MEAM Potential for W developed by Park et al. (2012) v002

Hyoungki Park; Michael Fellinger; Thomas Lenosky; William W. Tipton; Dallas R. Trinkle; Sven P. Rudin; Christopher Woodward; John W. Wilkins; Richard G. Hennig

doi:10.25950/fafad756

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MEAM_LAMMPS_ParkFellingerLenosky_2012_W__MO_560940542741_002

Interatomic potential for Tungsten (W).
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Title A single sentence description.	MEAM Potential for W developed by Park et al. (2012) 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.	Density-functional theory energies, forces, and elastic constants determine the parametrization of an empirical, modified embedded-atom method potential for tungsten.
Species The supported atomic species.	W
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	None
Content Origin	Obtained from the developer Thomas Lenosky and posted with his permission.
Content Other Locations	https://openkim.org/id/Sim_LAMMPS_MEAM_ParkFellingerLenosky_2012_W__SM_163270462402_000

Contributor	Yaser Afshar
Maintainer	Yaser Afshar
Developer	Hyoungki Park Michael Fellinger Thomas Lenosky William W. Tipton Dallas R. Trinkle Sven P. Rudin Christopher Woodward John W. Wilkins Richard G. Hennig
Published on KIM	2023
How to Cite	This Model originally published in [1-2] is archived in OpenKIM [3-6]. [1] Park H, Fellinger MR, Lenosky TJ, Tipton WW, Trinkle DR, Rudin SP, et al. Ab initio based empirical potential used to study the mechanical properties of molybdenum. Phys Rev B. 2012Jun;85:214121. doi:10.1103/PhysRevB.85.214121 — (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] Cereceda D, Stukowski A, Gilbert MR, Queyreau S, Ventelon L, Marinica M-C, et al. Assessment of interatomic potentials for atomistic analysis of static and dynamic properties of screw dislocations in W. Journal of Physics: Condensed Matter. 2013Jan;25(8):085702. doi:10.1088/0953-8984/25/8/085702 [3] Park H, Fellinger M, Lenosky T, Tipton WW, Trinkle DR, Rudin SP, et al. MEAM Potential for W developed by Park et al. (2012) v002. OpenKIM; 2023. doi:10.25950/fafad756 [4] 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 [5] 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 [6] Elliott RS, Tadmor EB. Knowledgebase of Interatomic Models (KIM) Application Programming Interface (API). OpenKIM; 2011. doi:10.25950/ff8f563a Click here to download the above citation in BibTeX format.
Citations This panel presents information regarding the papers that have cited the interatomic potential (IP) whose page you are on. The OpenKIM machine learning based Deep Citation framework is used to determine whether the citing article actually used the IP in computations (denoted by "USED") or only provides it as a background citation (denoted by "NOT USED"). For more details on Deep Citation and how to work with this panel, click the documentation link at the top of the panel. The word cloud to the right is generated from the abstracts of IP principle source(s) (given below in "How to Cite") and the citing articles that were determined to have used the IP in order to provide users with a quick sense of the types of physical phenomena to which this IP is applied. The bar chart shows the number of articles that cited the IP per year. Each bar is divided into green (articles that USED the IP) and blue (articles that did NOT USE the IP). Users are encouraged to correct Deep Citation errors in determination by clicking the speech icon next to a citing article and providing updated information. This will be integrated into the next Deep Citation learning cycle, which occurs on a regular basis. OpenKIM acknowledges the support of the Allen Institute for AI through the Semantic Scholar project for providing citation information and full text of articles when available, which are used to train the Deep Citation ML algorithm.	This panel provides information on past usage of this interatomic potential (IP) powered by the OpenKIM Deep Citation framework. The word cloud indicates typical applications of the potential. The bar chart shows citations per year of this IP (bars are divided into articles that used the IP (green) and those that did not (blue)). The complete list of articles that cited this IP is provided below along with the Deep Citation determination on usage. See the Deep Citation documentation for more information. Show Model Used Show All Help us to determine which of the papers that cite this potential actually used it to perform calculations. If you know, click the . Y. Lu et al., “Nanoscale ductile fracture and associated atomistic mechanisms in a body-centered cubic refractory metal,” Nature Communications. 2023. link Times cited: 1 M. Kotoul et al., “A novel multiscale approach to brittle fracture of nano/micro‐sized components,” Fatigue & Fracture of Engineering Materials & Structures. 2020. link Times cited: 5 S. Yi, G. Li, Z. Liu, P. H. Hopchev, and H. Deng, “First-Principles Calculations on the Wettability of Li Atoms on the (111) Surfaces of W and Mo Substrates,” Plasma Physics Reports. 2018. link Times cited: 3 C. Chen, Z. Deng, R. Tran, H. Tang, I. Chu, and S. Ong, “Accurate Force Field for Molybdenum by Machine Learning Large Materials Data,” arXiv: Computational Physics. 2017. link Times cited: 94 Abstract: In this work, we present a highly accurate spectral neighbor… read more Abstract: In this work, we present a highly accurate spectral neighbor analysis potential (SNAP) model for molybdenum (Mo) developed through the rigorous application of machine learning techniques on large materials data sets. Despite Mo's importance as a structural metal, existing force fields for Mo based on the embedded atom and modified embedded atom methods still do not provide satisfactory accuracy on many properties. We will show that by fitting to the energies, forces and stress tensors of a large density functional theory (DFT)-computed dataset on a diverse set of Mo structures, a Mo SNAP model can be developed that achieves close to DFT accuracy in the prediction of a broad range of properties, including energies, forces, stresses, elastic constants, melting point, phonon spectra, surface energies, grain boundary energies, etc. We will outline a systematic model development process, which includes a rigorous approach to structural selection based on principal component analysis, as well as a differential evolution algorithm for optimizing the hyperparameters in the model fitting so that both the model error and the property prediction error can be simultaneously lowered. We expect that this newly developed Mo SNAP model will find broad applications in large-scale, long-time scale simulations. read less Q. Sun et al., “Analytical interactomic potential for a molybdenum–erbium system,” Modelling and Simulation in Materials Science and Engineering. 2016. link Times cited: 3 Abstract: Analytical interatomic potentials of a molybdenum–erbium (Mo… read more Abstract: Analytical interatomic potentials of a molybdenum–erbium (Mo–Er) system are developed based on a Tersoff–Brenner-type form. The potentials well describes the bulk and defect properties of bcc Mo, including lattice parameter, cohesive energy, elastic constants, formation energies of point defects, surface energies and melting point. The adsorption behavior of Er on a Mo (1 1 0) surface is studied using ab initio calculations based on the density functional theory, which is used to fit the interatomic potential of a Mo–Er interaction. The growth mechanism of the Er film on a Mo substrate is investigated using the present potentials. The simulation results show that the microstructures and morphologies of Er films are sensitive to substrate temperatures. Columnar grains of hexagonal close-packed Er parallel to a Mo (1 1 0) surface are observed and the grain sizes increase with increasing substrate temperature. read less A. Stukowski, D. Cereceda, T. Swinburne, and J. Marian, “Thermally-activated non-Schmid glide of screw dislocations in W using atomistically-informed kinetic Monte Carlo simulations,” International Journal of Plasticity. 2014. link Times cited: 82 M. Zhang, H. Huang, B. Kong, T. Song, and T.-H. Chen, “Solubility and mechanical properties of hydrogen / carbon in Mo–Ta alloy,” Micro and Nanostructures. 2022. link Times cited: 0 D. Caillard, B. Bienvenu, and E. Clouet, “Anomalous slip in body-centred cubic metals,” Nature. 2022. link Times cited: 8 H. Gong, H. Huang, D. Guo, Q. Ren, Y. Liao, and G. Zhang, “The effect of impurity oxygen solution and segregation on Mo/Cr interface stability by multi-scale simulations,” The European Physical Journal B. 2022. link Times cited: 0 H. He, S. Ma, and S. Wang, “Survey of Grain Boundary Energies in Tungsten and Beta-Titanium at High Temperature,” Materials. 2021. link Times cited: 1 Abstract: Heat treatment is a necessary means to obtain desired proper… read more Abstract: Heat treatment is a necessary means to obtain desired properties for most of the materials. Thus, the grain boundary (GB) phenomena observed in experiments actually reflect the GB behaviors at relatively high temperature to some extent. In this work, 405 different GBs were systematically constructed for body-centered cubic (BCC) metals and the grain boundary energies (GBEs) of these GBs were calculated with molecular dynamics for W at 2400 K and β-Ti at 1300 K and by means of molecular statics for Mo and W at 0 K. It was found that high temperature may result in the GB complexion transitions for some GBs, such as the Σ11{332}{332} of W. Moreover, the relationships between GBEs and sin(θ) can be described by the functions of the same type for different GB sets having the same misorientation axis, where θ is the angle between the misorientation axis and the GB plane. Generally, the GBs tend to have lower GBE when sin(θ) is equal to 0. However, the GB sets with the <110> misorientation axis have the lowest GBE when sin(θ) is close to 1. Another discovery is that the local hexagonal-close packed α phase is more likely to form at the GBs with the lattice misorientations of 38.9°/<110>, 50.5°/<110>, 59.0°/<110> and 60.0°/<111> for β-Ti at 1300 K. read less M. Powers, B. Derby, S. N. Manjunath, and A. Misra, “Hierarchical morphologies in co-sputter deposited thin films,” Physical Review Materials. 2020. link Times cited: 5 Y. Li et al., “The evolution of dislocation loop and its interaction with pre-existing dislocation in He+-irradiated molybdenum: in-situ TEM observation and molecular dynamics simulation,” Acta Materialia. 2020. link Times cited: 53 S. Xu, E. Hwang, W. Jian, Y. Su, and I. Beyerlein, “Atomistic calculations of the generalized stacking fault energies in two refractory multi-principal element alloys,” Intermetallics. 2020. link Times cited: 39 D. Fernández-Pello, J. M. Fernández-Díaz, M. A. Cerdeira, C. González, and R. Iglesias, “Energetic, electronic and structural DFT analysis of point defects in refractory BCC metals,” Materials today communications. 2020. link Times cited: 1 S. Starikov and V. Tseplyaev, “Two-scale simulation of plasticity in molybdenum: Combination of atomistic simulation and dislocation dynamics with non-linear mobility function,” Computational Materials Science. 2020. link Times cited: 9 Y. Chen, X. Liao, N. Gao, W. Hu, F. Gao, and H. Deng, “Interatomic potentials of W–V and W–Mo binary systems for point defects studies,” Journal of Nuclear Materials. 2020. link Times cited: 13 E. Fransson and P. Erhart, “Defects from phonons: Atomic transport by concerted motion in simple crystalline metals,” Acta Materialia. 2019. link Times cited: 11 N. Beets, Y. Cui, D. Farkas, and A. Misra, “Mechanical response of a bicontinuous copper–molybdenum nano-composite: Experiments and simulations,” Acta Materialia. 2019. link Times cited: 17 T. Liang et al., “Properties of Ti/TiC Interfaces from Molecular Dynamics Simulations,” Journal of Physical Chemistry C. 2016. link Times cited: 25 Abstract: Titanium carbide is used as a primary component in coating m… read more Abstract: Titanium carbide is used as a primary component in coating materials, thin films for electronic devices, and composites. Here, the structure of coherent and semicoherent interfaces formed between close-packed TiC (111) and Ti (0001) is investigated in classical molecular dynamics simulations. The forces on the atoms in the simulations are determined using a newly developed TiC potential under the framework of the third-generation charge optimized many-body (COMB3) suite of potentials. The work of adhesion energies for the coherent interfaces is calculated and compared with the predictions of density functional theory calculations. In the case of relaxed semicoherent interfaces, a two-dimensional (2D) misfit dislocation network is predicted to form that separates the interface into different regions in which the positions of the atoms are similar to the positions at the corresponding coherent interfaces. After the interface is annealed at an elevated temperature, the climb of edge dislocations is activated... read less Y. Wang, C. Li, B. Xu, and W. Liu, “Hydrogen‐Induced Core Structures Change of Screw and Edge Dislocations in Tungsten.” 2016. link Times cited: 0 E. Hahn and M. Meyers, “Grain-size dependent mechanical behavior of nanocrystalline metals,” Materials Science and Engineering A-structural Materials Properties Microstructure and Processing. 2015. link Times cited: 162 D. Cereceda et al., “Assessment of interatomic potentials for atomistic analysis of static and dynamic properties of screw dislocations in W,” Journal of Physics: Condensed Matter. 2012. link Times cited: 50 Abstract: Screw dislocations in bcc metals display non-planar cores at… read more Abstract: Screw dislocations in bcc metals display non-planar cores at zero temperature which result in high lattice friction and thermally-activated strain rate behavior. In bcc W, electronic structure molecular statics calculations reveal a compact, non-degenerate core with an associated Peierls stress between 1.7 and 2.8 GPa. However, a full picture of the dynamic behavior of dislocations can only be gained by using more efficient atomistic simulations based on semiempirical interatomic potentials. In this paper we assess the suitability of five different potentials in terms of static properties relevant to screw dislocations in pure W. Moreover, we perform molecular dynamics simulations of stress-assisted glide using all five potentials to study the dynamic behavior of screw dislocations under shear stress. Dislocations are seen to display thermally-activated motion in most of the applied stress range, with a gradual transition to a viscous damping regime at high stresses. We find that one potential predicts a core transformation from compact to dissociated at finite temperature that affects the energetics of kink-pair production and impacts the mechanism of motion. We conclude that a modified embedded-atom potential achieves the best compromise in terms of static and dynamic screw dislocation properties, although at an expense of about ten-fold compared to central potentials. read less M. Luo, L. Liang, L. Lang, S. Xiao, W. Hu, and H. Deng, “Molecular dynamics simulations of the characteristics of Mo/Ti interfaces,” Computational Materials Science. 2018. link Times cited: 21 S. Sharma et al., “Machine Learning Methods for Multiscale Physics and Urban Engineering Problems,” Entropy. 2022. link Times cited: 0 Abstract: We present an overview of four challenging research areas in… read more Abstract: We present an overview of four challenging research areas in multiscale physics and engineering as well as four data science topics that may be developed for addressing these challenges. We focus on multiscale spatiotemporal problems in light of the importance of understanding the accompanying scientific processes and engineering ideas, where “multiscale” refers to concurrent, non-trivial and coupled models over scales separated by orders of magnitude in either space, time, energy, momenta, or any other relevant parameter. Specifically, we consider problems where the data may be obtained at various resolutions; analyzing such data and constructing coupled models led to open research questions in various applications of data science. Numeric studies are reported for one of the data science techniques discussed here for illustration, namely, on approximate Bayesian computations. read less J. A. Vita and D. Trinkle, “Exploring the necessary complexity of interatomic potentials,” Computational Materials Science. 2021. link Times cited: 8 A. H. M. Faisal and C. Weinberger, “Modeling twin boundary structures in body centered cubic transition metals,” Computational Materials Science. 2021. link Times cited: 6 Y. M. Gufan, E. N. Klimova, and R. Kutuev, “Symmetry of the Non-Atomic Interactions of N-Atomic Energy and the Atomistic Theory of High-Order Elastic Modules,” Bulletin of the Russian Academy of Sciences: Physics. 2021. link Times cited: 0 J. Roberts, J. R. S. Bursten, and C. Risko, “Genetic Algorithms and Machine Learning for Predicting Surface Composition, Structure, and Chemistry: A Historical Perspective and Assessment,” Chemistry of Materials. 2021. link Times cited: 7 X. Wang, S. Xu, W. Jian, X.-G. Li, Y. Su, and I. Beyerlein, “Generalized stacking fault energies and Peierls stresses in refractory body-centered cubic metals from machine learning-based interatomic potentials,” Computational Materials Science. 2021. link Times cited: 30 F. J. Domínguez-Gutiérrez, J. Byggmästar, K. Nordlund, F. Djurabekova, and U. Toussaint, “Computational study of crystal defect formation in Mo by a machine learning molecular dynamics potential,” Modelling and Simulation in Materials Science and Engineering. 2020. link Times cited: 2 Abstract: In this work, we study the damage in crystalline molybdenum … read more Abstract: In this work, we study the damage in crystalline molybdenum material samples due to neutron bombardment in a primary knock-on atom (PKA) range of 0.5–10 keV at room temperature. We perform classical molecular dynamics (MD) simulations using a previously derived machine learning (ML) interatomic potential based on the Gaussian approximation potential (GAP) framework. We utilize a recently developed software workflow for fingerprinting and visualizing defects in damaged crystal structures to analyze the Mo samples with respect to the formation of point defects during and after a collision cascade. As a benchmark, we report results for the total number of Frenkel pairs (a self-interstitial atom and a single vacancy) formed and atom displacements as a function of the PKA energy. A comparison to results obtained using an embedded atom method (EAM) potential is presented to discuss the advantages and limits of the MD simulations utilizing ML-based potentials. The formation of Frenkel pairs follows a sublinear scaling law as ξ b where b is a fitting parameter and ξ = E PKA/E 0 with E 0 as a scaling factor. We found that the b = 0.54 for the GAP MD results and b = 0.667 for the EAM simulations. Although the average number of total defects is similar for both methods, the MD results show different atomic geometries for complex point defects, where the formation of crowdions by the GAP potential is closer to the DFT-based expectation. Finally, ion beam mixing results for GAP MD simulations are in a good agreement with experimental mixing efficiency data. This indicates that the modeling of atom relocation in cascades by machine learned potentials is suited to interpret the corresponding experimental findings. read less X. Zhang et al., “First-principles study on the mechanical properties and thermodynamic properties of Mo–Ta alloys,” Plasma Science and Technology. 2020. link Times cited: 7 Abstract: The mechanical properties, thermodynamic properties and elec… read more Abstract: The mechanical properties, thermodynamic properties and electronic structure of Mo1−xTax (Mo–Ta) alloys (x = 0, 0.0625, 0.125, 0.25, 0.3125, 0.5 and 1) were calculated by using first-principles. The electronic structure of Mo–Ta alloys was analysed by the projected density of states (PDOS). The low temperature heat capacity was estimated by Fermi energy and Debye temperature. It is shown that the formation enthalpy will decrease with the increase of Ta content, and the cohesive energy will increase with the increase of the Ta content. On the other hand, the addition of Ta atoms will reduce the strength and improve the ductility of Mo–Ta alloys, the Debye temperature will decrease and the low temperature heat capacity will be improved with the increase of the Ta content. All these results will be useful for the research of new plasma grid (PG) materials, which is mainly used in neutral beam injection (NBI) systems to produce negative hydrogen ions. read less D. Smirnova et al., “Atomistic description of self-diffusion in molybdenum: A comparative theoretical study of non-Arrhenius behavior,” Physical Review Materials. 2020. link Times cited: 16 Abstract: According to experimental observations, the temperature depe… read more Abstract: According to experimental observations, the temperature dependence of self-diffusion coefficient in most body-centered cubic metals (bcc) exhibits non-Arrhenius behavior. The origin of this behavio ... read less S. He, E. Overly, V. Bulatov, J. Marian, and D. Cereceda, “Coupling 2D atomistic information to 3D kink-pair enthalpy models of screw dislocations in bcc metals,” Physical Review Materials. 2019. link Times cited: 6 Abstract: The kink-pair activation enthalpy is a fundamental parameter… read more Abstract: The kink-pair activation enthalpy is a fundamental parameter in the theory of plasticity of body-centered cubic (bcc) metals. It controls the thermally activated motion of screw dislocation at low and intermediate temperatures. While direct atomistic calculations of kink pairs on screw dislocations have reached a high degree of accuracy, they can only be practically performed using semiempirical interatomic force fields, as electronic structure methods have not yet reached the level of efficiency needed to capture the system sizes required to model kink-pair structures. In this context, an alternative approach based on standard three-dimensional elastic models, which are efficient but lack atomic-level information, coupled to a substrate potential that represents the underlying lattice, has been widely applied over the past few years. This class of methods, known as `line-on-substrate' (LOS) models, uses the substrate potential to calculate the lattice contribution to the kink-pair energies. In this work, we introduce the stress dependence of the substrate potential into LOS models to evaluate its impact on kink-pair energies. In addition, we include asymmetric dislocation core energies as an extra descriptor of the dislocation character. This asymmetry is also elevated to the continuum level by adding core energies to the general LOS formulation and used to explain potential energy differences known to exist between left and right kinks in bcc metals. More importantly, by matching the total LOS energies to previously calculated atomistic energies of kink-pair configurations, we issue a rule to establish the value of the so-called core width in nonsingular elasticity theories and reduce its arbitrariness as a mathematical construct. read less 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 C. Yang and L. Qi, “Modified embedded-atom method potential of niobium for studies on mechanical properties,” Computational Materials Science. 2019. link Times cited: 17 A. Hernandez, A. Balasubramanian, F. Yuan, S. Mason, and T. Mueller, “Fast, accurate, and transferable many-body interatomic potentials by symbolic regression,” npj Computational Materials. 2019. link Times cited: 51 B. Revard, “Development of an Evolutionary Algorithm for the ab Initio Discovery of Two-Dimensional Materials.” 2017. link Times cited: 0 V. Berdichevsky, “On a continuum theory of dislocation equilibrium,” International Journal of Engineering Science. 2016. link Times cited: 6 A. Lipnitskii and V. Saveliev, “Development of n-body expansion interatomic potentials and its application for V,” Computational Materials Science. 2016. link Times cited: 20 W. Ku� and A. Mrózek, “Quantum-inspired evolutionary optimization of SLMoS2 two-phase structures,” Computer Methods in Material Science. 2022. link Times cited: 0 Abstract: The paper focuses on applying a Quantum Inspired Evolutionar… read more Abstract: The paper focuses on applying a Quantum Inspired Evolutionary Algorithm to achieve the optimization of 2D material containing two phases, 2H and 1T, of Molybdenum Disulphide (MoS 2 ). The goal of the optimization is to obtain a nanostructure with tailored mechanical properties. The design variables describe the shape of inclusion made from phase 1T in the 2H unit cell. The modification of the size of the inclusions leads to changes in the mechanical properties. The problem is solved with the use of computed mechanical properties on the basis of the Molecular Statics approach with ReaxFF potentials. 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 G. Baldinozzi and V. Pontikis, “Phenomenological potentials for the refractory metals Cr, Mo and W,” Journal of Physics: Condensed Matter. 2022. link Times cited: 1 Abstract: Cohesion in the refractory metals Cr, Mo, and W is phenomeno… read more Abstract: Cohesion in the refractory metals Cr, Mo, and W is phenomenologically described in this work via a n-body energy functional with a set of physically motivated parameters that were optimized to reproduce selected experimental properties characteristic of perfect and defective crystals. The functional contains four terms accounting for the hard-core repulsion, the Thomas–Fermi kinetic energy repulsion and for contributions to the binding energy of s and d valence electrons. Lattice dynamics, molecular statics, and molecular dynamics calculations show that this model describes satisfactorily thermodynamic properties of the studied metals whereas, unlike other empirical approaches from the literature, predictions of phonon dispersion relations and of surface and point defect energetics reveal in fair good agreement with experiments. These results suggest that the present model is well adapted to large-scale simulations and whenever total energy calculations of thermodynamic properties are unfeasible. read less G. Nikoulis, J. Byggmästar, J. Kioseoglou, K. Nordlund, and F. Djurabekova, “Machine-learning interatomic potential for W–Mo alloys,” Journal of Physics: Condensed Matter. 2021. link Times cited: 9 Abstract: In this work, we develop a machine-learning interatomic pote… read more Abstract: In this work, we develop a machine-learning interatomic potential for W x Mo1−x random alloys. The potential is trained using the Gaussian approximation potential framework and density functional theory data produced by the Vienna ab initio simulation package. The potential focuses on properties such as elastic properties, melting, and point defects for the whole range of W x Mo1−x compositions. Moreover, we use all-electron density functional theory data to fit an adjusted Ziegler–Biersack–Littmarck potential for the short-range repulsive interaction. We use the potential to investigate the effect of alloying on the threshold displacement energies and find a significant dependence on the local chemical environment and element of the primary recoiling atom. 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. Byggmastar, K. Nordlund, and F. Djurabekova, “Gaussian approximation potentials for body-centered-cubic transition metals,” Physical Review Materials. 2020. link Times cited: 22 Abstract: We develop a set of machine-learning interatomic potentials … read more Abstract: We develop a set of machine-learning interatomic potentials for elemental V, Nb, Mo, Ta, and W using the Gaussian approximation potential framework. The potentials show good accuracy and transferability for elastic, thermal, liquid, defect, and surface properties. All potentials are augmented with accurate repulsive potentials, making them applicable to radiation damage simulations involving high-energy collisions. We study melting and liquid properties in detail and use the potentials to provide melting curves up to 400 GPa for all five elements. read less L. Lang et al., “Development of a Ni–Mo interatomic potential for irradiation simulation,” Modelling and Simulation in Materials Science and Engineering. 2019. link Times cited: 5 Abstract: An interatomic potential for the Ni–Mo binary alloy focusing… read more Abstract: An interatomic potential for the Ni–Mo binary alloy focusing on irradiation has been constructed with the modified analysis embedded atom method. The newly developed interatomic (Ni–Ni and Mo–Mo) potentials and the Ni–Mo cross-interactions are fitted to the ab initio results and experimental data, including defect energies, formation energies of three stable phases. The properties used for fitting are accurately reproduced by the present potentials for both pure elements and alloy systems. Those properties beyond the fitting ranges are also well predicted, demonstrating its excellent transferability. The advantages and certain weaknesses of the new potential are also discussed in detail compared with other existing potentials. The potential is expected to be especially suitable for irradiation simulations of Ni–Mo alloys. read less Y. Lysogorskiy, T. Hammerschmidt, J. Janssen, J. Neugebauer, and R. Drautz, “Transferability of interatomic potentials for molybdenum and silicon,” Modelling and Simulation in Materials Science and Engineering. 2019. link Times cited: 14 Abstract: Interatomic potentials are widely used in computational mate… read more Abstract: Interatomic potentials are widely used in computational materials science, in particular for simulations that are too computationally expensive for density functional theory (DFT). Most interatomic potentials have a limited application range and often there is very limited information available regarding their performance for specific simulations. We carried out high-throughput calculations for molybdenum and silicon with DFT and a number of interatomic potentials. We compare the DFT reference calculations and experimental data to the predictions of the interatomic potentials. We focus on a large number of basic materials properties, including the cohesive energy, atomic volume, elastic coefficients, vibrational properties, thermodynamic properties, surface energies and vacancy formation energies, which enables a detailed discussion of the performance of the different potentials. We further analyze correlations between properties as obtained from DFT calculations and how interatomic potentials reproduce these correlations, and suggest a general measure for quantifying the accuracy and transferability of an interatomic potential. From our analysis we do not establish a clearcut ranking of the potentials as each potential has its strengths and weaknesses. It is therefore essential to assess the properties of a potential carefully before application of the potential in a specific simulation. The data presented here will be useful for selecting a potential for simulations of Mo or Si. read less I. Novoselov et al., “Moment tensor potentials as a promising tool to study diffusion processes,” Computational Materials Science. 2018. link Times cited: 64 J. Haskins and J. Moriarty, “Polymorphism and melt in high-pressure tantalum. II. Orthorhombic phases,” Physical Review B. 2018. link Times cited: 2 Abstract: Continuing uncertainty in the high-pressure melt curves of b… read more Abstract: Continuing uncertainty in the high-pressure melt curves of bcc transition metals has spawned renewed research interest in the phase diagrams of these materials, with tantalum becoming an important prototype. The present paper extends the quantumbased investigation of high-T,P polymorphism and melt in Ta that was begun in Paper I [Phys. Rev. B 86, 224104 (2012)] on five candidate cubic and hexagonal structures (bcc, A15, fcc, hcp and hex-w) to here treat four promising orthorhombic structures (Pnma, Fddd, Pmma and a-U). Using DFT-based MGPT multi-ion potentials that allow accurate MD simulations of large systems, we showed in Paper I that the mechanically unstable fcc, hcp and hex-w structures can only be stabilized at high-T,P by large anharmonic vibrational effects, requiring systems of ~ 500 atoms to produce size-independent melt curves and reliable calculations of thermodynamic stability. This reversed a previous small-cell quantum-simulation prediction of a high-T,P hex-w phase. Subsequent DFT calculations have now suggested a more energetically favorable and mechanically stable Pnma structure, which again small-cell quantum simulations predict could be a high-T,P phase. Our present MGPT total-energy and phonon calculations show that not only Pnma, but all four orthorhombic structures considered here, are similarly energetically favorable, and that Fddd in addition to Pnma is mechanically stable up to 420 GPa. MGPT-MD simulations further reveal spontaneous temperature-induced Pnma bcc and Fddd bcc transformations at modest temperatures, peaking at ~ 1450 K near 100 GPa. At high temperatures near melt, we find T-dependent and axial ratios and large stabilizing anharmonicity present in all four orthorhombic structures. The → → c / a b / a read less A. Takahashi, A. Seko, and I. Tanaka, “Linearized machine-learning interatomic potentials for non-magnetic elemental metals: Limitation of pairwise descriptors and trend of predictive power.,” The Journal of chemical physics. 2017. link Times cited: 20 Abstract: Machine-learning interatomic potential (MLIP) has been of gr… read more Abstract: Machine-learning interatomic potential (MLIP) has been of growing interest as a useful method to describe the energetics of systems of interest. In the present study, we examine the accuracy of linearized pairwise MLIPs and angular-dependent MLIPs for 31 elemental metals. Using all of the optimal MLIPs for 31 elemental metals, we show the robustness of the linearized frameworks, the general trend of the predictive power of MLIPs, and the limitation of pairwise MLIPs. As a result, we obtain accurate MLIPs for all 31 elements using the same linearized framework. This indicates that the use of numerous descriptors is the most important practical feature for constructing MLIPs with high accuracy. An accurate MLIP can be constructed using only pairwise descriptors for most non-transition metals, whereas it is very important to consider angular-dependent descriptors when expressing interatomic interactions of transition metals. read less L. Hale and C. Becker, “Vacancy dissociation in body-centered cubic screw dislocation cores,” Computational Materials Science. 2017. link Times cited: 9 S. Saroukhani, “ATOMISTIC MODELING OF DISLOCATION MOTION AT EXPERIMENTAL TIME-SCALES.” 2017. link Times cited: 0 A. Mandal and Y. Gupta, “Elastic-plastic deformation of molybdenum single crystals shocked along [100],” Journal of Applied Physics. 2017. link Times cited: 16 Abstract: To understand the elastic-plastic deformation response of sh… read more Abstract: To understand the elastic-plastic deformation response of shock-compressed molybdenum (Mo) - a body-centered cubic metal, single crystal samples were shocked along the [100] crystallographic orientation to an elastic impact stress of 12.5 GPa. Elastic-plastic wave profiles, measured at different propagation distances ranging between ∼0.23 to 2.31 mm using laser interferometry, showed a time-dependent material response. Within the experimental scatter, the measured elastic wave amplitudes were nearly constant over the propagation distances examined. These data point to a large and rapid elastic wave attenuation near the impact surface, before reaching a threshold value (elastic limit) of ∼3.6 GPa. Numerical simulations of the measured wave profiles, performed using a dislocation-based continuum model, suggested that {110}⟨111⟩ and/or {112}⟨111⟩ slip systems are operative under shock loading. In contrast to shocked metal single crystals with close-packed structures, the measured wave profiles in Mo single c... read less P. Zhang and D. Trinkle, “A modified embedded atom method potential for interstitial oxygen in titanium,” Computational Materials Science. 2016. link Times cited: 13 S. Winczewski, J. Dziedzic, and J. Rybicki, “Central-force decomposition of spline-based modified embedded atom method potential,” Modelling and Simulation in Materials Science and Engineering. 2016. link Times cited: 0 Abstract: Central-force decompositions are fundamental to the calculat… read more Abstract: Central-force decompositions are fundamental to the calculation of stress fields in atomic systems by means of Hardy stress. We derive expressions for a central-force decomposition of the spline-based modified embedded atom method (s-MEAM) potential. The expressions are subsequently simplified to a form that can be readily used in molecular-dynamics simulations, enabling the calculation of the spatial distribution of stress in systems treated with this novel class of empirical potentials. We briefly discuss the properties of the obtained decomposition and highlight further computational techniques that can be expected to benefit from the results of this work. To demonstrate the practicability of the derived expressions, we apply them to calculate stress fields due to an edge dislocation in bcc Mo, comparing their predictions to those of linear elasticity theory. read less J. B. Yang, Z. J. Zhang, and Z. Zhang, “Quantitative understanding of anomalous slip in Mo,” Philosophical Magazine. 2015. link Times cited: 4 Abstract: Hexagonal dislocation networks (HDNs) formed by the reaction… read more Abstract: Hexagonal dislocation networks (HDNs) formed by the reaction of <1 1 1>/2 screw dislocations are frequently observed in association with anomalous slip in body-centred cubic (bcc) metals. However, its role assigned in anomalous slip remains obscure due to the absence of quantitative description of its response to uniaxial loading. Here, systematic atomistic simulations are performed in molybdenum (Mo) to study the responses of a typical HDN to different applied loadings. The simulation results are used to develop a quantitative yield criterion for the HDN motion under uniaxial loading. Based on this criterion together with the yield equation that can account for the non-Schmid behaviours of an isolated <1 1 1>/2 screw dislocation, the transition from primary to anomalous slips with the loading direction is predicted to be consistent with the experimental observations in many bcc metals including Mo. This work also sheds light on other experimental results such as the lack of dead-band and the displacement accompanying anomalous slip. In addition, the reason for the absence of anomalous slip in bcc iron (Fe) is found by comparison of the reaction between <1 1 1>/2 screw dislocations in Mo and Fe. read less D. Smirnova et al., “Atomistic modeling of the self-diffusion in γ-U and γ-U-Mo,” The Physics of Metals and Metallography. 2015. link Times cited: 31 G. Bonny, D. Terentyev, A. Bakaev, P. Grigorev, and D. V. Neck, “Many-body central force potentials for tungsten,” Modelling and Simulation in Materials Science and Engineering. 2014. link Times cited: 79 Abstract: Tungsten and tungsten-based alloys are the primary candidate… read more Abstract: Tungsten and tungsten-based alloys are the primary candidate materials for plasma facing components in fusion reactors. The exposure to high-energy radiation, however, severely degrades the performance and lifetime limits of the in-vessel components. In an effort to better understand the mechanisms driving the materials' degradation at the atomic level, large-scale atomistic simulations are performed to complement experimental investigations. At the core of such simulations lies the interatomic potential, on which all subsequent results hinge. In this work we review 19 central force many-body potentials and benchmark their performance against experiments and density functional theory (DFT) calculations. As basic features we consider the relative lattice stability, elastic constants and point-defect properties. In addition, we also investigate extended lattice defects, namely: free surfaces, symmetric tilt grain boundaries, the 1/2〈1 1 1〉{1 1 0} and 1/2〈1 1 1〉 {1 1 2} stacking fault energy profiles and the 1/2〈1 1 1〉 screw dislocation core. We also provide the Peierls stress for the 1/2〈1 1 1〉 edge and screw dislocations as well as the glide path of the latter at zero Kelvin. The presented results serve as an initial guide and reference list for both the modelling of atomically-driven phenomena in bcc tungsten, and the further development of its potentials. read less I. A. Osipenko, O. V. Kukin, A. Gufan, and Y. M. Gufan, “Many-atom interactions in the theory of higher order elastic moduli: A general theory,” Physics of the Solid State. 2013. link Times cited: 5 W. Tipton and R. Hennig, “A grand canonical genetic algorithm for the prediction of multi-component phase diagrams and testing of empirical potentials,” Journal of Physics: Condensed Matter. 2013. link Times cited: 64 Abstract: We present an evolutionary algorithm which predicts stable a… read more Abstract: We present an evolutionary algorithm which predicts stable atomic structures and phase diagrams by searching the energy landscape of empirical and ab initio Hamiltonians. Composition and geometrical degrees of freedom may be varied simultaneously. We show that this method utilizes information from favorable local structure at one composition to predict that at others, achieving far greater efficiency of phase diagram prediction than a method which relies on sampling compositions individually. We detail this and a number of other efficiency-improving techniques implemented in the genetic algorithm for structure prediction code that is now publicly available. We test the efficiency of the software by searching the ternary Zr–Cu–Al system using an empirical embedded-atom model potential. In addition to testing the algorithm, we also evaluate the accuracy of the potential itself. We find that the potential stabilizes several correct ternary phases, while a few of the predicted ground states are unphysical. Our results suggest that genetic algorithm searches can be used to improve the methodology of empirical potential design. read less I. A. Osipenko, O. V. Kukin, and A. Gufan, “Computing lattice sums for calculating the elastic moduli of bcc metals via cluster decomposition,” Bulletin of the Russian Academy of Sciences: Physics. 2013. link Times cited: 3 P. Zhang and D. Trinkle, “Database optimization for empirical interatomic potential models,” Modelling and Simulation in Materials Science and Engineering. 2013. link Times cited: 8 Abstract: Weighted least squares fitting to a database of quantum mech… read more Abstract: Weighted least squares fitting to a database of quantum mechanical calculations can determine the optimal parameters of empirical potential models. While algorithms exist to provide optimal potential parameters for a given fitting database of structures with corresponding energy-related predictions and to estimate prediction errors using Bayesian sampling, defining an optimal fitting database based on potential predictions remains elusive. A testing set of structures and energy-related predictions provides an empirical measure of potential transferability. Here, we propose an objective function for fitting databases based on testing set errors. The objective function allows the optimization of the weights in a fitting database, the assessment of the adding or removing of structures in the fitting database, or the comparison of two different fitting databases. To showcase this technique, we consider an example Lennard-Jones potential for Ti, where modeling multiple complicated crystal structures is difficult for a radial pair potential. The algorithm finds different optimal fitting databases, depending on the objective function of potential prediction error for a testing set. read less B. Revard, W. Tipton, and R. Hennig, “Structure and stability prediction of compounds with evolutionary algorithms.,” Topics in current chemistry. 2014. link Times cited: 36
Funding	Not available

Short KIM ID The unique KIM identifier code.	MO_560940542741_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_ParkFellingerLenosky_2012_W__MO_560940542741_002
DOI	10.25950/fafad756 https://doi.org/10.25950/fafad756 https://commons.datacite.org/doi.org/10.25950/fafad756
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_ParkFellingerLenosky_2012_W__MO_560940542741_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 5.71154e-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
N/A Unable to perform verification check due to an error.	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: W

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: W

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: W

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.

Species: W

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: W

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: W

FCC Stacking Fault Energies

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

(No matching species)

FCC Surface Energies

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

(No matching species)

SC Lattice Constant

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

Species: W

Cubic Crystal Basic Properties Table

Species: W

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 W v004	view	3232
Cohesive energy versus lattice constant curve for diamond W v004	view	3242
Cohesive energy versus lattice constant curve for fcc W v004	view	5232
Cohesive energy versus lattice constant curve for sc W v004	view	3163

DislocationCoreEnergyCubic__TD_452950666597_002

Dislocation core energy for cubic crystals at a set of dislocation core cutoff radii v002

Creators:
Contributor: qyc081025
Publication Year: 2023
DOI: https://doi.org/10.25950/ebecf626

This Test Driver computes the dislocation core energy of a cubic crystal at zero temperature and pressure for a specific set of dislocation core cutoff radii. First, it generates several periodic atomistic supercells containing a dislocation dipole. 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. The supercell is increased in size until the disolcation core energy converges. Finally, after checking the independence of the results from the simulation cell geometry, the dislocation core energies are determined for each dislocation core radius.

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)
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, 0] v000	view	10932644
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, 1] v000	view	34773663
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, 2] v000	view	27769947
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, 3] v000	view	111501423
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, 4] v000	view	127234261
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, 5] v000	view	277075409
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, 6] v000	view	204144465
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, -1] v000	view	545826951
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [2, 2, 3] v000	view	190705807
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [2, 2, 5] v000	view	501482085

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 W at zero temperature v006	view	16049
Elastic constants for diamond W at zero temperature v001	view	19436
Elastic constants for fcc W at zero temperature v006	view	25841
Elastic constants for sc W at zero temperature v006	view	12761

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 W in AFLOW crystal prototype A_cF4_225_a v002	view	93277
Equilibrium crystal structure and energy for W in AFLOW crystal prototype A_cI2_229_a v002	view	76011
Equilibrium crystal structure and energy for W in AFLOW crystal prototype A_cP8_223_ac v002	view	63190

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 W v007	view	8703
Equilibrium zero-temperature lattice constant for diamond W v007	view	19246
Equilibrium zero-temperature lattice constant for fcc W v007	view	9180
Equilibrium zero-temperature lattice constant for sc W v007	view	8573

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 W v005		view	87147

LinearThermalExpansionCoeffCubic__TD_522633393614_002

Linear thermal expansion coefficient of cubic crystal structures v002

Creators:
Contributor: mjwen
Publication Year: 2024
DOI: https://doi.org/10.25950/9d9822ec

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

Test	Test Results	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Linear thermal expansion coefficient of bcc W at 293.15 K under a pressure of 0 MPa v002		view	5381270

SurfaceEnergyCubicCrystalBrokenBondFit__TD_955413365818_004

High-symmetry surface energies in cubic lattices and broken bond model v004

Creators: Matt Bierbaum
Contributor: mattbierbaum
Publication Year: 2019
DOI: https://doi.org/10.25950/6c43a4e6

Calculates the surface energy of several high symmetry surfaces and produces a broken-bond model fit. In latex form, the fit equations are given by:

E_{FCC} (\vec{n}) = p_1 (4 \left( |x+y| + |x-y| + |x+z| + |x-z| + |z+y| +|z-y|\right)) + p_2 (8 \left( |x| + |y| + |z|\right)) + p_3 (2 ( |x+ 2y + z| + |x+2y-z| + |x-2y + z| + |x-2y-z| + |2x+y+z| + |2x+y-z| +|2x-y+z| +|2x-y-z| +|x+y+2z| +|x+y-2z| +|x-y+2z| +|x-y-2z| ) + c

E_{BCC} (\vec{n}) = p_1 (6 \left( | x+y+z| + |x+y-z| + |-x+y-z| + |x-y+z| \right)) + p_2 (8 \left( |x| + |y| + |z|\right)) + p_3 (4 \left( |x+y| + |x-y| + |x+z| + |x-z| + |z+y| +|z-y|\right)) +c.

In Python, these two fits take the following form:

def BrokenBondFCC(params, index):

import numpy
x, y, z = index
x = x / numpy.sqrt(x**2.+y**2.+z**2.)
y = y / numpy.sqrt(x**2.+y**2.+z**2.)
z = z / numpy.sqrt(x**2.+y**2.+z**2.)

return params[0]*4* (abs(x+y) + abs(x-y) + abs(x+z) + abs(x-z) + abs(z+y) + abs(z-y)) + params[1]*8*(abs(x) + abs(y) + abs(z)) + params[2]*(abs(x+2*y+z) + abs(x+2*y-z) +abs(x-2*y+z) +abs(x-2*y-z) + abs(2*x+y+z) +abs(2*x+y-z) +abs(2*x-y+z) +abs(2*x-y-z) + abs(x+y+2*z) +abs(x+y-2*z) +abs(x-y+2*z) +abs(x-y-2*z))+params[3]

def BrokenBondBCC(params, x, y, z):

import numpy
x, y, z = index
x = x / numpy.sqrt(x**2.+y**2.+z**2.)
y = y / numpy.sqrt(x**2.+y**2.+z**2.)
z = z / numpy.sqrt(x**2.+y**2.+z**2.)

return params[0]*6*(abs(x+y+z) + abs(x-y-z) + abs(x-y+z) + abs(x+y-z)) + params[1]*8*(abs(x) + abs(y) + abs(z)) + params[2]*4* (abs(x+y) + abs(x-y) + abs(x+z) + abs(x-z) + abs(z+y) + abs(z-y)) + params[3]

Test	Test Results	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Broken-bond fit of high-symmetry surface energies in bcc W v004		view	126215

VacancyFormationEnergyRelaxationVolume__TD_647413317626_001

Monovacancy formation energy and relaxation volume for cubic and hcp monoatomic crystals v001

Creators:
Contributor: efuem
Publication Year: 2023
DOI: https://doi.org/10.25950/fca89cea

Computes the monovacancy formation energy and relaxation volume for cubic and hcp monoatomic crystals.

Test	Test Results	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Monovacancy formation energy and relaxation volume for bcc W		view	1295500

VacancyFormationMigration__TD_554849987965_001

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

Creators:
Contributor: efuem
Publication Year: 2023
DOI: https://doi.org/10.25950/c27ba3cd

Computes the monovacancy formation and migration energies for cubic and hcp monoatomic crystals.

Test	Test Results	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Vacancy formation and migration energy for bcc W		view	969582

Errors

DislocationCoreEnergyCubic__TD_452950666597_002

Test	Error Categories	Link to Error page
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [0, 0, 1] v000	other	view
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, 7] v000	other	view
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [1, 1, -2] v000	other	view
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [2, 2, 1] v000	other	view
Dislocation core energy for bcc W computed at zero temperature for a set of dislocation core cutoff radii with burgers vector [0.5, 0.5, 0.5] along line direction [2, 2, -3] v000	other	view

ElasticConstantsHexagonal__TD_612503193866_004

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

SurfaceEnergyCubicCrystalBrokenBondFit__TD_955413365818_004

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

No Driver

Verification Check	Error Categories	Link to Error page
DimerContinuityC1__VC_303890932454_005	other	view

Files

CMakeLists.txt
LICENSE
W_Lenosky_V2.meam.spline
elems.meam
kimprovenance.edn
kimspec.edn

Download

MEAM_LAMMPS_ParkFellingerLenosky_2012_W__MO_560940542741_002.txz	Tar+XZ	Linux and OS X archive
MEAM_LAMMPS_ParkFellingerLenosky_2012_W__MO_560940542741_002.zip	Zip	Windows archive

Download Dependency

This Model requires a Model Driver. Archives for the Model Driver MEAM_LAMMPS__MD_249792265679_002 appear below.

MEAM_LAMMPS__MD_249792265679_002.txz	Tar+XZ	Linux and OS X archive
MEAM_LAMMPS__MD_249792265679_002.zip	Zip	Windows archive

Wiki

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MEAM_LAMMPS_ParkFellingerLenosky_2012_W__MO_560940542741_002

Verification Check Dashboard

Visualizers (in-page)

BCC Lattice Constant

Cohesive Energy Graph

Diamond Lattice Constant

Dislocation Core Energies

FCC Elastic Constants

FCC Lattice Constant

FCC Stacking Fault Energies

FCC Surface Energies

SC Lattice Constant

Cubic Crystal Basic Properties Table

Tests

Errors

Files

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Wiki