LAMMPS ADP potential for the Zr-Nb system developed by Smirnova and Starikov (2017) v000

Daria Smirnova; Sergey Starikov

doi:10.25950/8f9857b3

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Sim_LAMMPS_ADP_SmirnovaStarikov_2017_ZrNb__SM_937902197407_000

Interatomic potential for Niobium (Nb), Zirconium (Zr).
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Title A single sentence description.	LAMMPS ADP potential for the Zr-Nb system developed by Smirnova and Starikov (2017) v000
Description	We report a new attempt to study properties of Zr-Nb structural alloys. For this purpose we constructed an angular-dependent many-body interatomic potential. The potential functions were fitted towards the ab initio data computed for a large set of reference structures. The fitting procedure is described, and its accuracy is discussed. We show that the structure and properties of all Nb and Zr phases existing in the Zr-Nb binary system are reproduced with good accuracy. The interatomic potential is appropriate for study of the high-pressure hexagonal ω-phase of Zr. We also estimated characteristics of the point defects in α-Zr, β-Zr and Nb; results are proven to correlate with the existing experimental and theoretical data. In case of α-Zr the model reveals anisotropy of the vacancy diffusion, in agreement with previous calculations and experiments. The potential provides an opportunity for simulation of Zr-Nb alloys based on α-Zr and β-Zr. This conclusion is illustrated by the results obtained for the alloys with different niobium concentrations: up to 7% in case of hcp alloys and up to 50% for bcc alloys.
Species The supported atomic species.	Nb, Zr
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	None
Content Origin	NIST IPRP (https://www.ctcms.nist.gov/potentials/Zr.html#Zr-Nb)

Contributor	Ronald E. Miller
Maintainer	Ronald E. Miller
Developer	Daria Smirnova Sergey Starikov
Published on KIM	2019
How to Cite	This Simulator Model originally published in [1] is archived in OpenKIM [2-4]. [1] Smirnova DE, Starikov SV. An interatomic potential for simulation of Zr-Nb system. Computational Materials Science [Internet]. 2017Mar;129:259–72. Available from: https://doi.org/10.1016/j.commatsci.2016.12.016 doi:10.1016/j.commatsci.2016.12.016 — (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] Smirnova D, Starikov S. LAMMPS ADP potential for the Zr-Nb system developed by Smirnova and Starikov (2017) v000. OpenKIM; 2019. doi:10.25950/8f9857b3 [3] 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 [4] 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. 33 Citations (27 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 . M. Basaadat and M. Payami, “Elastic stiffness tensors of Zr–xNb alloy in the presence of defects: A molecular dynamics study,” International Journal of Modern Physics C. 2019. link Times cited: 3 Abstract: In a nuclear reactor, the Zr–[Formula: see text]Nb alloy, wh… read more Abstract: In a nuclear reactor, the Zr–[Formula: see text]Nb alloy, which is used as a structural material in the core region, is irradiated by energetic particles that cause the atoms to be displaced from their lattice sites and giving rise to crystal defects. The local changes in the atomic arrangements lead to local deformations of the solid and thereby changes of its local mechanical properties. Understanding the mechanisms behind this evolution in the core region of a reactor, and its monitoring or controlling is a critical task in nuclear industry. In this work, using extensive molecular dynamics simulations, we have studied the effects of radiation damage on the local mechanical properties of Zr–[Formula: see text]Nb alloy. In the first step, the effect of Nb-concentration on the mechanical stability of homogeneous Zr–[Formula: see text]Nb alloy is investigated. In the second step, we have studied the local changes of the elastic constants due to local changes of the microstructure. These local changes include presence and accumulation of vacancies in the form of dislocation loops or voids, accumulation of Nb atoms in the form of clusters of different morphologies. This study covers both cases of [Formula: see text]K and finite temperatures up to [Formula: see text]K. read less D. Singh and A. Parashar, “Atomistic simulations to study the effect of Nb precipitate on fracture properties of bi-crystalline Zr,” Journal of Physics D: Applied Physics. 2019. link Times cited: 7 Abstract: In this article, molecular dynamics based simulations were c… read more Abstract: In this article, molecular dynamics based simulations were carried out to study the effect of Nb in conjunction with grain boundary configurations on the fracture behaviour of bi-crystalline zirconium–niobium alloy (Zr–Nb). A separate set of simulations were performed with a varying percentage of Nb to study its effect on fracture behaviour of Zr–Nb alloy. Simulations were carried out with the crack orientation either perpendicular or parallel to the grain boundary plane. The distance of the crack tip from the grain boundary (GB) plane and percentage of Nb significantly affects the fracture behaviour of alloy. It was concluded from the atomistic simulations that the GB plane in vicinity of the crack tip helps in mitigating the stresses experienced at the tip; whereas the crack tip experienced higher level of stresses when at a distance from the GB plane. Higher angle grain boundaries generate a higher shielding effect at the crack tip as compared to bi-crystals containing lower angle GBs. So far, Zr–Nb alloys are developed with a range of Nb constituent ranging from 0.5% to 5%, results of this article will help in optimising the percentage of Nb in Zr–Nb alloy with desired structural strength. read less I. Gordeev and S. Starikov, “Comparison of Different Methods of Atomistic Simulation To Calculate the Temperature of Phase Transition Using the Example of Zirconium,” Journal of Experimental and Theoretical Physics. 2019. link Times cited: 5 E. Y. Chen, C. Deo, and R. Dingreville, “Irradiation resistance of nanostructured interfaces in Zr–Nb metallic multilayers,” Journal of Materials Research. 2019. link Times cited: 21 Abstract: Irradiation resistance of metallic nanostructured multilayer… read more Abstract: Irradiation resistance of metallic nanostructured multilayers is determined by the interactions between defects and phase boundaries. However, the dose-dependent interfacial morphology evolution can greatly change the nature of the defect–boundary interaction mechanisms over time. In the present study, we used atomistic models combined with a novel technique based on the accumulation of Frenkel pairs to simulate irradiation processes. We examined dose effects on defect evolutions near zirconium–niobium multilayer phase boundaries. Our simulations enabled us to categorize defect evolution mechanisms in bulk phases into progressing stages of dislocation accumulation, saturation, and coalescence. In the metallic multilayers, we observed a phase boundary absorption mechanism early on during irradiation, while at higher damage levels, the increased irradiation intermixing triggered a phase transformation in the Zr–Nb mixture. This physical phenomenon resulted in the emission of a large quantity of small immobile dislocation loops from the phase boundaries. read less M. M. Hasan, S. G. Srinivasan, and D. Choudhuri, “Transformation- and twinning-induced plasticity in phase-separated bcc Nb-Zr alloys: an atomistic study,” Journal of Materials Science. 2023. link Times cited: 0 M. Basaadat and S. Sheykhi, “Molecular Dynamics Study of Microstructural Evolution and Damage-Depth Induced by Isotropic Irradiation on Zr-1%Nb Alloy,” Journal of Nuclear Research and Applications. 2023. link Times cited: 0 Abstract: Zirconium alloys with niobium have extensive applications in… read more Abstract: Zirconium alloys with niobium have extensive applications in the nuclear industry, especially in fuel cladding. In this study, we consider the lattice structure of Zr-1%Nb alloy and study the damage depth (DD) due to irradiation on the structure of this alloy which results from the collision cascade (CC) phenomenon. It has been shown that the DD in the structure is directly related to Primary Knocked-on Atom (PKA) energy. Because the structure of Zr-1%Nb is not homogeneous, DD is highly affected by the incident direction of irradiation. Both Zr and Nb atoms were considered as PKA’s and the results show that the average of DD is larger for Nb than Zr. Next, the CC phenomenon has been considered for this alloy, and microstructure evolution has been studied at low temperatures and low PKA energy. The results show the formation of some self-interstitials (SI’s) during the CC phenomenon and no SI clusters are observed. read less H. Mei et al., “Development of Machine Learning and Empirical Interatomic Potentials for the Binary Zr-Sn System,” Journal of Nuclear Materials. 2023. link Times cited: 0 D. D. Zuo, J. Chang, Q. Wang, and H. P. Wang, “Thermophysical properties and atomic structure of liquid Zr–Nb alloys investigated by electrostatic levitation and molecular dynamics simulation,” Journal of Physics: Condensed Matter. 2023. link Times cited: 0 Abstract: The investigation of the thermophysical properties of liquid… read more Abstract: The investigation of the thermophysical properties of liquid Zr–Nb alloys holds great significance for theoretical research and technical application in liquid physics. However, the high temperatures involved make their experimental measurement challenging. In this study, the densities of liquid Zr-x wt.% Nb (x= 1.0, 2.5, 6.0) alloys were examined by electrostatic levitation and molecular dynamics calculation. Remarkably, the alloys achieved maximum undercooling of 335 K, 311 K and 326 K, respectively. Correspondingly, the densities are 6.20, 6.22 and 6.26 g·cm−3 at the liquidus temperatures (T L), respectively. The corresponding temperature coefficients are 2.61 × 10−4, 2.75 × 10−4 and 2.84 × 10−4 g·cm−3·K−1, respectively. Notably, the experimental density results align well with the simulated results. Moreover, the molar volume (V m), thermal expansion coefficient (α) and diffusion coefficient (D) were derived based on the experimental data and simulations. The thermal expansion coefficients reduce linearly with decreasing temperature. The analysis of the pair distribution function, coordination number (CN) and the radial distribution function reveals the temperature-dependent evolution of the atomic structure. The CN total and CN Zr–Zr initially increase and then decrease with decreasing temperature, while the change trends for CN Zr–Nb and CN Nb–Nb varied among the three alloys. The radial distribution function of three liquid alloys reveals that the atomic number density increases as the temperature drops. Additionally, the total diffusion coefficients decrease with the reduction of temperature and the rise of Nb content from 1.0 wt.% Nb to 6.0 wt.% Nb. read less M. Basaadat, M. Payami, and S. Sheykhi, “Analysis of Irradiation Induced Defect Clusterization for Zr-1%Nb Alloy Using Atomistic Simulation,” Journal of Nuclear Research and Applications. 2023. link Times cited: 0 Abstract: Nuclear-grade zirconium alloys' properties are very sim… read more Abstract: Nuclear-grade zirconium alloys' properties are very similar to those of pure zirconium (Zr) because in most cases they contain more than 95% of Zr atoms. They have extensive applications in the nuclear industry, especially in fuel cladding. In this work, for the atomic simulations, we have used an ADP model interatomic potential. The calculated lattice properties of Zr-1%Nb show a very good agreement with experiments. Investigation of the possibility of a di-vacancy formation showed that it is possible only for the first and second nearest neighbor positions. It shows that at zero pressure, the Nb atoms in the alloy tend to join and create Nb clusters. However, under external pressure, the Nb clusters become less stable, tending to decay into smaller ones. read less A. T. AlMotasem, N. Daghbouj, H. Sen, S. Mirzaei, M. Callisti, and T. Polcar, “Influence of HCP/BCC interface orientation on the tribological behavior of Zr/Nb multilayer during nanoscratch: A combined experimental and atomistic study,” Acta Materialia. 2023. link Times cited: 10 S. Liu, X. Liu, R. Xie, X. Feng, C. He, and J.-X. Liu, “Mechanism and influence factors on energy-release capacity under the high-velocity impact fragmentation of Zr-Nb alloys,” Journal of Alloys and Compounds. 2022. link Times cited: 1 C. Dai and N. Ofori-Opoku, “Deformation mechanism in the mechanical response of nano polycrystalline HCP Zr and Zr-2.5 Nb: an atomistic study,” Materials Today Communications. 2022. link Times cited: 0 V. Neaga, L. Benea, and E. R. Axente, “Corrosion Assessment of Zr2.5Nb Alloy in Ringer’s Solution by Electrochemical Methods,” Applied Sciences. 2022. link Times cited: 2 Abstract: This study aims to investigate the anticorrosive properties … read more Abstract: This study aims to investigate the anticorrosive properties of Zr2.5Nb alloy intended for possible applications in the human body; it was tested for 2 days in Ringer solution (an artificial analogue for human blood, considered the most corrosive body fluid). For Zr2.5Nb samples, in situ electrochemical measurements to assess the anticorrosive properties were applied, such as open circuit potential (OCP), polarization resistance (Rp), potentiodynamic polarization (PD) and cyclic voltammetry (CV). The electrochemical results show that the Zr2.5Nb alloy shows a positive and stable trend according to the open circuit potential, but with a modest corrosion rate in the form of pitting, deduced from the analysis of the polarization resistance and cyclic voltammetry data. read less M. Zhou, B. Fu, Q. Hou, L. Wu, and R. Pan, “Determining the diffusion behavior of point defects in zirconium by a multiscale modelling approach,” Journal of Nuclear Materials. 2022. link Times cited: 3 S. Kumar and V. Jindal, “Thermodynamic Re-assessment of the Nb-Zr System Using the CE–CVM Model for Solid Solution Phases,” Journal of Phase Equilibria and Diffusion. 2022. link Times cited: 0 N. Daghbouj et al., “Revealing Nanoscale Strain Mechanisms in Ion-Irradiated Multilayers,” Acta Materialia. 2022. link Times cited: 25 Abstract: Tailoring of interfaces is a powerful way of reducing the ac… read more Abstract: Tailoring of interfaces is a powerful way of reducing the accumulation of radiation defects. Understanding strain evolution induced by ions bombardment in nuclear materials with high interface density is crucial for next-generation reactors since induced defects are responsible for volumetric swelling and catastrophic failure. X-ray and SADPs measurements reveal that, after Cu implantation, a relatively high out-of-plane strain is created in thin Zr/Nb 6 multilayers, while the thick Zr/Nb 96 is barely distorted. The absence of the layer deformation in Zr/Nb 96 is explained by Astar strain mapping showing the presence of two oppositely distorted regions (inner and interface-affected regions) within one layer producing only a small overall strain, whereas the whole individual layers of Zr/Nb 6 are affected by the interface manifesting high strain. Using MD simulations, the type of defects responsible for layer distortion is identified. The opposite distortion within the layer is attributed to the inequality of the defect flux from the inner to interface-affected region due to the difference in migration energy barriers of the point defects. Moreover, the interface sink efficiency (defect annihilation) is determined for Zr/Nb as an illustration which provides a strategy for designing new derivate structures of multilayers with high radiation damage resistance. read less S. S. Kliavinek and L. Kolotova, “Modeling of glass transition process and elastic properties of Zr-Nb amorphous alloys,” Journal of Non-crystalline Solids. 2021. link Times cited: 1 V. Maksimenko, A. Lipnitskii, V. Saveliev, I. Nelasov, and A. Kartamyshev, “Prediction of the diffusion characteristics of the V-Cr system by molecular dynamics based on N-body interatomic potentials,” Computational Materials Science. 2021. link Times cited: 5 S. Starikov and D. Smirnova, “Optimized interatomic potential for atomistic simulation of Zr-Nb alloy,” Computational Materials Science. 2021. link Times cited: 15 B. Lin, J. Li, Z. Wang, and J. Wang, “Dislocation nucleation from Zr–Nb bimetal interfaces cooperating with the dynamic evolution of interfacial dislocations,” International Journal of Plasticity. 2020. link Times cited: 13 X.-long An, H. Zhang, S. Ni, X. Ou, X. Liao, and M. Song, “Effects of temperature and alloying content on the phase transformation and 101¯1 twinning in Zr during rolling,” Journal of Materials Science & Technology. 2020. link Times cited: 19 D. Singh, A. Parashar, and R. Kapoor, “Effect of Nb precipitate on defect formation and migration energies in bi-crystalline Zr,” Materials Chemistry and Physics. 2019. link Times cited: 4 K. V. Reddy and S. Pal, “Evaluation of glass forming ability of Zr–Nb alloy systems through liquid fragility and Voronoi cluster analysis,” Computational Materials Science. 2019. link Times cited: 14 D. Smirnova, S. Starikov, and A. Vlasova, “New interatomic potential for simulation of pure magnesium and magnesium hydrides,” Computational Materials Science. 2018. link Times cited: 17 D. Smirnova, S. Starikov, and I. Gordeev, “Evaluation of the structure and properties for the high-temperature phase of zirconium from the atomistic simulations,” Computational Materials Science. 2018. link Times cited: 13 S. Starikov, N. Lopanitsyna, D. Smirnova, and S. Makarov, “Atomistic simulation of Si-Au melt crystallization with novel interatomic potential,” Computational Materials Science. 2018. link Times cited: 20 D. Smirnova and S. Starikov, “Study of Niobium Diffusion and Clusterization in hcp Zr-Nb Dilute Alloys,” Defect and Diffusion Forum. 2017. link Times cited: 3 Abstract: We perform atomistic simulations aimed on study of diffusion… read more Abstract: We perform atomistic simulations aimed on study of diffusion of constituents and niobium precipitation in hcp Zr-Nb. We report diffusivities of Zr and Nb in hcp Zr-Nb alloys computed for the models containing up to 5 at.% of niobium. The calculated diffusivity of niobium rises with increase of its content in the alloy. The simulations also show that for a studied concentration range addition of niobium slightly enhances self-diffusion of zirconium in the alloys. The work is also devoted to description of niobium incorporation and clusterization in hcp zirconium. It is confirmed that for a single niobium atom incorporated in hcp zirconium lattice the octahedral position is the most favorable. We estimated the energy describing niobium cluster formation in pure hcp zirconium. According to the simulation results, we can suggest that the minimum niobium cluster size that can be expected in hcp Zr corresponds to about 80 atoms. read less O. G. Nicholls, D. Frost, V. Tuli, J. Smutná, M. Wenman, and P. Burr, “Transferability of Zr-Zr interatomic potentials,” Journal of Nuclear Materials. 2022. link Times cited: 6 W. Muftah, J. Allport, and V. Vishnyakov, “Corrosion performance and mechanical properties of FeCrSiNb amorphous equiatomic HEA thin film,” Surface & Coatings Technology. 2021. link Times cited: 17 B. Lin, J. Wang, J. Li, and Z. Wang, “A neural-network based framework of developing cross interaction in alloy embedded-atom method potentials: application to Zr–Nb alloy,” Journal of Physics: Condensed Matter. 2020. link Times cited: 2 Abstract: Interaction potentials are critical to molecular dynamics si… read more Abstract: Interaction potentials are critical to molecular dynamics simulations on fundamental mechanisms at atomic scales. Combination of well-developed single-element empirical potentials via cross interaction (CI) is an important and effective way to develop alloy embedded-atom method (EAM) potentials. In this work, based on neural-network (NN) models, firstly we proposed a framework to construct CI potential functions via utilizing single-element potentials. The framework contained four steps: (1) extracting characteristic points from single-element potential functions, (2) constructing CI functions by cubic spline interpolation, (3) evaluating the accuracy of CI functions by referring to first-principle (FP) data, and (4) searching for reasonable CI functions via NN models. Then with this framework, we developed a Zr–Nb alloy CI potential utilizing the MA-III (pure Zr potential developed by Mendelev and Ackland in 2007) and the Fellinger, Park and Wilkins (FPW) (pure Nb potential developed by FPW in 2010) potentials as single-element parts. The calculated results with this Zr–Nb alloy potential showed that: (1) the newly developed CI potential functions could simultaneously present the potential-function features of Zr and Nb; (2) the normalized energy–volume curves of L12 Zr3Nb, B2 ZrNb and L12 ZrNb3 calculated by this CI potential reasonably agreed with FP results; (3) the referred MA-III Zr and FPW Nb potentials can satisfactorily reproduce the priority of prismatic slip in Zr and the tension–compression asymmetry of 〈111〉{112} slip in Nb, while other ab initio developed Zr–Nb alloy potentials cannot. Our study indicates that, this NN based framework can take full advantage of single-element potentials, and is very convenient to develop EAM potentials of alloys; moreover, the new-developed Zr–Nb alloy EAM potential can reasonably describe the complicated deformation behaviors in Zr–Nb systems. read less S. S. Kliavinek and L. Kolotova, “Molecular Dynamics Simulation of Glass Transition of the Supercooled Zr–Nb Melt,” Journal of Experimental and Theoretical Physics. 2020. link Times cited: 4 W. Setyawan, N. Gao, and R. Kurtz, “A tungsten-rhenium interatomic potential for point defect studies,” Journal of Applied Physics. 2018. link Times cited: 22 Abstract: A tungsten-rhenium (W-Re) classical interatomic potential is… read more Abstract: A tungsten-rhenium (W-Re) classical interatomic potential is developed within the embedded atom method interaction framework. A force-matching method is employed to fit the potential to ab initio forces, energies, and stresses. Simulated annealing is combined with the conjugate gradient technique to search for an optimum potential from over 1000 initial trial sets. The potential is designed for studying point defects in W-Re systems. It gives good predictions of the formation energies of Re defects in W and the binding energies of W self-interstitial clusters with Re. The potential is further evaluated for describing the formation energy of structures in the σ and χ intermetallic phases. The predicted convex-hulls of formation energy are in excellent agreement with ab initio data. In pure Re, the potential can reproduce the formation energies of vacancies and self-interstitial defects sufficiently accurately and gives the correct ground state self-interstitial configuration. Furthermore, by including liquid structures in the fit, the potential yields a Re melting temperature (3130 K) that is close to the experimental value (3459 K).A tungsten-rhenium (W-Re) classical interatomic potential is developed within the embedded atom method interaction framework. A force-matching method is employed to fit the potential to ab initio forces, energies, and stresses. Simulated annealing is combined with the conjugate gradient technique to search for an optimum potential from over 1000 initial trial sets. The potential is designed for studying point defects in W-Re systems. It gives good predictions of the formation energies of Re defects in W and the binding energies of W self-interstitial clusters with Re. The potential is further evaluated for describing the formation energy of structures in the σ and χ intermetallic phases. The predicted convex-hulls of formation energy are in excellent agreement with ab initio data. In pure Re, the potential can reproduce the formation energies of vacancies and self-interstitial defects sufficiently accurately and gives the correct ground state self-interstitial configuration. Furthermore, by including liqu... read less H. Wang et al., “Effects of Nb concentration and temperature on generalized stacking fault energy of Zr–Nb alloys by molecular dynamics simulations,” Materials Research Express. 2021. link Times cited: 0 Abstract: The effects of Nb concentration and temperature on the gener… read more Abstract: The effects of Nb concentration and temperature on the generalized stacking fault energy (GSFE) of basal, prismatic I, pyramidal I and II plane for Zr-Nb alloys are investigated by molecular dynamics simulations (MD). The stable and unstable SFEs of different slip systems show no significant change with the increasing Nb concentration (0, 0.5, 1.0, 1.5, 2.0, and 2.5 at.%) in Zr-Nb alloys at 0 K. Basal, pyramidal I and II planes slip of Zr-Nb alloys prefer to deform by full dislocation with the temperature increases. Additionally, plastic deformation anisotropy of Zr-Nb alloy is improved with the increasing temperature using both embedded atom method (EAM) and angular-dependent potentials (ADP). The present work provides a theoretical basis for understanding enhanced plasticity of Zr-Nb alloys under finite temperature. read less
Funding	Not available

Short KIM ID The unique KIM identifier code.	SM_937902197407_000
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_ADP_SmirnovaStarikov_2017_ZrNb__SM_937902197407_000
DOI	10.25950/8f9857b3 https://doi.org/10.25950/8f9857b3 https://commons.datacite.org/doi.org/10.25950/8f9857b3
KIM Item Type	Simulator Model
KIM API Version	2.1
Simulator Name The name of the simulator as defined in kimspec.edn.	LAMMPS
Potential Type	adp
Simulator Potential	adp
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% Tcl

Verification Check Dashboard

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Grade	Name	Category	Brief Description	Full Results	Aux File(s)
P All elements claimed by model are supported in at least one of the tested configurations.	vc-species-supported-as-stated	mandatory	The model supports all species it claims to support; see full description.	Results	Files
P Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.	vc-periodicity-support	mandatory	Periodic boundary conditions are handled correctly; see full description.	Results	Files
P Model energy has permutation symmetry for all configurations the model was able to compute.	vc-permutation-symmetry	mandatory	Total energy and forces are unchanged when swapping atoms of the same species; see full description.	Results	Files
B The letter grade B was assigned because the normalized error in the computation was 9.84675e-09 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.	vc-forces-numerical-derivative	consistency	Forces computed by the model agree with numerical derivatives of the energy; see full description.	Results	Files
F The model is C^-1 continuous. This means that the model has discontinuous energy.	vc-dimer-continuity-c1	informational	The energy versus separation relation of a pair of atoms is C1 continuous (i.e. the function and its first derivative are continuous); see full description.	Results	Files
P Model energy and forces are invariant with respect to rigid-body motion (translation and rotation) for all configurations the model was able to compute.	vc-objectivity	informational	Total energy is unchanged and forces transform correctly under rigid-body translation and rotation; see full description.	Results	Files
P Model energy has inversion symmetry for all configurations the model was able to compute.	vc-inversion-symmetry	informational	Total energy is unchanged and forces change sign when inverting a configuration through the origin; see full description.	Results	Files
F 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
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: Zr

Species: Nb

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: Zr

Species: Nb

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: Nb

Species: Zr

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: Nb

Species: Zr

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: Zr

Species: Nb

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: Nb

Species: Zr

Cubic Crystal Basic Properties Table

Species: Nb

Species: Zr

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 Nb v004	view	3720
Cohesive energy versus lattice constant curve for bcc Zr v004	view	3899
Cohesive energy versus lattice constant curve for diamond Nb v004	view	4564
Cohesive energy versus lattice constant curve for diamond Zr v004	view	4491
Cohesive energy versus lattice constant curve for fcc Nb v004	view	4417
Cohesive energy versus lattice constant curve for fcc Zr v004	view	4417
Cohesive energy versus lattice constant curve for sc Nb v004	view	4417
Cohesive energy versus lattice constant curve for sc Zr v004	view	3610

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 Nb at zero temperature v006	view	2399
Elastic constants for bcc Zr at zero temperature v006	view	7773
Elastic constants for diamond Nb at zero temperature v001	view	31957
Elastic constants for diamond Zr at zero temperature v001	view	15195
Elastic constants for fcc Nb at zero temperature v006	view	8189
Elastic constants for fcc Zr at zero temperature v006	view	5662
Elastic constants for sc Nb at zero temperature v006	view	2399
Elastic constants for sc Zr at zero temperature v006	view	2527

ElasticConstantsHexagonal__TD_612503193866_004

Elastic constants for hexagonal crystals at zero temperature v004

Creators: Junhao Li
Contributor: jl2922
Publication Year: 2019
DOI: https://doi.org/10.25950/d794c746

Computes the elastic constants for hcp crystals by calculating the hessian of the energy density with respect to strain. An estimate of the error associated with the numerical differentiation performed is reported.

Test	Test Results	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Elastic constants for hcp Nb at zero temperature v004		view	1846
Elastic constants for hcp Zr at zero temperature v004		view	2356

EquilibriumCrystalStructure__TD_457028483760_003

Equilibrium structure and energy for a crystal structure at zero temperature and pressure v003

Creators:
Contributor: ilia
Publication Year: 2025
DOI: https://doi.org/10.25950/866c7cfa

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 Nb in AFLOW crystal prototype A_cF4_225_a v003	view	215789
Equilibrium crystal structure and energy for Zr in AFLOW crystal prototype A_cF4_225_a v003	view	207382
Equilibrium crystal structure and energy for Nb in AFLOW crystal prototype A_cI2_229_a v003	view	174073
Equilibrium crystal structure and energy for Zr in AFLOW crystal prototype A_cI2_229_a v003	view	137561
Equilibrium crystal structure and energy for Zr in AFLOW crystal prototype A_hP2_194_c v003	view	184562

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 Nb v007	view	5566
Equilibrium zero-temperature lattice constant for bcc Zr v007	view	6846
Equilibrium zero-temperature lattice constant for diamond Nb v007	view	8733
Equilibrium zero-temperature lattice constant for diamond Zr v007	view	9917
Equilibrium zero-temperature lattice constant for fcc Nb v007	view	11004
Equilibrium zero-temperature lattice constant for fcc Zr v007	view	6558
Equilibrium zero-temperature lattice constant for sc Nb v007	view	6302
Equilibrium zero-temperature lattice constant for sc Zr v007	view	5854

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 Nb v005		view	48072
Equilibrium lattice constants for hcp Zr v005		view	38522

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 Nb v004		view	74055

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 Nb		view	7063004
Monovacancy formation energy and relaxation volume for hcp Zr		view	6072219

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 Nb		view	13132646
Vacancy formation and migration energy for hcp Zr		view	10496516

Errors

EquilibriumCrystalStructure__TD_457028483760_000

Test	Error Categories	Link to Error page
Equilibrium crystal structure and energy for Zr in AFLOW crystal prototype A_hP2_194_c v000	other	view

Files

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Zr_Nb.adp
kimprovenance.edn
kimspec.edn
smspec.edn

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BCC Lattice Constant

Cohesive Energy Graph

Diamond Lattice Constant

Dislocation Core Energies

FCC Elastic Constants

FCC Lattice Constant

FCC Stacking Fault Energies

FCC Surface Energies

SC Lattice Constant

Cubic Crystal Basic Properties Table

Tests

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