MEAM potential for Cu developed by Asadi et al. (2015) v002

Ebrahim Asadi; Mohsen Asle Zaeem; Sasan Nouranian; Michael I. Baskes

doi:10.25950/d439eda9

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MEAM_LAMMPS_AsadiZaeemNouranian_2015_Cu__MO_390178379548_002

Interatomic potential for Copper (Cu).
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Title A single sentence description.	MEAM potential for Cu developed by Asadi et al. (2015) 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.	The two-phase solid-liquid coexisting structures of Ni, Cu, and Al are studied by molecular dynamics (MD) simulations using the second nearest-neighbor (2NN) modified-embedded atom method (MEAM) potential. For this purpose, the existing 2NN-MEAM parameters for Ni and Cu were modified to make them suitable for the MD simulations of the problems related to the two-phase solid-liquid coexistence of these elements. Using these potentials, we compare calculated low-temperature properties of Ni, Cu, and Al, such as elastic constants, structural energy differences, vacancy formation energy, stacking fault energies, surface energies, specific heat, and thermal expansion coefficient with experimental data. The solid-liquid coexistence approach is utilized to accurately calculate the melting points of Ni, Cu, and Al. The MD calculations of the expansion in melting, latent heat, and the liquid structure factor are also compared with experimental data. In addition, the solid-liquid interface free energy and surface anisotropy of the elements are determined from the interface fluctuations, and the predictions are compared to the experimental and computational data in the literature.
Species The supported atomic species.	Cu
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	None
Content Origin	NIST IPRP (https://www.ctcms.nist.gov/potentials/Cu.html)
Content Other Locations	https://openkim.org/id/Sim_LAMMPS_MEAM_AsadiZaeemNouranian_2015_Cu__SM_239791545509_000

Contributor	Yaser Afshar
Maintainer	Yaser Afshar
Developer	Ebrahim Asadi Mohsen Asle Zaeem Sasan Nouranian Michael I. Baskes
Published on KIM	2023
How to Cite	This Model originally published in [1] is archived in OpenKIM [2-5]. [1] Asadi E, Zaeem MA, Nouranian S, Baskes MI. Two-phase solid–liquid coexistence of Ni, Cu, and Al by molecular dynamics simulations using the modified embedded-atom method. Acta Materialia. 2015;86:169–81. doi:10.1016/j.actamat.2014.12.010 — (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] Asadi E, Zaeem MA, Nouranian S, Baskes MI. MEAM potential for Cu developed by Asadi et al. (2015) v002. OpenKIM; 2023. doi:10.25950/d439eda9 [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. 91 Citations (66 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 . T. Isensee and D. Tourret, “Convective effects on columnar dendritic solidification – A multiscale dendritic needle network study,” Acta Materialia. 2022. link Times cited: 10 S. M. Elahi, R. Tavakoli, A. K. Boukellal, T. Isensee, I. Romero, and D. Tourret, “Multiscale simulation of powder-bed fusion processing of metallic alloys,” Computational Materials Science. 2022. link Times cited: 16 F. Gitzhofer, J. Aluha, P.-O. Langlois, F. Barandehfard, T. Ntho, and N. Abatzoglou, “Proven Anti-Wetting Properties of Molybdenum Tested for High-Temperature Corrosion-Resistance with Potential Application in the Aluminum Industry,” Materials. 2021. link Times cited: 0 Abstract: The behavior of Mo in contact with molten Al was modelled by… read more Abstract: The behavior of Mo in contact with molten Al was modelled by classical molecular dynamics (CMD) simulation of a pure Mo solid in contact with molten Al at 1200 K using the Materials Studio®. Results showed that no reaction or cross diffusion of atoms occurs at the Mo(s)–Al(l) interface, and that molten Al atoms exhibit an epitaxial alignment with the exposed solid Mo crystal morphology. Furthermore, the two phases {Mo(s) and Al(l)} are predicted to interact with weak van der Waals forces and give interfacial energy of about 203 mJ/m2. Surface energy measurements by the sessile drop experiment using the van Oss–Chaudhury–Good (VCG) theory established a Mo(s)–Al(l) interface energy equivalent to 54 mJ/m2, which supports the weak van der Waals interaction. The corrosion resistance of a high purity (99.97%) Mo block was then tested in a molten alloy of 5% Mg mixed in Al (Al-5 wt.%Mg) at 1123 K for 96 h, using the ALCAN’s standard “immersion” test, and the results are presented. No Mo was found to be dissolved in the molten Al-Mg alloy. However, a 20% mass loss in the Mo block was due to intergranular corrosion scissoring the Mo block in the ALCAN test, but not as a result of the reaction of pure Mo with the molten Al-Mg alloy. It was observed that the Al-Mg alloy did not stick to the Mo block. read less A. Mahata, M. A. Zaeem, and M. Baskes, “Understanding homogeneous nucleation in solidification of aluminum by molecular dynamics simulations,” Modelling and Simulation in Materials Science and Engineering. 2017. link Times cited: 65 Abstract: Homogeneous nucleation from aluminum (Al) melt was investiga… read more Abstract: Homogeneous nucleation from aluminum (Al) melt was investigated by million-atom molecular dynamics simulations utilizing the second nearest neighbor modified embedded atom method potentials. The natural spontaneous homogenous nucleation from the Al melt was produced without any influence of pressure, free surface effects and impurities. Initially isothermal crystal nucleation from undercooled melt was studied at different constant temperatures, and later superheated Al melt was quenched with different cooling rates. The crystal structure of nuclei, critical nucleus size, critical temperature for homogenous nucleation, induction time, and nucleation rate were determined. The quenching simulations clearly revealed three temperature regimes: sub-critical nucleation, super-critical nucleation, and solid-state grain growth regimes. The main crystalline phase was identified as face-centered cubic, but a hexagonal close-packed (hcp) and an amorphous solid phase were also detected. The hcp phase was created due to the formation of stacking faults during solidification of Al melt. By slowing down the cooling rate, the volume fraction of hcp and amorphous phases decreased. After the box was completely solid, grain growth was simulated and the grain growth exponent was determined for different annealing temperatures. read less N. T. Brown, E. Martínez, and J. Qu, “Interfacial free energy and stiffness of aluminum during rapid solidification,” Acta Materialia. 2017. link Times cited: 12 J. Davoodi, S. Dadashi, and M. Yarifard, “Molecular dynamics simulations of the melting of Al–Ni nanowires,” Philosophical Magazine. 2016. link Times cited: 6 Abstract: Molecular dynamics (MD) simulations were performed to invest… read more Abstract: Molecular dynamics (MD) simulations were performed to investigate the influence of nickel (Ni) composition and nanowire thickness on the thermal properties of Al-x%Ni (at%) nanowires using the embedded atom model (EAM) potential. The melting of the nanowire was characterised by studying the temperature dependence of the cohesive energy and mean square displacement. The effect of the nanowire thickness on the cohesive energy, melting temperature, heat capacity as well as latent heat was studied in canonical ensemble. Moreover, the crystal stability of Al, Al-20%Ni, Al-40%Ni, Al-60%Ni, Al-80%Ni, Al3Ni, Ni3Al and Ni nanowires was studied at different temperatures using mean square displacement and cohesive energy. read less L. H. Li, L. Hu, S. J. Yang, W. Wang, and B. Wei, “Thermodynamic properties and solidification kinetics of intermetallic Ni7Zr2 alloy investigated by electrostatic levitation technique and theoretical calculations,” Journal of Applied Physics. 2016. link Times cited: 16 Abstract: The thermodynamic properties, including the density, volume … read more Abstract: The thermodynamic properties, including the density, volume expansion coefficient, ratio of specific heat to emissivity of intermetallic Ni7Zr2 alloy, have been measured using the non-contact electrostatic levitation technique. These properties vary linearly with temperature at solid and liquid states, even down to the obtained maximum undercooling of 317 K. The enthalpy, glass transition, diffusion coefficient, shear viscosity, and surface tension were obtained by using molecular dynamics simulations. Ni7Zr2 has a relatively poor glass forming ability, and the glass transition temperature is determined as 1026 K. The inter-diffusivity of Ni7Zr2 alloy fitted by Vogel–Fulcher–Tammann law yields a fragility parameter of 8.49, which indicates the fragile nature of this alloy. Due to the competition of increased thermodynamic driving force and decreased atomic diffusion, the dendrite growth velocity of Ni7Zr2 compound exhibits double-exponential relationship to the undercooling. The maximum growth velocity is... read less S. M. Handrigan and S. Nakhla, “Generation of viable nanocrystalline structures using the melt-cool method: the influence of force field selection,” Philosophical Magazine. 2023. link Times cited: 0 O. Klimanova, T. Miryashkin, and A. Shapeev, “Accurate melting point prediction through autonomous physics-informed learning,” Physical Review B. 2023. link Times cited: 0 Abstract: We present an algorithm for computing melting points by auto… read more Abstract: We present an algorithm for computing melting points by autonomously learning from coexistence simulations in the NPT ensemble. Given the interatomic interaction model, the method makes decisions regarding the number of atoms and temperature at which to conduct simulations, and based on the collected data predicts the melting point along with the uncertainty, which can be systematically improved with more data. We demonstrate how incorporating physical models of the solid-liquid coexistence evolution enhances the algorithm's accuracy and enables optimal decision-making to effectively reduce predictive uncertainty. To validate our approach, we compare the results of 20 melting point calculations from the literature to the results of our calculations, all conducted with same interatomic potentials. Remarkably, we observe significant deviations in about one-third of the cases, underscoring the need for accurate and reliable algorithms for materials property calculations. read less S. Kavousi, V. Ankudinov, P. Galenko, and M. A. Zaeem, “Atomistic-informed kinetic phase-field modeling of non-equilibrium crystal growth during rapid solidification,” Acta Materialia. 2023. link Times cited: 1 D. Tourret et al., “Morphological Stability of Solid-Liquid Interfaces Under Additive Manufacturing Conditions,” Acta Materialia. 2023. link Times cited: 8 B. Zhai and H. P. Wang, “Accurate interatomic potential for the nucleation in liquid Ti-Al binary alloy developed by deep neural network learning method,” Computational Materials Science. 2023. link Times cited: 2 J. Zhang, F. Han, Z. Yang, and J. Cui, “Coupling of an atomistic model and bond-based peridynamic model using an extended Arlequin framework,” Computer Methods in Applied Mechanics and Engineering. 2023. link Times cited: 5 D. Cui et al., “Atomistic insights into sluggish crystal growth in an undercooled CoNiCrFe multi-principal element alloy,” Journal of Alloys and Compounds. 2023. link Times cited: 1 C. Zhang, Q. Liao, X. Zhang, F. Ma, M. Wu, and Q. Xu, “Characterization of porosity in lack of fusion pores in selective laser melting using the wavefunction,” Materials Research Express. 2022. link Times cited: 0 Abstract: Selective laser melting (SLM) is used extensively in the man… read more Abstract: Selective laser melting (SLM) is used extensively in the manufacture of components for both production and domestic applications. However, the lack of fusion pores is one of the most common defects in the SLM process, affecting the performance and life of the part and hindering the development of the SLM process. Meanwhile, the defects are particularly sensitive to changes in SLM process parameters. The micro-selective laser melting (μ SLM) model was established by molecular dynamics simulation, and the lack of fusion pores in the melt pool was analyzed by a multifunctional wavefunction analyzer to understand the difference of the porosities under different processes. The results show that both laser power and scanning speed can prolong the existence time of the melt pool by changing the input energy density. The melted powder has more time to fill the lack of fusion pores, thus reducing the porosity. The larger scanning spacing hinders the combination of adjacent melt pools, leading to an increase in porosity. Reducing scanning spacing will lead to sintering or remelting, thus improving the bonding quality of adjacent melt pools and effectively reducing porosity. read less 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 H. Deng, J. Comer, and B. Liu, “A high-dimensional neural network potential for molecular dynamics simulations of condensed phase nickel and phase transitions,” Molecular Simulation. 2022. link Times cited: 0 Abstract: ABSTRACT A high-dimensional neural network interatomic poten… read more Abstract: ABSTRACT A high-dimensional neural network interatomic potential was developed and used in molecular dynamics simulations of condensed phase Ni and Ni systems with liquid–solid phase coexistence. The reference data set was generated by sampling the potential energy surface over a broad temperature-pressure domain using ab initio MD simulations to train a unified potential. Excellent agreement was achieved between bulk face-centred cubic nickel thermal expansion simulations and relevant experimental data. The same potential also yields accurate structures and diffusivities in the liquid state. The phase transition between liquid and solid phases was simulated using the two-phase interface method. The predicted melting point temperature is within a few kelvins of the literature value. The general methodology could be applied to describe crystals with much more complex phase behaviours. read less Y. Wang, B. Yang, S. Li, X.-L. Cao, Z. Liu, and H.-juan Xing, “Seaweed pattern formation in the non-axially directional solidification of 2D-like and 3D Al-3 wt.% Mg single crystal,” Journal of Materials Science & Technology. 2022. link Times cited: 1 L. Zepeda-Ruiz, “Melting temperature, critical nucleus size, and interfacial free energy in single FCC metals — A Molecular Dynamics study of liquid–solid phase equilibria,” Journal of Crystal Growth. 2022. link Times cited: 0 X. Chen et al., “Effects of Cooling Rate on the Solidification Process of Pure Metal Al: Molecular Dynamics Simulations Based on the MFPT Method,” Metals. 2022. link Times cited: 3 Abstract: Isothermal solidification process of pure metal Al was studi… read more Abstract: Isothermal solidification process of pure metal Al was studied by molecular dynamics (MD) simulation using EAM potential. The effects of different cooling rates on the isothermal solidification process of metallic Al were studied. Al was first subjected to a rapid cooling process, and then it was annealing under isothermal conditions. The mean first-passage times (MFPT) method and Johnson-Mehl-Avrami (JMA) law were used to qualify the solidification kinetic processing, and the nucleation rate, critical nucleus size, Avrami exponent and growth exponent of grains were calculated. Results show that the nucleation rate and critical size decrease as the cooling rate increases. Also, an increase in the cooling rate leads to the increase of grain growth rate. At all investigated cooling rates, nucleation and growth processes are in the typical three-dimensional growth mode. read less M. Haapalehto, T. Pinomaa, L. Wang, and A. Laukkanen, “An atomistic simulation study of rapid solidification kinetics and crystal defects in dilute Al–Cu alloys,” Computational Materials Science. 2022. link Times cited: 9 R. Liu, Z. Wang, and L. Xu, “Determining the melting temperature of three-dimensional atomic crystal using molecular dynamics simulation,” Other Conferences. 2022. link Times cited: 0 Abstract: Copper was one of the initial metals to be used by human. Be… read more Abstract: Copper was one of the initial metals to be used by human. Because of its good ductility, thermal conductivity and high electrical conductivity, copper is still widely used today. Typically, the processing of dealing with copper is to melt it and then cool it down into the desired shape. Therefore, the accurate measurement of copper melting point will make a great contribution to industrial production. In this experiment, we simply use LAMMPS to simulate both the copper’s melting process by using pair distribution function to determine the copper crystal melting point and using the Liquid-solid coexistence method to determine the melting point. Therefore, the result is that the melting point obtained by heating from lower temperatures to higher ones is approximately higher than 1300K, and it is 1349.73K by using Liquid-solid coexistence method. read less G. Azizi, S. Kavousi, and M. A. Zaeem, “Interactive Effects of Interfacial Energy Anisotropy and Solute Transport on Solidification Patterns of Al-Cu Alloys,” Acta Materialia. 2022. link Times cited: 16 S. A. Etesami, M. Laradji, and E. Asadi, “The influence of Pb content on the interfacial free energy of solid Sn in eutectic Pb–Sn liquid mixtures using molecular dynamics simulations,” Molecular Simulation. 2022. link Times cited: 2 Abstract: ABSTRACT The solid–liquid interfacial free energy (γ) for bi… read more Abstract: ABSTRACT The solid–liquid interfacial free energy (γ) for binary Pb–Sn systems at different concentrations and crystal orientations is calculated using molecular dynamics (MD) simulation that employs a modified-embedded atom method interatomic potential. First, the solid–liquid interface is constructed in MD simulations according to its calculated phase diagram. Then, the capillary fluctuation method (CFM) is employed for the calculation of the solid–liquid interfacial stiffness. A novel systematic approach is proposed that eliminates the error in the linear approximation of the CFM. The results show that orientation of the solid Sn crystal does not have a significant influence on the value of the stiffness, which explains the experimentally observed spherical shape of Sn particles in eutectic liquid Pb–Sn mixtures. The calculated γ for pure Sn is in good agreement with experimental counterparts. In addition, this study finds that γ slightly increases with increasing the concentration of Pb in the eutectic liquid Pb–Sn mixture, which agrees with available experimental data. read less S. Xu, W. Wu, J. Chang, S. Sha, and B. Wei, “Duplex Solidification Mechanisms of Glass Forming Zr55Cu30Al10Ni5 Alloy During Electromagnetic Levitation Processing,” Metallurgical and Materials Transactions A. 2022. link Times cited: 3 Y. Liu, F. Yang, X. Zhang, J. Zhang, and Z. Zhong, “Crack propagation in gradient nano-grained metals with extremely small grain size based on molecular dynamic simulations,” International Journal of Fracture. 2022. link Times cited: 7 A. Mahata, T. Mukhopadhyay, and M. A. Zaeem, “Modified embedded-atom method interatomic potentials for Al-Cu, Al-Fe and Al-Ni binary alloys: From room temperature to melting point,” Computational Materials Science. 2022. link Times cited: 27 M. T. Curnan, D. Shin, W. Saidi, J. C. Yang, and J. Han, “Universally characterizing atomistic strain via simulation, statistics, and machine learning: low-angle grain boundaries,” Acta Materialia. 2022. link Times cited: 3 M. Wu and W. Ji, “Nanoscale Origin of the Crystalline-to-Amorphous Phase Transformation and Damage Tolerance of Cantor Alloys at Cryogenic Temperatures,” SSRN Electronic Journal. 2022. link Times cited: 13 J. A. Vita and D. Trinkle, “Exploring the necessary complexity of interatomic potentials,” Computational Materials Science. 2021. link Times cited: 8 G. Singh, A. Waas, and V. Sundararaghavan, “Understanding defect structures in nanoscale metal additive manufacturing via molecular dynamics,” Computational Materials Science. 2021. link Times cited: 11 L. Shi et al., “Achieving high strength and ductility in copper matrix composites with graphene network,” Materials Science and Engineering: A. 2021. link Times cited: 18 M. Khalid, J. Friis, P. H. Ninive, K. Marthinsen, I. G. Ringdalen, and A. Strandlie, “Modified embedded atom method potential for Fe-Al intermetallics mechanical strength: A comparative analysis of atomistic simulations,” Physica B-condensed Matter. 2021. link Times cited: 4 M. O’Masta, C. CloughEric, and J. H. Martin, “Island formation and the heterogeneous nucleation of aluminum,” Computational Materials Science. 2021. link Times cited: 4 J. F. Hickman, Y. Mishin, V. Ozoliņš, and A. Ardell, “Coarsening of solid β -Sn particles in liquid Pb-Sn alloys: Reinterpretation of experimental data in the framework of trans-interface-diffusion-controlled coarsening,” Physical Review Materials. 2021. link Times cited: 3 Abstract: James F. Hickman,1 Yuri Mishin ,2 Vidvuds Ozoliņš ,3 and Ala… read more Abstract: James F. Hickman,1 Yuri Mishin ,2 Vidvuds Ozoliņš ,3 and Alan J. Ardell 4,* 1Materials Science and Engineering Division, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899-8910, USA 2Department of Physics and Astronomy, George Mason University, Fairfax, Virginia 22030-4444, USA 3Department of Applied Physics, Energy Sciences Institute, Yale University, New Haven, Connecticut 06511, USA 4Department of Materials Science and Engineering, UCLA Samueli School of Engineering, Los Angeles, California 90095-1595, USA read less M. T. Curnan, W. Saidi, J. C. Yang, and J. Han, “Universal prediction of strain footprints via simulation, statistics, and machine learning: low-Σ grain boundaries,” Acta Materialia. 2021. link Times cited: 4 Z. Aitken, V. Sorkin, Z. Yu, S. Chen, Z. Wu, and Y.-W. Zhang, “Modified embedded-atom method potentials for the plasticity and fracture behaviors of unary fcc metals,” Physical Review B. 2021. link Times cited: 5 M. Bahramyan, R. T. Mousavian, J. Carton, and D. Brabazon, “Nano-scale simulation of directional solidification in TWIP stainless steels: A focus on plastic deformation mechanisms,” Materials Science and Engineering: A. 2021. link Times cited: 4 A. Agrawal and R. Mirzaeifar, “Copper-graphene composites; developing the MEAM potential and investigating their mechanical properties,” Computational Materials Science. 2021. link Times cited: 9 S. Kavousi, B. R. Novak, J. Hoyt, and D. Moldovan, “Interface kinetics of rapid solidification of binary alloys by atomistic simulations: Application to Ti-Ni alloys,” Computational Materials Science. 2020. link Times cited: 20 S. A. Etesami, M. Laradji, and E. Asadi, “Reliability of molecular dynamics interatomic potentials for modeling of titanium in additive manufacturing processes,” Computational Materials Science. 2020. link Times cited: 5 G. Hu, C. Luo, L. Wu, Q. Tang, Z. Ren, and B. Xu, “Molecular dynamics simulation of solid/liquid interfacial energy of uranium,” Journal of Nuclear Materials. 2020. link Times cited: 7 Y. Wang, S. Li, Z. Liu, B. Yang, H. Zhong, and H. Xing, “Anisotropy-dependent seaweed growth during directional solidification of Al-4.5%Cu single crystal,” Scripta Materialia. 2020. link Times cited: 5 R. Yan, S. Ma, W. Sun, T. Jing, and H. Dong, “The solid–liquid interface free energy of Al: A comparison between molecular dynamics calculations and experimental measurements,” Computational Materials Science. 2020. link Times cited: 8 K. Bai, K. Wang, M. Sullivan, and Y. Zhang, “Prediction of the solid-liquid interface energy of a multicomponent metallic alloy via a solid-liquid interface sublattice model,” Journal of Alloys and Compounds. 2020. link Times cited: 3 C. Skelland et al., “Atomistic study on the pressure dependence of the melting point of NdFe12,” AIP Advances. 2020. link Times cited: 1 Abstract: We investigated, using molecular dynamics, how pressure affe… read more Abstract: We investigated, using molecular dynamics, how pressure affects the melting point of the recently theorised and epitaxially grown structure NdFe12. We modified Morse potentials using experimental constants and a genetic algorithm code, before running two-phase solid-liquid coexistence simulations of NdFe12 at various temperatures and pressures. The refitting of the Morse potentials allowed us to significantly improve the accuracy in predicting the melting temperature of the constituent elements. read less I. Aslam et al., “Thermodynamic and kinetic behavior of low-alloy steels: An atomic level study using an Fe-Mn-Si-C modified embedded atom method (MEAM) potential,” Materialia. 2019. link Times cited: 12 A. Mahata and M. A. Zaeem, “Effects of solidification defects on nanoscale mechanical properties of rapid directionally solidified Al-Cu Alloy: A large scale molecular dynamics study,” Journal of Crystal Growth. 2019. link Times cited: 21 N. T. Brown, E. Martínez, and J. Qu, “Solid-liquid metal interface definition studies using capillary fluctuation method,” Computational Materials Science. 2019. link Times cited: 3 Y. Zuo et al., “A Performance and Cost Assessment of Machine Learning Interatomic Potentials.,” The journal of physical chemistry. A. 2019. link Times cited: 413 Abstract: Machine learning of the quantitative relationship between lo… read more Abstract: Machine learning of the quantitative relationship between local environment descriptors and the potential energy surface of a system of atoms has emerged as a new frontier in the development of interatomic potentials (IAPs). Here, we present a comprehensive evaluation of ML-IAPs based on four local environment descriptors --- atom-centered symmetry functions (ACSF), smooth overlap of atomic positions (SOAP), the Spectral Neighbor Analysis Potential (SNAP) bispectrum components, and moment tensors --- using a diverse data set generated using high-throughput density functional theory (DFT) calculations. The data set comprising bcc (Li, Mo) and fcc (Cu, Ni) metals and diamond group IV semiconductors (Si, Ge) is chosen to span a range of crystal structures and bonding. All descriptors studied show excellent performance in predicting energies and forces far surpassing that of classical IAPs, as well as predicting properties such as elastic constants and phonon dispersion curves. We observe a general trade-off between accuracy and the degrees of freedom of each model, and consequently computational cost. We will discuss these trade-offs in the context of model selection for molecular dynamics and other applications. read less S. Kavousi, B. R. Novak, M. A. Zaeem, and D. Moldovan, “Combined molecular dynamics and phase field simulation investigations of crystal-melt interfacial properties and dendritic solidification of highly undercooled titanium,” Computational Materials Science. 2019. link Times cited: 28 A. Mahata and M. A. Zaeem, “Evolution of solidification defects in deformation of nano-polycrystalline aluminum,” Computational Materials Science. 2019. link Times cited: 25 S. A. Etesami, M. Baskes, M. Laradji, and E. Asadi, “Thermodynamics of solid Sn and Pb Sn liquid mixtures using molecular dynamics simulations,” Acta Materialia. 2018. link Times cited: 21 R. Yan et al., “Structural and mechanical properties of homogeneous solid-liquid interface of Al modelled with COMB3 potential,” Computational Materials Science. 2018. link Times cited: 9 X.-G. Li, C. Hu, C. Chen, Z. Deng, J. Luo, and S. Ong, “Quantum-accurate spectral neighbor analysis potential models for Ni-Mo binary alloys and fcc metals,” Physical Review B. 2018. link Times cited: 61 Abstract: In recent years, efficient interatomic potentials approachin… read more Abstract: In recent years, efficient interatomic potentials approaching the accuracy of density functional theory (DFT) calculations have been developed using rigorous atomic descriptors satisfying strict invariances, for example, for translation, rotation, permutation of homonuclear atoms, among others. In this paper, we generalize the spectral neighbor analysis potential (SNAP) model to bcc-fcc binary alloy systems. We demonstrate that machine-learned SNAP models can yield significant improvements even over the well-established high-performing embedded atom method (EAM) and modified EAM potentials for fcc Cu and Ni. We also report on the development of a SNAP model for the fcc Ni-bcc Mo binary system by machine learning a carefully constructed large computed data set of elemental and intermetallic compounds. We demonstrate that this binary Ni-Mo SNAP model can achieve excellent agreement with experiments in the prediction of a Ni-Mo phase diagram as well as near-DFT accuracy in the prediction of many key properties, such as elastic constants, formation energies, melting points, etc., across the entire binary composition range. In contrast, the existing Ni-Mo EAM has significant errors in the prediction of the phase diagram and completely fails in binary compounds. This paper provides a systematic model development process for multicomponent alloy systems, including an efficient procedure to optimize the hyperparameters in the model fitting, and paves the way for long-time large-scale simulations of such systems. read less A. Nourian-Avval and E. Asadi, “Thermodynamics of FCC metals at melting point in one-mode phase-field crystals model,” Computational Materials Science. 2018. link Times cited: 7 M. A. Zaeem and E. Asadi, “Phase‐Field Crystal Modeling: Integrating Density Functional Theory, Molecular Dynamics, and Phase‐Field Modeling.” 2018. link Times cited: 2 X. Gan, S. Xiao, H. Deng, X. Li, and W. Hu, “Orientation dependences of the Fe-Li solid-liquid interface properties: Atomistic simulations,” Journal of Alloys and Compounds. 2016. link Times cited: 13 C. Qi, J. Li, B. Xu, L. Kong, and S. Zhao, “Atomistic characterization of solid-liquid interfaces in the Cu-Ni binary alloy system,” Computational Materials Science. 2016. link Times cited: 15 Y. Shibuta, S. Sakane, T. Takaki, and M. Ohno, “Submicrometer-scale molecular dynamics simulation of nucleation and solidification from undercooled melt: Linkage between empirical interpretation and atomistic nature,” Acta Materialia. 2016. link Times cited: 73 E. Asadi and M. A. Zaeem, “Predicting Solidification Properties of Magnesium by Molecular Dynamics Simulations.” 2016. link Times cited: 0 E. Asadi, M. A. Zaeem, S. Nouranian, and M. Baskes, “Quantitative Modeling of the Equilibration of Two-Phase Solid-Liquid Fe by Atomistic Simulations on Diffusive Time Scales,” Physical Review B. 2015. link Times cited: 61 Abstract: (Received 10 July 2014; revised manuscript received 10 Decem… read more Abstract: (Received 10 July 2014; revised manuscript received 10 December 2014; published 12 January 2015) In this paper, molecular dynamics (MD) simulations based on the modified-embedded atom method (MEAM) and a phase-field crystal (PFC) model are utilized to quantitatively investigate the solid-liquid properties of Fe. A set of second nearest-neighbor MEAM parameters for high-temperature applications are developed for Fe, and the solid-liquid coexisting approach is utilized in MD simulations to accurately calculate the melting point, expansion in melting, latent heat, and solid-liquid interface free energy, and surface anisotropy. The required input properties to determine the PFC model parameters, such as liquid structure factor and fluctuations of atoms in the solid, are also calculated from MD simulations. The PFC parameters are calculated utilizing an iterative procedure from the inputs of MD simulations. The solid-liquid interface free energy and surface anisotropy are calculated using the PFC simulations. Very good agreement is observed between the results of our calculations from MEAM-MD and PFC simulations and the available modeling and experimental results in the literature. As an application of the developed model, the grain boundary free energy of Fe is calculated using the PFC model and the results are compared against experiments. read less A. Mahata, T. Mukhopadhyay, and M. A. Zaeem, “Liquid ordering induced heterogeneities in homogeneous nucleation during solidification of pure metals,” Journal of Materials Science & Technology. 2022. link Times cited: 11 K. Wang, X. Chen, X. Chen, Y. Huang, and Z. Wang, “Modified extended Finnis Sinclair potential for cubic crystal metal,” Computational Materials Science. 2022. link Times cited: 4 S. A. Etesami and E. Asadi, “Molecular dynamics for near melting temperatures simulations of metals using modified embedded-atom method,” Journal of Physics and Chemistry of Solids. 2018. link Times cited: 71 M. A. Zaeem and L. Hogan, “Dendritic Solidification of Crystals.” 2014. link Times cited: 0 Z. Bjelobrk, D. Mendels, T. Karmakar, M. Parrinello, and M. Mazzotti, “Solubility Prediction of Organic Molecules with Molecular Dynamics Simulations.” 2021. link Times cited: 14 Abstract: We present a molecular dynamics simulation method for the co… read more Abstract: We present a molecular dynamics simulation method for the computation of the solubility of organic crystals in solution. The solubility is calculated based on the equilibrium free energy difference between the solvated solute and its crystallized state at the crystal surface kink site. In order to efficiently sample the growth and dissolution process, we have carried out well-tempered Metadynamics simulations with a collective variable that captures the slow degrees of freedom, namely the solute diffusion to and adsorption at the kink site together with the desolvation of the kink site. Simulations were performed at different solution concentrations using constant chemical potential molecular dynamics and the solubility was identified at the concentration at which the free energy values between the grown and dissolved kink states were equal. The effectiveness of this method is demonstrated by its success in reproducing the experimental trends of solubility of urea and naphthalene in a variety of solvents. read less D. Tourret, H. Liu, and J. Llorca, “Phase-field modeling of microstructure evolution: Recent applications, perspectives and challenges,” Progress in Materials Science. 2021. link Times cited: 61 J. Zhao et al., “Liquid Structure and Thermophysical Properties of Ternary Ni-Fe-Co Alloys Explored by Molecular Dynamics Simulations and Electrostatic Levitation Experiments,” Metallurgical and Materials Transactions A. 2021. link Times cited: 6 G. P. P. Pun, V. Yamakov, J. Hickman, E. Glaessgen, and Y. Mishin, “Development of a general-purpose machine-learning interatomic potential for aluminum by the physically informed neural network method,” Physical Review Materials. 2020. link Times cited: 13 Abstract: Interatomic potentials constitute the key component of large… read more Abstract: Interatomic potentials constitute the key component of large-scale atomistic simulations of materials. The recently proposed physically-informed neural network (PINN) method combines a high-dimensional regression implemented by an artificial neural network with a physics-based bond-order interatomic potential applicable to both metals and nonmetals. In this paper, we present a modified version of the PINN method that accelerates the potential training process and further improves the transferability of PINN potentials to unknown atomic environments. As an application, a modified PINN potential for Al has been developed by training on a large database of electronic structure calculations. The potential reproduces the reference first-principles energies within 2.6 meV per atom and accurately predicts a wide spectrum of physical properties of Al. Such properties include, but are not limited to, lattice dynamics, thermal expansion, energies of point and extended defects, the melting temperature, the structure and dynamic properties of liquid Al, the surface tensions of the liquid surface and the solid-liquid interface, and the nucleation and growth of a grain boundary crack. Computational efficiency of PINN potentials is also discussed. read less W. Jiang, Y. Zhang, L. Zhang, and H. Wang, “Accurate Deep Potential model for the Al–Cu–Mg alloy in the full concentration space,” arXiv: Materials Science. 2020. link Times cited: 24 Abstract: Combining first-principles accuracy and empirical-potential … read more Abstract: Combining first-principles accuracy and empirical-potential efficiency for the description of the potential energy surface (PES) is the philosopher's stone for unraveling the nature of matter via atomistic simulation. This has been particularly challenging for multi-component alloy systems due to the complex and non-linear nature of the associated PES. In this work, we develop an accurate PES model for the Al-Cu-Mg system by employing Deep Potential (DP), a neural network based representation of the PES, and DP Generator (DP-GEN), a concurrent-learning scheme that generates a compact set of ab initio data for training. The resulting DP model gives predictions consistent with first-principles calculations for various binary and ternary systems on their fundamental energetic and mechanical properties, including formation energy, equilibrium volume, equation of state, interstitial energy, vacancy and surface formation energy, as well as elastic moduli. Extensive benchmark shows that the DP model is ready and will be useful for atomistic modeling of the Al-Cu-Mg system within the full range of concentration. read less Y. Zhang, C. Hu, and B. Jiang, “Accelerating atomistic simulations with piecewise machine-learned ab Initio potentials at a classical force field-like cost.,” Physical chemistry chemical physics : PCCP. 2020. link Times cited: 12 Abstract: Recently, machine learning methods have become easy-to-use t… read more Abstract: Recently, machine learning methods have become easy-to-use tools for constructing high-dimensional interatomic potentials with ab initio accuracy. Although machine-learned interatomic potentials are generally orders of magnitude faster than first-principles calculations, they remain much slower than classical force fields, at the price of using more complex structural descriptors. To bridge this efficiency gap, we propose an embedded atom neural network approach with simple piecewise switching function-based descriptors, resulting in a favorable linear scaling with the number of neighbor atoms. Numerical examples validate that this piecewise machine-learning model can be over an order of magnitude faster than various popular machine-learned potentials with comparable accuracy for both metallic and covalent materials, approaching the speed of the fastest embedded atom method (i.e. several μs per atom per CPU core). The extreme efficiency of this approach promises its potential in first-principles atomistic simulations of very large systems and/or in a long timescale. read less J.-H. Fu, C. Zhang, T. Liu, and J. Liu, “Room temperature liquid metal: its melting point, dominating mechanism and applications,” Frontiers in Energy. 2020. link Times cited: 27 J.-yu Yang, Y. Zhang, Y. Liu, W. Hu, and X. Dai, “A comparative atomic simulation study of the configurations in M-Al (M = Mg, Ni, and Fe) nanoalloys: influence of alloying ability, surface energy, atomic radius, and atomic arrangement,” Journal of Nanoparticle Research. 2020. link Times cited: 3 J.-H. Fu, C. Zhang, T. Liu, and J. Liu, “Room temperature liquid metal: its melting point, dominating mechanism and applications,” Frontiers in Energy. 2019. link Times cited: 0 S. Kavousi, B. R. Novak, M. Baskes, M. A. Zaeem, and D. Moldovan, “Modified embedded-atom method potential for high-temperature crystal-melt properties of Ti–Ni alloys and its application to phase field simulation of solidification,” Modelling and Simulation in Materials Science and Engineering. 2019. link Times cited: 21 Abstract: We developed new interatomic potentials, based on the second… read more Abstract: We developed new interatomic potentials, based on the second nearest-neighbor modified embedded-atom method (2NN-MEAM) formalism, for Ti, Ni, and the binary Ti–Ni system. These potentials were fit to melting points, latent heats, the binary phase diagrams for the Ti rich and Ni rich regions, and the liquid phase enthalpy of mixing for binary alloys, therefore they are particularly suited for calculations of crystal-melt (CM) interface thermodynamic and transport properties. The accuracy of the potentials for pure Ti and pure Ni were tested against both 0 K and high temperature properties by comparing various properties obtained from experiments or density functional theory calculations including structural properties, elastic constants, point-defect properties, surface energies, temperatures and enthalpies of phase transformations, and diffusivity and viscosity in the liquid phase. The fitted binary potential for Ti–Ni was also tested against various non-fitted properties at 0 K and high temperatures including lattice parameters, formation energies of different intermetallic compounds, and the temperature dependence of liquid density at various concentrations. The CM interfacial free energies obtained from simulations, based on the newly developed Ti–Ni potential, show that the bcc alloys tend to have smaller anisotropy compared with fcc alloys which is consistent with the finding from the previous studies comparing single component bcc and fcc materials. Moreover, the interfacial free energy and its anisotropy for Ti-2 atom% Ni were also used to parameterize a 2D phase field (PF) model utilized in solidification simulations. The PF simulation predictions of microstructure development during solidification are in good agreement with a geometric model for dendrite primary arm spacing. read less A. Mahata and M. A. Zaeem, “Size effect in molecular dynamics simulation of nucleation process during solidification of pure metals: investigating modified embedded atom method interatomic potentials,” Modelling and Simulation in Materials Science and Engineering. 2019. link Times cited: 8 Abstract: Due to the significant increase in computing power in recent… read more Abstract: Due to the significant increase in computing power in recent years, the simulation size of atomistic methods for studying the nucleation process during solidification has been gradually increased, even to billion atom simulations (sub-micron length scale). But the question is how big of a model is required for size-independent and accurate simulations of the nucleation process during solidification? In this work, molecular dynamics simulations with model sizes ranging from ∼2000 to ∼8 million atoms were used to study nucleation during solidification. To draw general conclusions independent of crystal structures, the most advanced second nearest-neighbor modified embedded atom method interatomic potentials for Al (face-centered cubic), Fe (body-centered cubic), and Mg (hexagonal-close packed) were utilized for molecular dynamics simulations. We have analyzed several quantitative characteristics such as nucleation time, density of nuclei, nucleation rate, self-diffusion coefficient, and change in free energy during solidification. The results showed that by increasing the model size to about two million atoms, the simulations and measurable quantities become entirely independent of simulation cell size. The prediction of cell size required for size-independent computed data can considerably reduce the computational costs of atomistic simulations and at the same time increase the accuracy and reliability of the computational data. read less V. Korolev, V. Samsonov, and P. Protsenko, “Molecular Dynamics Simulation of Unstable Equilibrium of a Spherical Nucleus for Determining the Interfacial Energy in a Pb–Cu Two-Component System,” Colloid Journal. 2019. link Times cited: 0 S. A. Etesami, M. Laradji, and E. Asadi, “Transferability of interatomic potentials in predicting the temperature dependency of elastic constants for titanium, zirconium and magnesium,” Modelling and Simulation in Materials Science and Engineering. 2019. link Times cited: 4 Abstract: We present our investigation of the current state of the art… read more Abstract: We present our investigation of the current state of the art for the transferability of molecular dynamics (MD) interatomic potentials for high temperature simulations of material processes in terms of elastic constants. With the current advancement of computer power, nanoscale computational models such as MD have the potential to accelerate optimization and development of high temperature material processes provided a robust and transferable interatomic potential. Temperature dependency of elastic constants, despite the low temperature elastic constants, is not commonly used as one of the target material properties to develop interatomic potentials for metals; thus, it is a reliable index to determine the transferability of interatomic potentials for high temperature simulations. We consider all five independent elastic constants and their temperature dependency as an index for our evaluations of available interatomic potentials for titanium (Ti), zirconium (Zr), and magnesium (Mg) as representative metals with a relatively complex crystal structure (hcp). The calculated elastic constants and their deviation from their corresponding experimental values are presented. We provide a through discussion on the transferability of each potential and summarize with the most suitable potentials for high temperature material process simulations for each considered material. read less L. Wu et al., “Calculation of solid–liquid interfacial free energy and its anisotropy in undercooled system,” Rare Metals. 2018. link Times cited: 6 M. A. Zaeem, “Recent Advances in Study of Solid-Liquid Interfaces and Solidification of Metals.” 2018. link Times cited: 1 Abstract: Solidification occurs in several material processing methods… read more Abstract: Solidification occurs in several material processing methods, such as in casting, welding, and laser additive manufacturing of metals, and it controls the nano- and microstructures, as well as the overall properties of the products[...] read less S. D. Nath, Y. Shibuta, M. Ohno, T. Takaki, and T. Mohri, “A Molecular Dynamics Study of Partitionless Solidification and Melting of Al–Cu Alloys,” Isij International. 2017. link Times cited: 13 Abstract: Title A Molecular Dynamics Study of Partitionless Solidifica… read more Abstract: Title A Molecular Dynamics Study of Partitionless Solidification and Melting of Al‒Cu Alloys Author(s) Deb Nath, Sankar Kumar; Shibuta, Yasushi; Ohno, Munekazu; Takaki, Tomohiro; Mohri, Tetsuo Citation ISIJ International, 57(10), 1774-1779 https://doi.org/10.2355/isijinternational.ISIJINT-2017-221 Issue Date 2017-10-15 Doc URL http://hdl.handle.net/2115/75395 Rights 著作権は日本鉄鋼協会にある Type article File Information ISIJ Int. 57(10)_ 1774-1779 (2017).pdf read less M. Muralles, D. Choi, and B. Lee, “A comparative study of mechanical properties of Ni <001> nanowires from atomistic calculations,” Journal of Mechanical Science and Technology. 2017. link Times cited: 3 E. Asadi and M. A. Zaeem, “Quantitative Phase-Field Crystal Modeling of Solid-Liquid Interfaces for FCC Metals,” Computational Materials Science. 2017. link Times cited: 8 C. D. Paola and J. P. Brodholt, “Modeling the melting of multicomponent systems: the case of MgSiO3 perovskite under lower mantle conditions,” Scientific Reports. 2016. link Times cited: 9 C. Paola and J. Brodholt, “Modeling the melting of multicomponent systems: the case of MgSiO3 perovskite under lower mantle conditions,” Scientific Reports. 2016. link Times cited: 5 J.-yu Yang and W. Hu, “Nucleation and solid–liquid interfacial energy of Li nanoparticles: A molecular dynamics study,” physica status solidi (b). 2016. link Times cited: 3 Abstract: The nucleation and growth processes of lithium nanoparticles… read more Abstract: The nucleation and growth processes of lithium nanoparticles are simulated by molecular dynamics and embedded atom method. A critical temperature dividing, shrinking, or growing of lithium nanoparticles is determined. The linear relationship between the depression of the melting point of the lithium nanoparticle and the reciprocal of the critical nuclei is determined when the critical nuclei are between 1.0 and 2.0 nm. Solid–liquid interfacial energies of lithium nanoparticles are estimated from the Gibbs–Thomson effect. These results are consistent with the experimental values of other metals. read less S. Wilson and M. Mendelev, “A unified relation for the solid-liquid interface free energy of pure FCC, BCC, and HCP metals.,” The Journal of chemical physics. 2016. link Times cited: 37 Abstract: We study correlations between the solid-liquid interface (SL… read more Abstract: We study correlations between the solid-liquid interface (SLI) free energy and bulk material properties (melting temperature, latent heat, and liquid structure) through the determination of SLI free energies for bcc and hcp metals from molecular dynamics (MD) simulation. Values obtained for the bcc metals in this study were compared to values predicted by the Turnbull, Laird, and Ewing relations on the basis of previously published MD simulation data. We found that of these three empirical relations, the Ewing relation better describes the MD simulation data. Moreover, whereas the original Ewing relation contains two constants for a particular crystal structure, we found that the first coefficient in the Ewing relation does not depend on crystal structure, taking a common value for all three phases, at least for the class of the systems described by embedded-atom method potentials (which are considered to provide a reasonable approximation for metals). read less E. Asadi and M. A. Zaeem, “The anisotropy of hexagonal close-packed and liquid interface free energy using molecular dynamics simulations based on modified embedded-atom method,” Acta Materialia. 2016. link Times cited: 37 Y. Shibuta, M. Ohno, and T. Takaki, “Solidification in a Supercomputer: From Crystal Nuclei to Dendrite Assemblages,” JOM*. 2015. link Times cited: 83 S. Kavousi, “Combined Molecular Dynamics and Phase Field Simulation of Crystal Melt Interfacial Properties and Microstructure Evolution during Rapid Solidification of TI-NI Alloys.” 2019. link Times cited: 0
Funding	Not available

Short KIM ID The unique KIM identifier code.	MO_390178379548_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_AsadiZaeemNouranian_2015_Cu__MO_390178379548_002
DOI	10.25950/d439eda9 https://doi.org/10.25950/d439eda9 https://commons.datacite.org/doi.org/10.25950/d439eda9
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_AsadiZaeemNouranian_2015_Cu__MO_390178379548_001

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
A The letter grade A was assigned because the normalized error in the computation was 3.55947e-10 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^0 continuous. This means that the model has continuous energy, but a discontinuous 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: Cu

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: Cu

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: Cu

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: Cu

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: Cu

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: Cu

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: Cu

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: Cu

Cubic Crystal Basic Properties Table

Species: Cu

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 Cu v004	view	2871
Cohesive energy versus lattice constant curve for diamond Cu v004	view	3332
Cohesive energy versus lattice constant curve for fcc Cu v004	view	2945
Cohesive energy versus lattice constant curve for sc Cu v004	view	2945

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 Cu at zero temperature v006	view	38750
Elastic constants for diamond Cu at zero temperature v001	view	19068
Elastic constants for fcc Cu at zero temperature v006	view	23264
Elastic constants for sc Cu at zero temperature v006	view	10601

EquilibriumCrystalStructure__TD_457028483760_001

Equilibrium structure and energy for a crystal structure at zero temperature and pressure v001

Creators:
Contributor: ilia
Publication Year: 2023
DOI: https://doi.org/10.25950/e8a7ed84

Computes the equilibrium crystal structure and energy for an arbitrary crystal at zero temperature and applied stress by performing symmetry-constrained relaxation. The crystal structure is specified using the AFLOW prototype designation. Multiple sets of free parameters corresponding to the crystal prototype may be specified as initial guesses for structure optimization. No guarantee is made regarding the stability of computed equilibria, nor that any are the ground state.

Test	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 crystal structure and energy for Cu in AFLOW crystal prototype A_cF4_225_a v001		view	72884
Equilibrium crystal structure and energy for Cu in AFLOW crystal prototype A_cI2_229_a v001		view	82970

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 Cu v001	view	11012629
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in fcc Cu v001	view	32414173
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in fcc Cu v001	view	15170226
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in fcc Cu v001	view	74590057

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 Cu v007	view	8225
Equilibrium zero-temperature lattice constant for diamond Cu v007	view	9497
Equilibrium zero-temperature lattice constant for fcc Cu v007	view	8908
Equilibrium zero-temperature lattice constant for sc Cu v007	view	8653

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 Cu v005		view	39187

LinearThermalExpansionCoeffCubic__TD_522633393614_001

Linear thermal expansion coefficient of cubic crystal structures v001

Creators: Mingjian Wen
Contributor: mjwen
Publication Year: 2019
DOI: https://doi.org/10.25950/fc69d82d

This Test Driver uses LAMMPS to compute the linear thermal expansion coefficient at a finite temperature under a given pressure for a cubic lattice (fcc, bcc, sc, diamond) of a single given species.

Test	Test Results	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Linear thermal expansion coefficient of fcc Cu at 293.15 K under a pressure of 0 MPa v001		view	61323008

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 Cu v004		view	99768

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 Cu v002		view	18197221

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 Cu v004		view	102752

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 Cu		view	322973

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 Cu		view	4247682

Errors

ElasticConstantsHexagonal__TD_612503193866_004

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

PhononDispersionCurve__TD_530195868545_004

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

SurfaceEnergyCubicCrystalBrokenBondFit__TD_955413365818_004

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

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elems.meam
kimprovenance.edn
kimspec.edn
library.Cu_asadi.meam

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MEAM_LAMMPS_AsadiZaeemNouranian_2015_Cu__MO_390178379548_002

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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

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