Ti

EAM Potential: Ti.lammps.eam  (unpublished)

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    Potential plots

Pair function

Density function

Embedding energy function        

    Titanium EAM potentials available in the literature

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 

     

        

      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

        

        

Deformation Path

      Deformation path {211} plane

Liquid Structure

    Liquid density: EAM vs. experiment   

    Pair correlation functions

    Structure factors

    Comparison of experimental structure factors and EAM calculations