Ti

EAM Potential: Ti.lammps.eam  (unpublished)

    Other formats            

 imd    dl_poly    xmd    xml    gulp      

    Potential plots

Pair function

Density function

Embedding energy function        

    Titanium EAM potentials available in the literature

• 1. R. G. Hennig, T. J. Lenosky, D. R. Trinkle, S. P. Rudin, and J. W. Wilkins, Classical potential describes martensitic phase transformations between the alpha., beta, and omega titanium phases, Phys. Rev. B 78, 054121 .(2008)  

  2. D. R. Trinkle, M. D. Jones, R. G. Hennig, S. P. Rudin, R. C. Albers, and J. W. Wilkins, An Empirical Tight-Binding Model for Titanium Phase Transformations,  Phys. Rev. B 73, 094123 (2006) 

Properties of Tantalum Predicted by the Present EAM Model 

Ref. 2.1    http://www.webelements.com/tantalum/crystal_structure.html

Ref. 2.2    C. Kittel, Introduction to Solid State Physics (Wiley, New York, 2004)

Ref. 2.3    G. Simons and H. Wang, Single Crystal Elastic Constants and Calculated Aggregate Properties (MIT Press, Cambridge,MA, 1977)

Ref. 2.4    Metals: Phonon and Electron States, Fermi Surfaces, Edited by  K.H. Hellwege et al., New York 1981 (p.142)         

Ref. 2.5    Ab initio calculation (vasp) in the present work.  paw_gga, 5d34s2, encut=279.6 eV. 

Ref. 2.6    K. Maier, M. Peo, B. Saile, H. E. Schaefer, and A. Seeger, Philos. Mag. A 40, 701 (1979)

Ref. 2.7    Ullmaier H, editor. Properties and interaction of atomic defects in metals and alloys. Landolt-Bornstein, New Series, Group III, vol.25. Springer: Berlin; 1991. p. 88.

Ref. 2.8    W. R. Tyson and W. A. Miller, Surf. Sci. 62, 267 (1977)

Ref. 2.9    Y. Mishin and A.Y. Lozovoi, Angular-dependent interatomic potential for tantalum, Acta Materialia 54, 5013 (2006)

Ref. 2.10    R. E. Bedford, G. Bonnier, H. Maas, and F. Pavese, Metrologia 33,133 (1996).

Ref. 2.11    P.F. Paradis, T. Ishikawa, S. Yoda, Noncontact density measurements of tantalum and rhenium in the liquid and undercooled states, Appl. Phys. Lett. 83, 4047 (2003); http://dx.doi.org/10.1063/1.1624475

Melting temperature of Ti 

lammps script to estimate the melting temperature of Ti: Ti.melting.in

MD simulation of two co-existing phases of Tantalum (bcc vs. liquid) in equilibrium at T = K

Lattice Dynamics

            Phonon Dispersion Curve   

Elastic constant:

E. S. Fisher and C. J. Renken, Single-Crystal Elastic Moduli and the hcp → bcc Transformation in Ti, Zr, and Hf, Phys. Rev. 135, A482–A494 (1964)

Thermal expansion of h.c.p titanium

J.W. Edwards, R. Speiser and H.L. Johnson, High Temperature Structure and Thermal Expansion of Some Metals as Determined by X‐Ray Diffraction Data. I. Platinum, Tantalum, Niobium, and Molybdenum, J. Appl. Phy., 22, 424 (1951) 

Crystal Structures

         Pressure-volume relationship of hcp titanium

     Phase diagram of Titanium 

• D. R. Trinkle, R. G. Hennig, S. G. Srinivasan, D. M. Hatch, M. D. Jones, H. T. Stokes, R. C. Albers, and J. W. Wilkins. A New Mechanism for the Alpha to Omega Martensitic Transformation in Pure Titanium, Phys. Rev. Lett. 91, 025701 (2003)       

      Molecular dynamics simulation of the formation of beta-Ti 

Generalized Stacking Fault Energy

   Tantalum {211} gamma surface (unrelaxed) evaluated with the EAM potential

    Atomic packing on plane {211} of bcc Tantalum 

            Directions: upward [111], horizontal [110]

            Atomic packing on plane {110} of bcc Tantalum 

    Comparison of ab initio and EAM calculations of SF energies

Simulation of a/2 <111> screw dislocation

      Differential displacement map showing the 3-fold compact dislocation core of Ta

    The screw component of the Nye tensor of a relaxed a/2<111> screw dislocation in Tantalum

• Y. Mishin and A.Y. Lozovoi, Angular-dependent interatomic potential for tantalum, Acta Materialia 54, 5013 (2006)

  • C.S. Hartley, Y. Mishin, Characterization and visualization of the lattice misfit associate with dislocation cores, Acta Materialia 53, 1313 (2005)

• C. Begau, J. Hua, A. Hartmaier A novel approach to study dislocation density tensors and lattice-rotation patterns in atomistic simulations, Journal of the Mechanics and Physics of Solids 60, 711-722, (2012)

Deformation Path

      Deformation path {211} plane

Liquid Structure

    Liquid density: EAM vs. experiment   

• • P.F. Paradis, T. Ishikawa, S. Yoda, Noncontact density measurements of tantalum and rhenium in the liquid and undercooled states, Appl. Phys. Lett. 83, 4047 (2003); http://dx.doi.org/10.1063/1.1624475

•  http://www.webelements.com/tantalum/crystal_structure.html

    Pair correlation functions

    Structure factors

    Comparison of experimental structure factors and EAM calculations