Finnis-Sinclair potential (LAMMPS cubic hermite tabulation) for Ti for the hcp-fcc transition developed by Ackland (1992) v005

Graeme J. Ackland

doi:10.25950/276be3c4

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EAM_Dynamo_Ackland_1992_Ti__MO_748534961139_005

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Interatomic potential for Titanium (Ti).
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Title A single sentence description.	Finnis-Sinclair potential (LAMMPS cubic hermite tabulation) for Ti for the hcp-fcc transition developed by Ackland (1992) v005
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.	It is shown that any force model using short-range pair-functional interactions can only have three independent h.c.p. elastic constants. Empirical data show that these elastic properties are nearly realized in a number of materials. A new parametrization of a Finnis-Sinclair-type many-body potential for titanium is presented using these relations. Particular care is taken to describe the anisotropy of the shear constants and the deviation of the c/a lattice parameter ratio from ideal, while maintaining smooth monotonic functions. Energies, stresses and reconstruction modes of various low-index surfaces are calculated and general rules for surface stability are proposed. Various stacking faults on the basal and pyramidal plane are investigated. This potential is widely used for radiation damage and gives a nice hcp-bcc martensitic transition. Available with early cross potentials for complete Ti3Al TiAl and TiAl3 system.
Species The supported atomic species.	Ti
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	Stacking fault energy in hcp is too low. Basal dislocations can be formed, and well as prismatic.
Content Origin	NIST IPRP(http://www.ctcms.nist.gov/potentials/Ti.html)
Content Other Locations	http://homepages.ed.ac.uk/graeme/moldy/moldy.html

Contributor	Graeme J. Ackland
Maintainer	Graeme J. Ackland
Developer	Graeme J. Ackland
Published on KIM	2018
How to Cite	Click here to download this 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. 142 Citations (70 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 . Q. Yang and P. Olsson, “Full energy range primary radiation damage model,” Physical Review Materials. 2021. link Times cited: 9 Abstract: A full energy range primary radiation damage model is presen… read more Abstract: A full energy range primary radiation damage model is presented here. It is based on the athermal recombination corrected displacements per atom (arc-dpa) model but includes a proper treatment of the near threshold conditions for metallic materials. Both ab initio (AIMD) and classical molecular dynamics (MD) simulations are used here for various metals with body-centered cubic (bcc), face-centered cubic (fcc), and hexagonal close-packed (hcp) structures to validate the model. For bcc and hcp metals, the simulation results fit very well with the model. For fcc metals, although there are slight deviations between the model and direct simulation results, it is still a clear improvement on the arc-dpa model. The deviations are due to qualitative differences in the threshold energy surfaces of fcc metals with respect to bcc and hcp metals according to our classical MD simulations. We introduce the minimum threshold displacement energy (TDE) as a term in our damage model. We calculated minimum TDEs for various metal materials using AIMD. In general, the calculated minimum TDEs are in very good agreement with experimental results. Moreover, we noticed a discrepancy in the literature for fcc Ni and estimated the average TDE of Ni using both classical MD and AIMD. It was found that the average TDE of Ni should be \ensuremath{\sim}70 eV based on simulation and experimental data, not the commonly used literature value of 40 eV. The most significant implications of introducing this full energy range damage model will be for estimating the effect of weak particle-matter interactions, such as for \ensuremath{\gamma}- and electron-radiation-induced damage. read less W. Tang et al., “Mechanical properties and enhancement mechanisms of titanium-graphene nanocomposites,” Acta Mechanica Sinica. 2020. link Times cited: 8 W. Tang et al., “Mechanical properties and enhancement mechanisms of titanium-graphene nanocomposites,” Acta Mechanica Sinica. 2020. link Times cited: 0 H. Wang et al., “Dynamic recrystallization initiated by direct grain reorientation at high-angle grain boundary in α-titanium,” Journal of Materials Research. 2019. link Times cited: 3 Abstract: Employing atomic-scale simulations, the response of a high-a… read more Abstract: Employing atomic-scale simulations, the response of a high-angle grain boundary (GB), the soft/hard GB, against external loading was systematically investigated. Under tensile loading close to the hard orientation, strain-induced dynamic recrystallization was observed to initiate through direct soft-to-hard grain reorientation, which was triggered by stress mismatch, inhibited by surface tension from the soft-hard GB, and proceeded by interface ledges. Such grain reorientation corresponds with expansion and contraction of the hard grain along and perpendicular to the loading direction, respectively, accompanied by local atomic shuffling, providing relatively large normal strain of 8.3% with activation energy of 0.04 eV per atom. Tensile strain and residual dislocations on the hard/soft GB facilitate the initiation of dynamic recrystallization by lowering the energy barrier and the critical stress for grain reorientation, respectively. read less A. Ready, P. Haynes, D. Rugg, and A. Sutton, “Stacking faults and the -surface on first-order pyramidal planes in -titanium,” Philosophical Magazine. 2017. link Times cited: 6 Abstract: Using first principles methods, we calculated the entire -su… read more Abstract: Using first principles methods, we calculated the entire -surface of the first-order pyramidal planes in -titanium. Slip on these planes involving dislocations with -type Burgers vectors is one means by which -titanium polycrystals may supplement slip on prism planes with -type Burgers vectors to maintain ductility. We find one low energy and one high energy stacking fault with energies of 163 and 681 , respectively. Contrary to previous suggestions, we do not find a stable stable stacking fault at . read less J.-Q. Ren, Q. Sun, L. Xiao, X. Ding, and J. Sun, “Phase transformation behavior in titanium single-crystal nanopillars under [0 0 0 1] orientation tension: A molecular dynamics simulation,” Computational Materials Science. 2014. link Times cited: 66 A. Poty et al., “Classification of the critical resolved shear stress in the hexagonal-close-packed materials by atomic simulation: Application to α-zirconium and α-titanium,” Journal of Applied Physics. 2011. link Times cited: 71 Abstract: We have studied the hierarchy of the activation of dislocati… read more Abstract: We have studied the hierarchy of the activation of dislocation glide in zirconium and titanium alloys and presented experimental results in zirconium alloys. We have compared the experimental results with simulations obtained by two different approaches. The first is by using the stacking fault energy maps (γ surfaces) obtained by molecular dynamics (MD) and by ab initio approaches. A good agreement was observed between the two approaches and with recent published work. The second is to compare the experimental critical resolved shear stresses (CRSS) with those determined by MD simulations based on embedded atom method (EAM) potentials. The CRSS for slip in the -direction for the basal, prismatic (type 1) and pyramidal (type 2) planes for edge dislocations are obtained. Finally, we discuss the hierarchy of the glide systems with the energy criterion of the γ surfaces and with the CRSS values and we compare with both experimental and modeling data. read less A. Girshick, D. Pettifor, and V. Vítek, “Atomistic simulation of titanium. II. Structure of 1/3 screw dislocations and slip systems in titanium,” Philosophical Magazine. 1998. link Times cited: 66 Abstract: The bond-order potential for hcp Ti, constructed in part I, … read more Abstract: The bond-order potential for hcp Ti, constructed in part I, and a central-force Finnis-Sinclair-type potential have been used to study atomistically the core structure of the ⅓ 〈1210〉 screw dislocation. The qualitative features of the core structures are similar in the two cases. The dislocation may either dissociate into Shockley partials on the basal plane or spread in a continuous manner into the prism plane. However, the spreading of the dislocation core into the prism plane is always energetically favoured over the splitting into the basal plane in the case of the bond-order potential whilst the opposite is found in the case of the centralforce Finnis-Sinclair-type potential. Hence, the results obtained using the bond-order potential explain the strong preference for the prism slip over the basal slip in Ti. The most important global parameter is the energy of the intrinsic stacking fault on the basal plane which is so high in the case of the bond-order potential that splitting into Shockley... read less C. Grégoire, “Dynamic behaviour of nano-sized voids in hexagonal close-packed materials.” 2018. link Times cited: 0 Abstract: The dynamic behaviour and failure mechanisms of nano-sized v… read more Abstract: The dynamic behaviour and failure mechanisms of nano-sized voids in single crystals is studied for three hexagonal close-packed materials by means of molecular dynamics simulations. Our study reveals that in Magnesium the response is highly anisotropic leading to a brittle to ductile transition in the failure modes under different load orientations. This transition is accompanied by different mechanisms of deformation and is associated with the anisotropic HCP lattice structure of Mg and the associated barrier for dislocation motion. Remarkably, brittle failure is observed when external loads produce a high stress triaxiality while the response is more ductile when the stress triaxiality decreases. On the other hand, the failure in other two hexagonal close-packed materials studied in this work, i.e, Titanium and Zirconium, is more ductile, in high contrast with the brittle failure observed in Magnesium. We find that this difference is due to the fact that nano-sized voids in Titanium and Zirconium emit substantially more dislocations than Magnesium, allowing for large displacements of the atoms and plastic work, including non-basal planes. Based on our findings, we postulate that this brittle failure in Magnesium is due to a competition between dislocations emission in the basal plane and crack propagation in non-basal planes. Thus, we propose to use the ratio between unstable stacking fault and surface energy in these materials to assess the tendency of hexagonal close-packed materials and alloys to fail under brittle or ductile modes. Using this ratio, we critically identify the low surface energy of Mg as responsible for this brittle behaviour and recommend that Mg-based alloys with large surface energies can lead to better performance for dynamic applications. The fundamental mechanisms observed, therefore, explain the low spall strength of Mg and suggest the possibility of manipulating some mechanisms to increase ductility and spall strength of new lightweight Mg alloys. read less L. Li and M. Han, “Shear behaviors of single crystal hcp Ti at different temperatures from molecular dynamics simulations,” Physica Scripta. 2014. link Times cited: 3 Abstract: Shear behaviors of single crystal hcp titanium in a close-pa… read more Abstract: Shear behaviors of single crystal hcp titanium in a close-packed (0001) basal plane along the [ 1 ¯ 2 1 ¯ 0 ] ?> , [ 1 2 ¯ 10 ?> ], [ 10 1 ¯ 0 ?> ], and [ 1 ¯ 010 ?> ] directions at different temperatures were studied via molecular dynamics simulation using an embedded atom method (EAM) potential. Results show that periods of shear stress–shear strain curves along four directions occur, where shear displacement for one period of the curve relates to one period of atomic configuration in the corresponding direction, and that the trajectory of the free atoms also shows periodic characteristics. It is demonstrated that shear behaviors along two orthogonal directions are different, while they perform the same in opposite directions. In addition, the shear modulus can be obtained from the slope of the shear stress–shear strain curves and shows independence from the shear directions and the height of the models. The modulus was extracted over a temperature range of 0 to 1050 K, showing a decreasing trend with increasing temperature. Furthermore, this work also demonstrates that the classical description of shear modulus is still valid on the nanoscale, which might suggest a simple and direct way to obtain the shear modulus on the atomic scale. read less J. Singh and R. Kumar, “Mechanical and fracture behaviour of pristine and defective single/bi-crystal graphene/Ti nanocomposites using molecular dynamics simulations,” Computational Materials Science. 2024. link Times cited: 0 T.-M. Lin, S.-xia Liu, P. Qu, and X. Zhao, “Investigation on plastic deformation mechanism of gradient nano-polycrystalline pure titanium by atomic simulation,” Vacuum. 2023. link Times cited: 0 Z. Li, W. Zhao, H. Zhang, G. Xiao, and K. Yu, “Microstructure and corrosion resistance of fusion zone in Ti-6Al-4V alloy welded using pulsed- and continuous-wave lasers,” Corrosion Science. 2023. link Times cited: 1 Z. Li et al., “Impact of microstructure evolution on the corrosion behaviour of the Ti-6Al-4V alloy welded joint using high-frequency pulse wave laser,” Journal of Materials Research and Technology. 2023. link Times cited: 5 X. Gao, N. Li, Z. Song, K. Wu, Y. Cheng, and B.-yang Xiao, “Atomic structure evolution and linear regression fitting models for pre-breakdown electric field strength of FCC, BCC and HCP metal nano-emitters under high electric field from PIC-ED–MD simulations,” Journal of Physics D: Applied Physics. 2023. link Times cited: 1 Abstract: Multi-scale and multi-physics simulations are carried out fo… read more Abstract: Multi-scale and multi-physics simulations are carried out for nano-emitters consisting of FCC (Al, Cu and Au), BCC (V, Mo and W) and HCP (Ti, Zn and Zr) metals, using hybrid electrodynamics coupled with molecular dynamics-particle in cell simulations (PIC-ED–MD). We show that the tilting of the nano-emitter at low temperature and small electric field (E-field) is mainly caused either by the movement of partial dislocations at the apex of the nanotip or by the elastic local distortions of atomic registries away from their ideal lattice sites (FCC/BCC/HCP). At high E-field, the intense resistive heating due to the strong electron emission leads to the direct melting of the apex of nano-emitters. For nano-emitters consisting of low melting point metals such as Al, Zn and Au, the thermal runaway is driven by the elongation, thinning and necking of the molten region. Meanwhile, the elongation, thinning and sharpening produce the nano-protrusion at the apex of metal nano-emitters, and the detachment of atoms or atomic clusters from the nano-protrusion mainly contributes to the thermal runaway event for refractor metals such as Ti, Zr, Mo and W. The critical E-field strength of metal nano-emitters is found to be strongly correlated with structural parameters (atomic coordination number of liquid and equilibrium lattice constant), thermodynamic quantities (cohesive energy and enthalpy of evaporation) and phase transition temperatures (melting point and boiling point). These correlations enable us to establish either single-variable linear fitting models or multi-variable linear regression models to predict the critical E-field value for metal nano-emitters with good credibility. read less K. A. Nair and S. Ghosh, “Crack tip enhanced phase-field model for crack evolution in crystalline Ti6Al from concurrent crystal plasticity FE-molecular dynamics simulations,” European Journal of Mechanics - A/Solids. 2023. link Times cited: 1 Z. Kou et al., “Stress-induced phase transformation and phase boundary sliding in Ti: An atomically resolved in-situ analysis,” Journal of Materials Science & Technology. 2023. link Times cited: 1 O. Bachurina, R. Murzaev, A. A. Kudreyko, S. Dmitriev, and D. Bachurin, “Atomistic study of two-dimensional discrete breathers in hcp titanium,” The European Physical Journal B. 2022. link Times cited: 2 L. Chang, X. Liu, J. Zhao, and C.-yu Zhou, “Effect of interatomic potential on modelling fracture behavior in hcp titanium: A molecular dynamics study,” Journal of Materials Research and Technology. 2022. link Times cited: 3 N. Miyazawa, T. Hirayama, and S. Onaka, “Molecular dynamics study of interactions between prismatic slip and oxygen-segregated twin boundaries in α-Ti,” Materialia. 2022. link Times cited: 1 L. Chang, Z. Tao, S. Yang, X. Liu, and C.-yu Zhou, “Anisotropic deformation behavior of 112-0, 101-0 and 0001-textured nanocrystalline titanium,” Results in Physics. 2022. link Times cited: 0 R. Qiu et al., “Finnis–Sinclair-type potential for atomistic simulation of defects behaviour in V-Ti-Ta ternary system,” Journal of Nuclear Materials. 2021. link Times cited: 7 A. Kedharnath, R. Kapoor, and A. Sarkar, “Classical molecular dynamics simulations of the deformation of metals under uniaxial monotonic loading: A review,” Computers & Structures. 2021. link Times cited: 16 H. Wang, Y. Sun, B. Qiao, and X. Chen, “Crack propagation mechanism of titanium nano-bicrystal: a molecular dynamics study,” The European Physical Journal B. 2021. link Times cited: 1 S. Kiselev and V. Kiselev, “Numerical Simulation of Fracture of Titanium and Aluminum Nanocrystals by the Molecular Dynamics Method,” Combustion, Explosion, and Shock Waves. 2021. link Times cited: 1 Abstract: Results of numerical simulations of fracture of titanium and… read more Abstract: Results of numerical simulations of fracture of titanium and aluminum nanocrystals by the molecular dynamics method are reported. The nanocrystals are subjected to uniaxial tension in a wide temperature range (300–1270 K). It is demonstrated that tension of titanium nanocrystals heated to temperatures above 0.7 of the melting temperature in a non-stressed nanocrystal first leads to a phase transition from the crystalline to liquid state, followed by fracture. This effect is not observed in the case of tension of the aluminum nanocrystal. read less S. Kiselev and V. Kiselev, “Numerical Simulation of Fracture of Titanium and Aluminum Nanocrystals by the Molecular Dynamics Method,” Combustion, Explosion, and Shock Waves. 2021. link Times cited: 0 L. Chang, T. Kitamura, C.-yu Zhou, and X.-hua He, “Comparison of anisotropic crack tip behavior in hcp titanium by two-dimensional and three-dimensional atomistic simulations,” Theoretical and Applied Fracture Mechanics. 2021. link Times cited: 3 J. Li, L. Dong, X. Zang, X.-ming Zhang, W. Zhao, and F. Wang, “Study on micro-crack propagation behavior of single-crystal α-Ti under shear stress based on molecular dynamics,” Materials today communications. 2020. link Times cited: 8 L. Chang, T. Kitamura, and C.-yu Zhou, “Atomic simulation of the orientation effects on crack tip behavior in titanium single crystal,” Theoretical and Applied Fracture Mechanics. 2020. link Times cited: 8 J. Jiang, X. Zhang, F. Ma, S. Dong, W. Yang, and M. Wu, “Molecular dynamics simulation of the crystal structure evolution of titanium under different Tdamp values and heating/cooling rates,” Chemical Physics Letters. 2020. link Times cited: 2 J. Li et al., “Molecular dynamics simulation of nanocrack propagation mechanism of polycrystalline titanium under tension deformation in nanoscale,” Materials Today Communications. 2020. link Times cited: 7 S. Rawat and S. Chaturvedi, “Strain-rate effect on plasticity and ω-phase transformation in single crystal titanium: A molecular dynamics study,” Mechanics of Materials. 2020. link Times cited: 5 A. B. Patel and H. Sheng, “Structure and atomic transport of liquid titanium from a pair potential model,” Physical Review B. 2020. link Times cited: 1 Q. Zu, Y.-F. Guo, and X. Yao, “Surface and orientation effects on stress-induced hcp-fcc phase transformation in Ti nanopillars,” Applied Surface Science. 2020. link Times cited: 9 J. Li, X. Lin, P. Guo, M. Song, and W. Huang, “Electrochemical behaviour of laser solid formed Ti–6Al–4V alloy in a highly concentrated NaCl solution,” Corrosion Science. 2018. link Times cited: 51 J.-Q. Ren, Q. Sun, L. Xiao, and J. Sun, “Atomistic simulation of tension-compression asymmetry and its mechanism in titanium single-crystal nanopillars oriented along the [1 1 2¯ 0] direction,” Computational Materials Science. 2018. link Times cited: 2 L. Chang, C.-yu Zhou, X. Pan, and X.-hua He, “Size-dependent deformation mechanism transition in titanium nanowires under high strain rate tension,” Materials & Design. 2017. link Times cited: 18 F. Meyer et al., “Energy dependence of He-ion-induced tungsten nanofuzz formation at non-normal incidence angles,” Nuclear materials and energy. 2017. link Times cited: 14 Z. Zheng, D. Balint, and F. Dunne, “Investigation of slip transfer across HCP grain boundaries with application to cold dwell facet fatigue,” Acta Materialia. 2017. link Times cited: 65 L. Chang, C.-yu Zhou, H.-xi Liu, J. Li, and X.-hua He, “Orientation and strain rate dependent tensile behavior of single crystal titanium nanowires by molecular dynamics simulations,” Journal of Materials Science & Technology. 2017. link Times cited: 34 L. Chang, C.-yu Zhou, L. Wen, J. Li, and X.-hua He, “Molecular dynamics study of strain rate effects on tensile behavior of single crystal titanium nanowire,” Computational Materials Science. 2017. link Times cited: 52 K. Mackenchery and A. Dongare, “Shock Hugoniot behavior of single crystal titanium using atomistic simulations.” 2017. link Times cited: 4 Abstract: Atomistic shock simulations are performed for single crystal… read more Abstract: Atomistic shock simulations are performed for single crystal titanium using four different interatomic potentials at impact velocities ranging from 0.5 km/s to 2.0 km/s. These potentials comprise of three parameterizations in the formulation of the embedded atom method and one formulation of the modified embedded atom method. The capability of the potentials to model the shock deformation and failure behavior is investigated by computing the shock hugoniot response of titanium and comparing to existing experimental data. In addition, the capability to reproduce the shock induced alpha (α) to omega (ω) phase transformation seen in Ti is investigated. The shock wave structure is discussed and the velocities for the elastic, plastic and the α-ω phase transformation waves are calculated for all the interatomic potentials considered. read less I. A. Alhafez and H. Urbassek, “Scratching of hcp metals: A molecular-dynamics study,” Computational Materials Science. 2016. link Times cited: 39 C. Ni, H. Ding, M. Asta, and X. Jin, “Computational study of symmetric tilt grain boundaries in Mg and Ti,” Scripta Materialia. 2015. link Times cited: 19 F. T. Latypov and A. Mayer, “Shear strength of metals under uniaxial deformation and pure shear,” Journal of Physics: Conference Series. 2015. link Times cited: 5 Abstract: In this paper, we investigate the dynamic shear strength of … read more Abstract: In this paper, we investigate the dynamic shear strength of perfect monocrystalline metals using the molecular dynamics simulation. Three types of deformation (single shear, uniaxial compression and tension) are investigated for five metals of different crystallographic systems (fcc, bcc and hcp). A strong dependence of the calculated shear strength on the deformation type is observed. In the case of bcc (iron) and hcp (titanium) metals, the maximal shear strength is achieved at the uniaxial compression, while the minimal shear strength is observed at the uniaxial tension. In the case of fcc metals (aluminum, copper, nickel) the largest strength is achieved at the pure shear, the lowest strength is obtained at the uniaxial compression. read less E. Hahn and M. Meyers, “Grain-size dependent mechanical behavior of nanocrystalline metals,” Materials Science and Engineering A-structural Materials Properties Microstructure and Processing. 2015. link Times cited: 162 T. Malama, A. Hamweendo, and I. Botef, “Molecular Dynamics Simulation of Ti and Ni Particles on Ti Substrate in the Cold Gas Dynamic Spray (CGDS) Process,” Materials Science Forum. 2015. link Times cited: 14 Abstract: This paper presents simulation of molecular dynamics for the… read more Abstract: This paper presents simulation of molecular dynamics for the deposition of Titanium (Ti) and Nickel (Ni) particles on Ti substrate during Cold Gas Dynamic Spray (CGDS) process. The influencing factors of the deposition process, such as particle incident velocity, particle size and particle temperature are taken into consideration. Ti and Ni were selected because of their potential applications in the aerospace, marine and bio-medical industries. CGDS is preferred because it is a state of the art technique by which coatings are created without significant heating of the sprayed powder. In CGDS, particles are accelerated to supersonic velocities using a high speed gas stream. However, there are inherent difficulties in relating particle deposition characteristics with influencing factors of the deposition process. Moreover, there is limited literature on molecular dynamics simulation of CGDS process. For this reason, this paper develops a simulation process for Ti and Ni particles under influence of many factors using molecular dynamics. In this process, particles are allowed to interact for a short time, giving a view of their motion. The trajectories of these particles are determined by numerically solving the Newton's equations of motion for a system of interacting particles, in which the forces between the particles are defined. The results of the simulation process show that higher incident velocities and larger particle sizes result in stronger interface between the particle and the substrate. Further, higher temperatures of the substrate and particles improve the bond strength. read less H. Khater and D. Bacon, “Dislocation core structure and dynamics in two atomic models of α-zirconium,” Acta Materialia. 2010. link Times cited: 55 C. Domain, “Ab initio modelling of defect properties with substitutional and interstitials elements in steels and Zr alloys,” Journal of Nuclear Materials. 2006. link Times cited: 96 T. Hammerschmidt, A. Kersch, and P. Vogl, “Embedded atom simulations of titanium systems with grain boundaries,” Physical Review B. 2005. link Times cited: 23 Abstract: The atomistic simulation of polycrystalline growth with an e… read more Abstract: The atomistic simulation of polycrystalline growth with an empirical potential requires an accurate modeling of the atomic configurations at grain boundaries. We refine an existing embedded-atom potential for bulk titanium to reproduce systems with small atomic coordination, namely, clusters of up to nine atoms, the relaxation of the s0001d surface and the adatom diffusion on this surface. We find that simulating Ti growth can be limited to the s0001d surface and the rather small class of grain boundaries with angles of coincidence-site lattices. We determine the atomic structure of the Tis0001d S = 7 grain boundary with molecular statics and find exclusively pentagonal elementary structural units. The potential energy surface shows that this grain boundary imposes a massive barrier on surface diffusion. We use the elementary cells of the coincidence-site lattice to construct two periodic systems with grain boundaries: an isolated grain within an environment of different crystalline orientation and two antiparallel grain boundaries. Molecular dynamic simulations show that this isolated grain is not stable and that the growth evolution of the system with two antiparallel grain boundaries depends strongly on the angle of incidence. read less Q. Xu, T. Yoshiie, and H. C. Huang, “Molecular dynamics simulation of vacancy diffusion in tungsten induced by irradiation,” Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms. 2003. link Times cited: 58 Y.-mei Kang, N. Chen, and J. Shen, “Atomistic simulation of the lattice constants and lattice vibrations in RT4Al8 (R=Nd, Sm; T=Cr, Mn, Cu, Fe),” Journal of Alloys and Compounds. 2003. link Times cited: 16 A. Serra, “Atomic computer simulation: Large scale calculations of defect properties by empirical potentials,” Physica Status Solidi B-basic Solid State Physics. 2001. link Times cited: 2 Abstract: This paper is aimed at introducing computer simulation of ex… read more Abstract: This paper is aimed at introducing computer simulation of extended defects in crystalline materials by means of empirical potentials. In this context we understand by large scale calculations those related to a number of atoms from 10 3 to 10 6 and/or a time scale of few nanoseconds (10 2 -10 4 ps) for the evolution of the processes studied. read less J. R. Fernández, A. M. Monti, and R. Pasianot, “Vibrational Entropy in Static Simulations of Point Defects,” Physica Status Solidi B-basic Solid State Physics. 2000. link Times cited: 11 K. Ito and V. Vítek, “An atomistic study of segregation to lamellar interfaces in non-stoichiometric TiAl alloys,” Acta Materialia. 1998. link Times cited: 10 T. Braisaz et al., “Nanocrystalline thin titanium films grown on potassium bromide single crystals,” Thin Solid Films. 1998. link Times cited: 3 A. Serra and D. Bacon, “A new model for 1012 twin growth in hcp metals,” Philosophical Magazine. 1996. link Times cited: 228 Abstract: Computer simulation has been used to study the interaction o… read more Abstract: Computer simulation has been used to study the interaction of a perfect, basal dislocation with a {1012} twin boundary in a hcp metal for the situation where the 1/3{1120} Burgers vector is inclined at 60° to the interface. It is found that slip is not transferred from one crystal to the other with a residual dislocation left at the interface. Instead, the matrix dislocation decomposes into interfacial defects. We show that as a result of this decomposition the matrix dislocation becomes a new source of twinning dislocations that produce twin growth when the appropriate stress is applied to the crystal. The mechanism described does not require twinning dislocations to multiply by a pole process. read less S. J. Wooding, D. Bacon, and W. Phythian, “A computer simulation study of displacement cascades in α-titanium,” Philosophical Magazine. 1995. link Times cited: 38 Abstract: The damage produced by displacement cascades in the h.c.p. m… read more Abstract: The damage produced by displacement cascades in the h.c.p. metal α-titanium at 100K has been investigated by molecular dynamics using a many-body interatomic potential. This has been the first simulation of cascades in the h.c.p. structure. 32 cascades ranging in energy from 0.3 to 5 keV were generated in order to study the effects of the crystal structure and cascade energy. Computer-generated plots have been used to visualize the nature and arrangement of the point defects produced in the cascade events. There is no discernible effect of the primary knock-on atom direction, and individual replacement sequences make only a minor contribution to the final damage state. Views of the displaced atoms looking along the basal planes show very clearly regions with a liquid-like disorder, but they are small, even at 5 ke V, and do not lead to vacancy clustering when crystalline order is restored. The efficiency of production of Frenkel pairs declines with increasing cascade energy in a similar fashion t... read less T. Braisaz, P. Ruterana, B. Lebouvier, and G. Nouet, “Atomic Structure Analysis of the (10 1 2) Twin in Zinc by HREM and Energetical Calculations,” Physica Status Solidi B-basic Solid State Physics. 1995. link Times cited: 20 Abstract: The atomic structure of the (10 1 2) twin boundary in zinc i… read more Abstract: The atomic structure of the (10 1 2) twin boundary in zinc is investigated theoretically by atomistic calculations and experimentally by high resolution electron microscopy. For computer simulations, the atomic interactions are described by a many-body potential of the Finnis-Sinclair type and are applied to a h.c.p. structure with a large c/a_ratio (1.856). Using this potential, only one planar atomic structure is found to exist for the (10 1 2) twin. This is in agreement with the previous results for h.c.p. metals with c/a ratio close to the ideal value (1.633). In contrast, two atomic structures are observed experimentally: a planar and symmetric interface similar to the one obtained by calculations, and a microfaceted structure. The microfaceted structure is observed for the first time in the (10 1 2) twin. La structure atomique de la macle (10 1 2) du zinc est atudiae a la fois thaoriquement grǎce aux calculs de relaxation et experimentalement par la technique de microscopie electronique haute resolution. Le potentiel a plusieurs corps utilise pour la simulation atomistique est du type Finnis-Sinclair et est applique a une structure h.c. au rapport c/a (1,856) tres different du rapport ideal (1,633). Nous concluons que quelque soit le modele de depart etudie, la relaxation conduit a une structure unique, symetrique et planaire. Ceci est en accord avec les resultats anterieures obtenus pour des metaux h.c. ayant un rapport c/a proche de la valeur ideale. D'autre part, les observations experimentales montrent que deux types de structure peuvent coexister: l'une est microfacettee, l'autre est planaire et symetrique comme l'indique les calculs de relaxation. La structure microfacettee est observee pour la premiere fois. read less S. J. Wooding and D. Bacon, “Computer simulation of low-energy displacement events in pure HCP metals,” Radiation Effects and Defects in Solids. 1994. link Times cited: 9 Abstract: Molecular dynamics simulations of low-energy atomic recoils … read more Abstract: Molecular dynamics simulations of low-energy atomic recoils have been carried out for α-Ti (HCP) with a view to investigating the displacement threshold energy, Ed, in detail. These have been undertaken at 0 K and 100 K, using a many-body interatomic potential modified to reflect the dominant two-body interaction at short range. This is the first systematic study of atomic displacement events in the HCP structure using such a potential. The mechanisms of these threshold events have been investigated and the strong orientation dependence of the threshold energy has been interpreted in terms of the HCP crystal structure. Also, a correlation has been found between the magnitude of the threshold displacement energy and the maximum number of atoms temporarily displaced into interstitial positions during a cascade. read less D. Bacon, A. Calder, J. Harder, and S. J. Wooding, “Computer simulation of low-energy displacement events in pure bcc and hcp metals,” Journal of Nuclear Materials. 1993. link Times cited: 35 N. Diego and D. Bacon, “Vacancy properties in twin boundaries in hcp metals simulated by many-body interatomic potentials,” Journal of Nuclear Materials. 1993. link Times cited: 3 D. Kulp, T. Egami, D. Luzzi, and V. Vítek, “A molecular dynamics study of atomic level stress distributions in defective intermetallics,” Journal of Alloys and Compounds. 1993. link Times cited: 5 C. Gu, M. Su, Z. Tian, J. Zhao, and Y. Wang, “Multi-scale simulation study on the evolution of stress waves and dislocations in Ti alloy during laser shock peening processing,” Optics & Laser Technology. 2023. link Times cited: 1 J. Ren et al., “Deformation Behavior of Pure Titanium With a Rare HCP/FCC Boundary: An Atomistic Study,” Materials Research. 2020. link Times cited: 5 Abstract: The compressive and tensile behaviors in a Ti nanopillar wit… read more Abstract: The compressive and tensile behaviors in a Ti nanopillar with a biphasic hexagonal close-packed (HCP) /face-centered cubic (FCC) phase boundary are theoretically researched using classic molecular dynamic simulation. The results indicate that the HCP/FCC interface and free surface of the nanopillar are the sources of dislocation nucleation. The plastic deformation is mainly concentrated in the metastable FCC phase of the biphasic nanopillar. Under compressive loading, a reverse phase transformation of FCC to the HCP phase is induced by the dislocation glide of multiple Shockley partial dislocations 1 6 <121> under compressive loading. However, for tensile loading a large number read less J.-Q. Ren, Q. Sun, L. Xiao, and J. Sun, “Temperature and strain rate effect of the deformation-induced phase transformation in pure titanium nanopillars oriented along [0 0 0 1],” Computational Materials Science. 2017. link Times cited: 18 K. Yan-mei, C. Nan‐xian, and S. Jiang, “Site preference and vibrational properties of ScFexAl12−x,” Journal of Magnetism and Magnetic Materials. 2003. link Times cited: 12 D. Bacon, R. Pond, and A. Serra, “The Structure of Defects Formed by Absorption of Crystal Dislocations in Interfaces in the HCP Metals,” MRS Proceedings. 1999. link Times cited: 8 Abstract: Atomic-scale computer simulation has been used to investigat… read more Abstract: Atomic-scale computer simulation has been used to investigate the interaction of crystal dislocations with two interfaces in hexagonal-close-packed (HCP) metals, namely the {1012} twin boundary and a /90° tilt boundary that is incommensurate in the direction perpendicular to the tilt axis. Crystal dislocations are absorbed in the tilt boundary with concomitant reconstruction of their cores. In the twin boundary, a broader range of interactions is observed, including defect transmission from matrix to twin and decomposition in the interface into discrete defects. The role of crystallographic features and interfacial structure is elucidated by comparing interaction processes in the two interfaces. The core structure of interfacial defects can be complex and contributes significantly to total defect energy. read less L. Zhang and J.-sheng Wu, “Stoichiometric and Off-Stoichiometric Alloying in Silicide Compound Ti 5 Si 3 By Nb or Cr Additions,” MRS Proceedings. 1998. link Times cited: 0 Abstract: Titanium silicide Ti{sub 5}Si{sub 3} whose melting temperatu… read more Abstract: Titanium silicide Ti{sub 5}Si{sub 3} whose melting temperature is 2,130 C bears the potential for very high temperature application. This paper reports their results on the alloying behavior of Nb or Cr addition to this compound. Total energy calculation shows that the substitution of Ti by Nb or Cr atoms in Ti{sub 5}Si{sub 3} crystal stiffens the bonding between the atoms. In experiment, two means of alloying are considered: stoichiometric and off-stoichiometric alloying. Stoichiometric alloying in Ti{sub 5}Si{sub 3} results in compounds consisting of single Ti{sub 5}Si{sub 3} phase while off-stoichiometric alloying yields hypereutectic microstructure with Ti{sub 5}Si{sub 3} being the primary phase. The Ti{sub 5}Si{sub 3} phase in both cases dissolves certain amount of Nb or Cr alloying element and its composition agrees with the stoichiometric composition of (Ti,Nb){sub 5}Si{sub 3} or (Ti,Cr){sub 5}Si{sub 3}. The moduli of the stoichiometric alloys increase with the increase of alloying element addition, indicating an enhancement in Ti{sub 5}Si{sub 3} crystal. read less V. Vítek, A. Girshick, R. Siegl, H. Inui, and M. Yamaguchi, “Atomic Structure and Properties of Dislocations and Interfaces in Two-Phase TiAl Compounds.” 1997. link Times cited: 6 S. Chen, Z. Aitken, V. Sorkin, Z. Yu, Z. Wu, and Y.-W. Zhang, “Modified Embedded‐Atom Method Potentials for the Plasticity and Fracture Behaviors of Unary HCP Metals,” Advanced Theory and Simulations. 2021. link Times cited: 3 Abstract: Modified embedded‐atom method (MEAM) potentials have been wi… read more Abstract: Modified embedded‐atom method (MEAM) potentials have been widely used in molecular dynamics (MD) simulations to describe the interatomic interactions in metallic systems. However, conventional MEAM potentials are almost exclusively fit to a limited number of key single‐value properties, limiting the predictability of MD simulations, especially for complex hexagonal‐close‐packed (HCP) metals with multiple slip systems. Here, three MEAM potentials for unary HCP metals (Mg, Co, and Ti) are fit to conventional target properties, as well as continuous‐energy curves and their gradients obtained from density‐functional theory calculations. These targets include the lattice parameters, cohesive energy, elastic constants, and surface energies as well as the cohesive energy curve, basal plane decohesion energy curve, and generalized stacking fault energy curves for basal, prismatic, pyramidal I, and pyramidal II planes. These interatomic potentials demonstrate excellent reproduction of relevant properties and enable accurate MD simulations of volumetric and plastic deformations, as well as fracture in Mg, Co, and Ti HCP metals. Importantly, the interatomic potentials demonstrate better performance than all existing EAM/MEAM potentials readily available from the literature. read less M. S. Nitol, D. Dickel, and C. Barrett, “Machine learning models for predictive materials science from fundamental physics: An application to titanium and zirconium,” Acta Materialia. 2021. link Times cited: 12 C. A. Hirst et al., “Revealing hidden defects through stored energy measurements of radiation damage,” Science Advances. 2021. link Times cited: 11 Abstract: With full knowledge of a material’s atomistic structure, it … read more Abstract: With full knowledge of a material’s atomistic structure, it is possible to predict any macroscopic property of interest. In practice, this is hindered by limitations of the chosen characterization techniques. For example, electron microscopy is unable to detect the smallest and most numerous defects in irradiated materials. Instead of spatial characterization, we propose to detect and quantify defects through their excess energy. Differential scanning calorimetry of irradiated Ti measures defect densities five times greater than those determined using transmission electron microscopy. Our experiments also reveal two energetically distinct processes where the established annealing model predicts one. Molecular dynamics simulations discover the defects responsible and inform a new mechanism for the recovery of irradiation-induced defects. The combination of annealing experiments and simulations can reveal defects hidden to other characterization techniques and has the potential to uncover new mechanisms behind the evolution of defects in materials. read less R. Murzaev, D. Bachurin, A. Mukhametgalina, M. Murzinova, and A. Nazarov, “Ultrasonic treatment of ultrafine-grained titanium,” Physics Letters A. 2020. link Times cited: 3 S. A. Etesami, M. Laradji, and E. Asadi, “Reliability of molecular dynamics interatomic potentials for modeling of titanium in additive manufacturing processes,” Computational Materials Science. 2020. link Times cited: 5 C. Cheng et al., “Development and application of EAM potentials for Ti, Al and Nb with enhanced planar fault energy of Ti,” Computational Materials Science. 2020. link Times cited: 4 J. Cai, C. Mi, Q. Deng, and C. Zheng, “Effects of crystalline orientation, twin boundary and stacking fault on the crack-tip behavior of a mode I crack in nanocrystalline titanium,” Mechanics of Materials. 2019. link Times cited: 8 A. Kartamyshev, A. Lipnitskii, V. Saveliev, V. Maksimenko, I. Nelasov, and D. Poletaev, “Development of an interatomic potential for titanium with high predictive accuracy of thermal properties up to melting point,” Computational Materials Science. 2019. link Times cited: 8 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 L. Chang, C.-yu Zhou, J. Li, and X.-hua He, “Investigation on tensile properties of nanocrystalline titanium with ultra-small grain size,” Computational Materials Science. 2018. link Times cited: 13 A. Ready, P. Haynes, and A. Sutton, “Comment on ‘Development of an interatomic potential for the simulation of defects, plasticity, and phase transformations in titanium’ [J. Chem. Phys. 145, 154102 (2016)].,” The Journal of chemical physics. 2017. link Times cited: 0 Abstract: Recently Mendelev, Underwood, and Ackland1 (MUA) published t… read more Abstract: Recently Mendelev, Underwood, and Ackland1 (MUA) published three interatomic potentials (IPs) Ti1, Ti2, and Ti3 for pure Ti. These IPs were developed to model atomistically defects, plasticity, and phase changes in Ti. In this comment we compare quantitatively the γsurfaces predicted by these IPs on the basal and {11̄01} first order pyramidal or pyramidal I planes of hexagonal close-packed Ti with those we computed recently by density functional theory (DFT)2. We also compare with the γ-surfaces computed with the IP developed by Ackland3, which we call Ti0. Local minima in the γ-surface4 correspond to stable stacking faults, which indicate the possibility, depending on the energy of the local minimum, of dissociation of lattice dislocations into partial dislocations separated by the stacking fault. In addition, the slope of the γ-surface determines the force per unit area tending to constrict the core of dislocations in the slip plane5. The accuracy of a γ-surface is therefore of some importance for modelling plasticity on that slip plane. read less A. Ready, A. Sutton, P. Haynes, and D. Rugg, “Point, Linear and Planar Defects in Titanium.” 2016. link Times cited: 2 X.-jie Li, J. Fu, Y. Qin, S. Hao, and J. Zhao, “Gupta potentials for five HCP rare earth metals,” Computational Materials Science. 2016. link Times cited: 6 Y.-xia Liu, H. Wang, H. Wu, D. Xu, and R. Yang, “A mean-field interatomic potential for a multi-component β-type titanium alloy,” Computational Materials Science. 2014. link Times cited: 2 G. Ackland, “Temperature dependence in interatomic potentials and an improved potential for Ti,” Journal of Physics: Conference Series. 2012. link Times cited: 11 Abstract: The process of deriving an interatomic potentials represents… read more Abstract: The process of deriving an interatomic potentials represents an attempt to integrate out the electronic degrees of freedom from the full quantum description of a condensed matter system. In practice it is the derivatives of the interatomic potentials which are used in molecular dynamics, as a model for the forces on a system. These forces should be the derivative of the free energy of the electronic system, which includes contributions from the entropy of the electronic states. This free energy is weakly temperature dependent, and although this can be safely neglected in many cases there are some systems where the electronic entropy plays a significant role. Here a method is proposed to incorporate electronic entropy in the Sommerfeld approximation into empirical potentials. The method is applied as a correction to an existing potential for titanium. Thermal properties of the new model are calculated, and a simple method for fixing the melting point and solid-solid phase transition temperature for existing models fitted to zero temperature data is presented. read less X.-J. Yuan, N. Chen, J. Shen, and W. Hu, “Embedded-atom-method interatomic potentials from lattice inversion,” Journal of Physics: Condensed Matter. 2010. link Times cited: 26 Abstract: The present work develops a physically reliable procedure fo… read more Abstract: The present work develops a physically reliable procedure for building the embedded-atom-method (EAM) interatomic potentials for the metals with fcc, bcc and hcp structures. This is mainly based on Chen–Möbius lattice inversion (Chen et al 1997 Phys. Rev. E 55 R5) and first-principles calculations. Following Baskes (Baskes et al 2007 Phys. Rev. B 75 094113), this new version of the EAM eliminates all of the prior arbitrary choices in the determination of the atomic electron density and pair potential functions. Parameterizing the universal form deduced from the calculations within the density-functional scheme for homogeneous electron gas as the embedding function, the new-type EAM potentials for Cu, Fe and Ti metals have successfully been constructed by considering interatomic interactions up to the fifth neighbor, the third neighbor and the seventh neighbor, respectively. The predictions of elastic constants, structural energy difference, vacancy formation energy and migration energy, activation energy of vacancy diffusion, latent heat of melting and relative volume change on melting all satisfactorily agree with the experimental results available or first-principles calculations. The predicted surface energies for low-index crystal faces and the melting point are in agreement with the experimental data to the same extent as those calculated by other EAM-type potentials such as the FBD-EAM, 2NN MEAM and MS-EAM. In addition, the order among the predicted low-index surface energies is also consistent with the experimental information. read less J. Schneider and L. Ciacchi, “First principles and classical modeling of the oxidized titanium (0001) surface,” Surface Science. 2010. link Times cited: 35 T. Hammerschmidt, R. Drautz, and D. Pettifor, “Atomistic modelling of materials with bond-order potentials,” International Journal of Materials Research. 2009. link Times cited: 26 Abstract: The atomistic modelling of materials with effective model po… read more Abstract: The atomistic modelling of materials with effective model potentials requires a reliable description of the breaking and making of interatomic bonds in different atomic environments. The bond-order potentials provide such a transferable description of atomic bonding while at the same time they are computationally efficient for application in large-scale atomistic simulations. We give an overview of the fundamentals of bond-order potentials and their derivation from the tight-binding electronic structure by linking the atomic structure to the electronic structure. We discuss the application of the structural energy difference theorem for studying trends in crystal phase stability and provide a brief summary of representative examples for modelling metals, hydrocarbons, and semiconductors with analytic and numerical bond-order potentials. read less Y.-xia Liu, X. Wang, Y. Ma, C. Zhang, J.-xing Sun, and J.-xing Sun, “Austenite composition design at the atomic scale for the iron-based multi-component alloy as cast,” Computational Materials Science. 2008. link Times cited: 1 M. Aoki, D. Nguyen-Manh, D. Pettifor, and V. Vítek, “Atom-based bond-order potentials for modelling mechanical properties of metals,” Progress in Materials Science. 2007. link Times cited: 52 Y.-M. Kim, B.-J. Lee, and M. Baskes, “Modified embedded-atom method interatomic potentials for Ti and Zr,” Physical Review B. 2006. link Times cited: 193 Abstract: Semiempirical interatomic potentials for hcp elements, Ti an… read more Abstract: Semiempirical interatomic potentials for hcp elements, Ti and Zr, have been developed based on the MEAM (modified embedded-atom method) formalism. The new potentials do not cause the stability problem previously reported in MEAM for hcp elements, and describe wide range of physical properties (bulk properties, point defect properties, planar defect properties, and thermal properties) of pure Ti and Zr, in good agreement with experimental information. The applicability of the potentials to atomistic approaches for investigation of various materials behavior (slip, irradiation, amorphous behavior, etc.) in Ti or Zr-based alloys is demonstrated by showing that the related material properties are correctly reproduced using the present potentials and that the potentials can be easily extended to multicomponent systems. read less S. Erdin, Y. Lin, and J. W. Halley, “Self-consistent tight-binding study of low-index titanium surfaces,” Physical Review B. 2005. link Times cited: 10 A. Serra, D. Bacon, and R. Pond, “Twins as barriers to basal slip in hexagonal-close-packed metals,” Metallurgical and Materials Transactions A. 2002. link Times cited: 74 W. Tian-min, W. Bao-yi, J. Xin, G. Qiang, W. Yue-xia, and G. Fei, “Many-Body Potentials for Intermetallic TiAl Alloy and Its Point Defect Properties,” Chinese Physics Letters. 2001. link Times cited: 6 Abstract: For the intermetallic compound TiAl, the interatomic potenti… read more Abstract: For the intermetallic compound TiAl, the interatomic potentials in the Finnis-Sinclair model were constructed by empirically fitting to the properties of L10 TiAl tetragonal phase and the pressure-volume relations. In the calculations of the point defect properties of the TiAl alloy with this potential, it was shown that the thermal concentration of anti-site defects was higher than that of other point defects. With similar formation energies, five possible interstitial configurations were stable. This model was consistent with the embedded atom method or embedded defect method and adequate for simulation of defects in the TiAl alloy. read less A. Béré, J. Chen, A. Hairie, G. Nouet, and E. Paumier, “Determination of the high c/a ratio of hexagonal metals with a semi-empirical tight-binding method,” Computational Materials Science. 2000. link Times cited: 10 A. Serra, D. Bacon, and R. Pond, “Dislocations in interfaces in the h.c.p. metals—I. Defects formed by absorption of crystal dislocations,” Acta Materialia. 1999. link Times cited: 104 A. Mikhin and N. Diego, “A many-body potential model for Zn,” Philosophical Magazine. 1996. link Times cited: 11 Abstract: A many-body potential model based on the second moment of th… read more Abstract: A many-body potential model based on the second moment of the tight-binding approximation is proposed for computer simulation of lattice defects in Zn. The constructed potential satisfactorily reproduces the experimental data: cohesive energy, equilibrium lattice constants, vacancy formation energy and elastic constants, except C 33. Mechanical and structural stability has been ensured and the stacking-fault energy has been determined to be close to the lower end of experimental estimates. As an application of the model, the monovacancy migration energies and the formation energy of single self-interstitials are calculated. A significant anisotropy of vacancy migration and a low value of interstitial formation energy is found, in full accordance with the results of previous experimental and theoretical studies. The shortcomings of spherically symmetric potentials applied to the hcp metals with c/a ratios strongly deviating from the ideal value are discussed. read less A. Serra and D. Bacon, “Computer simulation of screw dislocation interactions with twin boundaries in h.c.p. metals,” Acta Metallurgica Et Materialia. 1995. link Times cited: 110 N. Diego and D. Bacon, “A computer simulation study of interstitial-twin boundary interactions in h.c.p. metals,” Modelling and Simulation in Materials Science and Engineering. 1995. link Times cited: 3 Abstract: The formation of stable interstitial configurations in the (… read more Abstract: The formation of stable interstitial configurations in the (1121), (1122), (1011) and (1012) twin boundaries in hexagonal closed packed metals has been studied by computer simulation. The crystals have been modelled by either a pair potential for a crystal with a near-ideal c/a lattice parameter ratio or a many-body potential for titanium. These potentials have proved to be satisfactory for the simulation of both twin boundaries and point defects. It is found that the twin boundary gives rise to stable interstitial configurations exhibiting a high binding energy. These configurations are not found in the perfect lattice and are highly dependent on the twin crystallography. The variation of the twin-interstitial binding energy as a function of the defect distance to the interface depends also on the twin structure. The features are qualitatively the same for both potentials for the (1121) and (1122) twins, but differences between the two model potentials are observed for the (1011) and (1012) twin boundaries. read less D. Bacon, “Point defects and clusters in the hcp metals : their role in the dose transition,” Journal of Nuclear Materials. 1993. link Times cited: 35 H. Guo et al., “Twin junctions with geometric compatibility and mobility in titanium and magnesium,” Scripta Materialia. 2023. link Times cited: 0 V. Vítek and V. Paidar, “Chapter 87 - Non-planar Dislocation Cores: A Ubiquitous Phenomenon Affecting Mechanical Properties of Crystalline Materials.” 2008. link Times cited: 104 P. Komninou et al., “Electron Microscopy Studies of Defects in Deformed Hexagonal Materials.” 2000. link Times cited: 1 R. Pasianot and A. M. Monti, “A many body potential for α-Zr. Application to defect properties,” Journal of Nuclear Materials. 1999. link Times cited: 65 T. Braisaz et al., “HREM study of Ultra Thin Titanium Films,” MRS Proceedings. 1997. link Times cited: 1 Z. Tang, Y. Chen, and W. Ye, “Calculation of Surface Properties of Cubic and Hexagonal Crystals through Molecular Statics Simulations,” Crystals. 2020. link Times cited: 8 Abstract: Surface property is an important factor that is widely consi… read more Abstract: Surface property is an important factor that is widely considered in crystal growth and design. It is also found to play a critical role in changing the constitutive law seen in the classical elasticity theory for nanomaterials. Through molecular static simulations, this work presents the calculation of surface properties (surface energy density, surface stress and surface stiffness) of some typical cubic and hexagonal crystals: face-centered-cubic (FCC) pure metals (Cu, Ni, Pd and Ag), body-centered-cubic (BCC) pure metals (Mo and W), diamond Si, zincblende GaAs and GaN, hexagonal-close-packed (HCP) pure metals (Mg, Zr and Ti), and wurzite GaN. Sound agreements of the bulk and surface properties between this work and the literature are found. New results are first reported for the surface stiffness of BCC pure metals, surface stress and surface stiffness of HCP pure metals, Si, GaAs and GaN. Comparative studies of the surface properties are carried out to uncover trends in their behaviors. The results in this work could be helpful to the investigation of material properties and structure performances of crystals. read less C.-G. Jon, H.-S. Jin, C. Ri, and P. Song, “The first Brillouin zone of the hexagonal close-packed structure and study on the properties of vacancies and phonon dispersions by the improved ones of the modified analytic embedded atom method potentials for Ru, Sc, Ti, Y, and Zr,” Philosophical Magazine. 2019. link Times cited: 5 Abstract: ABSTRACT We studied the first Brillouin zone of the hexagona… read more Abstract: ABSTRACT We studied the first Brillouin zone of the hexagonal close-packed (HCP) structure and the improved ones of the modified analytical embedded atom method (EAM) potentials were adopted to calculate the properties of the mono- and bi-vacancies and the phonon dispersions for HCP transition metals Ru, Sc, Ti, Y, and Zr. The agreements with the experimental data showed that the improved potentials for the HCP transition metals are available. read less A. Takahashi, A. Seko, and I. Tanaka, “Conceptual and practical bases for the high accuracy of machine learning interatomic potential,” arXiv: Materials Science. 2017. link Times cited: 29 Abstract: Machine learning interatomic potentials (MLIPs) based on a l… read more Abstract: Machine learning interatomic potentials (MLIPs) based on a large dataset obtained by density functional theory (DFT) calculation have been developed recently. This study gives both conceptual and practical bases for the high accuracy of MLIPs, although MLIPs have been considered to be simply an accurate black-box description of atomic energy. We also construct the most accurate MLIP of the elemental Ti ever reported using a linearized MLIP framework and many angular-dependent descriptors, which also corresponds to a generalization of the modified embedded atom method (MEAM) potential. read less O. V. Lopatina, Y. Koroteev, and I. Chernov, “Atomic structure of the Zr–He, Zr–vac, and Zr–vac–He systems: First-principles calculation,” Physics of the Solid State. 2017. link Times cited: 2 Y.-hua Zhou, R. Smith, S. Kenny, and A. L. Lloyd, “Development of an empirical interatomic potential for the Ag–Ti system,” Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms. 2017. link Times cited: 5 M. Mendelev, T. L. Underwood, and G. Ackland, “Development of an interatomic potential for the simulation of defects, plasticity, and phase transformations in titanium.,” The Journal of chemical physics. 2016. link Times cited: 122 Abstract: New interatomic potentials describing defects, plasticity, a… read more Abstract: New interatomic potentials describing defects, plasticity, and high temperature phase transitions for Ti are presented. Fitting the martensitic hcp-bcc phase transformation temperature requires an efficient and accurate method to determine it. We apply a molecular dynamics method based on determination of the melting temperature of competing solid phases, and Gibbs-Helmholtz integration, and a lattice-switch Monte Carlo method: these agree on the hcp-bcc transformation temperatures to within 2 K. We were able to develop embedded atom potentials which give a good fit to either low or high temperature data, but not both. The first developed potential (Ti1) reproduces the hcp-bcc transformation and melting temperatures and is suitable for the simulation of phase transitions and bcc Ti. Two other potentials (Ti2 and Ti3) correctly describe defect properties and can be used to simulate plasticity or radiation damage in hcp Ti. The fact that a single embedded atom method potential cannot describe both low and high temperature phases may be attributed to neglect of electronic degrees of freedom, notably bcc has a much higher electronic entropy. A temperature-dependent potential obtained from the combination of potentials Ti1 and Ti2 may be used to simulate Ti properties at any temperature. read less Gui-Jun 贵钧 Cheng 程, B. Fu 付, Q. Hou 侯, X. Zhou 周, and Jun 俊 Wang 汪, “Diffusion behavior of helium in titanium and the effect of grain boundaries revealed by molecular dynamics simulation,” Chinese Physics B. 2016. link Times cited: 11 Abstract: The microstructures of titanium (Ti), an attractive tritium … read more Abstract: The microstructures of titanium (Ti), an attractive tritium (T) storage material, will affect the evolution process of the retained helium (He). Understanding the diffusion behavior of He at the atomic scale is crucial for the mechanism of material degradation. The novel diffusion behavior of He has been reported by molecular dynamics (MD) simulation for the bulk hcp-Ti system and the system with grain boundary (GB). It is observed that the diffusion of He in the bulk hcp-Ti is significantly anisotropic (the diffusion coefficient of the [0001] direction is higher than that of the basal plane), as represented by the different migration energies. Different from convention, the GB accelerates the diffusion of He in one direction but not in the other. It is observed that a twin boundary (TB) can serve as an effective trapped region for He. The TB accelerates diffusion of He in the direction perpendicular to the twinning direction (TD), while it decelerates the diffusion in the TD. This finding is attributable to the change of diffusion path caused by the distortion of the local favorable site for He and the change of its number in the TB region. read less I. A. Alhafez, C. Ruestes, Y. Gao, and H. Urbassek, “Nanoindentation of hcp metals: a comparative simulation study of the evolution of dislocation networks,” Nanotechnology. 2016. link Times cited: 66 Abstract: Using molecular dynamics simulation, we study the nanoindent… read more Abstract: Using molecular dynamics simulation, we study the nanoindentation of three hcp metals: Mg, Ti, and Zr. Both the basal and two prismatic surface planes are considered. We focus on the characterization of the plasticity generated in the crystal. The similarities to, and the differences from, the behavior of the more commonly investigated fcc and bcc metals are highlighted. We find that hcp metals show a larger variety than the fcc and bcc metals studied up until now. The prolific emission of prismatic loops can lead to extended plastic zones. The size of the plastic zone is quantified by the ratio f of the plastic zone radius to the radius of the contact area. We find values of between 1.6 (an almost collapsed zone) and >5; in the latter case, complex dislocation networks build up which are extended in the direction of easy glide. read less J.-Q. Ren, Q. Sun, L. Xiao, X. Ding, and J. Sun, “Size-dependent of compression yield strength and deformation mechanism in titanium single-crystal nanopillars orientated [0001] and [112̄0],” Materials Science and Engineering A-structural Materials Properties Microstructure and Processing. 2014. link Times cited: 23 H. Kim, N. H. Shaik, X. Xu, A. Raman, and A. Strachan, “Multiscale contact mechanics model for RF–MEMS switches with quantified uncertainties,” Modelling and Simulation in Materials Science and Engineering. 2013. link Times cited: 12 Abstract: We introduce a multiscale model for contact mechanics betwee… read more Abstract: We introduce a multiscale model for contact mechanics between rough surfaces and apply it to characterize the force–displacement relationship for a metal-dielectric contact relevant for radio frequency micro-electromechanicl system (MEMS) switches. We propose a mesoscale model to describe the history-dependent force–displacement relationships in terms of the surface roughness, the long-range attractive interaction between the two surfaces, and the repulsive interaction between contacting asperities (including elastic and plastic deformation). The inputs to this model are the experimentally determined surface topography and the Hamaker constant as well as the mechanical response of individual asperities obtained from density functional theory calculations and large-scale molecular dynamics simulations. The model captures non-trivial processes including the hysteresis during loading and unloading due to plastic deformation, yet it is computationally efficient enough to enable extensive uncertainty quantification and sensitivity analysis. We quantify how uncertainties and variability in the input parameters, both experimental and theoretical, affect the force–displacement curves during approach and retraction. In addition, a sensitivity analysis quantifies the relative importance of the various input quantities for the prediction of force–displacement during contact closing and opening. The resulting force–displacement curves with quantified uncertainties can be directly used in device-level simulations of micro-switches and enable the incorporation of atomic and mesoscale phenomena in predictive device-scale simulations. read less J.-Q. Ren, Q. Sun, L. Xiao, X. Ding, and J. Sun, “Molecular dynamics simulations of the size effect of titanium single-crystal nanopillars orientated for double prismatic slips,” Philosophical Magazine Letters. 2013. link Times cited: 9 Abstract: An inverse “smaller is stronger” trend is predicted on the b… read more Abstract: An inverse “smaller is stronger” trend is predicted on the basis of molecular dynamics simulations of α-titanium (Ti) single-crystal nanopillars orientated for double prismatic slips when the nanopillars are less than 7 nm wide. This trend is attributed to a significant increase in the surface energy due to the nucleation and propagation of edge dislocations on the surface of the pillars. read less M. A. Karolewski, R. Cavell, R. Gordon, C. Glover, M. Cheah, and M. Ridgway, “Predicting XAFS scattering path cumulants and XAFS spectra for metals (Cu, Ni, Fe, Ti, Au) using molecular dynamics simulations.,” Journal of synchrotron radiation. 2013. link Times cited: 5 Abstract: The ability of molecular dynamics (MD) simulations to suppor… read more Abstract: The ability of molecular dynamics (MD) simulations to support the analysis of X-ray absorption fine-structure (XAFS) data for metals is evaluated. The low-order cumulants (ΔR, σ(2), C3) for XAFS scattering paths are calculated for the metals Cu, Ni, Fe, Ti and Au at 300 K using 28 interatomic potentials of the embedded-atom method type. The MD cumulant predictions were evaluated within a cumulant expansion XAFS fitting model, using global (path-independent) scaling factors. Direct simulations of the corresponding XAFS spectra, χ(R), are also performed using MD configurational data in combination with the FEFF ab initio code. The cumulant scaling parameters compensate for differences between the real and effective scattering path distributions, and for any errors that might exist in the MD predictions and in the experimental data. The fitted value of ΔR is susceptible to experimental errors and inadvertent lattice thermal expansion in the simulation crystallites. The unadjusted predictions of σ(2) vary in accuracy, but do not show a consistent bias for any metal except Au, for which all potentials overestimate σ(2). The unadjusted C3 predictions produced by different potentials display only order-of-magnitude consistency. The accuracy of direct simulations of χ(R) for a given metal varies among the different potentials. For each of the metals Cu, Ni, Fe and Ti, one or more of the tested potentials was found to provide a reasonable simulation of χ(R). However, none of the potentials tested for Au was sufficiently accurate for this purpose. read less K. Hammond, H.-J. L. Voigt, L. A. Marus, N. Juslin, and B. Wirth, “Simple pair-wise interactions for hybrid Monte Carlo–molecular dynamics simulations of titania/yttria-doped iron,” Journal of Physics: Condensed Matter. 2013. link Times cited: 13 Abstract: We present pair-wise, charge-neutral model potentials for an… read more Abstract: We present pair-wise, charge-neutral model potentials for an iron–titanium–yttrium–oxygen system. These simple models are designed to provide a tractable method of simulating nanostructured ferritic alloys (NFAs) using off-lattice Monte Carlo and molecular dynamics techniques without deviating significantly from the formalism employed in existing Monte Carlo simulations. The model is fitted to diamagnetic density functional theory (DFT) calculations of the various species over a range of densities and concentrations. The resulting model potentials provide reasonable and in some cases even excellent mechanical and thermodynamic properties for the pure metals. The model replicates the qualitative trends in formation energy predicted by DFT, though the energies of formation do not agree as well for dilute systems as they do for more concentrated systems. We find that on-lattice models will consistently favor tetrahedral oxygen interstitial sites over octahedral interstitial sites, while relaxed systems typically favor octahedral sites. This emphasizes the need for the off-lattice simulations for which this potential was designed. read less J. Chu and C. Steeves, “Thermal expansion and recrystallization of amorphous Al and Ti: A molecular dynamics study,” Journal of Non-crystalline Solids. 2011. link Times cited: 23 I. Konovalenko, D. Kryzhevich, K. P. Zol’nikov, and S. Psakhie, “Atomic mechanisms of local structural rearrangements in strained crystalline titanium grain,” Technical Physics Letters. 2011. link Times cited: 20 Y. Dai, J. Li, and B. Liu, “Long-range empirical potential model: extension to hexagonal close-packed metals,” Journal of Physics: Condensed Matter. 2009. link Times cited: 33 Abstract: An n-body potential is developed and satisfactorily applied … read more Abstract: An n-body potential is developed and satisfactorily applied to hcp metals, Co, Hf, Mg, Re, Ti, and Zr, in the form of long-range empirical potential. The potential can well reproduce the lattice constants, c/a ratios, cohesive energies, and the bulk modulus for their stable structures (hcp) and metastable structures (bcc or fcc). Meanwhile, the potential can correctly predict the order of structural stability and distinguish the energy differences between their stable hcp structure and other structures. The energies and forces derived by the potential can smoothly go to zero at cutoff radius, thus completely avoiding the unphysical behaviors in the simulations. The developed potential is applied to study the vacancy, surface fault, stacking fault and self-interstitial atom in the hcp metals. The calculated formation energies of vacancy and divacancy and activation energies of self-diffusion by vacancies are in good agreement with the values in experiments and in other works. The calculated surface energies and stacking fault energies are also consistent with the experimental data and those obtained in other theoretical works. The calculated formation energies generally agree with the results in other works, although the stable configurations of self-interstitial atoms predicted in this work somewhat contrast with those predicted by other methods. The proposed potential is shown to be relevant for describing the interaction of bcc, fcc and hcp metal systems, bringing great convenience for researchers in constructing potentials for metal systems constituted by any combination of bcc, fcc and hcp metals. read less A. T. Raji, S. Scandolo, R. Mazzarello, S. Nsengiyumva, M. Härting, and D. T. Britton, “Ab initio pseudopotential study of vacancies and self-interstitials in hcp titanium,” Philosophical Magazine. 2009. link Times cited: 48 Abstract: By means of an ab initio plane-wave pseudopotential method, … read more Abstract: By means of an ab initio plane-wave pseudopotential method, monovacancy, divacancy and self-interstitials in hcp titanium are investigated. The calculated monovacancy formation energy is 1.97 eV, which is in excellent agreement with other theoretical calculations, and agrees qualitatively with published experimental results. The relaxation of the atoms around a single vacancy is observed to be small. Two divacancy configurations, the in-plane and the off-plane, have also been shown to be equally stable. With regards to the interstitials, of the eight configurations studied, two (octahedral and basal octahedral) have relatively lower formation energies and are, thus, the most likely stable configurations. We find small energy differences between them, suggesting their possible co-existence. It is also observed that the tetrahedral configuration decays to a split dumbbell configuration, whereas both the basal tetrahedral and the basal pseudocrowdion interstitials decay to the basal octahedral configuration. Using the nudged elastic band method (NEB), we determine a possible minimum energy path (MEP) for the diffusion of self-interstitial titanium atoms from an octahedral site to the nearest octahedral site. The energy barrier for this migration mechanism is shown to be about 0.20 eV. read less A. Béré, T. Braisaz, P. Ruterana, and G. Nouet, “Twinning and extended defects in hcp metals with large c/a ratio: modelling and microscopic observations,” physica status solidi (a). 2005. link Times cited: 2 Abstract: In hexagonal metals of largest c/a ratio, experimental obser… read more Abstract: In hexagonal metals of largest c/a ratio, experimental observations hardly agree with the theoretical models of extended defects. For Zn and Cd, we have developed a semi‐empirical tight‐binding method to calculate the energy of extended defects. It was then possible to obtain a good correlation for polytypes or basal stacking faults. For the (10$ \bar 1 $2) twin, two possible interfaces have been shown to be stable in agreement with the available experimental results for Zn. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) read less C. D. * and A. Legris, “Ab initio atomic-scale determination of point-defect structure in hcp zirconium,” Philosophical Magazine. 2005. link Times cited: 81 Abstract: Microstructure evolution under irradiation is very sensitive… read more Abstract: Microstructure evolution under irradiation is very sensitive to point defects mobility. Here we present state-of-the-art ab initio calculations of the point defects structure (vacancy and self-interstitial atoms; SIAs) in hexagonal zirconium. Contrary to previous results obtained using empirical potentials, we found that the octahedral configuration should be the most stable SIA, immediately followed by the basal octahedral and the basal crowdion, the three structures having very close formation energy. read less J. R. M. †, Y. Ye, and M. Yoo, “First-principles examination of the twin boundary in hcp metals,” Philosophical Magazine. 2005. link Times cited: 39 Abstract: We have performed total-energy electronic structure calculat… read more Abstract: We have performed total-energy electronic structure calculations to examine competing structures for the twin boundary, which can form under tensile stress along the c axis. The twin boundary structures are significantly different, most notably in their symmetry. These calculations show that, for all materials studied, the different structures have nearly the same energy, in agreement with calculations from empirical potentials. This result is surprising, given the difference in the structures, and the fact that previous first-principles calculations of the energies of compression twin boundaries have shown significant differences from empirical potentials. read less A. Béré, J. Chen, A. Hairie, G. Nouet, and E. Paumier, “Basal stacking faults and (10&1macr;2) twin energies by a semi‐empirical tight‐binding method for zinc and cadmium,” physica status solidi (b). 2004. link Times cited: 1 Abstract: The study of extended defects requires atomic modelisation a… read more Abstract: The study of extended defects requires atomic modelisation able to give theoretical values characterizing the defects to be compared to experimental observations. In the case of zinc and cadmium which are hexagonal metals with high c/a ratio, such a comparison is still controversial due to the difficulty of using known potentials. A previously developed semi‐empirical tight‐binding method is now applied to calculate the energy of extended defects in Zn and Cd. A good correlation is obtained for hypothetical polytypes and for basal stacking faults. For the (10&1macr;2) twin, two possible interfaces are found and discussed with respect to the experimental results. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) read less W. Hu, H. Deng, X. Yuan, and M. Fukumoto, “Point-defect properties in HCP rare earth metals with analytic modified embedded atom potentials,” The European Physical Journal B - Condensed Matter and Complex Systems. 2003. link Times cited: 64 A. Kersch and U. Hansen, “Atomistic feature scale modeling of the titanium ionized physical vapor deposition process,” Journal of Vacuum Science and Technology. 2002. link Times cited: 8 Abstract: We develop a fundamental model to simulate the ionized physi… read more Abstract: We develop a fundamental model to simulate the ionized physical vapor deposition process of a titanium barrier into submicron features. Using molecular dynamics techniques we calculate for typical energies the energy and angular dependent reaction rates of Ti+ with Ti and Ar+ with Ti including the distribution of the etched away particles. The interaction potential is based on Ackland’s model [G. J. Ackland, Philos. Mag. A 66, 917 (1992)] and is extended for particles with a kinetic energy up to 150 eV. The reaction rates are implemented into a cellular automaton feature scale simulator modeling the thin film growth. The reactor and plasma sheath conditions are described in a simple model providing the energy and angular distribution for the feature scale simulator. The multiscale model is applied to barrier deposition into a high aspect ratio feature with different substrate bias conditions. The results show that the barrier growth at high energy is dominated by kinetic energy driven processes. read less D. Bacon and V. Vítek, “Atomic-scale modeling of dislocations and related properties in the hexagonal-close-packed metals,” Metallurgical and Materials Transactions A. 2002. link Times cited: 76 W. Hu, B. Zhang, B.-yun Huang, F. Gao, and D. Bacon, “Analytic modified embedded atom potentials for HCP metals,” Journal of Physics: Condensed Matter. 2001. link Times cited: 164 Abstract: Analytic modified embedded atom method (AMEAM) type many-bod… read more Abstract: Analytic modified embedded atom method (AMEAM) type many-body potentials have been constructed for ten hcp metals: Be, Co, Hf, Mg, Re, Ru, Sc, Ti, Y and Zr. The potentials are parametrized using analytic functions and fitted to the cohesive energy, unrelaxed vacancy formation energy, five independent second-order elastic constants and two equilibrium conditions. Hence, each of the constructed potentials represents a stable hexagonal close-packed lattice with a particular non-ideal c/a ratio. In order to treat the metals with negative Cauchy pressure, a modified term has been added to the total energy. For all the metals considered, the hcp lattice is shown to be energetically most stable when compared with the fcc and bcc structure and the hcp lattice with ideal c/a. The activation energy for vacancy diffusion in these metals has been calculated. They agree well with experimental data available and those calculated by other authors for both monovacancy and divacancy mechanisms and the most possible diffusion paths are predicted. Stacking fault and surface energy have also been calculated and their values are lower than typical experimental data. Finally, the self-interstitial atom (SIA) formation energy and volume have been evaluated for eight possible sites. This calculation suggests that the basal split or crowdion is the most stable configuration for metals with a rather large deviation from the ideal c/a value and the non-basal dumbbell (C or S) is the most stable configuration for metals with c/a near ideal. The relationship between SIA formation energy and melting temperature roughly obeys a linear relation for most metals except Ru and Re. read less T. Ochs, C. Elsässer, M. Mrovec, V. Vítek, J. Belak, and J. Moriarty, “Symmetrical tilt grain boundaries in bcc transition metals: Comparison of semiempirical with ab-initio total-energy calculations,” Philosophical Magazine A. 2000. link Times cited: 34 Abstract: Five different semiempirical total-energy methods, provided … read more Abstract: Five different semiempirical total-energy methods, provided in the literature and applicable for atomistic simulations of extended defects in bcc transition metals, are investigated in a comparative study. The comparison is made with recent theoretical ab-initio (local-density-functional theory) and experimental (high-resolution transmission electron microscopy) studies for the specific case of the Σ = 5, (310)[001] symmetrical tilt grain boundaries (Σ = 5 STGBs) in Nb and Mo. The considered semiempirical real-space approaches based on different approximations of the tight-binding and related methods are the Finnis–Sinclair central-force potentials, non-central-force bond-order potentials recently advanced by Pettifor and co-workers, and non-central-force potentials based on the model-generalized pseudopotential theory of Moriarty. As semiempirical reciprocal-space methods, a very simple d-basis tight-binding model by Paxton and an elaborate environment dependent spd-basis orthogonal tight-binding model by Haas et al. are included in the analysis. The virtues and deficiencies of these models in their ability to predict the translation states and interfacial energies of the ∑ = 5 STGB are discussed. read less J. R. Fernández, A. M. Monti, R. C. Pasianott, and V. Vitek, “An atomistic study of formation and migration of vacancies in (1121) twin boundaries in Ti and Zr,” Philosophical Magazine A. 2000. link Times cited: 15 Abstract: The formation and migration of vacancies in (1121) twin boun… read more Abstract: The formation and migration of vacancies in (1121) twin boundaries in α-Ti and α-Zr are studied by computer modelling. Three empirical central force potentials constructed within the embedded-atom method are used to represent atomic interactions. Minimum-energy structures for the grain boundary are found first and the vacancy is then introduced by removing an atom and allowing further relaxation of the structure. Formation energies, entropies and relaxation volumes are calculated for different positions of vacancies. In order to analyse the vacancy migration, and thus the boundary self-diffusion, various vacancy jumps have been investigated and the corresponding migration energies and entropies calculated. The most probable paths composed of these simple jumps are then proposed. Both the formation and the migration free energies are significantly lower than in the bulk which demonstrates the role of the grain boundary as a vacancy sink and a fast diffusion channel. These free energies are then employed in evaluation of the diffusion coefficient tensor, the effective activation energies Qjj and the pre-exponential factors D 0jj when the jj component of this tensor is assumed to follow an Arrhenius relationship Djj = D 0jj exp (-Qjj /k B T). The boundary diffusion is then contrasted with the bulk diffusion and the calculated diffusion coefficients compared with available experimental data. read less M. Wen, C. Woo, and H.-C. Huang, “Atomistic studies of stress effects on self-interstitial diffusion in α-titanium,” Journal of Computer-Aided Materials Design. 2000. link Times cited: 7 V. Paidar, L. Wang, M. Šob, and V. Vítek, “A study of the applicability of many-body central force potentials in NiAl and TiAl,” Modelling and Simulation in Materials Science and Engineering. 1999. link Times cited: 45 Abstract: The applicability and characteristics of the central force m… read more Abstract: The applicability and characteristics of the central force many-body potentials of Finnis-Sinclair-type for NiAl and TiAl are investigated by studying the variation of the energy of these compounds with structural transformations that correspond to three distinct paths: tetragonal (B2L10), trigonal (B2L11) and hexagonal (B2B19). The energy was computed using both the central force potentials and the full potential linearized augmented plane waves (FLAPW) ab initio method. Comparison of these two calculations provides a means for the analysis of the efficacy of the potentials. The central force many-body potentials reproduce the results of ab initio calculations very satisfactorily for NiAl. This propounds that they are sufficient in atomistic modelling of lattice defects in this compound. For TiAl the central force potentials mimic the results of ab initio calculations qualitatively but are unable to differentiate adequately between structures with practically the same separations of the first and second neighbours. However, the present study provides a justification for the use of these potentials when investigating extended defects in which separations of the first and second nearest neighbours differ significantly from those in the L10 structure. read less A. Girshick, A. Bratkovsky, D. Pettifor, and V. Vítek, “Atomistic simulation of titanium. I. A bond-order potential,” Philosophical Magazine. 1998. link Times cited: 53 Abstract: The bond-order potential for hcp Ti has been constructed in … read more Abstract: The bond-order potential for hcp Ti has been constructed in the framework of a tight-binding description of the binding energy. In this scheme the energy consists of two parts: the bond part that comprises the d-electron contribution to bonding, and a pairwise part. Both parts contain fitting parameters but are treated independently. The bond part reproduces the most important characteristics of the d-band and Cauchy pressures, and the pairwise part complements the bond part so as to reproduce exactly the equilibrium lattice parameters and to a good approximation the elastic moduli. The potential is tested by examining the mechanical stability of the hcp lattice with respect to a variety of large deformations. It is applied to a study of dislocation behaviour in Ti in the accompanying paper, part II. read less A. Mikhin, N. Diego, and D. Bacon, “Defect clusters in Zn: A computer simulation study,” Philosophical Magazine. 1997. link Times cited: 4 Abstract: Calculations on point-defect clusters in Zn are performed us… read more Abstract: Calculations on point-defect clusters in Zn are performed using a static simulation technique in conjunction with a many-body potential. The results are compared with the available experimental observations, theoretical estimates and previous computations in hcp metals with c/a ratios below the ideal value. Both monovacancy and divacancy defects demonstrate an anisotropic migration with almost the same activation energy, corresponding to that observed in recovery stage IV. Small vacancy clusters are found to favour three-dimensional agglomerates. Stability conditions for vacancy clusters to nucleate or break up (recovery stage V) are discussed. Small clusters of interstitials are shown to grow on the basal plane in forms based on the octahedral point defect, although the most stable single interstitial is the non-basal crowdion. Large single- and double-layer interstitial clusters are assigned to embryos of the experimentally observed dislocation loops. read less D. Fuks, J. Pelleg, S. Rashkeev, and S. Dorfman, “The curvature of the self-diffusion Arrhenius plot through the mono-vacancy mechanism,” Zeitschrift für Physik B Condensed Matter. 1994. link Times cited: 4 D. Kulp, G. Ackland, M. Šob, V. Vítek, and T. Egami, “MANY-BODY POTENTIALS FOR CU-TI INTERMETALLIC ALLOYS AND A MOLECULAR-DYNAMICS STUDY OF VITRIFICATION AND AMORPHIZATION,” Modelling and Simulation in Materials Science and Engineering. 1993. link Times cited: 17 Abstract: The authors present central force many-body potentials for t… read more Abstract: The authors present central force many-body potentials for the Cu-Ti system which were constructed so as to reproduce a number of properties of the CuTi2 compound (tetragonal structure). The authors fitted the potentials not only to the available experimental data (equilibrium lattice parameters and enthalpy of mixing) but employed an ab initio method to determine additional data, in particular the bulk modulus. It is shown that these potentials ensure the stability of the CuTi2 crystal structure against alternate structures and changes in the c/a ratio and closely reproduce the melting temperature of CuTi2. The authors then employ these potentials in simulations of the glass transition and amorphization by irradiation and use the concept of atomic level stresses to interpret the results. read less S. Rawat and N. Mitra, “Molecular dynamics investigation of c-axis deformation of single crystal Ti under uniaxial stress conditions: Evolution of compression twinning and dislocations,” Computational Materials Science. 2018. link Times cited: 28 S. Rawat and N. Mitra, “Compression twinning and structural phase transformation of single crystal titanium under uniaxial compressive strain conditions: Comparison of inter-atomic potentials,” Computational Materials Science. 2017. link Times cited: 29 J. S. Gibson, S. G. Srinivasan, M. Baskes, R. E. Miller, and A. K. Wilson, “A multi-state modified embedded atom method potential for titanium,” Modelling and Simulation in Materials Science and Engineering. 2016. link Times cited: 3 Abstract: The continuing search for broadly applicable, predictive, an… read more Abstract: The continuing search for broadly applicable, predictive, and unique potential functions led to the invention of the multi-state modified embedded atom method (MS-MEAM) (Baskes et al 2007 Phys. Rev. B 75 094113). MS-MEAM replaced almost all of the prior arbitrary choices of the MEAM electron densities, embedding energy, pair potential, and angular screening functions by using first-principles computations of energy/volume relationships for multiple reference crystal structures and transformation paths connecting those reference structures. This strategy reasonably captured diverse interactions between atoms with variable coordinations in a face-centered-cubic (fcc)-stable copper system. However, a straightforward application of the original MS-MEAM framework to model technologically useful hexagonal-close-packed (hcp) metals proved elusive. This work describes the development of an hcp-stable/fcc-metastable MS-MEAM to model titanium by introducing a new angular function within the background electron density description. This critical insight enables the titanium MS-MEAM potential to reproduce first principles computations of reference structures and transformation paths extremely well. Importantly, it predicts lattice and elastic constants, defect energetics, and dynamics of non-ideal hcp and liquid titanium in good agreement with first principles computations and corresponding experiments, and often better than the three well-known literature models used as a benchmark. The titanium MS-MEAM has been made available in the Knowledgebase of Interatomic Models (https://openkim.org/) (Tadmor et al 2011 JOM 63 17). read less M. Benoit, N. Tarrat, and J. Morillo, “Density functional theory investigations of titanium γ-surfaces and stacking faults,” Modelling and Simulation in Materials Science and Engineering*. 2012. link Times cited: 40 Abstract: Bulk properties of hcp-Ti, relevant for the description of d… read more Abstract: Bulk properties of hcp-Ti, relevant for the description of dislocations, such as elastic constants, stacking faults and γ-surface, are computed using density functional theory (DFT) and two central force embedded atom interaction models (Zope and Mishin 2003 Phys. Rev. B 68 024102, Hammerschmidt et al 2005 Phys. Rev. B 71 205409). The results are compared with previously published calculations, except pair potential calculations, which are not appropriate for the description of the metallic bond. The comparison includes N-body central force (NB-CF) and N-body angular (NB-A) empirical potentials, tight-binding approximation to the electronic structure (TB), DFT pseudopotential (DFT-P) and all electron (DFT-A) calculations. None of the considered interaction models are fully satisfactory for the description of these properties. In particular, NB-CF, NB-A and TB interaction models are unable to describe the softening of the easy prismatic γ-surface leading to the appearance of a metastable stacking fault, as evidenced in all the DFT calculations. Most often, when the basal stacking fault excess energy is underevaluated, this leads to an inversion of the energetic stability between the I2 basal and the prismatic easy stacking faults. Even the DFT-pseudopotential calculations need to be improved regarding the description of the shear elastic constants. The implications of these results on the core structure and gliding properties of the screw dislocation are analyzed. The calculated dissociation lengths into Shockley partials in both the basal and prismatic planes for the different models compare well with the measured ones in the corresponding simulations of the dislocation core structure when available. Finally, the Peierls stress is also evaluated using the Peierls–Nabarro model and compared with the experimentally measured one. read less
Funding	Not available

Short KIM ID The unique KIM identifier code.	MO_748534961139_005
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.	EAM_Dynamo_Ackland_1992_Ti__MO_748534961139_005
DOI	10.25950/276be3c4 https://doi.org/10.25950/276be3c4 https://commons.datacite.org/doi.org/10.25950/276be3c4
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 EAM_Dynamo__MD_120291908751_005
Driver	EAM_Dynamo__MD_120291908751_005
KIM API Version	2.0
Potential Type	eam
Programming Language(s) The programming languages used in the code and the percentage of the code written in each one. "N/A" means "not applicable" and refers to model parameterizations which only include parameter tables and have no programming language.	N/A

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Grade	Name	Category	Brief Description	Full Results	Aux File(s)
P All elements claimed by model are supported in at least one of the tested configurations.	vc-species-supported-as-stated	mandatory	The model supports all species it claims to support; see full description.	Results	Files
P Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.	vc-periodicity-support	mandatory	Periodic boundary conditions are handled correctly; see full description.	Results	Files
P Model energy has permutation symmetry for all configurations the model was able to compute.	vc-permutation-symmetry	mandatory	Total energy and forces are unchanged when swapping atoms of the same species; see full description.	Results	Files
A The letter grade A was assigned because the normalized error in the computation was 4.77917e-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: 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: Ti

Tests

Disclaimer From Model Developer

Stacking fault energy in hcp is too low. Basal dislocations can be formed, and well as prismatic.

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	7698
Cohesive energy versus lattice constant curve for diamond Ti v004	view	9203
Cohesive energy versus lattice constant curve for fcc Ti v004	view	8086
Cohesive energy versus lattice constant curve for sc Ti v004	view	7778

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	4127
Elastic constants for fcc Ti at zero temperature v006	view	3871
Elastic constants for sc Ti at zero temperature v006	view	6110

ElasticConstantsHexagonal__TD_612503193866_004

Elastic constants for hexagonal crystals at zero temperature v004

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

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

Test	Test Results	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Elastic constants for hcp Ti at zero temperature v004		view	1655

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	87093
Equilibrium crystal structure and energy for Ti in AFLOW crystal prototype A_cI2_229_a v002	view	85621
Equilibrium crystal structure and energy for Ti in AFLOW crystal prototype A_hP2_194_c v002	view	79805
Equilibrium crystal structure and energy for Ti in AFLOW crystal prototype A_hP3_191_ad v002	view	47940

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	2495
Equilibrium zero-temperature lattice constant for diamond Ti v007	view	4223
Equilibrium zero-temperature lattice constant for fcc Ti v007	view	2719
Equilibrium zero-temperature lattice constant for sc Ti v007	view	2431

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 Ti v005		view	22349

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	253034

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	1192652

Errors

ElasticConstantsCubic__TD_011862047401_006

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

Files

CMakeLists.txt
LICENSE.CDDL
Ti.eam.fs
kimprovenance.edn
kimspec.edn

Download

EAM_Dynamo_Ackland_1992_Ti__MO_748534961139_005.txz	Tar+XZ	Linux and OS X archive
EAM_Dynamo_Ackland_1992_Ti__MO_748534961139_005.zip	Zip	Windows archive

Download Dependency

This Model requires a Model Driver. Archives for the Model Driver EAM_Dynamo__MD_120291908751_005 appear below.

EAM_Dynamo__MD_120291908751_005.txz	Tar+XZ	Linux and OS X archive
EAM_Dynamo__MD_120291908751_005.zip	Zip	Windows archive

Wiki

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EAM_Dynamo_Ackland_1992_Ti__MO_748534961139_005

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

Disclaimer From Model Developer

Errors

Files

Download

Download Dependency

Wiki