MEAM potential for Ti developed by Hennig et al. (2008) v002

Richard G. Hennig; Thomas Lenosky; Dallas R. Trinkle; Sven P. Rudin; John W. Wilkins

doi:10.25950/6bcb2fa8

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MEAM_LAMMPS_HennigLenoskyTrinkle_2008_Ti__MO_520569947398_002

Interatomic potential for Titanium (Ti).
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Title A single sentence description.	MEAM potential for Ti developed by Hennig et al. (2008) v002
Description A short description of the Model describing its key features including for example: type of model (pair potential, 3-body potential, EAM, etc.), modeled species (Ac, Ag, ..., Zr), intended purpose, origin, and so on.	A description of the martensitic transformations between the alpha, beta, and omega phases of titanium that includes nucleation and growth requires an accurate classical potential. Optimization of the parameters of a modified embedded atom potential to a database of density-functional calculations yields an accurate and transferable potential as verified by comparison to experimental and density-functional data for phonons, surface and stacking fault energies, and energy barriers for homogeneous martensitic transformations. Molecular-dynamics simulations map out the pressure-temperature phase diagram of titanium. For this potential, the martensitic phase transformation between a and 8 appears at ambient pressure and 1200 K, between alpha and omega at ambient conditions, between beta and omega at 1200 K and pressures above 8 GPa, and the triple point occurs at 8 GPa and 1200 K. Molecular-dynamics explorations of the kinetics of the martensitic alpha-omega transformation show a fast-moving interface with low interfacial energy of 30 meV/angstrom(2). The potential is applied to the study of defects and phase transformations of Ti.
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.	None
Content Origin	LAMMPS package 22-Sep-2017
Content Other Locations	https://openkim.org/id/Sim_LAMMPS_MEAM_HennigLenoskyTrinkle_2008_Ti__SM_318953488749_000

Contributor	Yaser Afshar
Maintainer	Yaser Afshar
Developer	Richard G. Hennig Thomas Lenosky Dallas R. Trinkle Sven P. Rudin John W. Wilkins
Published on KIM	2023
How to Cite	This Model originally published in [1] is archived in OpenKIM [2-5]. [1] Hennig RG, Lenosky TJ, Trinkle DR, Rudin SP, Wilkins JW. Classical potential describes martensitic phase transformations between the \upalpha, \upbeta, and \upomega titanium phases. Phys Rev B. 2008Aug;78(5):054121. doi:10.1103/PhysRevB.78.054121 — (Primary Source) A primary source is a reference directly related to the item documenting its development, as opposed to other sources that are provided as background information. [2] Hennig RG, Lenosky T, Trinkle DR, Rudin SP, Wilkins JW. MEAM potential for Ti developed by Hennig et al. (2008) v002. OpenKIM; 2023. doi:10.25950/6bcb2fa8 [3] Afshar Y, Hütter S, Rudd RE, Stukowski A, Tipton WW, Trinkle DR, et al. The modified embedded atom method (MEAM) potential v002. OpenKIM; 2023. doi:10.25950/ee5eba52 [4] Tadmor EB, Elliott RS, Sethna JP, Miller RE, Becker CA. The potential of atomistic simulations and the Knowledgebase of Interatomic Models. JOM. 2011;63(7):17. doi:10.1007/s11837-011-0102-6 [5] Elliott RS, Tadmor EB. Knowledgebase of Interatomic Models (KIM) Application Programming Interface (API). OpenKIM; 2011. doi:10.25950/ff8f563a Click here to download the above citation in BibTeX format.
Citations This panel presents information regarding the papers that have cited the interatomic potential (IP) whose page you are on. The OpenKIM machine learning based Deep Citation framework is used to determine whether the citing article actually used the IP in computations (denoted by "USED") or only provides it as a background citation (denoted by "NOT USED"). For more details on Deep Citation and how to work with this panel, click the documentation link at the top of the panel. The word cloud to the right is generated from the abstracts of IP principle source(s) (given below in "How to Cite") and the citing articles that were determined to have used the IP in order to provide users with a quick sense of the types of physical phenomena to which this IP is applied. The bar chart shows the number of articles that cited the IP per year. Each bar is divided into green (articles that USED the IP) and blue (articles that did NOT USE the IP). Users are encouraged to correct Deep Citation errors in determination by clicking the speech icon next to a citing article and providing updated information. This will be integrated into the next Deep Citation learning cycle, which occurs on a regular basis. OpenKIM acknowledges the support of the Allen Institute for AI through the Semantic Scholar project for providing citation information and full text of articles when available, which are used to train the Deep Citation ML algorithm.	This panel provides information on past usage of this interatomic potential (IP) powered by the OpenKIM Deep Citation framework. The word cloud indicates typical applications of the potential. The bar chart shows citations per year of this IP (bars are divided into articles that used the IP (green) and those that did not (blue)). The complete list of articles that cited this IP is provided below along with the Deep Citation determination on usage. See the Deep Citation documentation for more information. 146 Citations (46 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 . S. Rawat and N. Mitra, “101̄2 twinning in single-crystal titanium under shock loading,” Philosophical Magazine. 2021. link Times cited: 2 Abstract: ABSTRACT We employ molecular dynamics simulations to investi… read more Abstract: ABSTRACT We employ molecular dynamics simulations to investigate the evolution dynamics of twinning in single-crystal Ti under shock loading. The shock compression applied perpendicular to the c-axis leads to the activation of twins in single-crystal Ti. We find the twin variant activation for each case of the applied loading conditions follows Schmid criterion. However, the time for the activation of twin variants is not the same even with equal Schmid factor. The evolution and dominance of twin variants in each case of the applied loading conditions do not depend on the Schmid factor. High nucleation events and low overall twin volume fraction occur for the case where two conjugate pairs of twin variants activate while low nucleation events and high overall twin volume fraction occur for the case where only one conjugate pair of twin variants activate. Twin nucleation takes place throughout the simulation time for each case of the applied loading conditions. High twin growth occurs for the case where only one conjugate pair of twin variants activate in comparison to the case where two conjugate pairs of twin variants activate. This indicates that the number of activated twin variants affects the growth rate of the twins. read less A. H. Zahiri, J. Ombogo, T. Ma, P. Chakraborty, and L. Cao, “Transformation-induced plasticity in omega titanium,” Journal of Applied Physics. 2021. link Times cited: 6 Abstract: ω-titanium (Ti) is a high-pressure phase that is conventiona… read more Abstract: ω-titanium (Ti) is a high-pressure phase that is conventionally perceived to be brittle and nondeformable, although direct investigations of its deformation process remain scarce. In this work, we perform molecular dynamics simulations to study the deformation process of ω-Ti with initial defects and find that stress-induced ω → α martensitic transformation can cause extensive plasticity in ω-Ti under various loading directions. Moreover, for the first time, we demonstrate that four types of transformation twins— { 11 2 ¯ 1 }, { 11 2 ¯ 2 }, { 10 1 ¯ 2 }, and { 10 1 ¯ 1 } twins—can be formed through the ω → α martensitic phase transformation. This work advances the understanding of plastic deformation in ω-Ti and unveils the essential role of the metastable ω-phase in the formation of transformation twins. read less E. Fransson, M. Slabanja, P. Erhart, and G. Wahnström, “dynasor—A Tool for Extracting Dynamical Structure Factors and Current Correlation Functions from Molecular Dynamics Simulations,” Advanced Theory and Simulations. 2020. link Times cited: 11 Abstract: Perturbative treatments of the lattice dynamics are widely s… read more Abstract: Perturbative treatments of the lattice dynamics are widely successful for many crystalline materials; however, their applicability is limited for strongly anharmonic systems, metastable crystal structures and liquids. The full dynamics of these systems can, however, be accessed via molecular dynamics (MD) simulations using correlation functions, which includes dynamical structure factors providing a direct bridge to experiment. To simplify the analysis of correlation functions, here the dynasor package is presented as a flexible and efficient tool that enables the calculation of static and dynamical structure factors, current correlation functions as well as their partial counterparts from MD trajectories. The dynasor code can handle input from several major open source MD packages and thanks to its C/Python structure can be readily extended to support additional codes. The utility of dynasor is demonstrated via examples for both solid and liquid single and multi‐component systems. In particular, the possibility to extract the full temperature dependence of phonon frequencies and lifetimes is emphasized. read less Z. Brunson, A. Pilchak, S. Rao, E. Payton, and A. Stebner, “An Expanded Martensite Variant Selection Theory Accounting for Transformation Rotations and Applied Stress Fields: Predictions of Variant Clusters in Titanium,” JOM. 2020. link Times cited: 1 D. Giri, H. Elkadiri, K. Limmer, and C. Barrett, “An atomistic gateway into capturing twin nucleation in crystal plasticity,” Philosophical Magazine Letters. 2020. link Times cited: 6 Abstract: ABSTRACT Capturing twin nucleation in crystal plasticity is … read more Abstract: ABSTRACT Capturing twin nucleation in crystal plasticity is a long-standing problem due to its localisation and site sensitivity. Quantifying local energy to induce a stable twin is a unique challenge and profoundly informs the microstructural evolution. We performed nudged elastic band atomistic calculations identifying minimum energy path and activation energy for twin nucleation. This enables gauging the transformations from an initial state without twins to a final state with twins under various boundary conditions. The role of stress and atomic structure in twinning can be understood by the minimum energy path, energy barrier and relaxed energy. read less Y. Qi, X. Chen, and M. Feng, “Effect of void defect on c-axis deformation of single-crystal Ti under uniaxial stress conditions: Evolution of tension twinning and dislocations,” Journal of Materials Research. 2019. link Times cited: 2 Abstract: Deformation twins have a major role in the microstructure ev… read more Abstract: Deformation twins have a major role in the microstructure evolution of hexagonal close packed (HCP) metals. Voids are common defects in metals and have a significant impact on their properties. In this work, using molecular dynamics, a tension simulation of single-crystal titanium (Ti) with different void sizes under uniaxial stress conditions was performed. The results showed that the evolution and dominance of the $\left\{ {10\bar 12} \right\}$ { 10 1 ¯ 2 } twin system using the Henning potential was not consistent with the Schmid criterion when the single-crystal Ti contained void defects. From a microscopic perspective, the authors analyzed the relationship between the nucleation and growth of twins and the emission of dislocation loops. The authors found that the existence of voids not only contributes to the emission of dislocation loops but also hinders the movement of these loops. With the increase in void size, the peak dislocation density of ${{\bf{V}}_{\bf{2}}}:\left\{ {10\bar 12} \right\}\left\langle {\bar 1101} \right\rangle$ V 2 : { 10 1 ¯ 2 } 〈 1 ¯ 101 〉 partial dislocation loops decreased. This work is helpful to further investigate the nucleation and evolution of tension twins and to form an effective growth criterion for twins to study the twinning process of HCP metals during plastic deformation. read less 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 X. Liu, H. Zhang, and X. Cheng, “Interaction between Dislocation and Twinning Boundary under Incremental Loading in α -Titanium,” Chinese Physics Letters. 2018. link Times cited: 1 N. Walker, K.-M. Tam, B. R. Novak, and M. Jarrell, “Identifying structural changes with unsupervised machine learning methods,” Physical Review E. 2018. link Times cited: 8 Abstract: Unsupervised machine learning methods are used to identify s… read more Abstract: Unsupervised machine learning methods are used to identify structural changes using the melting point transition in classical molecular dynamics simulations as an example application of the approach. Dimensionality reduction and clustering methods are applied to instantaneous radial distributions of atomic configurations from classical molecular dynamics simulations of metallic systems over a large temperature range. Principal component analysis is used to dramatically reduce the dimensionality of the feature space across the samples using an orthogonal linear transformation that preserves the statistical variance of the data under the condition that the new feature space is linearly independent. From there, k-means clustering is used to partition the samples into solid and liquid phases through a criterion motivated by the geometry of the reduced feature space of the samples, allowing for an estimation of the melting point transition. This pattern criterion is conceptually similar to how humans interpret the data but with far greater throughput, as the shapes of the radial distributions are different for each phase and easily distinguishable by humans. The transition temperature estimates derived from this machine learning approach produce comparable results to other methods on similarly small system sizes. These results show that machine learning approaches can be applied to structural changes in physical systems. 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 M. Hooshmand, M. Mills, and M. Ghazisaeidi, “Atomistic modeling of dislocation interactions with twin boundaries in Ti,” Modelling and Simulation in Materials Science and Engineering. 2017. link Times cited: 27 Abstract: Dislocation/boundary interactions play a prominent role in m… read more Abstract: Dislocation/boundary interactions play a prominent role in mechanical properties and plastic deformation of materials. We study the interaction between prismatic screw 〈 a 〉 , prismatic edge 〈 c 〉 and pyramidal mixed 〈 c + a 〉 dislocations with ( 1 ¯ 011 ) and ( 1 ¯ 013 ) twin boundaries in titanium using atomistic simulations. Details of the dislocation reactions depend on the slip system, atomic structure of boundary and stress/strain states. All interactions lead to nucleation of twinning dislocations on both twin boundaries, confirming that the interaction with incoming dislocations is a twin growth mechanism. In addition, dissociation of 〈 c 〉 and 〈 c + a 〉 dislocations on the ( 1 ¯ 013 ) results in nucleation of a ( 1 ¯ 012 ) (tension twin) embryo in the second grain-a new twin nucleation mechanism for ( 1 ¯ 012 ) twins as a result of 〈 c 〉 and 〈 c + a 〉 slip. 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 H. Zong, X. Ding, T. Lookman, and J. Sun, “Twin boundary activated α → ω phase transformation in titanium under shock compression,” Acta Materialia. 2016. link Times cited: 29 H. Zong et al., “The kinetics of the ω to α phase transformation in Zr, Ti: Analysis of data from shock-recovered samples and atomistic simulations,” Acta Materialia. 2014. link Times cited: 41 Y.-T. Cheng, T.-R. Shan, T. Liang, R. Behera, S. Phillpot, and S. Sinnott, “A charge optimized many-body (comb) potential for titanium and titania,” Journal of Physics: Condensed Matter. 2014. link Times cited: 33 Abstract: This work proposes an empirical, variable charge potential f… read more Abstract: This work proposes an empirical, variable charge potential for Ti and TiO2 systems based on the charge-optimized many-body (COMB) potential framework. The parameters of the potential function are fit to the structural and mechanical properties of the Ti hcp phase, the TiO2 rutile phase, and the energetics of polymorphs of both Ti and TiO2. The relative stabilities of TiO2 rutile surfaces are predicted and compared to the results of density functional theory (DFT) and empirical potential calculations. The transferability of the developed potential is demonstrated by determining the adsorption energy of Cu clusters of various sizes on the rutile TiO2(1 1 0) surface using molecular dynamics simulations. The results indicate that the adsorption energy is dependent on the number of Cu–Cu bonds and Cu–O bonds formed at the Cu/TiO2 interface. The adsorption energies of Cu clusters on the reduced and oxidized TiO2(1 1 0) surfaces are also investigated, and the COMB potential predicts enhanced bonding between Cu clusters and the oxidized surface, which is consistent with both experimental observations and the results of DFT calculations for other transition metals (Au and Ag) on this oxidized surface. read less H. Zong, D. Xue, X. Ding, and T. Lookman, “Phase transformations in Titanium: Anisotropic deformation of ω phase,” Journal of Physics: Conference Series. 2014. link Times cited: 4 Abstract: We study the plastic deformation of the ω phase which is obt… read more Abstract: We study the plastic deformation of the ω phase which is obtained when Titanium undergoes a phase transformation under pressure. We perform molecular dynamics simulations under uniaxial loading and find that the ω phase not only shows brittle fracture upon loading in the [0001] direction, but also exhibits "superplastic" deformation features along the [101̄0] direction. The brittle fracture is analogous to that which occurs in metallic glass by means of shear banding whereas the ductility is mediated by the α (hcp) to ω (hexagonal) phase transformation. We further show that the elastic deformation of the m phase is anisotropic; it can be non-uniform upon [0001] uniaxial compression. Our results provide insight into the mechanical behaviour of the m phase and imply that the transformation mediated ductility can lead to improvement of the plasticity of co-containing Titanium alloys. read less M. Jafari, N. Zarifi, M. Nobakhti, A. Jahandoost, and M. Lame, “Pseudopotential calculation of the bulk modulus and phonon dispersion of the bcc and hcp structures of titanium,” Physica Scripta. 2011. link Times cited: 12 Abstract: The structural stability of Ti in the hexagonal-closed-packe… read more Abstract: The structural stability of Ti in the hexagonal-closed-packed and body-centered cubic structures was studied by means of the full potential linearized augmented plane wave method. The effect of pressure on the bulk modulus of the crystal structures was investigated. In this study, the plane wave ultrasoft pseudopotential method was used to calculate the elastic constants, bulk modulus and phonon frequency of Ti. Phonon calculations were performed by employing the density functional perturbation theory in real space, using the calculated lattice dynamical force constants. All calculations were based on the density functional theory with the generalized gradient approximation and local density approximation, which well describe the properties of the above-mentioned metal. read less A. Lipnitskii, D. A. Aksenov, and Y. Kolobov, “Ab initio calculation of characteristics of a hcpti–c system in α-titanium,” Russian Physics Journal. 2009. link Times cited: 1 I. Nelasov, A. Kartamyshev, A. Boev, A. Lipnitskii, Y. Kolobov, and T. Nguyen, “Molecular dynamics simulation of the behavior of titanium under high-speed deformation,” Modelling and Simulation in Materials Science and Engineering. 2021. link Times cited: 1 Abstract: We present molecular dynamics simulation to study the α–ω ph… read more Abstract: We present molecular dynamics simulation to study the α–ω phase transformation in titanium under different conditions simulating high-energy impacts. We employed the interatomic potential developed within the N-body method, which predicts the stability of the ω phase and the stacking fault energy in the α phase in excellent agreement with the experimental and theoretical data. The latter is crucial for the correct description of the deformation mechanisms. The dependence of the beginning and mechanism of the α–ω transition process on loading conditions are derived. In particular, at the uniaxial compression along the [0001] direction at 300 K, the ω phase is localized in deformation bands within the α phase, and the α–ω transition is observed at a pressure of more than 3 GPa. With this type of deformation, the residual inclusions of the α phase remain in the ω phase volume. A similar deformation at a temperature of 700 K does not lead to the formation of the ω phase. Meanwhile, at the hydrostatic compression, the α–ω transition is restrained and at a pressure of 20 GPa is not observed. In the case of anisotropic three-axis deformation along the α–ω transition pathways proposed by Trinkle et al at a constant pressure of 20 GPa, the transition mechanism includes the formation of dislocations, followed by the transformation of the regions between the dislocations into the ω phase. The simulation results demonstrate good agreement with the experimental data and confirm the applicability of the employed interatomic potential for simulating the deformation of titanium. read less S. Rawat and N. Mitra, “Evolution of tension twinning in single crystal Ti under compressive uniaxial strain conditions,” Computational Materials Science. 2018. link Times cited: 15 J. Raush, “Thermophysical and Thermochemical Property Measurement and Prediction of Liquid Metal Titanium Alloys with Applications in Additive Manufacturing.” 2016. link Times cited: 0 Abstract: ............................................................… read more Abstract: ........................................................................................................................................ xv Chapter 1 Motivation ...................................................................................................................... 1 1.1 Engineering Challenges.................................................................................................... 1 1.1.1 Additive Manufacturing ........................................................................................... 2 1.1.2 Powder Metallurgy.................................................................................................... 3 1.2 Materials Development Approach ................................................................................... 4 1.3 Focus of this Research...................................................................................................... 8 1.3.1 Objectives ............................................................................................................... 11 1.3.2 Project Timeline and Funding ................................................................................. 12 1.4 Outline of Dissertation ................................................................................................... 12 Chapter 2 Testing and Modeling Background .............................................................................. 14 2.1 Testing and Characterization of Liquid Metals .............................................................. 14 2.1.1 Traditional Thermophysical Property Measurement Techniques ........................... 14 2.1.2 Electrostatic Levitation ........................................................................................... 16 2.1.3 Additional Containerless Testing Techniques ........................................................ 31 2.2 Numerical Modeling ...................................................................................................... 31 2.2.1 CALPHAD .............................................................................................................. 32 2.2.2 Molecular Dynamics ............................................................................................... 33 Chapter 3 Test Method.................................................................................................................. 36 3. read less P. Wang et al., “Molecular dynamic simulations of the martensitic transformation for the dual-phase structure and dislocation activities in Ti80 alloys,” Mechanics of Materials. 2023. 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 T. Wen et al., “Modelling of dislocations, twins and crack-tips in HCP and BCC Ti,” International Journal of Plasticity. 2023. link Times cited: 4 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 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 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 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 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 L. Wang, L. Hu, J. Zhao, and B. Wei, “Ultrafast growth kinetics of titanium dendrites investigated by electrostatic levitation experiments and molecular dynamics simulations,” Chemical Physics Letters. 2020. link Times cited: 3 S. Rawat and N. Mitra, “Twinning, phase transformation and dislocation evolution in single crystal titanium under uniaxial strain conditions: A molecular dynamics study,” Computational Materials Science. 2020. link Times cited: 14 S. Kadkhodaei and A. Davariashtiyani, “Phonon-assisted diffusion in bcc phase of titanium and zirconium from first principles,” Physical Review Materials. 2019. link Times cited: 11 Abstract: Diffusion is the underlying mechanism for many complicated m… read more Abstract: Diffusion is the underlying mechanism for many complicated materials phenomena, and understanding it is basic to the discovery of novel materials with desired physical and mechanical properties. Certain groups of solid phases, such as the bcc phase of IIIB and IVB metals and their alloys, which are only stable when they reach high enough temperatures and experience anharmonic vibration entropic effects, exhibit ``anomalously fast diffusion.'' However, the underlying reason for the observed extraordinary fast diffusion is poorly understood and due to the existence of harmonic vibration instabilities in these phases the standard models fail to predict their diffusivity. Here, we indicate that the anharmonic phonon-phonon coupling effects can accurately describe the anomalously large macroscopic diffusion coefficients in the bcc phase of IVB metals and therefore yield understanding on the underlying mechanism for diffusion in these phases. We utilize temperature-dependent phonon analysis by combining ab initio molecular dynamics with lattice dynamics calculations to provide an approach to use the transition state theory beyond the harmonic approximation. We validate the diffusivity predictions for the bcc phase of titanium and zirconium with available experimental measurements, while we show that predictions based on harmonic transition state theory severely underestimate diffusivity in these phases. read less L. E. Atouani, E. E. koraychy, K. Sbiaai, M. Mazroui, and A. Hasnaoui, “Cluster adsorption and migration energetics on hcp Ti (0001) surfaces via atomistic simulations,” Thin Solid Films. 2019. link Times cited: 8 S. Kavousi, B. R. Novak, M. A. Zaeem, and D. Moldovan, “Combined molecular dynamics and phase field simulation investigations of crystal-melt interfacial properties and dendritic solidification of highly undercooled titanium,” Computational Materials Science. 2019. link Times cited: 28 L. Wang et al., “Orientation and grain-boundary dependence of shock-induced plasticity and transformation in nanocrystalline Ti,” Physical Review B. 2019. link Times cited: 12 R. Smith, “Atomistic simulation of martensitic transformations in zirconium nanoclusters,” Computational Condensed Matter. 2017. link Times cited: 5 A. Bolesta and V. Fomin, “Molecular dynamics simulation of shock-wave loading of copper and titanium.” 2017. link Times cited: 6 Abstract: At extreme pressures and temperatures common materials form … read more Abstract: At extreme pressures and temperatures common materials form new dense phases with compacted atomic arrangements. By classical molecular dynamics simulation we observe that FCC copper undergo phase transformation to BCC structure. The transition occurs under shock wave loading at the pressures above 80 GPa and corresponding temperatures above 2000 K. We calculate phase diagram, show that at these pressures and low temperature FCC phase of copper is still stable and discuss the thermodynamic reason for phase transformation at high temperature shock wave regime. Titanium forms new hexagonal phase at high pressure as well. We calculate the structure of shock wave in titanium and observe that shock front splits in three parts: elastic, plastic and phase transformation. The possibility of using a phase transition behind a shock wave with further unloading for designing nanocrystalline materials with a reduced grain size is also shown. read less 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 Y. Li, J. Li, and B.-xin Liu, “Homogeneous shear-driven reversible α-to-α″ phase transformation and superelasticity of titanium investigated by molecular dynamics simulations,” Acta Materialia. 2015. link Times cited: 8 D. Poletaev et al., “Ab initio-based prediction and TEM study of silicide precipitation in titanium,” Computational Materials Science. 2014. link Times cited: 17 H. Zhao and X.-S. Song, “Elastic and phonon instabilities in simple-cubic heavier alkali metals K, Rb and Cs under hydrostatic pressure studied using ab initio calculations,” Modern Physics Letters B. 2014. link Times cited: 1 Abstract: Using first-principles calculation based on density function… read more Abstract: Using first-principles calculation based on density functional theory, the elastic stability and dynamic stability of heavier alkali metals K, Rb and Cs in sc structure are investigated. Results reveal that the C44 instabilities are responsible for the mechanical instabilities for these heavier alkali metals and the spin-polarization phases are more stable than non-spin-polarization phases. Other than K-sc which presents BZ edge instability at the M-point at ambient condition, the K-sc and Rb-sc are dynamically stable for the range of the pressure in our calculation. But for Cs-sc, it becomes unstable starting from 7 GPa. Especially we demonstrate that the most stable phases of K at low temperatures and pressures around 20 GPa are ferromagnetic K in sc structure. read less K. Edalati et al., “High-pressure torsion of titanium at cryogenic and room temperatures: Grain size effect on allotropic phase transformations,” Acta Materialia. 2014. link Times cited: 68 S. Rao, A. Venkateswaran, and M. Letherwood, “Molecular statics and molecular dynamics simulations of the critical stress for motion of a /3 〈112¯0〉 screw dislocations in α-Ti at low temperatures using a modified embedded atom method potential,” Acta Materialia. 2013. link Times cited: 18 D. Aksyonov, A. Lipnitskii, and Y. Kolobov, “Ab initio study of Ti–C precipitates in hcp titanium: Formation energies, elastic moduli and theoretical diffraction patterns,” Computational Materials Science. 2012. link Times cited: 16 Z. Liu et al., “Tailoring microstructure and mechanical properties by laser powder bed fusion of Ti powder recycled and treated via discharge plasma modification,” Scripta Materialia. 2023. link Times cited: 0 M. Luo, L. Liang, L. Lang, S. Xiao, W. Hu, and H. Deng, “Molecular dynamics simulations of the characteristics of Mo/Ti interfaces,” Computational Materials Science. 2018. link Times cited: 21 A. D. Masto, J. Baccou, G. Tréglia, F. Ribeiro, and C. Varvenne, “Insights on the capabilities and improvement ability of classical many-body potentials: Application to α-zirconium,” Computational Materials Science. 2024. link Times cited: 0 H. Sun and A. Samanta, “Exploring structural transitions at grain boundaries in Nb using a generalized embedded atom interatomic potential,” Computational Materials Science. 2023. link Times cited: 0 J. Lee et al., “Stress-induced structural changes in superconducting Nb thin films,” Physical Review Materials. 2023. link Times cited: 1 Abstract: ,… read more Abstract: , read less T. Li and H. Zong, “Phase transformation mediated anomalous plasticity of titanium under severe loading conditions,” International Journal of Mechanical Sciences. 2022. link Times cited: 2 S. Sharma et al., “Machine Learning Methods for Multiscale Physics and Urban Engineering Problems,” Entropy. 2022. link Times cited: 0 Abstract: We present an overview of four challenging research areas in… read more Abstract: We present an overview of four challenging research areas in multiscale physics and engineering as well as four data science topics that may be developed for addressing these challenges. We focus on multiscale spatiotemporal problems in light of the importance of understanding the accompanying scientific processes and engineering ideas, where “multiscale” refers to concurrent, non-trivial and coupled models over scales separated by orders of magnitude in either space, time, energy, momenta, or any other relevant parameter. Specifically, we consider problems where the data may be obtained at various resolutions; analyzing such data and constructing coupled models led to open research questions in various applications of data science. Numeric studies are reported for one of the data science techniques discussed here for illustration, namely, on approximate Bayesian computations. read less M. Kriegel, M. H. Wetzel, O. Fabrichnaya, and D. Rafaja, “Binary Ti–Fe system. Part II: Modelling of pressure-dependent phase stabilities,” Calphad. 2022. link Times cited: 4 T. Wen, L. Zhang, H. Wang, W. E, and D. Srolovitz, “Deep Potentials for Materials Science,” Materials Futures. 2022. link Times cited: 54 Abstract: To fill the gap between accurate (and expensive) ab initio… read more Abstract: To fill the gap between accurate (and expensive) ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials, a new class of descriptions of atomic interactions has emerged and been widely applied; i.e., machine learning potentials (MLPs). One recently developed type of MLP is the Deep Potential (DP) method. In this review, we provide an introduction to DP methods in computational materials science. The theory underlying the DP method is presented along with a step-by-step introduction to their development and use. We also review materials applications of DPs in a wide range of materials systems. The DP Library provides a platform for the development of DPs and a database of extant DPs. We discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials. read less S. Li, Q. Yuan, J. Zhang, Y. Li, and D. He, “Towards Pure: The Single-phase Bulk Omega Titanium and Modulation on its Elastic Properties under Biaxial Strains,” Journal of Alloys and Compounds. 2022. link Times cited: 2 J. A. Vita and D. Trinkle, “Exploring the necessary complexity of interatomic potentials,” Computational Materials Science. 2021. link Times cited: 8 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 M. Kriegel, M. H. Wetzel, A. Treichel, O. Fabrichnaya, and D. Rafaja, “Binary Ti–Fe system. Part I: Experimental investigation at high pressure,” Calphad-computer Coupling of Phase Diagrams and Thermochemistry. 2021. link Times cited: 5 A. H. Zahiri, J. Ombogo, and L. Cao, “Formation of 112¯2 contraction twins in titanium through reversible martensitic phase transformation,” Scripta Materialia. 2021. link Times cited: 7 S. Macleod et al., “The phase diagram of Ti-6Al-4V at high-pressures and high-temperatures,” Journal of Physics: Condensed Matter. 2021. link Times cited: 8 Abstract: We report results from a series of diamond-anvil-cell synchr… read more Abstract: We report results from a series of diamond-anvil-cell synchrotron x-ray diffraction and large-volume-press experiments, and calculations, to investigate the phase diagram of commercial polycrystalline high-strength Ti-6Al-4V alloy in pressure–temperature space. Up to ∼30 GPa and 886 K, Ti-6Al-4V is found to be stable in the hexagonal-close-packed, or α phase. The effect of temperature on the volume expansion and compressibility of α–Ti-6Al-4V is modest. The martensitic α → ω (hexagonal) transition occurs at ∼30 GPa, with both phases coexisting until at ∼38–40 GPa the transition to the ω phase is completed. Between 300 K and 844 K the α → ω transition appears to be independent of temperature. ω–Ti-6Al-4V is stable to ∼91 GPa and 844 K, the highest combined pressure and temperature reached in these experiments. Pressure–volume–temperature equations-of-state for the α and ω phases of Ti-6Al-4V are generated and found to be similar to pure Ti. A pronounced hysteresis is observed in the ω–Ti-6Al-4V on decompression, with the hexagonal structure reverting back to the α phase at pressures below ∼9 GPa at room temperature, and at a higher pressure at elevated temperatures. Based on our data, we estimate the Ti-6Al-4V α–β–ω triple point to occur at ∼900 K and 30 GPa, in good agreement with our calculations. read less S. Sinha et al., “Initial texture dependence of nanocrystalline omega phase formation during high pressure torsion of commercially pure titanium,” Materials Science and Engineering A-structural Materials Properties Microstructure and Processing. 2020. link Times cited: 7 H. Zhang, X. Ou, S. Ni, and M. Song, “Toughening alpha-Ti by dislocation-induced phase transformation at crack tips,” Mechanics of Materials. 2020. link Times cited: 7 G. Smirnov, “Non-Arrhenius diffusion in bcc titanium: Vacancy-interstitialcy model,” Physical Review B. 2020. link Times cited: 6 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 Y. Chong et al., “Mechanistic basis of oxygen sensitivity in titanium,” Science Advances. 2020. link Times cited: 56 Abstract: A systematic study of Ti-O alloys reveals the mechanism behi… read more Abstract: A systematic study of Ti-O alloys reveals the mechanism behind acute oxygen sensitivity in titanium. One of the most potent examples of interstitial solute strengthening in metal alloys is the extreme sensitivity of titanium to small amounts of oxygen. Unfortunately, these small amounts of oxygen also lead to a markedly decreased ductility, which in turn drives the increased cost to purify titanium to avoid this oxygen poisoning effect. Here, we report a systematic study on the oxygen sensitivity of titanium that provides a clear mechanistic view of how oxygen impurities affect the mechanical properties of titanium. The increased slip planarity of Ti-O alloys is caused by an interstitial shuffling mechanism, which is sensitive to temperature, strain rate, and oxygen content and leads to the subsequent alteration of deformation twinning behavior. The insights from our experimental and computational work provide a rationale for the design of titanium alloys with increased tolerance to variations in interstitial content, with notable implications for more widespread use of titanium alloys. read less 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 J. Tseng et al., “Deformations of Ti-6Al-4V additive-manufacturing-induced isotropic and anisotropic columnar structures: Insitu measurements and underlying mechanisms,” Additive Manufacturing. 2020. link Times cited: 23 M. Hooshmand and M. Ghazisaeidi, “Solute/twin boundary interaction as a new atomic-scale mechanism for dynamic strain aging,” Acta Materialia. 2020. link Times cited: 15 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 E. Fransson and P. Erhart, “Defects from phonons: Atomic transport by concerted motion in simple crystalline metals,” Acta Materialia. 2019. link Times cited: 11 S. Kavousi, B. R. Novak, M. Baskes, M. A. Zaeem, and D. Moldovan, “Modified embedded-atom method potential for high-temperature crystal-melt properties of Ti–Ni alloys and its application to phase field simulation of solidification,” Modelling and Simulation in Materials Science and Engineering. 2019. link Times cited: 21 Abstract: We developed new interatomic potentials, based on the second… read more Abstract: We developed new interatomic potentials, based on the second nearest-neighbor modified embedded-atom method (2NN-MEAM) formalism, for Ti, Ni, and the binary Ti–Ni system. These potentials were fit to melting points, latent heats, the binary phase diagrams for the Ti rich and Ni rich regions, and the liquid phase enthalpy of mixing for binary alloys, therefore they are particularly suited for calculations of crystal-melt (CM) interface thermodynamic and transport properties. The accuracy of the potentials for pure Ti and pure Ni were tested against both 0 K and high temperature properties by comparing various properties obtained from experiments or density functional theory calculations including structural properties, elastic constants, point-defect properties, surface energies, temperatures and enthalpies of phase transformations, and diffusivity and viscosity in the liquid phase. The fitted binary potential for Ti–Ni was also tested against various non-fitted properties at 0 K and high temperatures including lattice parameters, formation energies of different intermetallic compounds, and the temperature dependence of liquid density at various concentrations. The CM interfacial free energies obtained from simulations, based on the newly developed Ti–Ni potential, show that the bcc alloys tend to have smaller anisotropy compared with fcc alloys which is consistent with the finding from the previous studies comparing single component bcc and fcc materials. Moreover, the interfacial free energy and its anisotropy for Ti-2 atom% Ni were also used to parameterize a 2D phase field (PF) model utilized in solidification simulations. The PF simulation predictions of microstructure development during solidification are in good agreement with a geometric model for dendrite primary arm spacing. read less P. Chen, F. Wang, and B. Li, “Transitory phase transformations during 101¯2 twinning in titanium,” Acta Materialia. 2019. link Times cited: 41 C. Yang and L. Qi, “Modified embedded-atom method potential of niobium for studies on mechanical properties,” Computational Materials Science. 2019. link Times cited: 17 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 O. Bachurina et al., “Two-dimensional discrete breathers in hcp titanium,” IOP Conference Series: Materials Science and Engineering. 2018. link Times cited: 2 Abstract: Recently delocalized nonlinear vibrational modes (DNVMs) hav… read more Abstract: Recently delocalized nonlinear vibrational modes (DNVMs) have been derived for a two-dimensional (2D) triangular lattice and their frequencies as the functions of amplitude have been calculated for a 2D Morse crystal. A 3D hcp lattice is formed by certain stacking of 2D triangular lattices. In the present work, we attempt to excite eight DNVMs with in-plane atomic displacements in a single plane of hcp titanium, modelled using many-body interatomic potentials. It is found that three of eight DNVMs produce long-lived 2D discrete breathers (DBs) in a titanium crystal. A 2D DB is delocalized in two spatial dimensions and localized in the third one, so that atoms of only one atomic plane have large vibrational amplitudes. The fFrequencies of the newly found DBs lie above the small-amplitude phonon spectrum of titanium and grow with increasing amplitude. Thus, we report on three novel 2D DBs in hcp metal. Our results open the route to finding new types of DBs in pure metals. read less D. Xu, H. Wang, J. Zhang, C. Bai, and R. Yang, “Titanium Alloys: From Properties Prediction to Performance Optimization,” Handbook of Materials Modeling. 2018. link Times cited: 7 M. Poschmann, J. Lin, H. Geerlings, I. Winter, and D. Chrzan, “Strain-induced variant selection in heterogeneous nucleation of α -Ti at screw dislocations in β -Ti,” Physical Review Materials. 2018. link Times cited: 4 Abstract: Heterogeneous nucleation of the α to β phase transition at 〈… read more Abstract: Heterogeneous nucleation of the α to β phase transition at 〈1 1 1〉β-type screw dislocations in pure titanium is examined through a combination of elasticity theory and molecular dynamics simulation using a modified embedded atom method potential. These screw dislocations act as heterogeneous nucleation sites and increase the α phase growth rate, but also restrict the orientation of the α nuclei to certain directions along which the strain field of the dislocation aligns with the strain required to complete the Burgers transformation path. Simulations and elasticity theory predict the same three α phase variants along the same preferential directions for α nucleus growth in the early stages of transformation. Previous elasticity theory calculations indicate that this growth does not result in the elastically preferred habit plane for the α nucleus. Molecular dynamics simulations on many-layer supercells presented here show that large α plates will change their growth direction towards the predicted habit plane, but this rotation is resisted by the line tension of the dislocation until the α precipitate detaches from the dislocation. read less P. Nandwana, N. Gupta, S. G. Srinivasan, and R. Banerjee, “A first principles study of commonly observed planar defects in Ti/TiB system,” Computational Materials Science. 2018. link Times cited: 17 S. Lu, W. Xiao, S.-hui Huang, J. Wang, and W. Ligen, “Improving the mechanical processing of titanium by hydrogen doping: A first-principles study,” International Journal of Hydrogen Energy. 2018. link Times cited: 11 W. Wang et al., “Insight into solid-solution strengthened bulk and stacking faults properties in Ti alloys: a comprehensive first-principles study,” Journal of Materials Science. 2018. link Times cited: 14 J. X. Yang, H. Zhao, H. Gong, M. Song, and Q. Ren, “Proposed mechanism of HCP → FCC phase transition in titianium through first principles calculation and experiments,” Scientific Reports. 2018. link Times cited: 71 A. Kilmametov, Y. Ivanisenko, B. Straumal, A. Gornakova, A. Mazilkin, and H. Hahn, “The α → ω Transformation in Titanium-Cobalt Alloys under High-Pressure Torsion.” 2017. link Times cited: 79 Abstract: The pressure influence on the α → ω transformation in Ti–Co … read more Abstract: The pressure influence on the α → ω transformation in Ti–Co alloys has been studied during high pressure torsion (HPT). The α → ω allotropic transformation takes place at high pressures in titanium, zirconium and hafnium as well as in their alloys. The transition pressure, the ability of high pressure ω-phase to retain after pressure release, and the pressure interval where α and ω phases coexist depend on the conditions of high-pressure treatment. During HPT in Bridgeman anvils, the high pressure is combined with shear strain. The presence of shear strain as well as Co addition to Ti decreases the onset of the α → ω transition from 10.5 GPa (under quasi-hydrostatic conditions) to about 3.5 GPa. The portion of ω-phase after HPT at 7 GPa increases in the following sequence: pure Ti → Ti–2 wt % Co → Ti–4 wt % Co → Ti–4 wt % Fe. read less B. G. D. Rio, O. Rodriguez, L. González, and D. González, “First principles determination of static, dynamic and electronic properties of liquid Ti near melting,” Computational Materials Science. 2017. link Times cited: 13 W. Mei and J. Sun, “Energy Landscape of Displace Phase Transition of β to ω in Ti-V alloys,” MRS Advances. 2017. link Times cited: 2 Abstract: The ground state properties of pure Ti with α, β and ω struc… read more Abstract: The ground state properties of pure Ti with α, β and ω structures and of the binary Ti-xV(x=5–30) at.% alloys with β and ω structures were calculated by first-principles method based on density functional theory, and subsequently the energy landscape of the displacive phase transition of β to ω were determined. The calculated results show that the energy barrier appears for the displacive phase transition of β to ω in Ti-(15–30) at.% V alloys at 300 K, but does not at 0 K. The energy barriers increase monotonously with increase of the temperature and the V content. These results can explain the formation of athermal ω phase and shear-assisted β to ω transition observed in as-quenched Ti-V base alloys. read less M. Wood, M. Cherukara, E. Antillon, and A. Strachan, “Molecular Dynamics Simulations of Shock Loading of Materials: A Review and Tutorial.” 2017. link Times cited: 14 D. Smirnova and S. Starikov, “An interatomic potential for simulation of Zr-Nb system,” Computational Materials Science. 2017. link Times cited: 37 B. Yin, Z. Wu, and W. Curtin, “Comprehensive first-principles study of stable stacking faults in hcp metals,” Acta Materialia. 2017. link Times cited: 138 P. Olsson, M. Mrovec, and M. Kroon, “First principles characterisation of brittle transgranular fracture of titanium hydrides,” Acta Materialia. 2016. link Times cited: 25 Z. Wu and W. Curtin, “Mechanism and energetics of 〈c + a〉 dislocation cross-slip in hcp metals,” Proceedings of the National Academy of Sciences. 2016. link Times cited: 94 Abstract: Significance For all hexagonal close-packed (hcp) metals, th… read more Abstract: Significance For all hexagonal close-packed (hcp) metals, the ability to plastically deform in the crystallographic c axis is crucial for achieving high ductility and high fracture toughness. 〈c+a〉 dislocation slip is the only sustainable mechanism to accommodate c-axis strain, but is difficult across the family of hcp metals. We reveal the mechanism, energy barrier, and unusual stress dependence of 〈c+a〉 dislocation cross-slip in Mg, using atomistic simulations. Our results provide mechanistic insights into 〈c+a〉 cross-slip behavior, rationalize observed changes in pyramidal I/II slip stability, enable predictions of slip trends across the family of hcp metals, and suggest that applied stresses and/or precise solid solution alloying can optimize cross-slip and enhance c-axis strain capacity, which can ultimately guide design of improved hcp alloys. Hexagonal close-packed (hcp) metals such as Mg, Ti, and Zr are lightweight and/or durable metals with critical structural applications in the automotive (Mg), aerospace (Ti), and nuclear (Zr) industries. The hcp structure, however, brings significant complications in the mechanisms of plastic deformation, strengthening, and ductility, and these complications pose significant challenges in advancing the science and engineering of these metals. In hcp metals, generalized plasticity requires the activation of slip on pyramidal planes, but the structure, motion, and cross-slip of the associated 〈c+a〉 dislocations are not well established even though they determine ductility and influence strengthening. Here, atomistic simulations in Mg reveal the unusual mechanism of 〈c+a〉 dislocation cross-slip between pyramidal I and II planes, which occurs by cross-slip of the individual partial dislocations. The energy barrier is controlled by a fundamental step/jog energy and the near-core energy difference between pyramidal 〈c+a〉 dislocations. The near-core energy difference can be changed by nonglide stresses, leading to tension–compression asymmetry and even a switch in absolute stability from one glide plane to the other, both features observed experimentally in Mg, Ti, and their alloys. The unique cross-slip mechanism is governed by common features of the generalized stacking fault energy surfaces of hcp pyramidal planes and is thus expected to be generic to all hcp metals. An analytical model is developed to predict the cross-slip barrier as a function of the near-core energy difference and applied stresses and quantifies the controlling features of cross-slip and pyramidal I/II stability across the family of hcp metals. read less L.-F. Huang et al., “From electronic structure to phase diagrams: A bottom-up approach to understand the stability of titanium–transition metal alloys,” Acta Materialia. 2016. link Times cited: 61 M. Murzinova, S. Zherebtsov, and G. Salishchev, “Dependence of the specific energy of the β/α interface in the VT6 titanium alloy on the heating temperature in the interval 600–975°C,” Journal of Experimental and Theoretical Physics. 2016. link Times cited: 8 A. Ready, A. Sutton, P. Haynes, and D. Rugg, “Point, Linear and Planar Defects in Titanium.” 2016. link Times cited: 2 D. Kryzhevich, “Structural transformation features in titanium crystallite under mechanical loading.” 2015. link Times cited: 0 Abstract: The features of defect structure generation and development … read more Abstract: The features of defect structure generation and development in titanium crystallites were studied on the basis of molecular dynamics method. Interatomic interaction was described using many-body potentials calculated in the approximation of the embedded atom method. It is shown that local structural changes begin to occur in the crystallite at the achievement of a threshold strain value, which is accompanied by a dramatic decrease of potential energy. The features of the formation of local structural changes, which are precursors of classical stacking faults, were studied. 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 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 I. Abrikosov et al., “Theoretical Modeling of Thermodynamic and Mechanical Properties of the Pure Components of Ti and Zr Based Alloys Using the Exact Muffin-Tin Orbitals Method,” Russian Physics Journal. 2014. link Times cited: 9 P. Kwaśniak, M. Muzyk, H. Garbacz, and K. Kurzydłowski, “Influence of oxygen content on the mechanical properties of hexagonal Ti—First principles calculations,” Materials Science and Engineering A-structural Materials Properties Microstructure and Processing. 2014. link Times cited: 46 I. Abrikosov, A. Nikonov, A. Ponomareva, A. Dmitriev, and S. Barannikova, “The Application of Method of Exact MT-orbitals for Modelling of Thermodynamic and Mechanical Properties in Pure Components of Ti- and Zr-Based Alloys.” 2013. link Times cited: 0 W. Tipton and R. Hennig, “A grand canonical genetic algorithm for the prediction of multi-component phase diagrams and testing of empirical potentials,” Journal of Physics: Condensed Matter. 2013. link Times cited: 64 Abstract: We present an evolutionary algorithm which predicts stable a… read more Abstract: We present an evolutionary algorithm which predicts stable atomic structures and phase diagrams by searching the energy landscape of empirical and ab initio Hamiltonians. Composition and geometrical degrees of freedom may be varied simultaneously. We show that this method utilizes information from favorable local structure at one composition to predict that at others, achieving far greater efficiency of phase diagram prediction than a method which relies on sampling compositions individually. We detail this and a number of other efficiency-improving techniques implemented in the genetic algorithm for structure prediction code that is now publicly available. We test the efficiency of the software by searching the ternary Zr–Cu–Al system using an empirical embedded-atom model potential. In addition to testing the algorithm, we also evaluate the accuracy of the potential itself. We find that the potential stabilizes several correct ternary phases, while a few of the predicted ground states are unphysical. Our results suggest that genetic algorithm searches can be used to improve the methodology of empirical potential design. read less Y. Ponosov, S. V. Streltsov, and K. Syassen, “Optical phonon self-energies in titanium phases: effects of electron–phonon interaction,” High Pressure Research. 2012. link Times cited: 3 Abstract: Temperature-dependent Raman investigations of titanium in th… read more Abstract: Temperature-dependent Raman investigations of titanium in the α and pressure-quenched ω-phase have been carried out. The results obtained suggest the possible coexistence of both phases at ambient pressure and low temperatures. Comparison of the low-temperature E2g phonon self-energies in both phases with simulations based on the calculated electronic structures for α- and ω-Ti implies significant contributions from non-adiabatic electron–phonon interactions. read less D. E. Smirnova, S. Starikov, S. Starikov, V. Stegailov, and V. Stegailov, “Interatomic potential for uranium in a wide range of pressures and temperatures,” Journal of Physics: Condensed Matter. 2012. link Times cited: 3 Abstract: Using the force-matching method we develop an interatomic po… read more Abstract: Using the force-matching method we develop an interatomic potential that allows us to study the structure and properties of α-U, γ-U and liquid uranium. The potential is fitted to the forces, energies and stresses obtained from ab initio calculations. The model gives a good comparison with the experimental and ab initio data for the lattice constants of α-U and γ-U, the elastic constants, the room-temperature isotherm, the normal density isochore, the bond-angle distribution functions and the vacancy formation energies. The calculated melting line of uranium at pressures up to 80 GPa and the temperature of the α–γ transition at 3 GPa agree well with the experimental phase diagram of uranium. read less D. Connétable, J. Huez, E. Andrieu, and C. Mijoule, “First-principles study of diffusion and interactions of vacancies and hydrogen in hcp-titanium,” Journal of Physics: Condensed Matter. 2011. link Times cited: 65 Abstract: We present a study of the stability of n-vacancies (V n) and… read more Abstract: We present a study of the stability of n-vacancies (V n) and hydrogens in the hexagonal close-packed titanium system computed by means of first-principles calculations. In this work, performed by using the generalized gradient approximation of density functional theory, we focused on the formation energies and the processes of migration of these defects. In the first part, the calculated formation energy of the monovacancy presents a disagreement with experimental data, as already mentioned in the literature. The activation energy is underestimated by almost 20%. The stability of compact divacancies was then studied. We show that a divacancy is more stable than a monovacancy if their migration energies are of the same order of magnitude. We also predict that the migration process in the basal plane of the divacancy is controlled by an intermediate state corresponding to a body-centered triangle (BO site). The case of the trivacancies is finally considered from an energetic point of view. In the second part, the insertion of hydrogen and the processes of its migration are discussed. We obtain a satisfactory agreement with experimental measurements. The chemical nature of the interactions between hydrogen and titanium are discussed, and we show that the H-atom presents an anionic behavior in the metal. The trapping energy of hydrogen in a monovacancy as a function of the number of hydrogen atoms is finally presented. read less C. Liang and H. Gong, “Structural stability, mechanical property and phase transition of the Ti–H system,” International Journal of Hydrogen Energy. 2010. link Times cited: 17 M. Fellinger, H. Park, and J. Wilkins, “Force-matched embedded-atom method potential for niobium,” Physical Review B. 2010. link Times cited: 115 Abstract: Large-scale simulations of plastic deformation and phase tra… read more Abstract: Large-scale simulations of plastic deformation and phase transformations in alloys require reliable classical interatomic potentials. We construct an embedded-atom method potential for niobium as the first step in alloy potential development. Optimization of the potential parameters to a well-converged set of density-functional theory (DFT) forces, energies, and stresses produces a reliable and transferable potential for molecular dynamics simulations. The potential accurately describes properties related to the fitting data, and also produces excellent results for quantities outside the fitting range. Structural and elastic properties, defect energetics, and thermal behavior compare well with DFT results and experimental data, e.g., DFT surface energies are reproduced with less than 4% error, generalized stacking-fault energies differ from DFT values by less than 15%, and the melting temperature is within 2% of the experimental value. read less Z. Mei, S. Shang, Y. Wang, and Z.-kui Liu, “Density-functional study of the thermodynamic properties and the pressure–temperature phase diagram of Ti,” Physical Review B. 2009. link Times cited: 81 D. Dickel, D. K. Francis, and C. Barrett, “Neural network aided development of a semi-empirical interatomic potential for titanium,” Computational Materials Science. 2020. link Times cited: 18 Y. Hida, E. Chaieb, A. Derkaoui, A. Tahani, and L. Elfarh, “Pure Titanium Corrosion inhibition by heat treatment in 3M HCl solution: An Electrochemical Impedance Spectroscopy (E.I.S) study,” Materials Today: Proceedings. 2019. link Times cited: 4 V. Zhakhovsky et al., “Shock-induced melting and crystallization in titanium irradiated by ultrashort laser pulse,” Physics of Fluids. 2023. link Times cited: 4 Abstract: Modification of titanium microstructure after propagation of… read more Abstract: Modification of titanium microstructure after propagation of a melting shock wave (SW) generated by a femtosecond laser pulse is investigated experimentally and analyzed using hydrodynamic and atomistic simulations. Scanning and transmission electron microscopy with analysis of microdiffraction is used to determine the microstructure of modified subsurface layers of titanium. We found that two layers are modified beneath the surface. A top surface polycrystalline layer of nanoscale grains is formed from shock-molten material via rapid crystallization. In a deeper subsurface layer, where the shock-induced melting changes into plastic deformation due to attenuation of SW, the grain structure of solid is considerably affected, which results in a grain size distribution differing from that in the intact titanium. Molecular dynamics simulation of single-crystal titanium reveals that the SW front continues to melt even after its temperature drops below the melting curve Tm(P). The enormous shear stress of ∼12 GPa generated in a narrow SW front leads to free slip of atomic planes, collapse of the crystal lattice, and formation of a supercooled metastable melt. Such melt crystallizes in an unloading tail of SW. The mechanical melting ceases after drop in the shear stress giving rise to the shock-induced plastic deformation. The last process triggers a long-term rearrangement of atomic structures in solid. The overall depth of modified layers is limited by SW attenuation to the Hugoniot elastic limit and can reach several micrometers. The obtained results reveal the basic physical mechanisms of surface hardening of metals by ultrashort laser pulses. read less T. Wen et al., “Atomistic Modelling of All Dislocations and Twins in HCP and BCC Ti,” SSRN Electronic Journal. 2022. link Times cited: 0 Abstract: Ti exhibits complex plastic deformation controlled by active… read more Abstract: Ti exhibits complex plastic deformation controlled by active dislocation and twinning systems. Understandings on dislocation cores and twin interfaces are currently not complete or quantitative, despite extensive experimental and simulation studies. Here, we determine all the core and twin interface properties in both HCP and BCC Ti using a Deep Potential (DP) and DFT. We determine the core structures, critical resolved shear stresses and mobilities of,,dislocations in HCP and<111>/2 dislocations in BCC Ti. Theslip consists of slow core migration on pyramidal-I planes and fast migration on prism-planes, and is kinetically limited by cross-slips among them. This behaviour is consistent with"locking-unlocking"phenomena in TEM and is likely an intrinsic property. Large-scale DFT calculations provide a peek at the screwcore and glide behaviour, which is further quantified using DP-Ti. The screwis unstable on pyramidal-II planes. The mixedis nearly sessile on pyramidal-I planes, consistent with observations of long dislocations in this orientation. The edge and mixedare unstable against a pyramidal-to-basal (PB) transition and become sessile at high temperatures, corroborate the difficulties in-axis compression of Ti. Finally, in BCC Ti, the<111>/2 screw has a degenerate core with average glide on {112} planes; the<111>/2 edge and mixed dislocations have non-dissociated cores on {110} planes. This work paints a self-consistent, complete picture on all dislocations in Ti, rationalises previous experimental observations and points to future HRTEM examinations of unusual dislocations such as the mixed and PB transformedcores. read less T. Wen et al., “Specialising neural network potentials for accurate properties and application to the mechanical response of titanium,” npj Computational Materials. 2021. link Times cited: 27 S. Xie, M. Rupp, and R. Hennig, “Ultra-fast interpretable machine-learning potentials,” npj Computational Materials. 2021. link Times cited: 9 C. Baruffi, A. Finel, Y. L. Bouar, B. Bacroix, and O. U. Salman, “Atomistic simulation of martensite microstructural evolution during temperature driven β→α transition in pure titanium,” Computational Materials Science. 2020. link Times cited: 4 A. Shapeev, E. Podryabinkin, K. Gubaev, F. Tasn’adi, and I. Abrikosov, “Elinvar effect in β-Ti simulated by on-the-fly trained moment tensor potential,” New Journal of Physics. 2020. link Times cited: 20 Abstract: A combination of quantum mechanics calculations with machine… read more Abstract: A combination of quantum mechanics calculations with machine learning techniques can lead to a paradigm shift in our ability to predict materials properties from first principles. Here we show that on-the-fly training of an interatomic potential described through moment tensors provides the same accuracy as state-of-the-art ab initio molecular dynamics in predicting high-temperature elastic properties of materials with two orders of magnitude less computational effort. Using the technique, we investigate high-temperature bcc phase of titanium and predict very weak, Elinvar, temperature dependence of its elastic moduli, similar to the behavior of the so-called GUM Ti-based alloys (Sato et al 2003 Science 300 464). Given the fact that GUM alloys have complex chemical compositions and operate at room temperature, Elinvar properties of elemental bcc-Ti observed in the wide temperature interval 1100–1700 K is unique. read less L. Fowler, A. J. van Vuuren, W. Goosen, H. Engqvist, C. Öhman-Mägi, and S. Norgren, “Investigation of Copper Alloying in a TNTZ-Cux Alloy,” Materials. 2019. link Times cited: 7 Abstract: Alloying copper into pure titanium has recently allowed the … read more Abstract: Alloying copper into pure titanium has recently allowed the development of antibacterial alloys. The alloying of biocompatible elements (Nb, Ta and Zr) into pure titanium has also achieved higher strengths for a new alloy of Ti-1.6 wt.% Nb-10 wt.% Ta-1.7 wt.% Zr (TNTZ), where strength was closer to Ti-6Al-4V and higher than grade 4 titanium. In the present study, as a first step towards development of a novel antibacterial material with higher strength, the existing TNTZ was alloyed with copper to investigate the resultant microstructural changes and properties. The initial design and modelling of the alloy system was performed using the calculation of phase diagrams (CALPHAD) methods, to predict the phase transformations in the alloy. Following predictions, the alloys were produced using arc melting with appropriate heat treatments. The alloys were characterized using energy dispersive X-ray spectroscopy in scanning transmission electron microscopy (STEM-EDS) with transmission Kikuchi diffraction (TKD). The manufactured alloys had a three-phased crystal structure that was found in the alloys with 3 wt.% Cu and higher, in line with the modelled alloy predictions. The phases included the α-Ti (HCP-Ti) with some Ta present in the crystal, Ti2Cu, and a bright phase with Ti, Cu and Ta in the crystal. The Ti2Cu crystals tended to precipitate in the grain boundaries of the α-Ti phase and bright phase. The hardness of the alloys increased with increased Cu addition, as did the presence of the Ti2Cu phase. Further studies to optimize the alloy could result in a suitable material for dental implants. read less D. Korbmacher, A. Glensk, A. Duff, M. Finnis, B. Grabowski, and J. Neugebauer, “Ab initio based method to study structural phase transitions in dynamically unstable crystals, with new insights on the β to ω transformation in titanium,” Physical Review B. 2019. link Times cited: 9 Abstract: We present an approach that enables an efﬁcient and accurate… read more Abstract: We present an approach that enables an efﬁcient and accurate study of dynamically unstable crystals over the full temperature range. The approach is based on an interatomic potential ﬁtted to ab initio molecular dynamics energies for both the high- and low-temperature stable phases. We verify by comparison to explicit ab initio simulations that such a bespoke potential, for which we use here the functional form of the embedded atom method, provides accurate transformation temperatures and atomistic features of the transformation. The accuracy of the potential makes it an ideal tool to study the important impact of ﬁnite size and ﬁnite time effects. We apply our approach to the dynamically unstable β (bcc) titanium phase and study in detail the transformation to the low-temperature stable hexagonal ω phase. We ﬁnd a large set of previously unreported linear-chain disordered (LCD) structures made up of three types of [111] β linear-chain defects that exhibit randomly disordered arrangements in the (111) β plane. read less D. Dickel and C. Barrett, “Methods for the determination of diffusionless transformation conditions from atomistic simulations,” Modelling and Simulation in Materials Science and Engineering. 2019. link Times cited: 3 Abstract: The phase transition process between solid phases plays a cr… read more Abstract: The phase transition process between solid phases plays a critical role in defining the microstructural characteristics of many metals and alloys. Therefore, accurate reproduction of phase transformations enables significant predictive abilities in material modeling which cannot be otherwise achieved. At the atomistic scale, phase transitions naturally occur in modeling as large numbers of atoms in a system relax to their equilibrium phase over a relatively long time scale. However, the accuracy of the simulations in predicting the equilibrium phase for a given pressure, temperature, and solute concentration are often inadequate. Sufficient calibration for a given atomistic potential to reliably reflect these properties is often not achieved because methods of determining the transformation face a number of limitations including high computational cost and sometimes poor accuracy of the results. Herein, we review the methods which have been used to determine equilibrium phase transition conditions at the discrete atom scale and compare their relative efficiency and efficacy. read less J. J. G. Moreno, D. Papageorgiou, G. Evangelakis, and C. E. Lekka, “An ab initio study of the structural and mechanical alterations of Ti-Nb alloys,” Journal of Applied Physics. 2018. link Times cited: 12 Abstract: This article describes a systematic theoretical investigatio… read more Abstract: This article describes a systematic theoretical investigation of the role of Nb substitution on the structural and mechanical properties of Ti-Nb alloys. The aim is to understand the origin of the ... read less D. Dickel, C. Barrett, R. Cariño, M. Baskes, and M. Horstemeyer, “Mechanical instabilities in the modeling of phase transitions of titanium,” Modelling and Simulation in Materials Science and Engineering. 2018. link Times cited: 16 Abstract: In this paper, we demonstrate that previously observed β to … read more Abstract: In this paper, we demonstrate that previously observed β to α transitions for titanium interatomic potentials available in the literature arose from a mechanical instability and thus the potentials underestimated the correct thermodynamic phase transition temperature by hundreds of degrees. Using a relative free energy method for the two phases to calculate the true transition temperature, we present a new modified embedded atom method potential for titanium that shows a transition temperature of 1155 ± 2 K in excellent agreement with the experimentally observed transition. This free energy approach avoids the problems of irreversibility which occur when one relies on direct observation of the phase transition in molecular dynamics simulation. Other transformation mechanisms in addition to the mechanical instability are also considered. Finally, the new potential predicts the proper c-axis plastic twinning for titanium under compression making it the only potential that correctly predicts the phase transition temperature and the plastic behavior of α Ti. read less T. White et al., “Identifying deformation mechanisms in molecular dynamics simulations of laser shocked matter,” J. Comput. Phys. 2017. link Times cited: 1 J. Paul et al., “Computational methods for 2D materials: discovery, property characterization, and application design,” Journal of Physics: Condensed Matter. 2017. link Times cited: 49 Abstract: The discovery of two-dimensional (2D) materials comes at a t… read more Abstract: The discovery of two-dimensional (2D) materials comes at a time when computational methods are mature and can predict novel 2D materials, characterize their properties, and guide the design of 2D materials for applications. This article reviews the recent progress in computational approaches for 2D materials research. We discuss the computational techniques and provide an overview of the ongoing research in the field. We begin with an overview of known 2D materials, common computational methods, and available cyber infrastructures. We then move onto the discovery of novel 2D materials, discussing the stability criteria for 2D materials, computational methods for structure prediction, and interactions of monolayers with electrochemical and gaseous environments. Next, we describe the computational characterization of the 2D materials’ electronic, optical, magnetic, and superconducting properties and the response of the properties under applied mechanical strain and electrical fields. From there, we move on to discuss the structure and properties of defects in 2D materials, and describe methods for 2D materials device simulations. We conclude by providing an outlook on the needs and challenges for future developments in the field of computational research for 2D materials. read less S. Kadkhodaei, Q.-J. Hong, and A. Walle, “Free energy calculation of mechanically unstable but dynamically stabilized bcc titanium,” Physical Review B. 2017. link Times cited: 37 Abstract: The phase diagram of numerous materials of technological imp… read more Abstract: The phase diagram of numerous materials of technological importance features high-symmetry high-temperature phases that exhibit phonon instabilities. Leading examples include shape-memory alloys, as well as ferroelectric, refractory, and structural materials. The thermodynamics of these phases have proven challenging to handle by atomistic computational thermodynamic techniques, due to the occurrence of constant anharmonicity-driven hopping between local low-symmetry distortions, while maintaining a high-symmetry time-averaged structure. To compute the free energy in such phases, we propose to explore the system's potential-energy surface by discrete sampling of local minima by means of a lattice gas Monte Carlo approach and by continuous sampling by means of a lattice dynamics approach in the vicinity of each local minimum. Given the proximity of the local minima, it is necessary to carefully partition phase space by using a Voronoi tessellation to constrain the domain of integration of the partition function, in order to avoid double-counting artifacts and enable an accurate harmonic treatment near each local minima. We consider the bcc phase of titanium as a prototypical examples to illustrate our approach. read less P. Zhang and D. Trinkle, “A modified embedded atom method potential for interstitial oxygen in titanium,” Computational Materials Science. 2016. link Times cited: 13 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 S. Winczewski, J. Dziedzic, and J. Rybicki, “Central-force decomposition of spline-based modified embedded atom method potential,” Modelling and Simulation in Materials Science and Engineering. 2016. link Times cited: 0 Abstract: Central-force decompositions are fundamental to the calculat… read more Abstract: Central-force decompositions are fundamental to the calculation of stress fields in atomic systems by means of Hardy stress. We derive expressions for a central-force decomposition of the spline-based modified embedded atom method (s-MEAM) potential. The expressions are subsequently simplified to a form that can be readily used in molecular-dynamics simulations, enabling the calculation of the spatial distribution of stress in systems treated with this novel class of empirical potentials. We briefly discuss the properties of the obtained decomposition and highlight further computational techniques that can be expected to benefit from the results of this work. To demonstrate the practicability of the derived expressions, we apply them to calculate stress fields due to an edge dislocation in bcc Mo, comparing their predictions to those of linear elasticity theory. read less Y. Ji, T. Heo, F. Zhang, and L.-Q. Chen, “Theoretical Assessment on the Phase Transformation Kinetic Pathways of Multi-component Ti Alloys: Application to Ti-6Al-4V,” Journal of Phase Equilibria and Diffusion. 2016. link Times cited: 15 Y. Ji, T. Heo, F. Zhang, and L.-qing Chen, “Theoretical Assessment on the Phase Transformation Kinetic Pathways of Multi-component Ti Alloys: Application to Ti-6Al-4V,” Journal of Phase Equilibria and Diffusion. 2015. link Times cited: 0 L.-F. Huang, B. Grabowski, E. McEniry, D. Trinkle, and J. Neugebauer, “Importance of coordination number and bond length in titanium revealed by electronic structure investigations,” physica status solidi (b). 2015. link Times cited: 31 Abstract: We study the influence of coordination number and bond lengt… read more Abstract: We study the influence of coordination number and bond length on the phase stability and orbital occupation in Ti using density functional theory. In particular, Ti under a wide range of conditions (equilibrium state, hydrostatic pressure, anisotropic strain, and phase transformations) is systematically investigated allowing us to derive generic energetic and electronic trends. Our analysis of the correlations between electronic structure and the atomic geometry reveals that the most suitable descriptors of the system are an effective coordination number and an effective bond length. Utilizing these descriptors, we show that (i) the phase stability of Ti increases with coordination number, because of the increased number of interatomic bonds; (ii) the occupation number of the d (s and p) orbital decreases (increases) with increasing the bond length, because of the localized (delocalized) character of the d (p and s) orbital. These dependencies are particularly evident after applying a simple harmonic strain correction to the energy and an electron‐transfer correction within the ω phase. The physical picture derived from pure Ti is used to explain the phase stability and orbital occupation of Ti–Nb and Ti–Zr alloys, which reveals the underlying mechanisms for various experimental phenomena in Ti alloys. read less Z.-Y. Zeng, C.-E. Hu, X. Liu, Z. Wei, and L. Cai, “High Pressure Phase Stability of Ti with Self-consistent ab initio Lattice Dynamics Approach,” Chinese Journal of Chemical Physics. 2015. link Times cited: 0 Abstract: The traditional quasiharmonic approximation cannot predict t… read more Abstract: The traditional quasiharmonic approximation cannot predict the phase diagram of Ti accurately, due to the well-known soften phonon modes of the β-Ti. By means of self-consistent ab initio lattice dynamics (SCAILD) method, in which the effects of phonon-phonon interactions are considered, the phonon dispersion relations at finite temperature for Ti are calculated. From the phonon dispersions, we extrapolat the acoustic velocities and harmonic elastic constants. The dynamical stable regions and phase diagram of Ti are also predicted successfully. The results show that SCAILD method can be designed to work for strongly anharmonic systems where the QHA fails. read less P. Zhang and D. Trinkle, “Database optimization for empirical interatomic potential models,” Modelling and Simulation in Materials Science and Engineering. 2013. link Times cited: 8 Abstract: Weighted least squares fitting to a database of quantum mech… read more Abstract: Weighted least squares fitting to a database of quantum mechanical calculations can determine the optimal parameters of empirical potential models. While algorithms exist to provide optimal potential parameters for a given fitting database of structures with corresponding energy-related predictions and to estimate prediction errors using Bayesian sampling, defining an optimal fitting database based on potential predictions remains elusive. A testing set of structures and energy-related predictions provides an empirical measure of potential transferability. Here, we propose an objective function for fitting databases based on testing set errors. The objective function allows the optimization of the weights in a fitting database, the assessment of the adding or removing of structures in the fitting database, or the comparison of two different fitting databases. To showcase this technique, we consider an example Lennard-Jones potential for Ti, where modeling multiple complicated crystal structures is difficult for a radial pair potential. The algorithm finds different optimal fitting databases, depending on the objective function of potential prediction error for a testing set. read less H. Park et al., “Ab initio based empirical potential used to study the mechanical properties of molybdenum,” Physical Review B. 2012. link Times cited: 70 Abstract: Density-functional theory energies, forces, and elastic cons… read more Abstract: Density-functional theory energies, forces, and elastic constants determine the parametrization of an empirical, modified embedded-atom method potential for molybdenum. The accuracy and transferability of the potential are verified by comparison to experimental and density-functional data for point defects, phonons, thermal expansion, surface and stacking fault energies, and ideal shear strength. Searching the energy landscape predicted by the potential using a genetic algorithm verifies that it reproduces not only the correct bcc ground state of molybdenum but also all low-energy metastable phases. The potential is also applicable to the study of plastic deformation and used to compute energies, core structures, and Peierls stresses of screw and edge dislocations. Molybdenum's high strength and high-temperature stability make this refractory metal very attractive for use in advanced process technologies. The motion of dislocations is generally accepted to be responsible for the complex deformation behavior of this transition metal. 1-8 In recent years progress has been made on the description of the properties of screw dislocations using density-functional theory (DFT), tight- binding calculations, and empirical potentials. 9-19 However, DFT and tight-binding techniques are limited to small system sizes, which is problematic due to the long-range strain field of dislocations, and current empirical potentials lack the required accuracy for the description of the dislocation structure. Simulations of dislocation motion and interactions require efficient interatomic potentials which accurately describe the dislocation energies, core structures, and motion. In this work we develop an empirical potential for Mo which predicts the ideal shear strength, generalized stacking fault en- ergies, energies of dislocations, and the Peierls stress and core structure of the � 111� /2 screw dislocation. The potential form is given by the modified embedded-atom method (MEAM) and the potential parameters are optimized usingabinitio energies, lattice parameters, forces, and elastic constants. Section II describes the calculations for the DFT database, the functional form of the MEAM potential, and the optimization of the potential parameters to the DFT database. The accuracy of the potential for structural, elastic, and defect properties is verified in Sec. III by comparison to DFT results and experiments. A genetic algorithm search of the energy landscape of the MEAM potential confirms that the potential reproduces the correct bcc ground state and predicts several low-energy metastable structures whose energies agree well with DFT results. Results of the MEAM potential for formation energies of point defects, phonon dispersion, thermal expansion, surface energies, ideal shear strength, and generalized stacking faults for the MEAM potential closely match DFT results and available experimental data. In Sec. IV we apply the potential to determine energies and Peierls stresses of the screw and edge dislocation in bcc Mo. The results show that the MEAM potential accurately describes the structural and mechanical properties of Mo and should be applicable to simulate the motion of dislocations and the plastic deformation of Mo. read less B. Tang, Y.-W. Cui, H. Chang, H. Kou, J. Li, and L. Zhou, “Modeling of Incommensurate ω Structure in the Zr-Nb Alloys,” Metallurgical and Materials Transactions A. 2012. link Times cited: 2 G. Grimvall, B. Magyari-Köpe, V. Ozoliņš, and K. Persson, “Lattice instabilities in metallic elements,” Reviews of Modern Physics. 2012. link Times cited: 347 Abstract: Most metallic elements have a crystal structure that is eith… read more Abstract: Most metallic elements have a crystal structure that is either body-centered cubic (bcc), face-centered close packed, or hexagonal close packed. If the bcc lattice is the thermodynamically most stable structure, the close-packed structures usually are dynamically unstable, i.e., have elastic constants violating the Born stability conditions or, more generally, have phonons with imaginary frequencies. Conversely, the bcc lattice tends to be dynamically unstable if the equilibrium structure is close packed. This striking regularity essentially went unnoticed until ab initio total-energy calculations in the 1990s became accurate enough to model dynamical properties of solids in hypothetical lattice structures. After a review of stability criteria, thermodynamic functions in the vicinity of an instability, Bain paths, and how instabilities may arise or disappear when pressure, temperature, and/or chemical composition is varied are discussed. The role of dynamical instabilities in the ideal strength of solids and in metallurgical phase diagrams is then considered, and comments are made on amorphization, melting, and low-dimensional systems. The review concludes with extensive references to theoretical work on the stability properties of metallic elements. read less X. Bai and B. Uberuaga, “Multi-timescale investigation of radiation damage near TiO2 rutile grain boundaries,” Philosophical Magazine. 2012. link Times cited: 31 Abstract: To understand the interactions between defects and grain bou… read more Abstract: To understand the interactions between defects and grain boundaries (GBs) in oxides, two atomistic modeling methods were used to examine the role of GBs in a model system, rutile TiO2, in modifying radiation-induced defect production and annealing. Molecular dynamics was used to investigate defect production near a symmetric tilt GB at both 300 K and 1000 K. The damage production is found to be sensitive to the initial distance of the primary knock-on atom from the GB. We find three distinct regimes in which GBs have different effects. Similar to GBs in metals, the GB absorbs more interstitials than vacancies at certain distances while this behavior of biased loading of interstitials diminishes at other distances. Further, we obtain the statistics of both interstitial and vacancy clusters produced in collision cascades in terms of their compositions at two temperatures. Perfectly stoichiometric defect clusters represent a small fraction of the total clusters produced. Moreover, a significant reduction in the number of interstitial clusters at 1000 K compared to 300 K is thought to be a consequence of enhanced migration of interstitials towards the GB. Finally, the kinetic properties of certain defect clusters were investigated with temperature accelerated dynamics, without any a priori assumptions of migration mechanisms. Small interstitial clusters become mobile at high temperatures while small vacancy clusters do not. Multiple migration pathways exist and are typically complex and non-intuitive. We use this kinetic information to explain experimental observations and predict their long-time migration behavior near GBs. read less N. Velisavljevic, S. Macleod, and H. Cynn, “Titanium Alloys at Extreme Pressure Conditions.” 2012. link Times cited: 18 Abstract: The electronic structures of the early transition metals are… read more Abstract: The electronic structures of the early transition metals are characterised by the relationship that exists between the occupied narrow d bands and the broad sp bands. Under pressure, the sp bands rise faster in energy, causing electrons to be transferred to the d bands (Gupta et al., 2008). This process is known as the s-d transition and it governs the structural properties of the transition metals. At ambient conditions, pure Ti crystallizes in the 2-atom hcp, or  phase crystal structure (space group P63/mmc) and has an axial ratio (c/a) ~ 1.58. Under pressure, the  phase undergoes a martensitic transformation at room temperature (RT) into the 3-atom hexagonal, or  phase structure (space group P6/mmm). The appearance of the ω phase at high pressure raises a number of scientific and engineering issues mainly because the  phase appears to be fairly brittle compared with the  phase, and this may significantly limit the use of Ti in high pressure applications. Furthermore, after pressure treatment the ω phase appears to be fully, or at least, partially recoverable at ambient conditions, thus raising questions as to which is the lowest thermodynamically stable crystallographic phase of Ti at RT and pressure. read less M. Ghazisaeidi and D. Trinkle, “Core structure of a screw dislocation in Ti from density functional theory and classical potentials,” Acta Materialia. 2012. link Times cited: 84 P. Souvatzis, S. Arapan, O. Eriksson, and M. Katsnelson, “Temperature-driven α-to-β phase transformation in Ti, Zr and Hf from first-principles theory combined with lattice dynamics,” EPL (Europhysics Letters). 2011. link Times cited: 17 Abstract: Lattice dynamical methods used to predict phase transformati… read more Abstract: Lattice dynamical methods used to predict phase transformations in crystals typically deal with harmonic phonon spectra and are therefore not applicable in important situations where one of the competing crystal structures is unstable in the harmonic approximation, such as the bcc structure involved in the hcp-to-bcc martensitic phase transformation in Ti, Zr and Hf. Here we present an expression for the free energy that does not suffer from such shortcomings, and we show by self-consistent ab initio lattice dynamical calculations (SCAILD), that the critical temperature for the hcp-to-bcc phase transformation in Ti, Zr and Hf, can be effectively calculated from the free-energy difference between the two phases. This opens up the possibility to study quantitatively, from first-principles theory, temperature-induced phase transitions. read less C.-E. Hu, Z.-Y. Zeng, L. Zhang, X.-R. Chen, L. Cai, and D. Alfé, “Theoretical investigation of the high pressure structure, lattice dynamics, phase transition, and thermal equation of state of titanium metal,” Journal of Applied Physics. 2010. link Times cited: 72 Abstract: We report a detailed first-principles calculation to investi… read more Abstract: We report a detailed first-principles calculation to investigate the structures, elastic constants, and phase transition of Ti. The axial ratios of both alpha-Ti and omega-Ti are nearly constant under hydrostatic compression, which confirms the latest experimental results. From the high pressure elastic constants, we find that the alpha-Ti is unstable when the applied pressures are larger than 24.2 GPa, but the omega-Ti is mechanically stable at all range of calculated pressure. The calculated phonon dispersion curves agree well with experiments. Under compression, we captured a large softening around Gamma point of alpha-Ti. When the pressure is raised to 35.9 GPa, the frequencies around the Gamma point along Gamma-M-K and Gamma-A in transverse acoustical branches become imaginary, indicating a structural instability. Within quasiharmonic approximation, we obtained the full phase diagram and accurate thermal equations of state of Ti. The phase transition omega-Ti ->alpha-Ti ->beta-Ti at zero pressure occurs at 146 K and 1143 K, respectively. The predicted triple point is at 9.78 GPa, 931 K, which is close to the experimental data. Our thermal equations of state confirm the available experimental results and are extended to a wider pressure and temperature range. (C) 2010 American Institute of Physics. [doi:10.1063/1.3407560] 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 M. Poschmann, M. Asta, and D. Chrzan, “Convergence of calculated dislocation core structures in hexagonal close packed titanium,” Modelling and Simulation in Materials Science and Engineering. 2017. link Times cited: 9 Abstract: The core structure of 〈 a 〉 -type screw dislocations in hexa… read more Abstract: The core structure of 〈 a 〉 -type screw dislocations in hexagonal close packed titanium is investigated computationally using periodic supercells with quadrupolar configurations in combination with density functional theory (DFT) and a modified embedded atom method (MEAM) classical potential. Two arrangements of the quadrupolar supercell configurations are examined, and within each arrangement two initial dislocation positions are compared. (Meta)stable pyramidal and prismatic dislocation core structures exist within both DFT and MEAM methods, and the relaxed structure from a given configuration resulting from our anisotropic elasticity theory solution depends only on the assumed initial dislocation positions. Within DFT we find the ground state core structure to be spread on the pyramidal plane. We find that it is necessary to include the semi-core 3p electrons as valence states in the DFT calculations in order to converge the ground state dislocation core configuration and difference in energy between structures. In terms of k-point sampling, it is found that at least a 1 × 1 × 15 k-point mesh is necessary to converge the dislocation core structure for a supercell one Burgers vector deep. Use of higher k-point densities or inclusion of additional semi-core electronic states as valence electrons results in the same core structure. With the MEAM potential considered in this work, we find the ground state core configuration to be spread predominantly on the prismatic plane, in contrast with the DFT results. read less 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 N. Wilson, K. Mcgregor, M. Gibson, and S. Russo, “The effect of dopant incorporation on the elastic properties of Ti metal,” Modelling and Simulation in Materials Science and Engineering. 2014. link Times cited: 5 Abstract: The effect of dopant atoms on the structural and elastic pro… read more Abstract: The effect of dopant atoms on the structural and elastic properties of α titanium is examined through the use of density functional theory. The effect of 66 dopant atoms, from H through the third row transition metal elements, were considered in this study. In all cases the dopant concentration was approximately 3 at%, with substitutional incorporation investigated for all atoms considered and interstitial incorporation investigated for a smaller subset of elements. Interstitial incorporation was calculated to be more energetically favourable for the elements H, B to F, S and Cl with these dopants coordinating octahedrally with the surrounding Ti atoms, while substitutional incorporation was found to be more stable for the other elements. The five independent single crystal elastic constants are calculated, along with the bulk and shear moduli. The energetics and mechanically stability associated with the alloying of various dopants is also discussed. read less E. Pechenik, I. Kelson, and G. Makov, “Formulation of wide-ranging embedded-atom-type potentials: the role of mechanical stability,” Modelling and Simulation in Materials Science and Engineering. 2012. link Times cited: 1 Abstract: Wide-ranging inter-atomic potentials are necessary for model… read more Abstract: Wide-ranging inter-atomic potentials are necessary for modeling many problems in material physics that involve multiple atomic environments and phases. The domains of thermodynamic and mechanical stability of embedded-atom-type potentials are examined for the cubic phases. It is shown that the choice of the pair potential is critical in determining the domain of stability of embedded-atom-type potentials. In particular, the Lennard-Jones embedded-atom potential is shown not to stabilize the bcc phase. A simple four-parameter universal equation of state-based embedded-atom potential is shown to have a domain of stability for all the cubic phases and to reproduce the high-pressure equation of state. A model phase diagram for the three cubic phases is presented. This potential is fitted to 17 elemental systems and found to be able to reproduce both the elastic constants and the ground state crystalline structure. For elements with a low degree of elastic anisotropy, this potential can also reproduce the high-pressure behavior. read less Y. Kolobov, A. Lipnitskii, M. Ivanov, I. Nelasov, and S. Manokhin, “Investigations of the thermal stability of the microstructure of titanium produced by intense plastic deformation,” Russian Physics Journal. 2012. link Times cited: 11 H. Zong, G. Pilania, X. Ding, G. Ackland, and T. Lookman, “Developing an interatomic potential for martensitic phase transformations in zirconium by machine learning,” npj Computational Materials. 2018. link Times cited: 78 C. Greeff, “A Model for Phase Transitions Under Dynamic Compression,” Journal of Dynamic Behavior of Materials. 2016. link Times cited: 10 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_520569947398_002
Extended KIM ID The long form of the KIM ID including a human readable prefix (100 characters max), two underscores, and the Short KIM ID. Extended KIM IDs can only contain alpha-numeric characters (letters and digits) and underscores and must begin with a letter.	MEAM_LAMMPS_HennigLenoskyTrinkle_2008_Ti__MO_520569947398_002
DOI	10.25950/6bcb2fa8 https://doi.org/10.25950/6bcb2fa8 https://commons.datacite.org/doi.org/10.25950/6bcb2fa8
KIM Item Type Specifies whether this is a Portable Model (software implementation of an interatomic model); Portable Model with parameter file (parameter file to be read in by a Model Driver); Model Driver (software implementation of an interatomic model that reads in parameters).	Portable Model using Model Driver MEAM_LAMMPS__MD_249792265679_002
Driver	MEAM_LAMMPS__MD_249792265679_002
KIM API Version	2.2
Potential Type	meam

Previous Version	MEAM_LAMMPS_HennigLenoskyTrinkle_2008_Ti__MO_520569947398_001

Verification Check Dashboard

(Click here to learn more about Verification Checks)

Grade	Name	Category	Brief Description	Full Results	Aux File(s)
P All elements claimed by model are supported in at least one of the tested configurations.	vc-species-supported-as-stated	mandatory	The model supports all species it claims to support; see full description.	Results	Files
P Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.	vc-periodicity-support	mandatory	Periodic boundary conditions are handled correctly; see full description.	Results	Files
P Model energy has permutation symmetry for all configurations the model was able to compute.	vc-permutation-symmetry	mandatory	Total energy and forces are unchanged when swapping atoms of the same species; see full description.	Results	Files
A The letter grade A was assigned because the normalized error in the computation was 6.34091e-11 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
P The model is C^1 continuous. This means that the model has continuous energy and continuous 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

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	2745
Cohesive energy versus lattice constant curve for diamond Ti v004	view	3534
Cohesive energy versus lattice constant curve for fcc Ti v004	view	4257
Cohesive energy versus lattice constant curve for sc Ti v004	view	2724

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	13924
Elastic constants for fcc Ti at zero temperature v006	view	17246
Elastic constants for sc Ti at zero temperature v006	view	23853

EquilibriumCrystalStructure__TD_457028483760_003

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

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

Computes the equilibrium crystal structure and energy for an arbitrary crystal at zero temperature and applied stress by performing symmetry-constrained relaxation. The crystal structure is specified using the AFLOW prototype designation. Multiple sets of free parameters corresponding to the crystal prototype may be specified as initial guesses for structure optimization. No guarantee is made regarding the stability of computed equilibria, nor that any are the ground state.

Test	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Equilibrium crystal structure and energy for Ti in AFLOW crystal prototype A_cF4_225_a v003	view	179838
Equilibrium crystal structure and energy for Ti in AFLOW crystal prototype A_cI2_229_a v003	view	141389
Equilibrium crystal structure and energy for Ti in AFLOW crystal prototype A_hP2_194_c v003	view	182320
Equilibrium crystal structure and energy for Ti in AFLOW crystal prototype A_hP3_191_ad v003	view	145216

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	8862
Equilibrium zero-temperature lattice constant for diamond Ti v007	view	8540
Equilibrium zero-temperature lattice constant for fcc Ti v007	view	6405
Equilibrium zero-temperature lattice constant for sc Ti v007	view	8687

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	65266

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	1116234

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	6308909

Errors

ElasticConstantsCubic__TD_011862047401_006

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

ElasticConstantsHexagonal__TD_612503193866_004

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

Files

CMakeLists.txt
LICENSE
Ti.meam.spline
elems.meam
kimprovenance.edn
kimspec.edn

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MEAM_LAMMPS__MD_249792265679_002.zip	Zip	Windows archive

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MEAM_LAMMPS_HennigLenoskyTrinkle_2008_Ti__MO_520569947398_002

Verification Check Dashboard

Visualizers (in-page)

BCC Lattice Constant

Cohesive Energy Graph

Diamond Lattice Constant

Dislocation Core Energies

FCC Elastic Constants

FCC Lattice Constant

FCC Stacking Fault Energies

FCC Surface Energies

SC Lattice Constant

Cubic Crystal Basic Properties Table

Tests

Errors

Files

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