MEAM Potential for the Ti-N system developed by Kim and Lee (2008) v002

Young-Min Kim; Byeong-Joo Lee

doi:10.25950/2e66694f

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MEAM_LAMMPS_KimLee_2008_TiN__MO_070542625990_002

Interatomic potential for Nitrogen (N), Titanium (Ti).
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Title A single sentence description.	MEAM Potential for the Ti-N system developed by Kim and Lee (2008) 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.	Modified embedded-atom method (MEAM) interatomic potentials for the Ti–N binary system has been developed using previously developed MEAM potentials of Ti, C and N. The potential parameters were determined by fitting to experimental data on the enthalpy of formation, lattice parameter, elastic constants, thermal linear expansion of NaCl-type TiN, and dilute heat of solution of carbon and nitrogen atoms in hexagonal close-packed Ti. In the original paper (Kim and Lee, Acta Materialia, 56(14), 2008), the potential can describe fundamental physical properties (structural, elastic, thermal and surface properties) of the alloys well, in good agreement with experimental information or first-principles calculations.
Species The supported atomic species.	N, Ti
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	Joonho Ji
Maintainer	Joonho Ji
Developer	Young-Min Kim Byeong-Joo Lee
Published on KIM	2023
How to Cite	This Model originally published in [1] is archived in OpenKIM [2-5]. [1] Kim Y-M, Lee B-J. Modified embedded-atom method interatomic potentials for the Ti–C and Ti–N binary systems. Acta materialia. 2008;56(14):3481–9. doi:10.1016/j.actamat.2008.03.027 — (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] Kim Y-M, Lee B-J. MEAM Potential for the Ti-N system developed by Kim and Lee (2008) v002. OpenKIM; 2023. doi:10.25950/2e66694f [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. 66 Citations (50 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 . H. Zhang, A. Pan, R. Hei, and P. Liu, “An atomistic simulation on the tensile and compressive deformation mechanisms of nano-polycrystalline Ti,” Applied Physics A. 2021. link Times cited: 3 B. Wang, Z. Wang, and W.-H. Song, “Electronic and elastic properties of TixZr1-xN.” 2016. link Times cited: 0 Abstract: The lattice parameter, elastic modulus, elastic constants an… read more Abstract: The lattice parameter, elastic modulus, elastic constants and electronic structure of Ti xZr1-xN(x=0, 0.25, 0.5, 0.75, 1) were studied with first-principle pseudopotential plane-waves method. The lattice parameters of TixZr1-xN increase with Zr atoms increasing. Bulk modulus B, shear modulus G and Young's Modulus E express a monotonously decreasing with Zr concentration. For the shear modulus is proportional to the hardness, the hardness is supposed to be decreasing with Zr concentration. By analyzing the density of states, N p and Ti(Zr) d states hybridized strongly, which form the strong p-d covalent bonds, having positive impact on the hardness. read less J. Chun and B. Lee, “Atomistic calculations of mechanical properties of Ni-Ti-C metallic glass systems,” Journal of Mechanical Science and Technology. 2013. link Times cited: 0 A. Goncharov, A. Yunda, I. Kolinko, G. Kornich, and D. Shyrokorad, “Modeling the Deposition of Thin Films of Transition Metal Nitrides,” Coatings. 2023. link Times cited: 0 Abstract: This paper presents an overview of studies dedicated to the … read more Abstract: This paper presents an overview of studies dedicated to the atomic-discrete modeling of the growth process of film coatings that comprise mononitrides of transition and post-transition metals. The main modeling approaches are the Monte Carlo and molecular dynamics methods as well as their combinations with analytical contributions. The molecular dynamics method is more accurate compared to the Monte Carlo method but has disadvantages related to the time scale. Given this, the adoption of accelerated molecular dynamics methods is viewed as a promising approach for directly simulating the specified processes. These methods can be implemented just after the relaxation of the collision stage in the area of the deposited particle between the deposition events to simulate the realistic density of the incident beam and accompanied long-term mass transfer processes. read less F. Guo et al., “Microstructure evolution under thermo-mechanical operating of rocksalt-structure TiN via neural network potential.,” The Journal of chemical physics. 2023. link Times cited: 0 Abstract: In the process of high temperature service, the mechanical p… read more Abstract: In the process of high temperature service, the mechanical properties of cutting tools decrease sharply due to the peeling of the protective coating. However, the mechanism of such coating failure remains obscure due to the complicated interaction between atomic structure, temperature, and stress. This dynamic evolution nature demands both large system sizes and accurate description on the atomic scale, raising challenges for existing atomic scale calculation methods. Here, we developed a deep neural network (DNN) potential for Ti-N binary systems based on first-principles study datasets to achieve quantum-accurate large-scale atomic simulation. Compared with empirical interatomic potential based on the embedded-atom-method, the developed DNN-potential can accurately predict lattice constants, phonon properties, and mechanical properties under various thermodynamic conditions. Moreover, for the first time, we present the atomic evolution of the fracture behavior of large-scale rocksalt-structure (B1) TiN systems coupled with temperature and stress conditions. Our study validates that interatomic brittle fractures occur when TiN stretches beyond its tensile yield point. Such simulation of coating fracture and cutting behavior based on large-scale atoms can shed new light on understanding the microstructure and mechanical properties of coating tools under extreme operating conditions. read less Z. Gong et al., “Young’s modulus prediction model for metal carbides based on first-principles calculations,” Materials Chemistry and Physics. 2023. link Times cited: 0 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 X. Lin, X. Feng, M. He, H. Liu, S. Liu, and B. Wen, “Temperature-Dependent Easy Slip System Transformation in WC and TiC,” Metallurgical and Materials Transactions A. 2023. link Times cited: 0 M. Lebeda, J. Drahokoupil, P. Veřtát, and P. Vlčák, “Quantifying low-energy nitrogen ion channeling in α-titanium by molecular dynamics simulations,” Materials Chemistry and Physics. 2023. link Times cited: 0 J. Li, S. Yang, L. Dong, J. Zhang, Z. Zheng, and J. Liu, “Effect of crystal orientation on the nanoindentation deformation behavior of TiN coating based on molecular dynamics,” Surface and Coatings Technology. 2023. link Times cited: 0 Z. Guo et al., “Atomic simulation for the effect of nano-cutting parameters on the 3D surface morphology of polycrystalline γ-TiAl alloy,” Modelling and Simulation in Materials Science and Engineering. 2023. link Times cited: 0 Abstract: γ-TiAl alloy is one of the most potentially lightweight and … read more Abstract: γ-TiAl alloy is one of the most potentially lightweight and high-temperature structural materials, and its machined surface quality has a significant effect on member service performance. Despite the extensive research on plastic removal and defect evolution under different cutting parameters, the forming mechanism of surface topography is not perfect under different cutting parameters. It is necessary to study the variation law of surface topography under the influence of different cutting parameters from the atomic scale. To this end, the influence of cutting depths and cutting speeds on the machined surface topography is investigated during nano-cutting of polycrystalline γ-TiAl alloys based on molecular dynamics simulation methods, and the effect of defective grain boundaries on cutting force fluctuations is analyzed. The results show that the effect of grain boundary on material deformation and dislocation obstruction is the main reason for the peak cutting force; with the increase of cutting depth, the average cutting force and friction coefficient increase, and both Sa and Sq show an increasing trend, which is the result of the joint action of plowing effect and grain boundary distribution; Sa and Sq show a decreasing and then increasing trend with the increase of cutting speed, and the critical cutting speed is 200 m s−1. This indicates that a smaller cutting depth and an appropriately higher cutting speed can effectively improve the surface quality of the polycrystalline γ-TiAl alloy, and optimize its nano-cutting process. read less J. Zhou et al., “Grain-size effects of TiC on mechanical properties in diamond/TiC combinations: A molecular dynamics exploration,” Diamond and Related Materials. 2023. link Times cited: 0 J. Li et al., “Molecular Dynamics Simulation of the Incident Energy Effect on the Properties of TiN Films,” Coatings. 2023. link Times cited: 2 Abstract: In this work, to investigate the physical vapor deposition (… read more Abstract: In this work, to investigate the physical vapor deposition (PVD)-deposited TiN coating on the TiN(001) substrate, the process was simulated using the molecular dynamics (MD) method with the 2NN-MEAM (nearest-neighbor modified embedded atom method) potential. The results revealed that the growth mode of TiN film is determined by incident energy. When the incident energy is low, the deposited atoms have weak mobility after momentum transfer with the substrate and cannot fill the vacancy in the TiN film, and thus the TiN film eventually grows in an island shape. When increasing the incident energy, the vibration of atoms on the deposited surface is intensified, and some atoms on the film surface jump. Therefore, the non-thermal diffusion occurs, resulting in defect reduction on the TiN film and forming a lamellar growth with a more continuous and complete film. The growing incident energy continuously reduces the surface roughness of the TiN film. read less Y. Kimura, K. K. Tanaka, Y. Inatomi, C. Aktas, and J. Blum, “Nucleation experiments on a titanium-carbon system imply nonclassical formation of presolar grains,” Science Advances. 2023. link Times cited: 1 Abstract: Just as the shapes of snowflakes provide us with information… read more Abstract: Just as the shapes of snowflakes provide us with information on the temperature and humidity of the upper atmosphere, the characteristics of presolar grains in meteorites place limits on their formation environment in a stellar outflow. However, even in the case of well-characterized presolar grains consisting of a titanium carbide core and a graphitic carbon mantle, it is not possible to delimit their formation environment. Here, we have demonstrated the formation of core-mantle grains in gravitational and microgravity environments and have found that core-mantle grains are formed by a nonclassical nucleation pathway involving the three steps: (i) primary nucleation of carbon at a substantially high supersaturation, (ii) heterogeneous condensation of titanium carbide on the carbon, and (iii) fusion of nuclei. We argue that the characteristics of not only core-mantle grains but also other presolar and solar grains might be accurately explained by considering a nonclassical nucleation pathway. read less J. Zhou et al., “Molecular dynamics simulation of the tensile response and deformation mechanism of diamond/TiC combinations,” Computational Materials Science. 2022. link Times cited: 3 N. Dhariwal, A. S. M. Miraz, W. Meng, and C. Wick, “Strengthening the Ti/Tin Interface Against Shear Failure with Al Dopants:A Molecular Dynamics Study,” SSRN Electronic Journal. 2022. link Times cited: 1 M. Zheng et al., “Study on Nanoscale Friction Behavior of TiC/Ni Composites by Molecular Dynamics Simulations,” Coatings. 2022. link Times cited: 1 Abstract: To systematically investigate the friction and wear behavior… read more Abstract: To systematically investigate the friction and wear behavior of TiC/Ni composites under microscopic, the molecular dynamics (MD) method was used to simulate nano-friction on the TiC/Ni composite. Mechanical properties, abrasion depth, wear rates, temperature change of the material during friction, the microscopic deformation behavior, and the evolution of nickel-based titanium carbide microstructure at high-speed friction have been systematically studied. It was found that the variation of tangential and normal forces is related to the relative position of the grinding ball and the TiC phase, when the grinding ball is located above the TiC phase, large fluctuations in the frictional force occur and extreme value of normal force appears, shallow abrasion depth and low wear rate. During the friction process, there is a high-stress area between the grinding ball and the TiC phase, generating a large number of dislocations. The presence of the TiC phase hinders the development and extension of defects, resulting in a significant increase in temperature. At the same time, dislocation entanglement occurs, which improves the wear resistance of the workpiece. In addition, it was also found that the internal atomic motion guided by the carbonized phase was related to the position of the grinding ball relative to the reinforced phase, with the reinforced phase presenting a tendency to rotate in different directions when the grinding ball was in different positions relative to the reinforced phase, which in turn affected the deformation of the whole workpiece. read less M. Lebeda, P. Vlčák, and J. Drahokoupil, “Influence of nitrogen interstitials in α-titanium and nitrogen vacancies in δ-titanium nitride on lattice parameters and bulk modulus - computational study,” Computational Materials Science. 2022. link Times cited: 2 T. Miyagawa, K. Mori, N. Kato, and A. Yonezu, “Development of neural network potential for MD simulation and its application to TiN,” Computational Materials Science. 2022. link Times cited: 3 M. Zheng et al., “Molecular dynamics study on the nanoscale repeated friction and wear mechanisms of TiC/Ni composites,” Applied Physics A. 2022. link Times cited: 7 M. Zheng et al., “Molecular dynamics study on the nanoscale repeated friction and wear mechanisms of TiC/Ni composites,” Applied Physics A. 2022. link Times cited: 0 A. Mahata, T. Mukhopadhyay, and M. A. Zaeem, “Modified embedded-atom method interatomic potentials for Al-Cu, Al-Fe and Al-Ni binary alloys: From room temperature to melting point,” Computational Materials Science. 2022. link Times cited: 27 P. Gholizadeh, H. Amini, J. Davoodi, and E. Poursaeidi, “Molecular dynamic simulation of crack growth in Ti/TiN multilayer coatings,” Materials Today Communications. 2021. link Times cited: 11 N. Dhariwal, A. S. M. Miraz, W. Meng, B. Ramachandran, and C. Wick, “Impact of metal/ceramic interactions on interfacial shear strength: Study of Cr/TiN using a new modified embedded-atom potential,” Materials & Design. 2021. link Times cited: 4 P. Huo, Z. Zhao, W. Du, Z. Zhang, P. Bai, and D. Tie, “Deformation strengthening mechanism of in situ TiC/TC4 alloy nanocomposites produced by selective laser melting,” Composites Part B: Engineering. 2021. link Times cited: 26 D. Yang, Y. Sun, Z. Yang, X. Chen, and C. Wang, “Multiscale modeling of unidirectional composites with interfacial debonding using molecular dynamics and micromechanics,” Composites Part B-engineering. 2021. link Times cited: 7 Y. Yang, M. Liu, S. Zhou, W. Ren, Q. Zhou, and S. Lan, “Breaking through the strength-ductility trade-off in graphene reinforced Ti6Al4V composites,” Journal of Alloys and Compounds. 2021. link Times cited: 22 V. Lenzi, A. Cavaleiro, F. Fernandes, and L. Marques, “Diffusion of silver in titanium nitride: Insights from density functional theory and molecular dynamics,” Applied Surface Science. 2021. link Times cited: 8 M. Deura et al., “Kinetic analysis of face-centered-cubic Ti1−Al N film deposition by chemical vapor deposition,” Materials Science and Engineering B-advanced Functional Solid-state Materials. 2021. link Times cited: 4 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 P. Liu, J. Xie, A. Wang, M. Douqin, and Z. Mao, “Molecular dynamics simulation on the deformation mechanism of monocrystalline and nano-twinned TiN under nanoindentation,” Materials Chemistry and Physics. 2020. link Times cited: 14 G. Plummer and G. Tucker, “Bond-order potentials for theTi3AlC2andTi3SiC2MAX phases,” Physical Review B. 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 N. Mediukh, V. Ivashchenko, P. Turchi, V. Shevchenko, J. Leszczynski, and L. Gorb, “Phase diagrams and mechanical properties of TiC-SiC solid solutions from first-principles,” Calphad. 2019. link Times cited: 3 L. Zhang, Y. Wu, W. Yu, and S. Shen, “Response of <110> symmetric tilt grain boundary in titanium nitride under shear,” Engineering Analysis with Boundary Elements. 2019. link Times cited: 9 L. E. Atouani, E. E. koraychy, K. Sbiaai, M. Mazroui, and A. Hasnaoui, “Cluster adsorption and migration energetics on hcp Ti (0001) surfaces via atomistic simulations,” Thin Solid Films. 2019. link Times cited: 8 L. Zhang, L. Wang, W. Yu, S. Shen, and T. Fu, “Structure and shear response of <001> tilt grain boundary in titanium nitride,” Ceramics International. 2019. link Times cited: 9 S. A. Etesami, M. Laradji, and E. Asadi, “Transferability of interatomic potentials in predicting the temperature dependency of elastic constants for titanium, zirconium and magnesium,” Modelling and Simulation in Materials Science and Engineering. 2019. link Times cited: 4 Abstract: We present our investigation of the current state of the art… read more Abstract: We present our investigation of the current state of the art for the transferability of molecular dynamics (MD) interatomic potentials for high temperature simulations of material processes in terms of elastic constants. With the current advancement of computer power, nanoscale computational models such as MD have the potential to accelerate optimization and development of high temperature material processes provided a robust and transferable interatomic potential. Temperature dependency of elastic constants, despite the low temperature elastic constants, is not commonly used as one of the target material properties to develop interatomic potentials for metals; thus, it is a reliable index to determine the transferability of interatomic potentials for high temperature simulations. We consider all five independent elastic constants and their temperature dependency as an index for our evaluations of available interatomic potentials for titanium (Ti), zirconium (Zr), and magnesium (Mg) as representative metals with a relatively complex crystal structure (hcp). The calculated elastic constants and their deviation from their corresponding experimental values are presented. We provide a through discussion on the transferability of each potential and summarize with the most suitable potentials for high temperature material process simulations for each considered material. read less W. Yang, G. Ayoub, I. Salehinia, B. Mansoor, and H. Zbib, “The effect of layer thickness ratio on the plastic deformation mechanisms of nanoindented Ti/TiN nanolayered composite,” Computational Materials Science. 2018. link Times cited: 18 M. Elkhateeb and Y. Shin, “Molecular dynamics-based cohesive zone representation of Ti6Al4V/TiC composite interface,” Materials & Design. 2018. link Times cited: 43 S. Sun et al., “First Principles Study of Mechanical Properties and Electronic Structures of Vanadium‐Doped TiC and TiN,” Advanced Engineering Materials. 2018. link Times cited: 8 Abstract: The mechanical properties and electronic structures of TiC a… read more Abstract: The mechanical properties and electronic structures of TiC and TiN with different doping ratio of vanadium (V) are studied in this work using the first principles calculations. The simulation results show that Ti1−xVxN has lower formation energy than Ti1−xVxC, suggesting higher chemical stability of Ti1−xVxN. Ti0.25V0.75C and TiN show larger hardness than other Ti1−xVxC and Ti1−xVxN compounds. The anisotropic Young's modulus of Ti1−xVxC and Ti1−xVxN models are plotted in 3D surface constructions, and VN exhibited the strongest anisotropy. The uniaxial tensile simulation of Ti1−xVxC and Ti1−xVxN are conducted along [111] direction. The tensile strength of Ti1−xVxN is stronger than Ti1−xVxC. The tensile strength increases with the increasing of V‐doping ratio. Furthermore, the electronic structures of Ti1−xVxC and Ti1−xVxN are estimated. The modeling techniques used in this work and the calculation results are helpful for systematically understanding the properties of Ti1−xVxC and Ti1−xVxN in nanoscale. read less S. Wang et al., “First‐principles study of the TiN(111)/ZrN(111) interface,” Surface and Interface Analysis. 2018. link Times cited: 12 Abstract: The TiN(111)/ZrN(111) interface was studied by first‐princip… read more Abstract: The TiN(111)/ZrN(111) interface was studied by first‐principles method to provide the theoretical basis for developing the TiN/ZrN coatings. Twelve geometry structures of TiN(111)/ZrN(111) interfaces were established. The calculated interfacial work of adhesion reveals that the N‐terminated TiN/N‐terminated ZrN interface with TL site shows the strongest stability. For this TiN(111)/ZrN(111) interface, the results of the partial density of state indicate that the chemical bonding at the interface appeals both ionic and covalent characteristic, which is same as that in the bulk materials. The partial density of states for Zr, Ti, and N atoms at the interface are very similar with those in the bulk, which reveals that the electronic structure transition at the interface is smooth. The results of charge density and charge density difference demonstrate that the lost charge of Ti atom is larger than that of Zr atom, indicating that TiN is more ionic than ZrN. Calculations of the work of fracture indicate that the mechanical failure of the ZrN(111)/TiN(111) interface will take place at the interface. Besides that, the calculation result of the TiN(111)/ZrN(111) interface implies that the TiZrN2 phase might be formed at the interface because the contacting of the N―N bond is the most stable. read less N. Zhang, Y. Hong, S. Yazdanparast, and M. A. Zaeem, “Superior structural, elastic and electronic properties of 2D titanium nitride MXenes over carbide MXenes: a comprehensive first principles study,” 2D Materials. 2018. link Times cited: 132 Abstract: The structural, elastic and electronic properties of two-dim… read more Abstract: The structural, elastic and electronic properties of two-dimensional (2D) titanium carbide/nitride based pristine (Tin+1Cn/Tin+1Nn) and functionalized MXenes (Tin+1CnT2/Tin+1NnT2, T stands for the terminal groups: –F, –O and –OH, n = 1, 2, 3) are investigated by density functional theory calculations. Carbide-based MXenes possess larger lattice constants and monolayer thicknesses than nitride-based MXenes. The in-plane Young’s moduli of Tin+1Nn are larger than those of Tin+1Cn, whereas in both systems they decrease with the increase of the monolayer thickness. Cohesive energy calculations indicate that MXenes with a larger monolayer thickness have a better structural stability. Adsorption energy calculations imply that Tin+1Nn have stronger preference to adhere to the terminal groups, which suggests more active surfaces for nitride-based MXenes. More importantly, nearly free electron states are observed to exist outside the surfaces of –OH functionalized carbide/nitride based MXenes, especially in Tin+1Nn(OH)2, which provide almost perfect transmission channels without nuclear scattering for electron transport. The overall electrical conductivity of nitride-based MXenes is determined to be higher than that of carbide-based MXenes. The exceptional properties of titanium nitride-based MXenes, including strong surface adsorption, high elastic constant and Young’s modulus, and good metallic conductivity, make them promising materials for catalysis and energy storage applications. read less V. Mishra and S. Chaturvedi, “First-principles study of high temperature and high-pressure behavior of carbides and nitrides of group IVB elements,” Phase Transitions. 2016. link Times cited: 3 Abstract: Full potential linearized augmented plane wave method combin… read more Abstract: Full potential linearized augmented plane wave method combined with quasi-harmonic approximation, has been used to perform the calculations of thermophysical properties of carbides and nitrides of the group IVB elements at high temperature and pressure. Relative accuracy of linear density approximation (LDA) and generalized gradient approximation (GGA) exchange correlation potentials have been tested. Specific heat () obtained through LDA and GGA agrees with experimental data up to 1500 K. Above 1500 K, GGA gives better agreement whereas LDA under-estimates the specific heat. LDA overestimates the bulk modulus, GGA gives better agreement with the experimental data. High-temperature bulk modulus follows the Wachtman formula. Calculated isotherms agree with published experimental results. The transformation pressures () from NaCl-type structure (B phase) to CsCl-type structure (B phase), and collapsed volumes () at () have been predicted. The stability and hardness of these compounds are related with the calculated density of states. read less J. M. Windajanti, R. Arifin, D. Santjojo, M. A. Pamungkas, and Abdurrouf, “Enhancing performance of nitrogen diffusion in HCP and BCC titanium by diffusion temperature: Molecular dynamics simulation study,” THE 11TH INTERNATIONAL CONFERENCE ON THEORETICAL AND APPLIED PHYSICS: The Spirit of Research and Collaboration Facing the COVID-19 Pandemic. 2023. link Times cited: 0 A. I. Dmitriev, A. Nikonov, and A. R. Shugurov, “Molecular dynamics study of the strength properties of TixAl1-xN coatings,” PHYSICAL MESOMECHANICS OF CONDENSED MATTER: Physical Principles of Multiscale Structure Formation and the Mechanisms of Nonlinear Behavior: MESO2022. 2023. link Times cited: 0 A. S. D. Honguelet, Y. J. M. Mimboui, R. B. Ondongo, and T. Nsongo, “Study of the Effect of Operating Temperatures (1320 K, 1420 K and 1520 K) on the Vacant Sites of TiN Alloy in B2 Structure at 45%, 50% and 55% N by MEAM Method,” Advances in Materials Physics and Chemistry. 2023. link Times cited: 0 Abstract: In this work, we have studied the vacancy formation energy o… read more Abstract: In this work, we have studied the vacancy formation energy of TiN alloy of structure B2 of size 10 × 10 × 10 for nitrogen percentages of 45%, 50% and 55% under the influence of temperature at 1320 K, 1420 K and 1520 K using the Modified Embedded Atom Method MEAM under the calculation code LAMMPS version 2020. This study has enabled us to understand the behavior of the TiN alloy under different nitrogen percentages in terms of total energy, vacancy formation energy, crystalline parameter, occupancy rate and order parameter. For total energy, we have shown that as temperature increases, total energy decreases, making it easier to obtain TiN at higher temperatures; reaching the value of −7344.9169 eV for the 55% nitrogen structure for the temperature of 1420 K. For the energy of formation, we have shown that the compounds obtained at 1320 K and 1520 K have a more considerable energy of formation than that obtained at 1420 K. The study of fractions and the order parameter showed us that the structure of TiN with 55% nitrogen is less likely, as the composition obtained is at most 53.35%. read less I. Shabalin, “Titanium Monocarbide,” Ultra-High Temperature Materials III. 2020. link Times cited: 5 A. Nikonov and A. Shugurov, “Numerical study of the effect of configurational ordering in Ti-Al-N atomic cells on the mechanical properties of resulting coating,” PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON ADVANCED MATERIALS WITH HIERARCHICAL STRUCTURE FOR NEW TECHNOLOGIES AND RELIABLE STRUCTURES 2019. 2019. link Times cited: 0 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 B. Yao, Z. R. Liu, D. Legut, and R. F. Zhang, “Hybrid potential model with high feasibility and flexibility for metallic and covalent solids,” Physical Review B. 2023. link Times cited: 0 R. Ahmed, M. Mahamudujjaman, M. A. Afzal, M. S. Islam, R. Islam, and S. Naqib, “Dft Based Comparative Analysis of the Physical Properties of Some Binary Transition Metal Carbides Xc (X = Nb, Ta, Ti),” SSRN Electronic Journal. 2023. link Times cited: 5 S. Attarian and S. Xiao, “Development of a 2NN-MEAM potential for Ti B system and studies of the temperature dependence of the nanohardness of TiB2,” Computational Materials Science. 2022. link Times cited: 3 P. Liu, J. Xie, A. Wang, D. Ma, and Z. Mao, “An interatomic potential for accurately describing the atomic-scale deformation behaviors of Ti2AlC crystal,” Computational Materials Science. 2020. link Times cited: 10 V. Zhakhovsky et al., “Shock-induced melting and crystallization in titanium irradiated by ultrashort laser pulse,” Physics of Fluids. 2023. link Times cited: 4 Abstract: Modification of titanium microstructure after propagation of… read more Abstract: Modification of titanium microstructure after propagation of a melting shock wave (SW) generated by a femtosecond laser pulse is investigated experimentally and analyzed using hydrodynamic and atomistic simulations. Scanning and transmission electron microscopy with analysis of microdiffraction is used to determine the microstructure of modified subsurface layers of titanium. We found that two layers are modified beneath the surface. A top surface polycrystalline layer of nanoscale grains is formed from shock-molten material via rapid crystallization. In a deeper subsurface layer, where the shock-induced melting changes into plastic deformation due to attenuation of SW, the grain structure of solid is considerably affected, which results in a grain size distribution differing from that in the intact titanium. Molecular dynamics simulation of single-crystal titanium reveals that the SW front continues to melt even after its temperature drops below the melting curve Tm(P). The enormous shear stress of ∼12 GPa generated in a narrow SW front leads to free slip of atomic planes, collapse of the crystal lattice, and formation of a supercooled metastable melt. Such melt crystallizes in an unloading tail of SW. The mechanical melting ceases after drop in the shear stress giving rise to the shock-induced plastic deformation. The last process triggers a long-term rearrangement of atomic structures in solid. The overall depth of modified layers is limited by SW attenuation to the Hugoniot elastic limit and can reach several micrometers. The obtained results reveal the basic physical mechanisms of surface hardening of metals by ultrashort laser pulses. read less R. Ahmed, M. Mahamudujjaman, M. A. Afzal, M. S. Islam, R. Islam, and S. Naqib, “Comparative Analysis of Physical Properties of Some Binary Transition Metal Carbides Xc (X = Nb, Ta, Ti): Insights From A Comprehensive Ab-Initio Study,” SSRN Electronic Journal. 2022. link Times cited: 0 Abstract: Binary metallic carbides belong to a technologically promine… read more Abstract: Binary metallic carbides belong to a technologically prominent class of materials. We have explored the structural, mechanical, electronic, optical, and some thermophysical properties of XC (X = Nb, Ta, Ti) binary metallic carbides in details employing density functional theory based first-principles method. Some of the results obtained are novel. Study of elastic constants and moduli shows that XC (X = Nb. Ta, Ti) compounds possess low level of elastic anisotropy, reasonably good machinability, mixed bonding characteristics with ionic and covalent contributions, brittle nature and high Vickers hardness with very high Debye temperatures. The mechanical and dynamical stability conditions are fulfilled. The bulk modulus and Young’s modulus of TiC are lower than those of NbC and TaC. All the XC (X = Nb, Ta, Ti) compounds are hard suitable for heavy duty engineering applications. The electronic band structures with finite electronic energy density of states at the Fermi level reveal metallic character of XC (X = Nb, Ta, Ti). Presence of both covalent and ionic bondings are also evident from the charge density distribution maps of XC (X = Nb, Ta, Ti) compounds. The vibrational properties such as phonon dispersion curves and phonon density of states for XC (X = Nb, Ta, Ti) compounds are also calculated. Positive phonon frequencies at the Γ -point suggest that the solids under investigation are dynamically stable and capable of efficient thermal transport. The optical parameters are found to be almost isotropic. The optical absorption, reflectivity spectra, and the static index of refractive of XC (X = Nb, Ta, Ti) show that the compounds hold promise to be used in optoelectronic device sectors. Debye temperature, melting temperature, lattice thermal conductivity, and minimum phonon thermal conductivity of the compounds under study are high and show excellent correspondence with the elastic and bonding characteristics. Extremely high melting temperature of TaC indicates that this compound is a good candidate material for high-temperature applications. read less 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 D. Zhao et al., “Structural Properties and Phase Stability of Primary Y Phase (Ti2SC) in Ti-Stabilized Stainless Steel from Experiments and First Principles,” Materials. 2019. link Times cited: 2 Abstract: The morphology and microstructural evaluation of Y phases in… read more Abstract: The morphology and microstructural evaluation of Y phases in AISI 321 (a Ti-stabilized stainless steel) were characterized after hot deformation. The electronic structure and phase stability of titanium carbosulfide were further discussed by first-principle calculations. It was found that Y phases, like curved strips or bones in AISI 321 stainless steel, mostly show a clustered distribution and are approximately arranged in parallel. The width of the Y phase is much less than the length, and the composition of the Y phase is close to that of Ti2SC. Y phases have exceptional thermal stability. The morphology of Y phases changed considerably after forging. During the first calculations, the Ti2SC with hexagonal structure does not spontaneously change into TiS and TiC; however Ti4S2C2 (Z = 2) can spontaneously change into the two phases. The Ti–S bonds are compressed in Ti4S2C2 cells, which leads to poor structural stability for Ti4S2C2. There is a covalent interaction between C/S and Ti, as well as an exchange of electrons between Ti and S/C atoms. Evidently, the mechanical stability of Ti4S2C2 is weak; however, Ti2SC shows high stability. Ti2SC, as a hard brittle phase, does not easily undergo plastic deformation. 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: 21 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 I. Plyushchay, T. L. Tsaregrads’ka, and O. I. Plyushchay, “Ab initio Modelling of Electronic Structure and Mechanical Properties of Substoichiometric TiC_x,” METALLOFIZIKA I NOVEISHIE TEKHNOLOGII. 2018. link Times cited: 3 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: 16 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 F. Montero-Chacón et al., “Multiscale thermo-mechanical analysis of multi-layered coatings in solar thermal applications,” Finite Elements in Analysis and Design. 2017. link Times cited: 16 S. Winczewski, J. Dziedzic, and J. Rybicki, “Central-force decomposition of spline-based modified embedded atom method potential,” Modelling and Simulation in Materials Science and Engineering. 2016. link Times cited: 0 Abstract: Central-force decompositions are fundamental to the calculat… read more Abstract: Central-force decompositions are fundamental to the calculation of stress fields in atomic systems by means of Hardy stress. We derive expressions for a central-force decomposition of the spline-based modified embedded atom method (s-MEAM) potential. The expressions are subsequently simplified to a form that can be readily used in molecular-dynamics simulations, enabling the calculation of the spatial distribution of stress in systems treated with this novel class of empirical potentials. We briefly discuss the properties of the obtained decomposition and highlight further computational techniques that can be expected to benefit from the results of this work. To demonstrate the practicability of the derived expressions, we apply them to calculate stress fields due to an edge dislocation in bcc Mo, comparing their predictions to those of linear elasticity theory. read less V. Borysiuk, V. Mochalin, and Y. Gogotsi, “Molecular dynamic study of the mechanical properties of two-dimensional titanium carbides Tin+1Cn (MXenes),” Nanotechnology. 2015. link Times cited: 190 Abstract: Two-dimensional materials beyond graphene are attracting muc… read more Abstract: Two-dimensional materials beyond graphene are attracting much attention. Recently discovered 2D carbides and nitrides (MXenes) have shown very attractive electrical and electrochemical properties, but their mechanical properties have not been characterized yet. There are neither experimental measurements reported in the literature nor predictions of strength or fracture modes for single-layer MXenes. The mechanical properties of two-dimensional titanium carbides were investigated in this study using classical molecular dynamics. Young’s modulus was calculated from the linear part of strain–stress curves obtained under tensile deformation of the samples. Strain-rate effects were observed for all Tin+1Cn samples. From the radial distribution function, it is found that the structure of the simulated samples is preserved during the deformation process. Calculated values of the elastic constants are in good agreement with published DFT data. read less 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 N. Vuksic, “New Zirconium Hydrogen Second Nearest Neighbor Modified Embedded Atom Method (MEAM) Potential For Simulation of Stacking Fault Energy Along the < 011̄0 > Path Of The Hexagonal Closely Packed Lattice Basal Plane.” 2014. link Times cited: 0 Abstract: A new Modified Embedded Atom Method (MEAM) potential for zir… read more Abstract: A new Modified Embedded Atom Method (MEAM) potential for zirconium and hydrogen, called the second nearest-neighbor MEAM (2nnMEAM), was created to more effectively simulate the stacking fault energy of different zirconium hydrogen solid solutions along the < 011̄0 > path of the hexagonal closely packed (hcp) lattice basal plane. The 2nnMEAM is a binary alloy MEAM with a less severe screening function that enables the potential to include longer range interactions between atoms. The 2nnMEAM is required because the existing MEAM potential for zirconium and hydrogen, developed by Dr.M.Baskes (in the text referred to as the MEAM potential), although useful for bulk tests of basic physical properties of different zirconium hydrogen phases, was not capable to model the energetics associated with basal slip. Several previous papers outlined the process of creating binary alloy MEAM potential out of the MEAM potentials of different pure elements. Due to the fact that there is no direct method of combining pure elements MEAM data, a trial and error approach was used to gradually achieve qualitative similarity with the first principles results. This translated into physical behavior, the goal was to show that the 2nnMEAM can be fine-tuned to replicate realistic response of the material during the tests and demonstrate the power of the MEAM methodology. The quantitative agreement was not achieved due to too many unknown MEAM parameters, lack of their physical meaning and functional influence on each other. Furthermore, none of the academic papers used as the basis for this research ventured into more complex tests like stacking fault, but bulk ones, and even then stressed the approximate nature of the MEAM methodology compared to much more precise first principles simulations. As a main tool for simulating behavior of different zirconium hydrogen solid solutions and testing of different MEAM versions, Large Scale Atomic/Molecular Massively read less
Funding	Not available

Short KIM ID The unique KIM identifier code.	MO_070542625990_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_KimLee_2008_TiN__MO_070542625990_002
DOI	10.25950/2e66694f https://doi.org/10.25950/2e66694f https://commons.datacite.org/doi.org/10.25950/2e66694f
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_KimLee_2008_TiN__MO_070542625990_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
B The letter grade B was assigned because the normalized error in the computation was 1.27142e-08 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.	vc-forces-numerical-derivative	consistency	Forces computed by the model agree with numerical derivatives of the energy; see full description.	Results	Files
N/A Unable to perform verification check due to an error.	vc-dimer-continuity-c1	informational	The energy versus separation relation of a pair of atoms is C1 continuous (i.e. the function and its first derivative are continuous); see full description.	Results	Files
P Model energy and forces are invariant with respect to rigid-body motion (translation and rotation) for all configurations the model was able to compute.	vc-objectivity	informational	Total energy is unchanged and forces transform correctly under rigid-body translation and rotation; see full description.	Results	Files
P Model energy has inversion symmetry for all configurations the model was able to compute.	vc-inversion-symmetry	informational	Total energy is unchanged and forces change sign when inverting a configuration through the origin; see full description.	Results	Files
P No memory leak detected.	vc-memory-leak	informational	The model code does not have memory leaks (i.e. it releases all allocated memory at the end); see full description.	Results	Files
P All threads give identical results for tested case. Model appears to be thread-safe.	vc-thread-safe	mandatory	The model returns the same energy and forces when computed in serial and when using parallel threads for a set of configurations. Note that this is not a guarantee of thread safety; see full description.	Results	Files
P Unit conversion successful	vc-unit-conversion	mandatory	The model is able to correctly convert its energy and/or forces to different unit sets; see full description.	Results	Files

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

Species: Ti

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: Ti

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: Ti

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: Ti

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: Ti

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: Ti

Cubic Crystal Basic Properties Table

Species: N

Species: Ti

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 Ti v004	view	3755
Cohesive energy versus lattice constant curve for diamond Ti v004	view	3755
Cohesive energy versus lattice constant curve for fcc Ti v004	view	3607
Cohesive energy versus lattice constant curve for sc Ti v004	view	3902

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 Ti at zero temperature v006	view	22896
Elastic constants for fcc Ti at zero temperature v006	view	13325
Elastic constants for sc Ti at zero temperature v006	view	33276

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 Ti in AFLOW crystal prototype A_cF4_225_a v002	view	92246
Equilibrium crystal structure and energy for N in AFLOW crystal prototype A_cI20_217_ce v002	view	92781
Equilibrium crystal structure and energy for Ti in AFLOW crystal prototype A_cI2_229_a v002	view	86210
Equilibrium crystal structure and energy for N in AFLOW crystal prototype A_cI8_199_a v002	view	58390
Equilibrium crystal structure and energy for N in AFLOW crystal prototype A_cP8_198_2a v002	view	65074
Equilibrium crystal structure and energy for N in AFLOW crystal prototype A_cP8_205_c v002	view	94161
Equilibrium crystal structure and energy for N in AFLOW crystal prototype A_hP2_194_c v002	view	72516
Equilibrium crystal structure and energy for Ti in AFLOW crystal prototype A_hP2_194_c v002	view	77302
Equilibrium crystal structure and energy for Ti in AFLOW crystal prototype A_hP3_191_ad v002	view	50872
Equilibrium crystal structure and energy for N in AFLOW crystal prototype A_hP4_194_f v002	view	75976
Equilibrium crystal structure and energy for N in AFLOW crystal prototype A_hR16_167_cf v002	view	957140
Equilibrium crystal structure and energy for N in AFLOW crystal prototype A_tP4_136_f v002	view	42774
Equilibrium crystal structure and energy for NTi in AFLOW crystal prototype AB2_tI12_141_a_e v002	view	56172
Equilibrium crystal structure and energy for NTi in AFLOW crystal prototype AB2_tP6_136_a_f v002	view	63093
Equilibrium crystal structure and energy for NTi in AFLOW crystal prototype AB_cF8_225_a_b v002	view	74492
Equilibrium crystal structure and energy for NTi in AFLOW crystal prototype AB_cP2_221_a_b v002	view	78038

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 Ti v007	view	9906
Equilibrium zero-temperature lattice constant for diamond Ti v007	view	11309
Equilibrium zero-temperature lattice constant for fcc Ti v007	view	10065
Equilibrium zero-temperature lattice constant for sc Ti v007	view	13252

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 N v005		view	58045
Equilibrium lattice constants for hcp Ti v005		view	59616

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 hcp Ti		view	384152

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 hcp Ti		view	3779897

Errors

ElasticConstantsCubic__TD_011862047401_006

Test	Error Categories	Link to Error page
Elastic constants for diamond Ti at zero temperature v001	other	view

ElasticConstantsHexagonal__TD_612503193866_004

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

EquilibriumCrystalStructure__TD_457028483760_002

Test	Error Categories	Link to Error page
Equilibrium crystal structure and energy for N in AFLOW crystal prototype A_oP2_51_e v002	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 diamond 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

No Driver

Verification Check	Error Categories	Link to Error page
DimerContinuityC1__VC_303890932454_005	other	view

Files

CMakeLists.txt
LICENSE
TiN.meam
elems.meam
kimprovenance.edn
kimspec.edn
library.meam

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MEAM_LAMMPS_KimLee_2008_TiN__MO_070542625990_002.txz	Tar+XZ	Linux and OS X archive
MEAM_LAMMPS_KimLee_2008_TiN__MO_070542625990_002.zip	Zip	Windows archive

Download Dependency

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

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

Wiki

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MEAM_LAMMPS_KimLee_2008_TiN__MO_070542625990_002

Verification Check Dashboard

Visualizers (in-page)

BCC Lattice Constant

Cohesive Energy Graph

Diamond Lattice Constant

Dislocation Core Energies

FCC Elastic Constants

FCC Lattice Constant

FCC Stacking Fault Energies

FCC Surface Energies

SC Lattice Constant

Cubic Crystal Basic Properties Table

Tests

Errors

Files

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Download Dependency

Wiki