LAMMPS EAM potential for Fe-Cr developed by Bonny et al. (2011) v001

Giovanni Bonny; Roberto C Pasianot; D. Terentyev; L. Malerba

doi:10.25950/d82afb9f

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Sim_LAMMPS_EAM_BonnyPasianotTerentyev_2011_FeCr__SM_237089298463_001

Interatomic potential for Chromium (Cr), Iron (Fe).
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Title A single sentence description.	LAMMPS EAM potential for Fe-Cr developed by Bonny et al. (2011) v001
Description	We present an Fe–Cr interatomic potential to model high-Cr ferritic alloys. The potential is fitted to thermodynamic and point-defect properties obtained from density functional theory (DFT) calculations and experiments. The developed potential is also benchmarked against other potentials available in literature. It shows particularly good agreement with the DFT obtained mixing enthalpy of the random alloy, the formation energy of intermetallics and experimental excess vibrational entropy and phase diagram. In addition, DFT calculated point-defect properties, both interstitial and substitutional, are well reproduced, as is the screw dislocation core structure. As a first validation of the potential, we study the precipitation hardening of Fe–Cr alloys via static simulations of the interaction between Cr precipitates and screw dislocations. It is concluded that the description of the dislocation core modification near a precipitate might have a significant influence on the interaction mechanisms observed in dynamic simulations. HISTORY: Changes in version 001: * Parameter files updated to match the latest (version 3) in NIST IPRP. This includes changing the values of 'Infinity' and 'NaN' in FeCr_d.eam.alloy to 1e+8 and 0.0, respectively, and adding missing rows of zero values to FeCr_s.eam.fs.
Species The supported atomic species.	Cr, Fe
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	The tabulated values of the s-embedding functions and their derivatives may deviate significantly from the corresponding analytical functions as the s-density approaches zero. See Appendix 1 of the Philosophical Magazine article and Appendix C of the technical report for more information.
Content Origin	NIST IPRP (https://www.ctcms.nist.gov/potentials/Fe.html#Fe-Cr)

Contributor	Daniel S. Karls
Maintainer	Daniel S. Karls
Developer	Giovanni Bonny Roberto C Pasianot D. Terentyev L. Malerba
Published on KIM	2021
How to Cite	This Simulator Model originally published in [1-2] is archived in OpenKIM [3-5]. [1] Bonny G, Pasianot RC, Terentyev D, Malerba L. Iron chromium potential to model high-chromium ferritic alloys. Philosophical Magazine. 2011;91(12):1724–46. doi:10.1080/14786435.2010.545780 — (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] Bonny G, Pasianot R, Terentyev D, Malerba L, Castin N. Interatomic Potential to Simulate Radiation Damage in Fe-Cr Alloys [Internet]. SCK CEN; 2011 Mar. Available from: https://publications.sckcen.be/portal/en/publications/interatomic-potential-to-simulate-radiation-damage-in-fecr-alloys(deceaab5-8760-4600-8ef9-924d028cc7a7).html [3] Bonny G, Pasianot RC, Terentyev D, Malerba L. LAMMPS EAM potential for Fe-Cr developed by Bonny et al. (2011) v001. OpenKIM; 2021. doi:10.25950/d82afb9f [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. 70 Citations (43 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 . X. Chen, R. Huang, T.-M. Shih, and Y. Wen, “Shape Stability of Metallic Nanoplates: A Molecular Dynamics Study,” Nanoscale Research Letters. 2019. link Times cited: 3 J. Sublet et al., “Neutron-induced damage simulations: Beyond defect production cross-section, displacement per atom and iron-based metrics,” The European Physical Journal Plus. 2019. link Times cited: 22 A. Hasanzadeh, A. Hamedani, G. Alahyarizadeh, A. Minuchehr, and M. Aghaei, “The role of chromium and nickel on the thermal and mechanical properties of FeNiCr austenitic stainless steels under high pressure and temperature: a molecular dynamics study,” Molecular Simulation. 2019. link Times cited: 8 Abstract: ABSTRACT The effect of Cr and Ni content on thermo-mechanica… read more Abstract: ABSTRACT The effect of Cr and Ni content on thermo-mechanical properties of FeNiCr austenitic stainless steel under ambient and high pressure and temperature were investigated by MD simulations. The FCC structure was selected as optimum structure for FeNiCr system based on obtained MD results from Bonny EAM potential and valid experimental results. The structural and mechanical properties of pure Fe, Ni, and Cr were also estimated based on this potential, indicating good agreement with experimental results. These properties were computed for four experimental case studies which showed less than 10% error. Moreover, the elastic constants of the Fe–(8–18)Ni–(18–25)Cr systems were estimated. Results showed that bulk modulus increases by increasing the Ni and Cr contents, which can be connected to the changes in bonding electrons. The thermal properties of FeNiCr were calculated in ambient and high pressure. Although thermo-mechanical properties confirm good agreement with experimental results at the ambient condition, however, they indicate that FeNiCr Bonny potential is not applicable at high pressure. In order to tackle this issue, a hybrid potential was used at high Pressure/Temperature. The results illustrate enhanced mechanical properties, increase of melting point and reduction of LTE in high pressure and deteriorated mechanical properties at high temperature. read less A. Takahashi and M. Kanazawa, “Atomistic-continuum hybrid analysis of dislocation behavior in spinodally decomposed Fe-Cr alloys.” 2017. link Times cited: 0 Abstract: In this study, we first present the molecular dynamics (MD) … read more Abstract: In this study, we first present the molecular dynamics (MD) simulation of dislocation behavior in a spinodally decomposed Fe-Cr alloy. The MD simulation is used for exploring the nature of the interaction between a dislocation and the spinodal decomposition without any specific assumptions. In order to classify the interaction mechanism, dislocation dynamics (DD) simulations of the interaction between a dislocation and the spinodal decomposition are performed. In the simulations, we controlled the interaction mechanism by adding and removing the atomistic mechanism. The simulation results clearly illustrate that the atomistic mechanism can be negligible in determining the critical resolved shear stress (CRSS) of spinodally decomposed Fe-Cr alloys, and the internal stress generated by the lattice constant mismatch is a dominant mechanism. These findings are very useful for simplifying the analysis of the mechanism of material strength change due to the spinodal decomposition. Particularly in the analysis using the DD simulations, the required computational effort for simulating the dislocation behavior is greatly reduced by taking into account only the internal stress without the atomistic dislocation core influence. read less Y. Dai et al., “Nucleation of Cr precipitates in Fe–Cr alloy under irradiation,” Computational Materials Science. 2015. link Times cited: 13 W. Setyawan, A. P. Selby, N. Juslin, R. Stoller, B. Wirth, and R. Kurtz, “Cascade morphology transition in bcc metals,” Journal of Physics: Condensed Matter. 2014. link Times cited: 44 Abstract: Energetic atom collisions in solids induce shockwaves with c… read more Abstract: Energetic atom collisions in solids induce shockwaves with complex morphologies. In this paper, we establish the existence of a morphological transition in such cascades. The order parameter of the morphology is defined as the exponent, b, in the defect production curve as a function of cascade energy . Response of different bcc metals can be compared in a consistent energy domain when the energy is normalized by the transition energy, μ, between the high- and the low-energy regime. Using Cr, Fe, Mo and W data, an empirical formula of μ as a function of displacement threshold energy, Ed, is presented for bcc metals. read less A. Karavaev, P. Chirkov, R. M. Kichigin, and V. Dremov, “Atomistic simulation of hardening in bcc iron-based alloys caused by nanoprecipitates,” Computational Materials Science. 2023. link Times cited: 1 M. Tikhonchev, “MD simulation of vacancy and interstitial diffusion in FeCr alloy,” Physica Scripta. 2023. link Times cited: 1 Abstract: The diffusion mobility of iron and chromium atoms in Fe-9%Cr… read more Abstract: The diffusion mobility of iron and chromium atoms in Fe-9%Cr and Fe-20%Cr alloys for temperature up to 1000 K has been studied by molecular dynamics simulation. Both vacancy and interstitial migration of atoms has been considered. Corresponding diffusion coefficients of iron and chromium atoms, as well as the diffusion coefficients of a vacancy and self-interstitial configuration, have been evaluated. The values obtained for the vacancy diffusion satisfactory agree with experimental results taken from the literature. read less N. Kvashin, D. Terentyev, A. Serra, and N. Anento, “Effect of irradiation defects on the plastic slip of 112 grain boundary: Atomic scale study,” Computational Materials Science. 2022. link Times cited: 0 L. Wei, F. Zhou, S. Wang, W. Hao, Y. Liu, and J. Zhu, “Description of crystal defect properties in BCC Cr with extended Finnis–Sinclair potential,” Multidiscipline Modeling in Materials and Structures. 2022. link Times cited: 0 Abstract: PurposeThe purpose of this study is to propose extended pote… read more Abstract: PurposeThe purpose of this study is to propose extended potentials and investigate the applicability of extended Finnis–Sinclair (FS) potential to Cr with the unit cell structure of body-centered cubic (BCC Cr).Design/methodology/approachThe parameters of each potential are determined by fitting the elastic constants, cohesive energy and mono-vacancy formation energy. Furthermore, the ability of the extended FS potential to describe the crystal defect properties is tested. Finally, the applicability of reproducing the thermal properties of Cr is discussed.FindingsThe internal relationship between physical properties and potential function is revealed. The mathematical relationship between physical properties and potential function is derived in detail. The extended FS potential performs well in reproducing physical properties of BCC Cr, such as elastic constants, cohesive energy, surface energy and the properties of vacancy et al. Moreover, good agreement is obtained with the experimental data for predicting the melting point, specific heat and coefficient of thermal expansion.Originality/valueIn this study, new extended potentials are proposed. The extended FS potential is able to reproduce the physical and thermal properties of BCC Cr. Therefore, the new extended potential can be used to describe the crystal defect properties of BCC Cr. read less Z. Bai, X. Yan, J. Yin, and H. Hou, “Influence of Chromium Atoms on the Shear-Coupled Motion of [110] Symmetric Tilt Grain Boundary in α-Iron: Atomic Simulation,” Metals. 2022. link Times cited: 0 Abstract: Shear-coupled grain boundary motion (SCGBM) is an important … read more Abstract: Shear-coupled grain boundary motion (SCGBM) is an important mechanism of plastic deformation, especially in the cases of ultrafine-grained or nanocrystalline materials at low temperatures. Much research work has been focused on the geometric rules of coupling, the grain boundary migration mechanisms, or the temperature effect of SCGBM, but the effect of the alloy atoms is seldom involved. In this work, molecular dynamics (MD) simulations were carried out to examine the SCGBM of the Σ17[110](223) and Σ9[110](221) grain boundaries (GBs) in iron-chromium alloys containing from 1 at.% to 9 at.% Cr. A constant shear velocity corresponding to 10 m/s parallel to the boundary plane was applied to the models. Our simulation results indicate that the critical stress of GB migration reduces due to the addition of Cr atoms for the Σ17(223) GB. As for the Σ9(221) GB, sliding occurs simultaneously with coupling in the shear process when the atomic amount of Cr reaches 3%. This phenomenon was also observed in the Σ9(221) GB in pure Fe when the temperature was elevated to 300 K, which was studied in our previous simulation work. The existence of new structural units was demonstrated to be responsible for the sliding of the grain boundary. read less G. Bonny, A. Bakaev, and D. Terentyev, “The combined effect of carbon and chromium enrichment on 〈1 0 0〉 loop absorption in iron,” Computational Materials Science. 2022. link Times cited: 1 A. Bakaev et al., “Effect of radiation defects on the early stages of nanoindentation tests in bcc Fe and Fe-Cr alloys,” Computational Materials Science. 2022. link Times cited: 3 L. Malerba et al., “Multiscale modelling for fusion and fission materials: the M4F project,” Nuclear Materials and Energy. 2021. link Times cited: 15 F. Baras, Q. Bizot, A. Fourmont, S. L. Gallet, and O. Politano, “Mechanical activation of metallic powders and reactivity of activated nanocomposites: a molecular dynamics approach,” Applied Physics A. 2021. link Times cited: 1 P. Kuopanportti et al., “Interatomic Fe–Cr potential for modeling kinetics on Fe surfaces,” Computational Materials Science. 2021. link Times cited: 1 H. Kim et al., “From Chaos to Control: Programmable Crack Patterning with Molecular Order in Polymer Substrates,” Advanced Materials. 2021. link Times cited: 10 Abstract: Cracks are typically associated with the failure of material… read more Abstract: Cracks are typically associated with the failure of materials. However, cracks can also be used to create periodic patterns on the surfaces of materials, as observed in the skin of crocodiles and elephants. In synthetic materials, surface patterns are critical to micro‐ and nanoscale fabrication processes. Here, a strategy is presented that enables freely programmable patterns of cracks on the surface of a polymer and then uses these cracks to pattern other materials. Cracks form during deposition of a thin film metal on a liquid crystal polymer network (LCN) and follow the spatially patterned molecular order of the polymer. These patterned sub‐micrometer scale cracks have an order parameter of 0.98 ± 0.02 and form readily over centimeter‐scale areas on the flexible substrates. The patterning of the LCN enables cracks that turn corners, spiral azimuthally, or radiate from a point. Conductive inks can be filled into these oriented cracks, resulting in flexible, anisotropic, and transparent conductors. This materials‐based processing approach to patterning cracks enables unprecedented control of the orientation, length, width, and depth of the cracks without costly lithography methods. This approach promises new architectures of electronics, sensors, fluidics, optics, and other devices with micro‐ and nanoscale features. read less X. Liao et al., “Interatomic potentials and defect properties of Fe–Cr–Al alloys,” Journal of Nuclear Materials. 2020. link Times cited: 12 T. Fukuya and Y. Shibuta, “Machine learning approach to automated analysis of atomic configuration of molecular dynamics simulation,” Computational Materials Science. 2020. link Times cited: 12 M. I. Pascuet, G. Bonny, G. Monnet, and L. Malerba, “The effect on the mechanical response of Cr and Ni segregation on dislocation lines in bcc Fe,” Journal of Nuclear Materials. 2020. link Times cited: 3 E. Antillon and M. Ghazisaeidi, “Efficient determination of solid-state phase equilibrium with the multicell Monte Carlo method.,” Physical review. E. 2020. link Times cited: 5 Abstract: Building on our previously introduced multicell Monte Carlo … read more Abstract: Building on our previously introduced multicell Monte Carlo (MC)^{2} method for modeling phase coexistence, this paper provides important improvements for efficient determination of phase equilibria in solids. The (MC)^{2} method uses multiple cells, representing possible phases. Mass transfer between cells is modeled virtually by solving the mass balance equation after the composition of each cell is changed arbitrarily. However, searching for the minimum free energy during this process poses a practical problem. The solution to the mass balance equation is not unique away from equilibrium, and consequently the algorithm is in risk of getting trapped in nonequilibrium solutions. Therefore, a proper stopping condition for (MC)^{2} is currently lacking. In this work, we introduce a consistency check via a predictor-corrector algorithm to penalize solutions that do not satisfy a necessary condition for equivalence of chemical potentials and steer the system toward finding equilibrium. The most general acceptance criteria for (MC)^{2} is derived starting from the isothermal-isobaric Gibbs ensemble for mixtures. Using this ensemble, translational MC moves are added to include vibrational excitations as well as volume MC moves to ensure the condition of constant pressure and temperature entirely with a MC approach, without relying on any other method for relaxation of these degrees of freedom. As a proof of concept the method is applied to two binary alloys with miscibility gaps and a model quaternary alloy, using classical interatomic potentials. read less T. Krauss and S. Eich, “Development of a segregation model beyond McLean based on atomistic simulations,” Acta Materialia. 2020. link Times cited: 6 K. Ueno and Y. Shibuta, “Composition dependence of solid-liquid interfacial energy of Fe-Cr binary alloy from molecular dynamics simulations,” Computational Materials Science. 2019. link Times cited: 17 J. Zhang, W. Liu, P. Chen, H. He, C. He, and D. Yun, “Molecular dynamics study of the interaction between symmetric tilt Σ5(2 1 0) 〈0 0 1〉 grain boundary and radiation-induced point defects in Fe-9Cr alloy,” Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms. 2019. link Times cited: 7 K. Ueno and Y. Shibuta, “Semi-grand canonical Monte Carlo simulation for derivation of thermodynamic properties of binary alloy,” IOP Conference Series: Materials Science and Engineering. 2019. link Times cited: 3 Abstract: Semi-grand canonical Monte Carlo (SGCMC) simulations are per… read more Abstract: Semi-grand canonical Monte Carlo (SGCMC) simulations are performed to derive thermodynamic properties of binary alloy from atomistic-based simulations. Particularly, solidus and liquidus compositions are directly derived for Fe-Cr alloy described by two different EAM potentials. Although the SGCMC simulation can derive relationship between the free energy and composition at any temperature straightforwardly, partial phase diagram obtained from SGCMC simulations strongly depends on the choice of interatomic potential. read less G. Bonny, C. Domain, N. Castin, P. Olsson, and L. Malerba, “The impact of alloying elements on the precipitation stability and kinetics in iron based alloys: An atomistic study,” Computational Materials Science. 2019. link Times cited: 27 K. Ueno and Y. Shibuta, “Solute partition at solid-liquid interface of binary alloy from molecular dynamics simulation,” Materialia. 2018. link Times cited: 6 A. Bakaev, D. Terentyev, and E. Zhurkin, “Effect of Segregation of Ni and Cr at Dislocation Loops on Their Interaction with Gliding Dislocations in Irradiated Fe−Ni−Cr BCC Alloys,” Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques. 2018. link Times cited: 1 G. Bonny, A. Bakaev, P. Olsson, C. Domain, E. Zhurkin, and M. Posselt, “Interatomic potential to study the formation of NiCr clusters in high Cr ferritic steels,” Journal of Nuclear Materials. 2017. link Times cited: 17 M. Abu-Shams, W. Haider, and I. Shabib, “Evolution of displacement cascades in Fe–Cr structures with different [001] tilt grain boundaries,” Radiation Effects and Defects in Solids. 2017. link Times cited: 3 Abstract: ABSTRACT Reduced-activation ferritic/martensitic steels of C… read more Abstract: ABSTRACT Reduced-activation ferritic/martensitic steels of Cr concentration between 2.25 and 12 wt% are candidate structural materials for next-generation nuclear reactors. In this study, molecular dynamics (MD) simulation is used to generate the displacement cascades in Fe–Cr structures with different Cr concentrations by using different primary knock-on atom (PKA) energies between 2 and 10 keV. A concentration-dependent model potential has been used to describe the interactions between Fe and Cr. Single crystals (SCs) of three different coordinate bases (e.g. [310], [510], and [530]) and bi-crystal (BC) structures with three different [001] tilt grain boundaries (GBs) (e.g. Σ5, Σ13, and Σ17) have been simulated. The Wigner–Seitz cell criterion has been used to identify the produced Frenkel pairs. The results show a marked difference between collisions observed in SCs and those in BC structures. The numbers of vacancies and interstitials are found to be significantly higher in BC structures than those found in SCs. The number of point defects exhibits a power relationship with the PKA energies; however, the Cr concentration does not seem to have any influence on the number of survived point defects. In BC models, a large fraction of the total survived point defects (between 59% and 93%) tends accumulate at the GBs, which seem to trap the generated point defects. The BC structure with Σ17 GB is found to trap more defects than Σ5 and Σ13 GBs. The defect trapping is found to be dictated by the crystallographic parameters of the GBs. For all studied GBs, self-interstitial atoms (SIAs) are easily trapped within the GB region than vacancies. An analysis of defect composition reveals an enrichment of Cr in SIAs, and in BC cases, more than half of the Cr-SIAs are found to be located within the GB region. read less M. Vairavel, B. Sundaravel, and B. Panigrahi, “Lattice location of O18 in ion implanted Fe crystals by Rutherford backscattering spectrometry, channeling and nuclear reaction analysis,” Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms. 2016. link Times cited: 3 I. Dopico, P. Castrillo, and I. Martín-Bragado, “Quasi-atomistic modeling of the microstructure evolution in binary alloys and its application to the FeCr case,” Acta Materialia. 2015. link Times cited: 16 D. Costa, G. Adjanor, C. Becquart, P. Olsson, and C. Domain, “Vacancy migration energy dependence on local chemical environment in Fe-Cr alloys : A Density Functional Theory study,” Journal of Nuclear Materials. 2014. link Times cited: 16 J. Emo, C. Pareige, S. Saillet, C. Domain, and P. Pareige, “Kinetics of secondary phase precipitation during spinodal decomposition in duplex stainless steels: A kinetic Monte Carlo model – Comparison with atom probe tomography experiments,” Journal of Nuclear Materials. 2014. link Times cited: 25 L. Malerba et al., “Microchemical effects in irradiated Fe–Cr alloys as revealed by atomistic simulation,” Journal of Nuclear Materials. 2013. link Times cited: 35 D. Terentyev, G. Bonny, C. Domain, G. Monnet, and L. Malerba, “Mechanisms of radiation strengthening in Fe–Cr alloys as revealed by atomistic studies,” Journal of Nuclear Materials. 2013. link Times cited: 52 D. Schwen, E. Martínez, and A. Caro, “On the analytic calculation of critical size for alpha prime precipitation in FeCr,” Journal of Nuclear Materials. 2013. link Times cited: 14 M. Levesque, E. Mart’inez, C. Fu, M. Nastar, and F. Soisson, “Simple concentration-dependent pair interaction model for large-scale simulations of Fe-Cr alloys,” Physical Review B. 2011. link Times cited: 57 Abstract: This work is motivated by the need for large-scale simulatio… read more Abstract: This work is motivated by the need for large-scale simulations to extract physical information on the iron-chromium system that is a binary model alloy for ferritic steels used or proposed in many nuclear applications. From first-principles calculations and the experimental critical temperature we build a new energetic rigid lattice model based on pair interactions with concentration and temperature dependence. Density functional theory calculations in both norm-conserving and projector augmented-wave approaches have been performed. A thorough comparison of these two different ab initio techniques leads to a robust parametrization of the Fe-Cr Hamiltonian. Mean-field approximations and Monte Carlo calculations are then used to account for temperature effects. The predictions of the model are in agreement with the most recent phase diagram at all temperatures and compositions. The solubility of Cr in Fe below 700 K remains in the range of about 6 to 12%. It reproduces the transition between the ordering and demixing tendency and the spinodal decomposition limits are also in agreement with the values given in the literature. read less G. Bonny, D. Terentyev, and L. Malerba, “Interaction of screw and edge dislocations with chromium precipitates in ferritic iron: An atomistic study,” Journal of Nuclear Materials. 2011. link Times cited: 21 Y. Zhang, Z. Xiao, and X. Bai, “Effect of Cr Concentration on ½<111> to <100> Dislocation Loop Transformation in Fe-Cr alloys,” Journal of Nuclear Materials. 2021. link Times cited: 10 J. Zhang, H. He, W. Liu, L. Kang, D. Yun, and P. Chen, “Effects of grain boundaries on the radiation-induced defects evolution in BCC Fe–Cr alloy: A molecular dynamics study,” Nuclear materials and energy. 2020. link Times cited: 11 G. Bonny, A. Bakaev, D. Terentyev, E. Zhurkin, and M. Posselt, “Atomistic study of the hardening of ferritic iron by Ni-Cr decorated dislocation loops,” Journal of Nuclear Materials. 2018. link Times cited: 16 R. Khanna and V. Sahajwalla, “Atomistic Simulations of Properties and Phenomena at High Temperatures.” 2014. link Times cited: 3 J. Ke and A. Jokisaari, “Effects of Aluminum and Molybdenum on the Phase Stability of Iron-Chromium Alloys: A First-Principles Study,” JOM. 2023. link Times cited: 1 Y. Lei et al., “An Embedded-Atom Method Potential for studying the properties of Fe-Pb solid-liquid interface,” Journal of Nuclear Materials. 2022. link Times cited: 1 N. Castin et al., “Advanced atomistic models for radiation damage in Fe-based alloys: Contributions and future perspectives from artificial neural networks,” Computational Materials Science. 2018. link Times cited: 21 T. Klaver, E. Río, G. Bonny, S. Eich, and A. Caro, “Inconsistencies in modelling interstitials in FeCr with empirical potentials,” Computational Materials Science. 2016. link Times cited: 6 S. Eich, D. Beinke, and G. Schmitz, “Embedded-atom potential for an accurate thermodynamic description of the iron–chromium system,” Computational Materials Science. 2015. link Times cited: 24 N. Castin, J. R. Fernández, and R. Pasianot, “Predicting vacancy migration energies in lattice-free environments using artificial neural networks,” Computational Materials Science. 2014. link Times cited: 23 L. Malerba, “Large Scale Integrated Materials Modeling Programs.” 2020. link Times cited: 2 С. Волегов, Р. М. Герасимов, and Р. П. Давлятшин, “MODELS OF MOLECULAR DYNAMICS: A REVIEW OF EAM-POTENTIALS. PART 2. POTENTIALS FOR MULTI-COMPONENT SYSTEMS.” 2018. link Times cited: 1 Abstract: Получена: 18 мая 2018 г. Принята: 25 июня 2018 г. Опубликова… read more Abstract: Получена: 18 мая 2018 г. Принята: 25 июня 2018 г. Опубликована: 29 июня 2018 г. В статье представлена вторая часть обзора современных подходов и работ, посвященных построению потенциалов межатомного взаимодействия с использованием методологии погруженного атома (EAM-потенциалы). Эта часть обзора посвящена одной из наиболее остро стоящих проблем в молекулярной динамике – вопросам построения потенциалов, которые были бы пригодны для описания структуры и физико-механических свойств многокомпонентных (в первую очередь – бинарных и тернарных) материалов. Отмечены первые работы, в которых предлагались подходы к построению функций перекрестного взаимодействия для сплавов никеля и меди – как с использованием методологии EAM, так и несколько отличающийся по процедуре построения потенциал типа Финисса-Синклера. Рассматриваются работы, в которых производится сопоставление различных подходов к построению потенциалов, а также к процедуре идентификации их параметров на примере одних и тех же многокомпонентных систем (типа Al-Ni или Cu-Au). Кроме того, особый интерес представляют некоторые тернарные системы, например Fe–Ni–Cr, W–H– He или U–Mo–Xe, которые являются ключевыми для материалов атомной энергетики и которые в последние годы активно изучаются как возможные материалы для использования в термоядерных ректорах. Приведены примеры работ, в которых предлагаются и исследуются потенциалы для описания многокомпонентных систем, пригодных для использования в аэрокосмической промышленности и изготовленных прежде всего на основе никеля. Рассмотрены результаты исследований различных интерметаллических соединений, отмечены работы, в которых при помощи построенного EAM потенциала удалось количественно точно описать фазовые диаграммы соединений и вычислить характеристики фазовых переходов. 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 N. Kvashin, N. Anento, D. Terentyev, A. Bakaev, and A. Serra, “Interaction of a dislocation pileup with 332 tilt grain boundary in bcc metals studied by MD simulations,” Physical Review Materials. 2021. link Times cited: 7 Abstract: The sustainability and capacity of macroscopic deformation b… read more Abstract: The sustainability and capacity of macroscopic deformation by polycrystalline metals and metallic alloys is controlled by the propagation of dislocation-mediated slip through grains. In this paper, the interaction of a pileup of $1/2\ensuremath{\langle}111\ensuremath{\rangle}$ dislocations with the ${332}$ tilt grain boundary (GB) is studied as a function of temperature in three bcc metals: iron (Fe), chromium (Cr), and tungsten (W). The interaction results in the transformation of the crystal dislocation into GB dislocations. The ${332}$ tilt GB absorbs the crystal dislocations of the pileup, neither the transmission nor reflection of dislocations was observed. The reaction product at the GB is determined by the crystallography of the GB and the features of the crystal dislocations involved, specifically, the orientation of the Burgers vector and the glide plane of the dislocation. In general, the decomposition results in the formation of a sessile GB dislocation with a riser that facets the GB and several elementary disconnections that glide away. In some cases, the riser increases its length with the number of dislocations absorbed and a new asymmetrical grain boundary of ${112}/{110}$ type is created. For a given external shear stress, the number of dislocations absorbed depends on the orientation of the Burgers vector, glide plane of the pileup, and material. read less V. E. Porsev, A. Ulyanov, and G. Dorofeev, “Structural-Phase Transformations and Short-Range Order Evolution in the Fe–Cr System during Mechanical Alloying,” Physics of the Solid State. 2020. link Times cited: 0 V. E. Porsev, A. Ulyanov, and G. Dorofeev, “Atomic Redistribution in a Fe-Cr System in the Course of Mechanical Alloying and Subsequent Annealing,” Metallurgical and Materials Transactions A. 2019. link Times cited: 1 I. Svistunov and A. S. Kolokol, “An analysis of interatomic potentials for vacancy diffusion simulation in concentrated Fe-Cr alloys.” 2018. link Times cited: 1 Abstract: В данном исследовании проверялась корректность работы трех м… read more Abstract: В данном исследовании проверялась корректность работы трех межатомных потенциалов взаимодействия, доступных в научной литературе, в молекулярно-динамическом моделировании вакансионной диффузии в концентрированных сплавах Fe–Cr. Проведенная работа была необходима для дальнейшего детального исследования механизма вакансионной диффузии в данных сплавах с содержанием хрома 5–25 ат.% в температурном диапазоне 600–1000 К. Анализ был выполнен на моделях сплава с содержанием хрома 10, 20, 50 ат.%. Рассмотрение модели сплава с 50 ат.% хрома было необходимо для дальнейшего исследования диффузионных процессов в обогащенных хромом преципитатах данных сплавов. Для всех потенциалов были рассчитаны и проанализированы энергии формирования вакансии в сплавах и диффузионные подвижности атомов железа и хрома через искусственно созданную одиночную вакансию. В качестве основной характеристики для анализа подвижностей атомов была выбрана временная зависимость их среднеквадратичного смещения. Моделирование энергий формирования вакансий не выявило качественных различий между исследуемыми моделями потенциалов. Проведенное исследование атомных подвижностей показало плохое воспроизведение диффузии вакансии в исследуемых сплавах концентрационно-зависимой моделью (CDM), которая сильно занижала подвижность атомов хрома через вакансию во всем исследуемом диапазоне температур и концентраций хрома. Установлено, что двусвязная модель потенциала (2BM) в своей оригинальной и модифицированной версии подобных недостатков не имеет. Это позволяет использовать эти потенциалы в моделированиях вакансионного механизма диффузии в исследуемых сплавах. Для обоих 2BM-потенциалов была зафиксирована существенная зависимость соотношения подвижностей хрома и железа от температуры и содержания хрома в сплавах. Количественные данные коэффициентов диффузии атомов, полученные этими потенциалами, также существенно различаются. read less G. Bonny, N. Castin, M. I. Pascuet, Y. Çelik, and G. Cruz, “Exact mean field concept to compute defect energetics in random alloys on rigid lattices,” Physica B-condensed Matter. 2017. link Times cited: 4 A. Bakaev, A. Bakaev, D. Terentyev, and E. Zhurkin, “Atomistic simulation of the segregation of alloying elements close to radiation-induced defects in irradiated Fe–Cr–Ni BCC alloys,” Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques. 2017. link Times cited: 4 G. Bonny et al., “Density functional theory-based cluster expansion to simulate thermal annealing in FeCrW alloys,” Philosophical Magazine. 2017. link Times cited: 10 Abstract: In this work, we develop a rigid lattice cluster expansion a… read more Abstract: In this work, we develop a rigid lattice cluster expansion as an ultimate goal to track the micro-structural evolution of Eurofer steel under neutron irradiation. The fact that all (defect) structures are mapped upon a rigid lattice allows a simplified computation and fitting procedure, thus enabling alloys of large chemical complexity to be modelled. As a first step towards the chemical complexity of Eurofer steels, we develop a cluster expansion (CE) for the FeCrW-vacancy system based on density functional theory (DFT) calculations in the dilute alloy limit. The DFT calculations suggest that only CrW clusters containing vacancies are stabilised. The cluster expansion was used to simulate thermal annealing in Fe–20Cr–xW alloys at 773 K. It is found that the addition of W to the alloy results in a non-linear decrease in the precipitation kinetics. The CE was found suitable to describe the energetics of the FeCrW-vacancy system in the Fe-rich limit. read less J. Cecilia, A. Hernández-Díaz, P. Castrillo, and J. Jiménez‐Alonso, “Enhanced calculation of eigen-stress field and elastic energy in atomistic interdiffusion of alloys,” Comput. Phys. Commun. 2017. link Times cited: 3 O. I. Gorbatov, O. I. Gorbatov, Y. Gornostyrev, P. Korzhavyi, and A. Ruban, “Ab initio modeling of decomposition in iron based alloys,” Physics of Metals and Metallography. 2016. link Times cited: 11 T. Kumagai, K. Nakamura, S. Yamada, and T. Ohnuma, “Simple bond-order-type interatomic potential for an intermixed Fe-Cr-C system of metallic and covalent bondings in heat-resistant ferritic steels,” Journal of Applied Physics. 2014. link Times cited: 1 Abstract: It is known that M23C6(M = Cr/Fe) behavior in heat-resistant… read more Abstract: It is known that M23C6(M = Cr/Fe) behavior in heat-resistant ferritic steels affects the strength of the material at high temperature. The ability to garner direct information regarding the atomic motion using classical molecular dynamics simulations is useful for investigating the M23C6 behavior in heat-resistant ferritic steels. For such classical molecular dynamics calculations, a suitable interatomic potential is needed. To satisfy this requirement, an empirical bond-order-type interatomic potential for Fe-Cr-C systems was developed because the three main elements to simulate the M23C6 behavior in heat-resistant ferritic steels are Fe, Cr, and C. The angular-dependent term, which applies only in non-metallic systems, was determined based on the similarity between a Finnis-Sinclair-type embedded-atom-method interatomic potential and a Tersoff-type bond-order potential. The potential parameters were determined such that the material properties of Fe-Cr-C systems were reproduced. These properties include... read less G. Bonny, N. Castin, and D. Terentyev, “Interatomic potential for studying ageing under irradiation in stainless steels: the FeNiCr model alloy,” Modelling and Simulation in Materials Science and Engineering. 2013. link Times cited: 215 Abstract: The degradation of austenitic stainless steels in a radiatio… read more Abstract: The degradation of austenitic stainless steels in a radiation environment is a known problem for the in-core components of nuclear light water reactors. For a better understanding of the prevailing mechanisms responsible for the materials' degradation, large-scale atomistic simulations are desirable. In this framework and as a follow-up on Bonny et al (2011 Modelling Simul. Mater. Sci. Eng. 19 085008), we developed an embedded atom method type interatomic potential for the ternary FeNiCr system to model the production and evolution of radiation defects. Special attention has been drawn to the Fe10Ni20Cr alloy, whose properties were ensured to be close to those of 316L austenitic stainless steels. The potential is extensively benchmarked against density functional theory calculations and the potential developed in our earlier work. As a first validation, the potential is used in AKMC simulations to simulate thermal annealing experiments in order to determine the self-diffusion coefficients of the components in FeNiCr alloys around the Fe10Ni20Cr composition. The results from these simulations are consistent with experiments, i.e., DCr > DNi > DFe. read less G. Bonny, N. Castin, J. Bullens, A. Bakaev, T. Klaver, and D. Terentyev, “On the mobility of vacancy clusters in reduced activation steels: an atomistic study in the Fe–Cr–W model alloy,” Journal of Physics: Condensed Matter. 2013. link Times cited: 29 Abstract: Reduced activation steels are considered as structural mater… read more Abstract: Reduced activation steels are considered as structural materials for future fusion reactors. Besides iron and the main alloying element chromium, these steels contain other minor alloying elements, typically tungsten, vanadium and tantalum. In this work we study the impact of chromium and tungsten, being major alloying elements of ferritic Fe–Cr–W-based steels, on the stability and mobility of vacancy defects, typically formed under irradiation in collision cascades. For this purpose, we perform ab initio calculations, develop a many-body interatomic potential (EAM formalism) for large-scale calculations, validate the potential and apply it using an atomistic kinetic Monte Carlo method to characterize the lifetime and diffusivity of vacancy clusters. To distinguish the role of Cr and W we perform atomistic kinetic Monte Carlo simulations in Fe–Cr, Fe–W and Fe–Cr–W alloys. Within the limitation of transferability of the potentials it is found that both Cr and W enhance the diffusivity of vacancy clusters, while only W strongly reduces their lifetime. The cluster lifetime reduction increases with W concentration and saturates at about 1–2 at.%. The obtained results imply that W acts as an efficient ‘breaker’ of small migrating vacancy clusters and therefore the short-term annealing process of cascade debris is modified by the presence of W, even in small concentrations. read less D. Terentyev, N. Castin, and C. Ortiz, “Correlated recombination and annealing of point defects in dilute and concentrated Fe–Cr alloys,” Journal of Physics: Condensed Matter. 2012. link Times cited: 12 Abstract: In this work, we present a comprehensive combined modelling … read more Abstract: In this work, we present a comprehensive combined modelling approach to study the annealing of lattice defects in dilute and concentrated metallic alloys. The developed approach consists in the combination of molecular dynamics, atomistic kinetic Monte Carlo (AKMC) and mean field rate theory methods, linked at appropriate time and space scales. For the first time, the AKMC tool has been designed to model the evolution of point defects (both vacancies and self-interstitial atoms) in random concentrated alloys, taking into account the influence of lattice distortion on the local migration energy barrier due to the mutual interaction of point defects and solutes. Good accuracy and outstanding speed of calculations has been achieved by introducing the artificial neural network regression as an engine of the AKMC applied to calculate migration barriers for mobile defects. The developed method was applied to study correlated recombination in bcc Fe and random Fe–Cr alloys, aiming at the reproduction of a set of experimental studies after electron irradiation. The obtained results agree well with the available experimental data, implying that the developed modelling procedure correctly captures the undergoing physical process. read less Y. Wang and M. Hou, “Ordering of bimetallic nanoalloys predicted from bulk alloy phase diagrams,” Journal of Physical Chemistry C. 2012. link Times cited: 31 Abstract: The Metropolis Monte Carlo method is used to demonstrate the… read more Abstract: The Metropolis Monte Carlo method is used to demonstrate the relationship between the bulk phase diagram of alloys with limited miscibility and the equilibrium configurations of nanoparticles. Using the Au–Pt system as a case study, an embedded atom potential is parametrized so as to match the phase diagram exactly. The smooth temperature dependence of the short-range order parameter is shown correlated with an onion-like configuration intermediate between solid solution and phase separated states. read less G. Bonny, D. Terentyev, R. Pasianot, S. Poncé, and A. Bakaev, “Interatomic potential to study plasticity in stainless steels: the FeNiCr model alloy,” Modelling and Simulation in Materials Science and Engineering. 2011. link Times cited: 180 Abstract: Austenitic stainless steels are commonly used materials for … read more Abstract: Austenitic stainless steels are commonly used materials for in-core components of nuclear light water reactors. In service, such components are exposed to harsh conditions: intense neutron irradiation, mechanical and thermal stresses, and aggressive corrosion environment which all contribute to the components' degradation. For a better understanding of the prevailing mechanisms responsible for the materials degradation, large-scale atomistic simulations are desirable. In this framework we developed an embedded atom method type interatomic potential for the ternary FeNiCr system to model movement of dislocations and their interaction with radiation defects. Special attention has been drawn to the Fe–10Ni–20Cr alloy, whose properties were ensured to be close to those of 316L austenitic stainless steel. In particular, the stacking fault energy and elastic constants are well reproduced. The fcc phase for the Fe–10Ni–20Cr random alloy was proven to be stable in the temperature range 0–900 K and under shear strain up to 5%. For the same alloy the stable glide of screw dislocations and stability of Frank loops was confirmed. read less E. Martínez, C. Fu, M. Levesque, M. Nastar, and F. Soisson, “Simulations of Decomposition Kinetics of Fe-Cr Solid Solutions during Thermal Aging,” Solid State Phenomena. 2011. link Times cited: 63 Abstract: The decomposition of Fe-Cr solid solutions during thermal ag… read more Abstract: The decomposition of Fe-Cr solid solutions during thermal aging is modeled by Atomistic Kinetic Monte Carlo (AKMC) simulations, using a rigid lattice approximation with composition dependant pair interactions that can reproduce the change of sign of the mixing energy with the alloy composition. The interactions are fitted on ab initio mixing energies and on the experimental phase diagram, as well as on the migration barriers in iron and chromium rich phases. Simulated kinetics is compared with 3D atom probe and neutron scattering experiments. read less X. Lian et al., “Evolution of Thermally‐Induced Microstructural Defects in the Fe‐9Cr Alloy,” physica status solidi (a). 2018. link Times cited: 5 Abstract: The purpose of the study detailed in this paper is to invest… read more Abstract: The purpose of the study detailed in this paper is to investigate the evolution of microstructural defects in the Fe‐9Cr binary alloy induced by isochronal annealing from 373 to 1223 K. Positron annihilation lifetime spectroscopy (PALS), Doppler broadening spectroscopy (DBS), positron annihilation lifetime calculation, and transmission electron microscope (TEM) are used to analyze and characterize the change of defect concentration, defect type and the micro‐morphology in the Fe‐9Cr alloy as a function of the annealing temperature. The experimental results showed that, a large number of vacancies and dislocations were found to exist in the untreated Fe‐9Cr alloy. The monovacancy (186.2 ps) in the Fe‐9Cr alloy migrated during annealing from room temperature to 573 K. The annealing temperature at 773 K produce aggregation of dislocations and the formation of dislocation networks, as well as their heterogeneous distribution. When the temperature is further increased to 1073 K, most of the vacancies and dislocations are recovered and a bcc‐fcc phase transmition occurred in Fe‐9Cr model alloy. The dislocation density is continuous decreased with the increase of annealing temperature, the recovery is obvious from 773 K annealing to 1073 K annealing in Fe‐9Cr alloy. read less M. Park, K. C. Alexander, and C. Schuh, “Diffusion of tungsten in chromium: Experiments and atomistic modeling,” Journal of Alloys and Compounds. 2014. link Times cited: 12
Funding	Not available

Short KIM ID The unique KIM identifier code.	SM_237089298463_001
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.	Sim_LAMMPS_EAM_BonnyPasianotTerentyev_2011_FeCr__SM_237089298463_001
DOI	10.25950/d82afb9f https://doi.org/10.25950/d82afb9f https://commons.datacite.org/doi.org/10.25950/d82afb9f
KIM Item Type	Simulator Model
KIM API Version	2.2
Simulator Name The name of the simulator as defined in kimspec.edn.	LAMMPS
Potential Type	eam
Simulator Potential	hybrid/overlay
Run Compatibility	portable-models
Programming Language(s) The programming languages used in the code and the percentage of the code written in each one.	100.00% F#

Previous Version	Sim_LAMMPS_EAM_BonnyPasianotTerentyev_2011_FeCr__SM_237089298463_000

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Grade	Name	Category	Brief Description	Full Results	Aux File(s)
P All elements claimed by model are supported in at least one of the tested configurations.	vc-species-supported-as-stated	mandatory	The model supports all species it claims to support; see full description.	Results	Files
P Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.	vc-periodicity-support	mandatory	Periodic boundary conditions are handled correctly; see full description.	Results	Files
P Model energy has permutation symmetry for all configurations the model was able to compute.	vc-permutation-symmetry	mandatory	Total energy and forces are unchanged when swapping atoms of the same species; see full description.	Results	Files
B The letter grade B was assigned because the normalized error in the computation was 8.75499e-08 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.	vc-forces-numerical-derivative	consistency	Forces computed by the model agree with numerical derivatives of the energy; see full description.	Results	Files
F The model is C^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
N/A Unable to perform verification check due to an error.	vc-memory-leak	informational	The model code does not have memory leaks (i.e. it releases all allocated memory at the end); see full description.	Results	Files
N/A Thread safety can only be checked for KIM Models.	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

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: Cr

Species: Fe

Cohesive Energy Graph

This graph shows the cohesive energy versus volume-per-atom for the current mode for four mono-atomic cubic phases (body-centered cubic (bcc), face-centered cubic (fcc), simple cubic (sc), and diamond). The curve with the lowest minimum is the ground state of the crystal if stable. (The crystal structure is enforced in these calculations, so the phase may not be stable.) Graphs are generated for each species supported by the model.

Species: Fe

Species: Cr

Diamond Lattice Constant

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

Species: Fe

Species: Cr

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: Cr

Species: Fe

FCC Lattice Constant

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

Species: Cr

Species: Fe

FCC Stacking Fault Energies

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

(No matching species)

FCC Surface Energies

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

(No matching species)

SC Lattice Constant

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

Species: Cr

Species: Fe

Cubic Crystal Basic Properties Table

Species: Cr

Species: Fe

Tests

Disclaimer From Model Developer

The tabulated values of the s-embedding functions and their derivatives may deviate significantly from the corresponding analytical functions as the s-density approaches zero. See Appendix 1 of the Philosophical Magazine article and Appendix C of the technical report for more information.

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 Cr v004	view	38332
Cohesive energy versus lattice constant curve for bcc Fe v004	view	43186
Cohesive energy versus lattice constant curve for diamond Cr v004	view	41017
Cohesive energy versus lattice constant curve for diamond Fe v004	view	40023
Cohesive energy versus lattice constant curve for fcc Cr v004	view	48737
Cohesive energy versus lattice constant curve for fcc Fe v004	view	41952
Cohesive energy versus lattice constant curve for sc Cr v004	view	50430
Cohesive energy versus lattice constant curve for sc Fe v004	view	47671

ElasticConstantsCrystal__TD_034002468289_000

Elastic constants for arbitrary crystals at zero temperature and pressure v000

Creators:
Contributor: ilia
Publication Year: 2024
DOI: https://doi.org/10.25950/888f9943

Computes the elastic constants for an arbitrary crystal. A robust computational protocol is used, attempting multiple methods and step sizes to achieve an acceptably low error in numerical differentiation and deviation from material symmetry. The crystal structure is specified using the AFLOW prototype designation as part of the Crystal Genome testing framework. In addition, the distance from the obtained elasticity tensor to the nearest isotropic tensor is computed.

Test	Test Results	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Elastic constants for CrFe in AFLOW crystal prototype A2B_cF24_227_c_b at zero temperature and pressure v000		view	9494394

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 Cr at zero temperature v006	view	190572
Elastic constants for bcc Fe at zero temperature v006	view	195566
Elastic constants for diamond Cr at zero temperature v001	view	388710
Elastic constants for diamond Fe at zero temperature v001	view	711656
Elastic constants for fcc Cr at zero temperature v006	view	279764
Elastic constants for fcc Fe at zero temperature v006	view	170166
Elastic constants for sc Cr at zero temperature v006	view	184273
Elastic constants for sc Fe at zero temperature v006	view	212227

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 CrFe in AFLOW crystal prototype A2B_cF24_227_c_b v002	view	276701
Equilibrium crystal structure and energy for CrFe in AFLOW crystal prototype A3B_cP4_221_c_a v002	view	128983
Equilibrium crystal structure and energy for Cr in AFLOW crystal prototype A_cF4_225_a v002	view	127732
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_cF4_225_a v002	view	269966
Equilibrium crystal structure and energy for Cr in AFLOW crystal prototype A_cI2_229_a v002	view	64345
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_cI2_229_a v002	view	115731
Equilibrium crystal structure and energy for Cr in AFLOW crystal prototype A_cP8_223_ac v002	view	307660
Equilibrium crystal structure and energy for Cr in AFLOW crystal prototype A_hP2_194_c v002	view	125155
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_hP2_194_c v002	view	80142
Equilibrium crystal structure and energy for Cr in AFLOW crystal prototype A_tP28_136_f2ij v002	view	472652
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_tP28_136_f2ij v002	view	232346
Equilibrium crystal structure and energy for CrFe in AFLOW crystal prototype AB2_cF24_227_a_d v002	view	833679
Equilibrium crystal structure and energy for CrFe in AFLOW crystal prototype AB3_cF16_225_a_bc v002	view	279537
Equilibrium crystal structure and energy for CrFe in AFLOW crystal prototype AB3_cP4_221_a_c v002	view	132296

GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle__TD_410381120771_003

Relaxed energy as a function of tilt angle for a symmetric tilt grain boundary within a cubic crystal v003

Creators:
Contributor: brunnels
Publication Year: 2022
DOI: https://doi.org/10.25950/2c59c9d6

Computes grain boundary energy for a range of tilt angles given a crystal structure, tilt axis, and material.

Test	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Relaxed energy as a function of tilt angle for a 100 symmetric tilt grain boundary in bcc Fe v001	view	5308926
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in bcc Fe v001	view	14902818
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in bcc Fe v001	view	7065559
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in bcc Fe v001	view	26745779
Relaxed energy as a function of tilt angle for a 100 symmetric tilt grain boundary in fcc Fe v001	view	21131699
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in fcc Fe v001	view	193071420
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in fcc Fe v001	view	142521643
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in fcc Fe v001	view	474387953

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 Cr v007	view	596986
Equilibrium zero-temperature lattice constant for bcc Fe v007	view	370894
Equilibrium zero-temperature lattice constant for diamond Cr v007	view	267090
Equilibrium zero-temperature lattice constant for diamond Fe v007	view	172225
Equilibrium zero-temperature lattice constant for fcc Cr v007	view	354569
Equilibrium zero-temperature lattice constant for fcc Fe v007	view	231422
Equilibrium zero-temperature lattice constant for sc Cr v007	view	243180
Equilibrium zero-temperature lattice constant for sc Fe v007	view	216401

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 Cr v005		view	4256835
Equilibrium lattice constants for hcp Fe v005		view	3838679

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 Cr at 293.15 K under a pressure of 0 MPa v002		view	408489
Linear thermal expansion coefficient of bcc Fe at 293.15 K under a pressure of 0 MPa v002		view	445675

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 Cr v004		view	3782006
Broken-bond fit of high-symmetry surface energies in bcc Fe v004		view	3966704

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 Cr		view	41454894
Monovacancy formation energy and relaxation volume for bcc Fe		view	33225668

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 Cr		view	50988012
Vacancy formation and migration energy for bcc Fe		view	121878222

Errors

ElasticConstantsHexagonal__TD_612503193866_004

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

EquilibriumCrystalStructure__TD_457028483760_002

Test	Error Categories	Link to Error page
Equilibrium crystal structure and energy for CrFe in AFLOW crystal prototype A3B_tI8_139_ad_b v002	other	view
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_tP1_123_a v002	other	view

SurfaceEnergyCubicCrystalBrokenBondFit__TD_955413365818_004

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

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Verification Check	Error Categories	Link to Error page
MemoryLeak__VC_561022993723_004	other	view

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