MEAM Potential for the Fe-N system developed by Lee, Lee and Kim. (2006) v002

Byeong-Joo Lee; Tae-Ho Lee; Sung-Joon Kim

doi:10.25950/22f2df58

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MEAM_LAMMPS_LeeLeeKim_2006_FeN__MO_432861766738_002

Interatomic potential for Iron (Fe), Nitrogen (N).
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Title A single sentence description.	MEAM Potential for the Fe-N system developed by Lee, Lee and Kim. (2006) v002
Description A short description of the Model describing its key features including for example: type of model (pair potential, 3-body potential, EAM, etc.), modeled species (Ac, Ag, ..., Zr), intended purpose, origin, and so on.	The potential parameters were determined by fitting to the dilute heat of solution and migration energy of nitrogen atoms, the vacancy–nitrogen binding energy and its configuration in body-centered cubic iron, and the enthalpy of formation and lattice parameter of Fe4N. The potential reproduces very well the known physical properties of nitrogen as an interstitial solute element in body- and face-centered cubic iron and of various nitrides. In the original paper (Lee et al., Acta Materialia, 54(17), 2006), the similarity and difference between nitrogen and carbon as equally important interstitial elements in iron are also examined. The applicability of the potential to atomistic approaches for investigating interactions between nitrogen atoms and other defects such as vacancies, dislocations, and grain boundaries, and also for investigating the effects of nitrogen on various deformation and mechanical behaviors of iron is demonstrated.
Species The supported atomic species.	Fe, N
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	None
Content Origin	http://cmse.postech.ac.kr/home_2nnmeam

Contributor	Hyeon-Seok Do
Maintainer	Hyeon-Seok Do
Developer	Byeong-Joo Lee Tae-Ho Lee Sung-Joon Kim
Published on KIM	2023
How to Cite	This Model originally published in [1] is archived in OpenKIM [2-5]. [1] Lee B-J, Lee T-H, Kim S-J. A modified embedded-atom method interatomic potential for the Fe–N system: a comparative study with the Fe–C system. Acta materialia. 2006;54(17):4597–607. doi:10.1016/j.actamat.2006.06.003 — (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] Lee B-J, Lee T-H, Kim S-J. MEAM Potential for the Fe-N system developed by Lee, Lee and Kim. (2006) v002. OpenKIM; 2023. doi:10.25950/22f2df58 [3] Afshar Y, Hütter S, Rudd RE, Stukowski A, Tipton WW, Trinkle DR, et al. The modified embedded atom method (MEAM) potential v002. OpenKIM; 2023. doi:10.25950/ee5eba52 [4] Tadmor EB, Elliott RS, Sethna JP, Miller RE, Becker CA. The potential of atomistic simulations and the Knowledgebase of Interatomic Models. JOM. 2011;63(7):17. doi:10.1007/s11837-011-0102-6 [5] Elliott RS, Tadmor EB. Knowledgebase of Interatomic Models (KIM) Application Programming Interface (API). OpenKIM; 2011. doi:10.25950/ff8f563a Click here to download the above citation in BibTeX format.
Citations This panel presents information regarding the papers that have cited the interatomic potential (IP) whose page you are on. The OpenKIM machine learning based Deep Citation framework is used to determine whether the citing article actually used the IP in computations (denoted by "USED") or only provides it as a background citation (denoted by "NOT USED"). For more details on Deep Citation and how to work with this panel, click the documentation link at the top of the panel. The word cloud to the right is generated from the abstracts of IP principle source(s) (given below in "How to Cite") and the citing articles that were determined to have used the IP in order to provide users with a quick sense of the types of physical phenomena to which this IP is applied. The bar chart shows the number of articles that cited the IP per year. Each bar is divided into green (articles that USED the IP) and blue (articles that did NOT USE the IP). Users are encouraged to correct Deep Citation errors in determination by clicking the speech icon next to a citing article and providing updated information. This will be integrated into the next Deep Citation learning cycle, which occurs on a regular basis. OpenKIM acknowledges the support of the Allen Institute for AI through the Semantic Scholar project for providing citation information and full text of articles when available, which are used to train the Deep Citation ML algorithm.	This panel provides information on past usage of this interatomic potential (IP) powered by the OpenKIM Deep Citation framework. The word cloud indicates typical applications of the potential. The bar chart shows citations per year of this IP (bars are divided into articles that used the IP (green) and those that did not (blue)). The complete list of articles that cited this IP is provided below along with the Deep Citation determination on usage. See the Deep Citation documentation for more information. 70 Citations (44 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. Wan et al., “Iron atom–cluster interactions increase activity and improve durability in Fe–N–C fuel cells,” Nature Communications. 2022. link Times cited: 84 A. Karimi and M. Auinger, “Nitrogen Diffusion in Vacancy-Rich Ferrite and Austenite, from First Principles to Applications,” EngRN: Process Engineering (Topic). 2021. link Times cited: 1 Abstract: This work contains a systematic study of the diffusion of ni… read more Abstract: This work contains a systematic study of the diffusion of nitrogen in Ferrite (α Fe, BCC) and Austenite (γ Fe, FCC) from first principles, using a robust multi scale model which combines Density Functional Theory (DFT) and Kinetic Monte Carlo (KMC). Both ferromagnetic BCC and non-magnetic FCC iron are considered using DFT to drive a diffusion model, which shows strong agreement with experimental diffusion data in literature. Further, quantified predictions are calculated for nitrogen diffusion in iron crystals which are vacancy-rich. In particular, it was found that an extended diffusion coefficient of nitrogen can be expressed as a function of nitrogen and vacancy concentration by fitting polynomial coefficients. These are calculated within the 100◦C < T < 1500◦C temperature range, and 0.01 at.% < cN < 10.0 at.% nitrogen concentration range. Such insights in vacancy-rich crystals may be useful to nitriding manufacturers, as enhanced diffusion models are an important factor in improving existing processes and avoiding common manufacturing problems such as the egg-shell-effect. read less A. T. AlMotasem, M. Posselt, and T. Polcar, “Deformation Behavior of Nanocrystalline Body-Centered Cubic Iron with Segregated, Foreign Interstitial: A Molecular Dynamics Study,” Materials. 2020. link Times cited: 3 Abstract: In the present work, modified embedded atom potential and la… read more Abstract: In the present work, modified embedded atom potential and large-scale molecular dynamics’ simulations were used to explore the effect of grain boundary (GB) segregated foreign interstitials on the deformation behavior of nanocrystalline (nc) iron. As a case study, carbon and nitrogen (about 2.5 at.%) were added to (nc) iron. The tensile test results showed that, at the onset of plasticity, grain boundary sliding mediated was dominated, whereas both dislocations and twinning were prevailing deformation mechanisms at high strain. Adding C/N into GBs reduces the free excess volume and consequently increases resistance to GB sliding. In agreement with experiments, the flow stress increased due to the presence of carbon or nitrogen and carbon had the stronger impact. Additionally, the simulation results revealed that GB reduction and suppressing GBs’ dislocation were the primary cause for GB strengthening. Moreover, we also found that the stress required for both intragranular dislocation and twinning nucleation were strongly dependent on the solute type. read less J. Kong, D. Du, A. Song, F. Zhang, and W. Huang, “Surface Physical and Chemical Modification of Pure Iron by Using Atmospheric Pressure Plasma Treatment,” Materials. 2020. link Times cited: 2 Abstract: To investigate the mechanism of surface modification of pure… read more Abstract: To investigate the mechanism of surface modification of pure iron by atmospheric pressure plasma treatment (APPT), the surface wettability of pure iron was characterized by using a contact-angle measuring instrument, and the mechanical properties of pure iron were measured by a tensile testing machine and nanoindentation instrument. Molecular dynamics simulations were used to explain the modification mechanism of the surface wettability and the mechanical behavior of pure iron by APPT. The experimental results show that pure iron treated by APPT is superhydrophilic, with reduced tensile strength and surface hardness. This result agrees with the molecular dynamics simulation, which shows that the pure iron material hydrophilicity improved after APPT. The behavior was attributed to the formation of hydrogen bonds on the surface of the pure iron after APPT. The surface binding energy of the pure iron material increased between the water molecule and the residual N atom that was induced by APPT. The N atom that was introduced by the APPT led to Fe bond fracture, and the N atom reduced the Fe bond strength, which resulted in a reduction of material yield strength and microhardness. read less J. Wang et al., “Greater diffusion rate of carbon atoms from nonlinear migration in micro-cell and spatially heterogeneous stable states in FCC iron,” Journal of Materials Science. 2018. link Times cited: 2 M. Mohammadzadeh and R. Mohammadzadeh, “Effect of interstitial and substitution alloying elements on the intrinsic stacking fault energy of nanocrystalline fcc-iron by atomistic simulation study,” Applied Physics A. 2017. link Times cited: 13 F. Ulomek and V. Mohles, “Molecular dynamics simulations of grain boundary mobility in Al, Cu and γ-Fe using a symmetrical driving force,” Modelling and Simulation in Materials Science and Engineering. 2014. link Times cited: 13 Abstract: We present a new artificial driving force for the determinat… read more Abstract: We present a new artificial driving force for the determination of grain boundary mobility by molecular dynamics. The new driving force is a symmetric version of the synthetic driving force formerly introduced by Janssens et al 2006 Nature Mater. 5 124–7. The new version depends on two orientation parameters instead of one. We analyze the advantages and disadvantages of these two driving force methods. Grain boundary mobilities are simulated for eight symmetric CSL tilt grain boundaries in Al, Cu and γ-Fe, and two MD potentials for each of these materials. Boundary conditions are kept as similar as possible to show the influence of the different materials and to compare to the influence of the different MD potential types on simulated GB mobilities. We find that the newly introduced artificial driving force is a slight improvement, but it cannot remove the shortcomings of the original approach. Also, it is found that the differences in calculated MD mobilities between different materials are of the same order as those between different MD potentials of any one element. Sources for such differences are identified and classified by severity. read less M. H. Wu, X. H. Liu, J. F. Gu, and Z. H. Jin, “First-principles simulations of iron with nitrogen: from surface adsorption to bulk diffusion,” Modelling and Simulation in Materials Science and Engineering. 2013. link Times cited: 14 Abstract: Adsorption, absorption and diffusion pathways of nitrogen ar… read more Abstract: Adsorption, absorption and diffusion pathways of nitrogen are studied for ferromagnetic body-centered cubic iron via spin-polarized density functional theory in combination with the climbing image nudged elastic band method. The computed data suggest that, depending on the coverage of N atoms, N prefers to stay on particular surface sites. Once pinned down well below the surface, N prefers to move into octahedral interstices rather than tetrahedral interstices. However, the tetrahedral interstices are crucial because they act as transition states and yield the saddle point energies of the corresponding minimum energy pathways. In comparison with carbon, we found that nitrogen prefers a different pathway from the (1 0 0) surface to the subsurface due to its strong repulsive interaction with Fe ions. read less M. Billah, M. S. Rabbi, K. A. Rahman, and P. Acar, “Temperature and strain rate dependent tensile properties of Titanium carbide/nitride MXenes,” Materials Chemistry and Physics. 2023. link Times cited: 0 S. Risal et al., “Development of the RF-MEAM Interatomic Potential for the Fe-C System to Study the Temperature-Dependent Elastic Properties,” Materials. 2023. link Times cited: 0 Abstract: One of the major impediments to the computational investigat… read more Abstract: One of the major impediments to the computational investigation and design of complex alloys such as steel is the lack of effective and versatile interatomic potentials to perform large-scale calculations. In this study, we developed an RF-MEAM potential for the iron-carbon (Fe-C) system to predict the elastic properties at elevated temperatures. Several potentials were produced by fitting potential parameters to the various datasets containing forces, energies, and stress tensor data generated using density functional theory (DFT) calculations. The potentials were then evaluated using a two-step filter process. In the first step, the optimized RSME error function of the potential fitting code, MEAMfit, was used as the selection criterion. In the second step, molecular dynamics (MD) calculations were employed to calculate ground-state elastic properties of structures present in the training set of the data fitting process. The calculated single crystal and poly-crystalline elastic constants for various Fe-C structures were compared with the DFT and experimental results. The resulting best potential accurately predicted the ground state elastic properties of B1, cementite, and orthorhombic-Fe7C3 (O-Fe7C3), and also calculated the phonon spectra in good agreement with the DFT-calculated ones for cementite and O-Fe7C3. Furthermore, the potential was used to successfully predict the elastic properties of interstitial Fe-C alloys (FeC-0.2% and FeC-0.4%) and O-Fe7C3 at elevated temperatures. The results were in good agreement with the published literature. The successful prediction of elevated temperature properties of structures not included in data fitting validated the potential’s ability to model elevated-temperature elastic properties. read less L. Liu, G. Wang, Y. Xiao, Z. Zhao, and Z. Yang, “Molecular dynamics simulation of Cr-N clusters formation in high nitrogen austenitic stainless steel,” Scripta Materialia. 2023. link Times cited: 0 J. Zhu and J. P. Wang, “Simulation of thermal decomposition of γ′-Fe4N using molecular dynamics method,” AIP Advances. 2023. link Times cited: 0 Abstract: α″-Fe16N2 is a promising environmentally friendly rare-earth… read more Abstract: α″-Fe16N2 is a promising environmentally friendly rare-earth-free permanent magnet material with ultra-high saturation magnetization. Recent research has demonstrated experimentally through a thermally quenching treatment using γ′ phase Fe4N as a precursor to synthesize α″-Fe16N2 in bulk format. In this research using Molecular Dynamics (MD) simulation, we investigated the γ′-Fe4N phase thermal decomposition process and the potential phase transition from face center cubic ( fcc)-phase to body center tetragonal ( bct)-phase. As nitrogen concentration is higher in γ′-Fe4N (5.9 wt. %) than that in α′-Fe8N or α″-Fe16N2 (3 wt. %), Nitrogen bond formation through atom diffusion is studied with a “Nitrogen-rich” grain boundary (GB) model to find out whether lower-Nitrogen content bct Fe–N solid solution can be formed. Modified Embedded Atom Method (MEAM) interatomic potential of Fe–N system is applied. Post-processing including Nitrogen bond mapping/tracking is also performed for the thermostat-controlled heating and quenching simulation process. We also applied virtual XRD computation to characterize the material crystallographic texture before and after the thermal treatment. read less S. Manda, S. Kumar, K. Pal, A. Bhattacharyya, A. Panwar, and I. Samajdar, “Correction: Snoek-Dominated Internal Friction Response in bcc Steel: Relating Experiments With a Multi-scale Atomistic Computational Framework,” Metallurgical and Materials Transactions A. 2022. link Times cited: 1 R. Salloom, M. Baskes, and S. G. Srinivasan, “Atomic level simulations of the phase stability and stacking fault energy of FeCoCrMnSi high entropy alloy,” Modelling and Simulation in Materials Science and Engineering. 2022. link Times cited: 4 Abstract: High entropy alloys (HEAs) have many promising properties be… read more Abstract: High entropy alloys (HEAs) have many promising properties beneficial to advanced technologies. However, their underlying deformation mechanisms are largely unclear. So, as a first step, we have developed a modified embedded atom method potential for FeCoCrMnSi alloys to study such mechanisms. We predict the phase stability, chemical short-range ordering (CSRO), and stacking fault energy (SFE) of a specific alloy system using molecular dynamics (MD) and hybrid Monte-Carlo and molecular dynamics (MC/MD) simulation techniques. Room temperature MD simulations showed that both the potential energy and free energy of the single phase ε-hcp alloy is marginally more stable than the γ-fcc phase alloy, which resulted in a large, negative SFE. However, the room temperature MC/MD simulation showed an opposite trend where the γ-fcc phase was found to be more stable than the ε-hcp phase, and this resulted in a small, positive SFE. The prediction of the lower energy γ-fcc phase and resultant SFE agreed well with the experimentally reported SFE and phase stability for the Fe40Co20Cr15Mn20Si5 HEA, illustrating the importance of CSRO. Also, the calculated basal SFE of the hcp phase was close to that of the fcc phase. Therefore, the MC/MD implementation is crucial for the proper prediction of the phase stability and structural evolution in this HEA system. Many previous studies showed the ability of hybrid MC/MD technique to obtain consistent structural and configurational information of different alloy systems. The current work illustrates the potential of accelerating HEA materials development by utilizing computational methods based on the MC/MD technique which can reduce time and cost associated with experimental methods. read less A. S. M. Miraz, N. Dhariwal, W. Meng, B. Ramachandran, and C. Wick, “Development and application of interatomic potentials to study the stability and shear strength of Ti/TiN and Cu/TiN interfaces,” Materials & Design. 2020. link Times cited: 15 I. Aslam et al., “Thermodynamic and kinetic behavior of low-alloy steels: An atomic level study using an Fe-Mn-Si-C modified embedded atom method (MEAM) potential,” Materialia. 2019. link Times cited: 12 S. Ding and X.-qiang Wang, “A systematic study on the MEAM interatomic potentials of the transition metal nitrides TMNs (TM=Ti, V, Cr, Fe) binary systems,” Journal of Alloys and Compounds. 2019. link Times cited: 10 K. Tong, F. Ye, and Y. K. Wang, “Short-range ordered structure and phase stability of supersaturated nitrided layer on austenitic stainless steel,” Acta Materialia. 2019. link Times cited: 15 Y. Cheng et al., “Dynamic and structural heterogeneity in undercooled miscible and immiscible metallic liquid,” Journal of Alloys and Compounds. 2019. link Times cited: 4 N. Razmara and R. Mohammadzadeh, “Effect of nitrogen content on the crack growth behavior in the Fe-N alloy at high temperatures via molecular dynamics simulations,” Theoretical and Applied Fracture Mechanics. 2018. link Times cited: 4 F. Ye, K. Tong, Y. K. Wang, Z. Li, and F. Zhou, “First-principles study of interaction between vacancies and nitrogen atoms in fcc iron,” Computational Materials Science. 2018. link Times cited: 8 P. Liu, X. Han, D. Sun, and Q. Wang, “Development and application of a ternary Ti-Al-N interatomic potential for Ti2AlN/TiAl composite,” Journal of Alloys and Compounds. 2018. link Times cited: 20 K. M. Wang, H. Wu, C. Wang, and X. Li, “Study on Preparation and MD Simulation of Nano Fe4N,” NANO. 2017. link Times cited: 2 Abstract: Nano Fe4N powder has been successfully prepared by the combi… read more Abstract: Nano Fe4N powder has been successfully prepared by the combination between high pressure combined method of reduction and nitriding and molecular dynamics (MD) simulation. The phase, composition, morphology, and magnetic properties have been preliminarily characterized by XRD, TEM, and VSM to investigate the influence of temperature, time, ammonia hydrogen ratio, and pressure during reaction process on the preparation. The results indicate that the preferable nano Fe4N powder of the average size around 35nm could be obtained nitriding at 0.4MPa and 673K for 2.5hours with the ammonia hydrogen ratio being 3:1. The results of magnetic detection show that the nano Fe4N produced here is a fairly desirable soft magnetic material with Ms=169.70emu/g. This process could reduce the reaction temperature and shorten the reaction time, which is of important significance to the industrial production of nano Fe4N powder. read less R. Mohammadzadeh, N. Razmara, and F. Razmara, “Molecular dynamics study of strain-induced diffusivity of nitrogen in pure iron nanocrystalline,” Physica A-statistical Mechanics and Its Applications. 2016. link Times cited: 3 M. Mohammadzadeh and R. Mohammadzadeh, “WITHDRAWN: Molecular dynamics study on the effect of interstitial and substitutional alloying elements on stacking fault energies of fcc iron,” Physica B-condensed Matter. 2016. link Times cited: 0 F. Ye, C. Yin, K. Tong, C. Zhang, and W. Liu, “Structural evolution of vacancy clusters by combination of cluster units in alpha-iron,” Materials Research Innovations. 2014. link Times cited: 0 Abstract: The development of vacancy clusters in α-Fe is essential for… read more Abstract: The development of vacancy clusters in α-Fe is essential for understanding the formation of irradiation damage. In this work, the structures and the development of vacancy clusters in α-Fe have been studied by atomistic computer simulation. It was found out that larger clusters can form by combinations of smaller cluster units including triangular trimers and square tetramers. Furthermore, the formation of stacking faults, cracks or voids can be explained by the development of the clusters. read less D. Sangiovanni, D. Edström, L. Hultman, I. Petrov, J. Greene, and V. Chirita, “Ab initio and classical molecular dynamics simulations of N2 desorption from TiN(001) surfaces,” Surface Science. 2014. link Times cited: 52 R. Neugebauer, R. Wertheim, and U. Semmler, “THE ATOMIC FINITE ELEMENT METHOD AS A BRIDGE BETWEEN MOLECULAR DYNAMICS AND CONTINUUM MECHANICS,” Journal of Multiscale Modelling. 2011. link Times cited: 6 Abstract: On cutting tools for high performance cutting (HPC) processe… read more Abstract: On cutting tools for high performance cutting (HPC) processes or for hard-to-cut materials, there is an increased importance in so-called superlattice coatings with hundreds of layers each of which is only a few nanometers in thickness. Homogeneity or average material properties based on the properties of single layers are not valid in these dimensions any more. Consequently, continuum mechanical material models cannot be used for modeling the behavior of nanolayers. Therefore, the interaction potentials between the single atoms should be considered. A new, so-called atomic finite element method (AFEM) is presented. In the AFEM the interatomic bonds are modeled as nonlinear spring elements. The AFEM is the connection between the molecular dynamics (MD) method and the crystal plasticity FEM (CPFEM). The MD simulates the atomic deposition process. The CPFEM considers the behavior of anisotropic crystals using the continuum mechanical FEM. On one side, the atomic structure data simulated by MD defines the interface to AFEM. On the other side, the boundary conditions (displacements and tractions) of the AFEM model are interpolated from the CPFEM simulations. In AFEM, the lattice deformation, the crack and dislocation behavior can be simulated and calculated at the nanometer scale. read less A. L. Nikolaev and T. Kurennykh, “On the interaction between radiation-induced defects and foreign interstitial atoms in α-iron,” Journal of Nuclear Materials. 2011. link Times cited: 14 X. Zhen, L. Yuan, D. Shan, and B. Guo, “A molecular dynamics simulation of TiN film growth on TiN(0 0 1),” Computational Materials Science. 2011. link Times cited: 22 B.-J. Lee, W. Ko, H.-K. Kim, and E.-H. Kim, “The modified embedded-atom method interatomic potentials and recent progress in atomistic simulations,” Calphad-computer Coupling of Phase Diagrams and Thermochemistry. 2010. link Times cited: 138 Y.-M. Kim, N. Kim, and B.-J. Lee, “Atomistic Modeling of pure Mg and Mg―Al systems,” Calphad-computer Coupling of Phase Diagrams and Thermochemistry. 2009. link Times cited: 117 H. Yu and F.-jiu Sun, “A modified embedded atom method interatomic potential for the Ti―N system,” Physica B-condensed Matter. 2009. link Times cited: 9 S. R. Hosseini and F. Ashrafizadeh, “Accurate measurement and evaluation of the nitrogen depth profile in plasma nitrided iron,” Vacuum. 2009. link Times cited: 24 I. Sa and B.-J. Lee, “Modified embedded-atom method interatomic potentials for the Fe-Nb and Fe-Ti binary systems,” Scripta Materialia. 2008. link Times cited: 47 H.-K. Kim, W. Jung, and B.-J. Lee, “Modified embedded-atom method interatomic potentials for the Fe–Ti–C and Fe–Ti–N ternary systems,” Acta Materialia. 2008. link Times cited: 120 E.-H. Kim, Y.-H. Shin, and B.-J. Lee, “A modified embedded-atom method interatomic potential for Germanium,” Calphad-computer Coupling of Phase Diagrams and Thermochemistry. 2008. link Times cited: 85 J. Jang, B.-J. Lee, and J.-H. Hong, “Influence of Cu, Cr and C on the irradiation defect in Fe: A molecular dynamics simulation study,” Journal of Nuclear Materials. 2008. link Times cited: 14 Y.-M. Kim and B.-J. Lee, “A modified embedded-atom method interatomic potential for the Cu–Zr system,” Journal of Materials Research. 2004. link Times cited: 65 J. Zhu, G. Guo, and J. P. Wang, “Study of γ′-F4N Annealing Process Through Molecular Dynamics Modeling,” TMS 2022 151st Annual Meeting & Exhibition Supplemental Proceedings. 2022. link Times cited: 0 Z. Xu, Q. Zeng, L. Yuan, Y. Qin, M. Chen, and D. Shan, “Molecular dynamics study of the interactions of incident N or Ti atoms with the TiN(001) surface,” Applied Surface Science. 2016. link Times cited: 17 W. Joost, “Modeling the Influence of Phase Boundaries and Oxygen Interstitials on the Nucleation and Growth of Deformation Twins in the Alpha-Phase of Titanium Alloys.” 2015. link Times cited: 0 Abstract: Title of dissertation: MODELING THE INFLUENCE OF PHASE BOUND… read more Abstract: Title of dissertation: MODELING THE INFLUENCE OF PHASE BOUNDARIES AND OXYGEN INTERSTITIALS ON THE NUCLEATION AND GROWTH OF DEFORMATION TWINS IN THE ALPHA-PHASE OF TITANIUM ALLOYS William Joseph Joost, Doctor of Philosophy, 2015 Dissertation directed by: Professor Sreeramamurthy Ankem Professor Maija M. Kuklja Department of Materials Science and Engineering Twinning is an important deformation mechanism in many hexagonal close packed metals, including α-titanium alloys. However, the processes of twin nucleation, growth, and interaction with other defects are not well understood. Further, many aspects of deformation twinning are difficult to interrogate experimentally owing to the small time and length scales of the governing mechanisms. In this study we apply a combination of theoretical and computational materials science techniques, leveraged with experimental data, to quantify the effects of α-β phase boundaries and oxygen interstitials on twin nucleation, twin growth, and ultimately mechanical behavior in titanium alloys. Combined results from finite element method and analytical dislocation modeling demonstrate that elastic and plastic interaction stresses across the interface between the αand β-phases are responsible for the experimentally observed anisotropy in the deformation behavior of dual-phase alloys. Interaction stresses also promote slip and twinning at up to 30% lower applied stress than predicted from Schmid’s Law, significantly affecting performance in many applications. The complex interactions of phase boundaries, dislocations, and deformation twins modify the preferred deformation mechanism and promote twinning for some loading orientations. In order to quantify the interaction between oxygen interstitials and (101̄2) twin boundaries, we employ atomistic simulations using a newly developed modified embedded atom method potential and density functional theory. Our investigation reveals that a twin boundary alters interstitial formation energy by as much as 0.5 eV while also stabilizing a tetrahedral interstitial, which is unstable in the bulk. Further, the activation barriers for diffusion in the region near a twin are uniformly lower than in the bulk; an atom diffusing across the twin boundary moves through several paths with peak activation barriers more than 0.3 eV lower than for comparable diffusion far from the twin. Despite accelerated kinetics, oxygen diffusion still occurs much more slowly than twin growth, suggesting that oxygen interstitials contribute to experimentally observed time-dependent twinning. Together, these results provide new insight while enabling predictive modeling and purposeful development of improved titanium alloys across a wide range of applications. MODELING THE INFLUENCE OF PHASE BOUNDARIES AND OXYGEN INTERSTITIALS ON THE NUCLEATION AND GROWTH OF DEFORMATION TWINS IN THE ALPHA-PHASE OF TITANIUM ALLOYS read less T. Prasanthi, C. Sudha, S. Saroja, and M. Vijayalakshmi, “Simulation of nitrogen diffusion in Ni vis-à-vis Fe – Identification of better structural material for neutron detectors,” Results in physics. 2014. link Times cited: 3 Y.-M. Kim, Y.-H. Shin, and B.-J. Lee, “Modified embedded-atom method interatomic potentials for pure Mn and the Fe–Mn system,” Acta Materialia. 2009. link Times cited: 64 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 Y. Sun, H. Wang, Z. He, B. Qiao, and X. Chen, “Role of initial stage nitridation on the mechanical properties of an α-Fe(100) nanofilm in NH3.,” Physical chemistry chemical physics : PCCP. 2021. link Times cited: 2 Abstract: Nitrogen is one of the most significant non-native interstit… read more Abstract: Nitrogen is one of the most significant non-native interstitial elements that is present in the structure of Fe. Initial stage nitridation dramatically influences the mechanical properties of steel, especially for micro to nanoscale applications, but is not yet fully understood. By means of reactive force field molecular dynamics (ReaxFF MD) simulations, the initial stage of the nitridation process of nanofilm Fe, as well as its role on the mechanical properties of the material, were investigated. To clarify the temperature effect, nitridation was simulated in the range of 500-900 K, demonstrating that the adsorption of both N and H atoms into Fe was enhanced by thermal actuation. Corresponding tension test simulations were performed, manifesting that the Fe nanofilm nitrided at 600 K presents the highest yield stress. Further analysis shows that there is a competitive mechanism between the inward diffusion of N atoms that enhances the strength and simultaneous adsorption of H atoms, which leads to brittleness of the material as the temperature increases. Hence, an intermediate temperature could lead to optimal mechanical properties due to the balance of improving the strength while controlling the brittleness of the material. To probe the deformation mechanism, evolutions of partial dislocation and twin boundary at plasticity beginning for pure Fe and the nitrided Fe nanofilm are discussed. The present results show the nitridation strengthening technology of Fe in NH3 and its related microscale mechanism, which may theoretically support the technical design and improvement in the properties of steel. read less K. Hyodo, S. Munetoh, T. Tsuchiyama, and S. Takaki, “Empirical interatomic potential for Fe-N binary system based on Finnis–Sinclair potential,” Computational Materials Science. 2020. link Times cited: 7 X. Chong, Y.-hua Jiang, and J. Feng, “Exploring the intrinsic ductile metastable Fe-C compounds: Complex chemical bonds, anisotropic elasticity and variable thermal expansion,” Journal of Alloys and Compounds. 2018. link Times cited: 27 B. Narayanan et al., “Development of a Modified Embedded Atom Force Field for Zirconium Nitride Using Multi-Objective Evolutionary Optimization,” Journal of Physical Chemistry C. 2016. link Times cited: 23 Abstract: Zirconium nitride (ZrN) exhibits exceptional mechanical, che… read more Abstract: Zirconium nitride (ZrN) exhibits exceptional mechanical, chemical, and electrical properties, which make it attractive for a wide range of technological applications, including wear-resistant coatings, protection from corrosion, cutting/shaping tools, and nuclear breeder reactors. Despite its broad usability, an atomic scale understanding of the superior performance of ZrN, and its response to external stimuli, for example, temperature, applied strain, and so on, is not well understood. This is mainly due to the lack of interatomic potential models that accurately describe the interactions between Zr and N atoms. To address this challenge, we develop a modified embedded atom method (MEAM) interatomic potential for the Zr–N binary system by training against formation enthalpies, lattice parameters, elastic properties, and surface energies of ZrN (and, in some cases, also Zr3N4) obtained from density functional theory (DFT) calculations. The best set of MEAM parameters are determined by employing a multiobj... read less B. Liu, H. Zhang, J. Tao, Z. R. Liu, X. Chen, and Y. Zhang, “Development of a second-nearest-neighbor modified embedded atom method potential for silicon–phosphorus binary system,” Computational Materials Science. 2016. link Times cited: 8 M. Zacate, “Modified embedded-atom method potential for cadmium,” Hyperfine Interactions. 2019. link Times cited: 0 P. Srinivasan, A. Duff, T. Mellan, M. Sluiter, L. Nicola, and A. Simone, “The effectiveness of reference-free modified embedded atom method potentials demonstrated for NiTi and NbMoTaW,” Modelling and Simulation in Materials Science and Engineering. 2019. link Times cited: 15 Abstract: One of the effective potentials that has proven to be very v… read more Abstract: One of the effective potentials that has proven to be very versatile and useful for describing metals is the modified embedded atom method (MEAM) potential. The reference-free version of the MEAM (RF-MEAM) potential provides more flexibility for fitting than the 2NN-MEAM because it also describes the pair potential as an explicit function. In this work, we present a methodology to fit RF-MEAM potentials to DFT data. We then evaluate the performance of the fitted potential by comparing MD simulations with experimental and DFT data. As an example, the methodology is applied to a binary and a quaternary alloy, namely NiTi and NbMoTaW. In the case of the equi-atomic NiTi shape memory alloy, our attention focuses on designing a potential that properly captures its mechanical behavior, given that the existing potentials fail to predict elastic constants in agreement with experiments. To reach our aim, we included the stress tensors of different high temperature NiTi configurations in the fitting database. The obtained RF-MEAM potential outperforms existing EAM and MEAM potentials in predicting the lattice and elastic constants of austenitic and martensitic phases as well as the corresponding transformation temperatures. To demonstrate the suitability of this methodology also for more complex systems, a RF-MEAM potential is fitted to model the multi-component NbMoTaW high-entropy alloy. Validation is achieved through comparison between observables obtained through the MD output and ab initio data. The article also reports key improvements to the optimization code MEAMfit v2 and the freely-available LAMMPS implementation of the RF-MEAM formalism. Most notably, resorting to analytic derivatives of the objective function with respect to the potential parameters rather than derivatives through finite differences, the time necessary for fitting has decreased by an order of magnitude. read less G. Almyras, D. Sangiovanni, and K. Sarakinos, “Semi-Empirical Force-Field Model for the Ti1−xAlxN (0 ≤ x ≤ 1) System,” Materials. 2019. link Times cited: 20 Abstract: We present a modified embedded atom method (MEAM) semi-empir… read more Abstract: We present a modified embedded atom method (MEAM) semi-empirical force-field model for the Ti1−xAlxN (0 ≤ x ≤ 1) alloy system. The MEAM parameters, determined via an adaptive simulated-annealing (ASA) minimization scheme, optimize the model’s predictions with respect to 0 K equilibrium volumes, elastic constants, cohesive energies, enthalpies of mixing, and point-defect formation energies, for a set of ≈40 elemental, binary, and ternary Ti-Al-N structures and configurations. Subsequently, the reliability of the model is thoroughly verified against known finite-temperature thermodynamic and kinetic properties of key binary Ti-N and Al-N phases, as well as properties of Ti1−xAlxN (0 < x < 1) alloys. The successful outcome of the validation underscores the transferability of our model, opening the way for large-scale molecular dynamics simulations of, e.g., phase evolution, interfacial processes, and mechanical response in Ti-Al-N-based alloys, superlattices, and nanostructures. read less D. Dickel, C. Barrett, R. Cariño, M. Baskes, and M. Horstemeyer, “Mechanical instabilities in the modeling of phase transitions of titanium,” Modelling and Simulation in Materials Science and Engineering. 2018. link Times cited: 17 Abstract: In this paper, we demonstrate that previously observed β to … read more Abstract: In this paper, we demonstrate that previously observed β to α transitions for titanium interatomic potentials available in the literature arose from a mechanical instability and thus the potentials underestimated the correct thermodynamic phase transition temperature by hundreds of degrees. Using a relative free energy method for the two phases to calculate the true transition temperature, we present a new modified embedded atom method potential for titanium that shows a transition temperature of 1155 ± 2 K in excellent agreement with the experimentally observed transition. This free energy approach avoids the problems of irreversibility which occur when one relies on direct observation of the phase transition in molecular dynamics simulation. Other transformation mechanisms in addition to the mechanical instability are also considered. Finally, the new potential predicts the proper c-axis plastic twinning for titanium under compression making it the only potential that correctly predicts the phase transition temperature and the plastic behavior of α Ti. read less S. Liu et al., “Refinement effect of TiC on ferrite by molecular statics/dynamics simulations and first-principles calculations,” Journal of Alloys and Compounds. 2018. link Times cited: 3 K. Tong, F. Ye, M. Gao, M. Lei, and C. Zhang, “Interatomic potential for Fe–Cr–Ni–N system based on the second nearest-neighbor modified embedded-atom method,” Molecular Simulation. 2016. link Times cited: 7 Abstract: The interatomic potential for Fe–Cr–Ni–N system based on the… read more Abstract: The interatomic potential for Fe–Cr–Ni–N system based on the second nearest-neighbour modified embedded-atom method has been developed in this work. The potential is based on those for the corresponding lower order systems. The potential parameters for the binary systems, Cr–N, Ni–N, Ni–Fe and Ni–Cr, were determined by fitting the lattice constants, elastic properties, heat of solution and defect binding energies. The potential parameters for the ternary systems were calculated based on the corresponding binary systems. Then, all of them were applied to the quaternary system Fe–Cr–Ni–N to confirm their validity by a simulation of the lattice constants of AISI 316 austenitic stainless steel with a range of nitrogen content. The results were in good agreement with the previous observations and calculations. read less C. P. Chui, W. Liu, Y. Xu, and Y. Zhou, “Molecular Dynamics Simulation of Iron — A Review.” 2015. link Times cited: 3 Abstract: Molecular dynamics (MD) is a technique of atomistic simulati… read more Abstract: Molecular dynamics (MD) is a technique of atomistic simulation which has facilitated scientific discovery of interactions among particles since its advent in the late 1950s. Its merit lies in incorporating statistical mechanics to allow for examination of varying atomic configurations at finite temperatures. Its contributions to materials science from modeling pure metal properties to designing nanowires is also remarkable. This review paper focuses on the progress of MD in understanding the behavior of iron — in pure metal form, in alloys, and in composite nanomaterials. It also discusses the interatomic potentials and the integration algorithms used for simulating iron in the literature. Furthermore, it reveals the current progress of MD in simulating iron by exhibiting some results in the literature. Finally, the review paper briefly mentions the development of the hardware and software tools for such large-scale computations. read less M. H. Wu, X. Liu, J. Gu, and Z. Jin, “DFT study of nitrogen–vacancy complexions in (fcc) Fe,” Modelling and Simulation in Materials Science and Engineering. 2014. link Times cited: 9 Abstract: Formation energies of nitrogen (N)/vacancy (v) monomers, N–N… read more Abstract: Formation energies of nitrogen (N)/vacancy (v) monomers, N–N and N–v dimers and N–v complexions in an ideal face-centered cubic (fcc) lattice of iron are obtained via DFT calculations. Based on a thermodynamic model, the occupancies of various complexions and the vacancy concentration as a function of the chemical potential of N and temperature T are predicted. We found that increasing the chemical potential or content of N can increase the vacancy concentration considerably, e.g. compared with the case without nitrogen, increasing the N content to 10 at% at 750 K can increase the vacancy concentration by about eight orders of magnitude when a saturated concentration is reached. read less K. Henriksson, C. Björkas, and K. Nordlund, “Atomistic simulations of stainless steels: a many-body potential for the Fe–Cr–C system,” Journal of Physics: Condensed Matter. 2013. link Times cited: 62 Abstract: Stainless steels found in real-world applications usually ha… read more Abstract: Stainless steels found in real-world applications usually have some C content in the base Fe–Cr alloy, resulting in hard and dislocation-pinning carbides—Fe3C (cementite) and Cr23C6—being present in the finished steel product. The higher complexity of the steel microstructure has implications, for example, for the elastic properties and the evolution of defects such as Frenkel pairs and dislocations. This makes it necessary to re-evaluate the effects of basic radiation phenomena and not simply to rely on results obtained from purely metallic Fe–Cr alloys. In this report, an analytical interatomic potential parameterization in the Abell–Brenner–Tersoff form for the entire Fe–Cr–C system is presented to enable such calculations. The potential reproduces, for example, the lattice parameter(s), formation energies and elastic properties of the principal Fe and Cr carbides (Fe3C, Fe5C2, Fe7C3, Cr3C2, Cr7C3, Cr23C6), the Fe–Cr mixing energy curve, formation energies of simple C point defects in Fe and Cr, and the martensite lattice anisotropy, with fair to excellent agreement with empirical results. Tests of the predictive power of the potential show, for example, that Fe–Cr nanowires and bulk samples become elastically stiffer with increasing Cr and C concentrations. High-concentration nanowires also fracture at shorter relative elongations than wires made of pure Fe. Also, tests with Fe3C inclusions show that these act as obstacles for edge dislocations moving through otherwise pure Fe. read less Y. You and M. Yan, “Many-body potential for nitrogen in α-iron,” Philosophical Magazine Letters. 2012. link Times cited: 3 Abstract: N atom is one of the most frequent foreign interstitial atom… read more Abstract: N atom is one of the most frequent foreign interstitial atoms in α-iron along with C atoms. The Fe–C potential has been well-developed and can reproduce many significant interactions of C with point defects present in α-iron. However, there exists no satisfactory Fe–N potential to describe the interactions of N with point defects. Here, we develop a many-body potential for N in α-iron. The potential parameters are determined by fitting to ab initio data, which includes energetics, configurations, and relaxations of Fe atoms close to N atom. This potential successfully describes the interactions of Fe–N across a wide range of defect environments. The potential employs the embedded atom method form and hence is appropriate for large-scale molecular dynamics simulation. read less J. Kang, B. Hosseinkhani, and P. Rivera-Diaz-Del-Castillo, “Rolling contact fatigue in bearings: multiscale overview,” Materials Science and Technology. 2012. link Times cited: 77 Abstract: For over a century, rolling contact fatigue in bearings has … read more Abstract: For over a century, rolling contact fatigue in bearings has been recognised as a key feature limiting bearing life. The phenomenon is manifested through dark etching regions, 30 and 80° white etching bands as well as white etching areas, the latter often forming intricate defects commonly referred to as butterflies. Their presence depends on testing conditions, such as contact pressure, temperature, number of revolutions and steel cleanliness. Microstructural inspection demonstrates that precipitate shearing, dissolution, cell and nanocrystal formation as well as matrix/inclusion debonding may take place throughout bearing life. Such microstructural features have a negative effect on bearing hardness, strength, ductility and toughness, usually preceding failure. The present review shows how such phenomena are interconnected, highlighting the need for integral characterisation and modelling across the scales. This will aid in the conception of new heat treatments, steel grades and microstructures for enhanced rolling contact fatigue, leading to increased bearing life. read less S. R. Hosseini, F. Ashrafizadeh, and A. Kermanpur, “Analytical–experimental approach for accurate depth profile evaluation of diffusion zone in plasma nitrided iron,” Surface Engineering. 2011. link Times cited: 3 Abstract: Nitrogen depth profile of diffusion zone in plasma nitrided … read more Abstract: Nitrogen depth profile of diffusion zone in plasma nitrided pure iron was analytically calculated and experimentally measured. Nitrogen concentration equation was obtained versus nitriding temperature, time and diffusion distance. Plasma nitriding was carried out on pure iron substrate at 550°C in an atmosphere of 75H2–25N2. Nitrogen concentration depth profile in compound layer was characterised by glow discharge optical emission spectroscopy (GDOES) and for detection of nitrogen within the diffusion zone, secondary ion mass spectroscopy (SIMS) technique was employed. Nitrogen diffusion depths were measured accurately by optical and scanning electron microscopy as well as SIMS technique at different nitriding times. Experimental results indicated good agreement with calculated diffusion depths for various nitriding cycles. The extent of nitrogen diffusion depth in alpha zone, detected in this work for 10 h plasma nitriding at 550°C, was in excess of 2000 μm; such values have not been reported in previous investigations that conventionally used EDS, GDS, XPS or EPMA technique. read less H.-K. Kim, W. Jung, and B.-J. Lee, “Modified embedded-atom method interatomic potentials for the Nb-C, Nb-N, Fe-Nb-C, and Fe-Nb-N systems,” Journal of Materials Research. 2010. link Times cited: 21 Abstract: Modified embedded-atom method (MEAM) interatomic potentials … read more Abstract: Modified embedded-atom method (MEAM) interatomic potentials for Nb-C, Nb-N, Fe-Nb-C, and Fe-Nb-N systems have been developed based on the previously developed MEAM potentials for lower order systems. The potentials reproduce various fundamental physical properties (structural properties, elastic properties, thermal properties, and surface properties) of NbC and NbN, and interfacial energy between bcc Fe and NbC or NbN, in generally good agreement with higher-level calculations or experimental information. The applicability of the present potentials to atomic-level investigations to the precipitation behavior of complex-carbonitrides (Nb,Ti)(C,N) as well as NbC and NbN, and their effects on the mechanical properties of steels are also discussed. read less B.-J. Lee, “A Semi-Empirical Atomistic Approach in Materials Research,” Journal of Phase Equilibria and Diffusion. 2009. link Times cited: 3 E. C. Do, Y.-H. Shin, and B.-J. Lee, “Atomistic modeling of III–V nitrides: modified embedded-atom method interatomic potentials for GaN, InN and Ga1−xInxN,” Journal of Physics: Condensed Matter. 2009. link Times cited: 25 Abstract: Modified embedded-atom method (MEAM) interatomic potentials … read more Abstract: Modified embedded-atom method (MEAM) interatomic potentials for the Ga–N and In–N binary and Ga–In–N ternary systems have been developed based on the previously developed potentials for Ga, In and N. The potentials can describe various physical properties (structural, elastic and defect properties) of both zinc-blende and wurtzite-type GaN and InN as well as those of constituent elements, in good agreement with experimental data or high-level calculations. The potential can also describe the structural behavior of Ga1−xInxN ternary nitrides reasonably well. The applicability of the potentials to atomistic investigations of atomic/nanoscale structural evolution in Ga1−xInxN multi-component nitrides during the deposition of constituent element atoms is discussed. read less L. A. Bol’shov, V. Bogdanov, and V. A. Gorbunov, “Thermodynamic analysis of the data on the solubility of nitrogen in gamma iron at a high pressure,” The Physics of Metals and Metallography. 2009. link Times cited: 2 B.-J. Lee, J. Shim, and J. Kwon, “Effects of crystallographic structure and Cr on the rate of void nucleation in BCC Fe: An atomistic simulation study,” Metals and Materials International. 2008. link Times cited: 1 Abstract: Atomistic Monte Carlo simulations based on modified embedded… read more Abstract: Atomistic Monte Carlo simulations based on modified embedded-atom method (MEAM) interatomic potentials have been carried out to clarify the differences in swelling rates between bcc and fcc Fe and between pure bcc Fe and bcc Fe−Cr alloys. Assuming that the transient regimes prior to the onset of steady-state swelling correspond to the void nucleation stage, the effect of crystallographic structure (bcc vs. fcc) or Cr alloying on the void nucleation rate under a given amount of supersaturated vacancies was examined. It was found that the void nucleation rate is much higher in fcc Fe than in bcc Fe. Randomly distributed Cr atoms slightly increase the void nucleation rate in bcc Fe, but microstructural evolutions such as the precipitation of Cr-rich phase have more decisive effects, serving as a vacancy sink. The reasons for the individual results are rationalized in terms of the binding energy of vacancy clusters and the size difference between Fe and Cr atoms. read less S. Valone and M. Baskes, “Self-Irradiation Cascade Simulations in Plutonium Metal: Model Behavior at High Energy,” Journal of Computer-Aided Materials Design. 2007. link Times cited: 10 N. Razmara and R. Mohammadzadeh, “Molecular dynamics study of nitrogen diffusion in nanocrystalline iron,” Journal of Molecular Modeling. 2016. link Times cited: 6 W. Joost, S. Ankem, and M. Kuklja, “A modified embedded atom method potential for the titanium–oxygen system,” Modelling and Simulation in Materials Science and Engineering. 2014. link Times cited: 16 Abstract: Small concentrations of impurity atoms can affect the behavi… read more Abstract: Small concentrations of impurity atoms can affect the behavior of metal alloys in many ways of interest to the science and engineering community. In some cases, such as for oxygen (O) interstitials and twins or dislocations in titanium (Ti) alloys, these interactions can be difficult to study experimentally due to the small time and length scales of the governing mechanisms. Theory and atomic-scale modeling offers a path toward understanding materials at very high resolution using a variety of techniques ranging from ab initio methods such as density functional theory (DFT) to empirical potential methods such as the Modified Embedded Atom Method (MEAM). In this study we present the first published MEAM potential for the Ti–O system; the potential is fit to experimental measurements and DFT calculations for the lattice constants, elastic constants and thermodynamic characteristics of several Ti–O structures with O concentration between 0 and 50 at%. We validate the effectiveness of the new potential by successfully reproducing properties such as lattice constants, elastic constants and diffusion energy barriers for other structures. In doing so, we have calculated and report properties for two new stable structures of TiO: a CsCl structure and a zinc blende structure. We also report the first theoretical study on the effects of O concentration on the elastic constants of hexagonal close packed Ti without the confounding effects of changing supercell size. Overall, this new potential will enable interrogation of Ti and O interactions at time and length scales below those available experimentally and above the range accessible by DFT. read less
Funding	Not available

Short KIM ID The unique KIM identifier code.	MO_432861766738_002
Extended KIM ID The long form of the KIM ID including a human readable prefix (100 characters max), two underscores, and the Short KIM ID. Extended KIM IDs can only contain alpha-numeric characters (letters and digits) and underscores and must begin with a letter.	MEAM_LAMMPS_LeeLeeKim_2006_FeN__MO_432861766738_002
DOI	10.25950/22f2df58 https://doi.org/10.25950/22f2df58 https://commons.datacite.org/doi.org/10.25950/22f2df58
KIM Item Type Specifies whether this is a Portable Model (software implementation of an interatomic model); Portable Model with parameter file (parameter file to be read in by a Model Driver); Model Driver (software implementation of an interatomic model that reads in parameters).	Portable Model using Model Driver MEAM_LAMMPS__MD_249792265679_002
Driver	MEAM_LAMMPS__MD_249792265679_002
KIM API Version	2.2
Potential Type	meam

Previous Version	MEAM_LAMMPS_LeeLeeKim_2006_FeN__MO_432861766738_001

Verification Check Dashboard

(Click here to learn more about Verification Checks)

Grade	Name	Category	Brief Description	Full Results	Aux File(s)
P All elements claimed by model are supported in at least one of the tested configurations.	vc-species-supported-as-stated	mandatory	The model supports all species it claims to support; see full description.	Results	Files
P Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.	vc-periodicity-support	mandatory	Periodic boundary conditions are handled correctly; see full description.	Results	Files
P Model energy has permutation symmetry for all configurations the model was able to compute.	vc-permutation-symmetry	mandatory	Total energy and forces are unchanged when swapping atoms of the same species; see full description.	Results	Files
A The letter grade A was assigned because the normalized error in the computation was 1.83987e-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^0 continuous. This means that the model has continuous energy, but a discontinuous first derivative.	vc-dimer-continuity-c1	informational	The energy versus separation relation of a pair of atoms is C1 continuous (i.e. the function and its first derivative are continuous); see full description.	Results	Files
P Model energy and forces are invariant with respect to rigid-body motion (translation and rotation) for all configurations the model was able to compute.	vc-objectivity	informational	Total energy is unchanged and forces transform correctly under rigid-body translation and rotation; see full description.	Results	Files
P Model energy has inversion symmetry for all configurations the model was able to compute.	vc-inversion-symmetry	informational	Total energy is unchanged and forces change sign when inverting a configuration through the origin; see full description.	Results	Files
P No memory leak detected.	vc-memory-leak	informational	The model code does not have memory leaks (i.e. it releases all allocated memory at the end); see full description.	Results	Files
P All threads give identical results for tested case. Model appears to be thread-safe.	vc-thread-safe	mandatory	The model returns the same energy and forces when computed in serial and when using parallel threads for a set of configurations. Note that this is not a guarantee of thread safety; see full description.	Results	Files
P Unit conversion successful	vc-unit-conversion	mandatory	The model is able to correctly convert its energy and/or forces to different unit sets; see full description.	Results	Files

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

Species: 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: N

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: N

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: 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: 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: Fe

Cubic Crystal Basic Properties Table

Species: Fe

Species: N

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 Fe v004	view	7141
Cohesive energy versus lattice constant curve for diamond Fe v004	view	6674
Cohesive energy versus lattice constant curve for diamond N v004	view	7141
Cohesive energy versus lattice constant curve for fcc Fe v004	view	7320
Cohesive energy versus lattice constant curve for sc Fe v004	view	6604

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 Fe at zero temperature v006	view	46627
Elastic constants for diamond Fe at zero temperature v001	view	47681
Elastic constants for diamond N at zero temperature v001	view	59268
Elastic constants for fcc Fe at zero temperature v006	view	44025
Elastic constants for sc Fe at zero temperature v006	view	24000

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 FeN in AFLOW crystal prototype A2B_oP12_60_d_c v002	view	78921
Equilibrium crystal structure and energy for FeN in AFLOW crystal prototype A3B_hP8_182_g_c v002	view	99388
Equilibrium crystal structure and energy for FeN in AFLOW crystal prototype A3B_oP16_62_cd_c v002	view	75342
Equilibrium crystal structure and energy for FeN in AFLOW crystal prototype A4B_cP5_221_ac_b v002	view	68541
Equilibrium crystal structure and energy for FeN in AFLOW crystal prototype A8B_tI18_139_deh_a v002	view	55049
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_cF4_225_a v002	view	146799
Equilibrium crystal structure and energy for N in AFLOW crystal prototype A_cI20_217_ce v002	view	137965
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_cI2_229_a v002	view	68688
Equilibrium crystal structure and energy for N in AFLOW crystal prototype A_cI8_199_a v002	view	102701
Equilibrium crystal structure and energy for N in AFLOW crystal prototype A_cP8_198_2a v002	view	89964
Equilibrium crystal structure and energy for N in AFLOW crystal prototype A_cP8_205_c v002	view	67504
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_hP2_194_c v002	view	63755
Equilibrium crystal structure and energy for N in AFLOW crystal prototype A_hP2_194_c v002	view	71338
Equilibrium crystal structure and energy for N in AFLOW crystal prototype A_hP4_194_f v002	view	39312
Equilibrium crystal structure and energy for N in AFLOW crystal prototype A_hR16_167_cf v002	view	149082
Equilibrium crystal structure and energy for N in AFLOW crystal prototype A_oP2_51_e v002	view	44962
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_tP28_136_f2ij v002	view	116615
Equilibrium crystal structure and energy for N in AFLOW crystal prototype A_tP4_136_f v002	view	40102
Equilibrium crystal structure and energy for FeN in AFLOW crystal prototype AB_cF8_216_a_c v002	view	121032
Equilibrium crystal structure and energy for FeN in AFLOW crystal prototype AB_cF8_225_a_b v002	view	80932

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	7426231
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in bcc Fe v001	view	22373189
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in bcc Fe v001	view	12566313
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in bcc Fe v001	view	46336186
Relaxed energy as a function of tilt angle for a 100 symmetric tilt grain boundary in fcc Fe v001	view	19983583
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in fcc Fe v001	view	76531049
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in fcc Fe v001	view	34641928

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 Fe v007	view	13258
Equilibrium zero-temperature lattice constant for diamond Fe v007	view	13109
Equilibrium zero-temperature lattice constant for diamond N v007	view	13099
Equilibrium zero-temperature lattice constant for fcc Fe v007	view	11338
Equilibrium zero-temperature lattice constant for sc Fe v007	view	10969

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 Fe v005		view	113817
Equilibrium lattice constants for hcp N v005		view	118750

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 Fe at 293.15 K under a pressure of 0 MPa v002		view	1506349

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 Fe v004		view	65902

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 Fe		view	299635

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 Fe		view	4206896

Errors

ElasticConstantsHexagonal__TD_612503193866_004

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

EquilibriumCrystalStructure__TD_457028483760_002

Test	Error Categories	Link to Error page
Equilibrium crystal structure and energy for FeN in AFLOW crystal prototype A2B_mC18_12_ij_ah v002	other	view
Equilibrium crystal structure and energy for FeN in AFLOW crystal prototype A2B_mC18_5_3c_2ab v002	other	view
Equilibrium crystal structure and energy for FeN in AFLOW crystal prototype A2B_oP12_29_2a_a v002	other	view
Equilibrium crystal structure and energy for FeN in AFLOW crystal prototype A3B_mC16_5_3c_ab v002	other	view
Equilibrium crystal structure and energy for FeN in AFLOW crystal prototype A3B_oC16_20_ac_b v002	other	view
Equilibrium crystal structure and energy for Fe in AFLOW crystal prototype A_tP1_123_a v002	other	view

GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle__TD_410381120771_003

Test	Error Categories	Link to Error page
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in fcc Fe v001	other	view

LatticeConstantCubicEnergy__TD_475411767977_007

Test	Error Categories	Link to Error page
Equilibrium zero-temperature lattice constant for bcc N v007	other	view
Equilibrium zero-temperature lattice constant for fcc N v007	other	view
Equilibrium zero-temperature lattice constant for sc N v007	other	view

SurfaceEnergyCubicCrystalBrokenBondFit__TD_955413365818_004

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

Files

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FeN.meam
LICENSE
elems.meam
kimprovenance.edn
kimspec.edn
library.meam

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MEAM_LAMMPS__MD_249792265679_002.zip	Zip	Windows archive

Wiki

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Parameter Choices in the SW Potential

In the original Stillinger-Weber paper (SW85: PRB 31:5262, 1985) it is stated that in order to obtain the correct “atomization energy” (cohesive energy) the following choice for epsilon must be made (see Eqn. (2.9) in [SW85]):

epsilon = 50 kcal/mol = 3.4723E-12 erg/atom

Unfortunately, there appears to be an error in the unit conversion here. (There is also an indeterminacy associated with the “kcal” unit which can mean different things.) The kcal and erg values have led to two different values for epsilon being used in articles that cite [SW85].

(a) If the kcal number is selected (assuming that S&W meant the thermochemical kcal unit), then epsilon = 2.1682 eV. This can be seen from the following conversion (which uses NIST conversion factors):

(50 kcal_th/mol)/(6.02214129 mol^-1) = 8.30269461E-23 kcal_th

8.30269461E-23 kcal_th x 4.184E+03 (J/kcal_th) = 3.47384742E-19 J

3.47384742E-19 J x 6.24150934E+18 (eV/J) = 2.168205112 eV

(b) If the erg number is selected, then epsilon = 2.1672 eV, which follows from:

3.4723E-12 erg x 6.24150934E+11 (eV/erg) = 2.16723929 eV

As noted above, both values have been used in simulations that cite the original [SW85] paper. However, it appears that S&W intended to use the 50 kcal_th/mol value since they refer to this number more than once in the paper. (See for example discussion after Eqn. (8.1) in [SW85].) Therefore we argue that the appropriate choice is

epsilon = 8.30269461E-23 kcal_th

or in eV units (reduced to 5-digit significant digits):

epsilon = 2.1682 eV

Note that in the Si.sw parameterization for this potential distributed with LAMMPS, a value of epsilon=2.1683 is used, which appears to be due to slightly different unit conversion.

Another source of confusion is that in [SW85] the potential is fitted to an incorrect value for the cohesive energy of silicon. This is corrected by Balamane in a 1992 paper. See https://openkim.org/cite/MO_113686039439_004 for more details.

SW Functions

See the Stillinger-Weber Model driver page (linked above) for the definition of the model and its functions. The graphs below are for the Stillinger-Weber parametrization for silicon.

The graph of function $f_{2}$ with the parameter values suggested by Stillinger and Weber ( $A = 7.049556277$ , $B = 0.6022245584$ , $p = 4$ , $q = 0$ , $a = 1.80$ ) is given in the following Figure:

The contour plot of the function $h$ in $f_{3}$ for $θ = \cos^{- 1} (- 0.25) = {104.48}^{\circ}$ , as a function of $r_{i j}$ and $r_{i k}$ is given below:

MEAM_LAMMPS_LeeLeeKim_2006_FeN__MO_432861766738_002

Verification Check Dashboard

Visualizers (in-page)

BCC Lattice Constant

Cohesive Energy Graph

Diamond Lattice Constant

Dislocation Core Energies

FCC Elastic Constants

FCC Lattice Constant

FCC Stacking Fault Energies

FCC Surface Energies

SC Lattice Constant

Cubic Crystal Basic Properties Table

Tests

Errors

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Parameter Choices in the SW Potential

SW Functions