hcp Co		view	297942

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 Al		view	991447
Vacancy formation and migration energy for hcp Co		view	4662386

Errors

ElasticConstantsCubic__TD_011862047401_006

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

EquilibriumCrystalStructure__TD_457028483760_002

Test	Error Categories	Link to Error page
Equilibrium crystal structure and energy for AlCo in AFLOW crystal prototype A13B4_oP102_31_17a11b_8a2b v002	other	view
Equilibrium crystal structure and energy for Co in AFLOW crystal prototype A_oC4_63_c v002	other	view

LatticeConstantCubicEnergy__TD_475411767977_006

Test	Error Categories	Link to Error page
Equilibrium zero-temperature lattice constant for diamond Al	other	view
Equilibrium zero-temperature lattice constant for diamond Co	other	view

No Driver

Verification Check	Error Categories	Link to Error page
DimerContinuityC1__VC_303890932454_005	other	view
MemoryLeak__VC_561022993723_004	other	view

Files

CMakeLists.txt
CoAl.eam.alloy
LICENSE.CDDL
kimprovenance.edn
kimspec.edn

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EAM_Dynamo_VailheFarkas_1997_CoAl__MO_284963179498_005.txz	Tar+XZ	Linux and OS X archive
EAM_Dynamo_VailheFarkas_1997_CoAl__MO_284963179498_005.zip	Zip	Windows archive

Download Dependency

This Model requires a Model Driver. Archives for the Model Driver EAM_Dynamo__MD_120291908751_005 appear below.

EAM_Dynamo__MD_120291908751_005.txz	Tar+XZ	Linux and OS X archive
EAM_Dynamo__MD_120291908751_005.zip	Zip	Windows archive

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EAM_Dynamo_VailheFarkas_1997_CoAl__MO_284963179498_005

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

Files

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