Pb

EAM Potential: Pb.lammps.eam

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Properties Predicted by EAM

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

Ref. 2.2     B.J. Lee, J.H. Shim and M.I. Baskes, Semiempirical atomic potentials for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, Al, and Pb based on first and second nearest-neighbor modified embedded atom method, Phys. Rev. B 68, 144112 (2003) 

Ref. 2.3     R. Stedman, L. Almqvist, G. Nilsson, and G. Raunio, Dispersion Relations for Phonons in Lead at 80 and 300°K, Phys Rev. 162, 545 (1967)

Ref. 2.5    http://en.wikipedia.org/wiki/Lead

Lattice Dynamics

    Lattice constants as a function of temperature  

Ref. 3.1   Y.S. Touloukian, R.K. Kirby, R.E. Taylor, P.D. Desai, Thermal Expansion, Metallic Elements and Alloys, Plenum Press, New York,        1975.

   Thermal expansion coefficient based on quasiharmonic approximation

    Elastic Constants

Ref. 3.2     G. Simons and H. Wang, Single Crystal Elastic Constants and Calculated Aggregate Properties (MIT Press, Cambridge, MA, 1977)

     Pressure-volume equation of state

        Ref. 3.3    R. G. McQueen and S.P. Marsh, Equation of State for Nineteen Metallic Elements from Shock‐Wave Measurements to Two Megabars, J. Appl. Phys. 31, 1253 (1960)

     Phonon Dispersion Curves

Ref. 3.3     PWSCF calculation. Ultrasoft pseudopotential Pb.pz-d-van.UPF has been used, with a kinetic energy cutoff ecutwfc = 30.0 Ry. Kpoint selection: 11x11x11. Energy minimization of fcc Pb yields the equilibrium lattice parameter of a = 4.800 Å. 

Ref. 3.4     R. Stedman, L. Almqvist, G. Nilsson, and G. Raunio, Dispersion Relations for Phonons in Lead at 80 and 300°K, Phys Rev. 162, 545 (1967)

Crystal Structures

Generalized Stacking Fault Energy

    Stacking fault along [101] and [121] directions

    Lead gamma surface calculated with the EAM potential

    Comparison of ab initio and EAM calculations of SF energies (F.C.C. Pb, a = 4.8905 Å)

Deformation Path

    The Bain path

    Engergy contours along the Bain deformation path (EAM calculations, Lead)

    Comparison of ab intio and EAM calculations along the Bain path

Surface Relaxation 

Liquid Structure

    Liquid density: EAM vs. experiment

Ref. 8.1     L.W. Wang, Q. Wang, A.P. Xian and K.Q. Lu, Precise measurement of the densities of liquid Bi, Sn, Pb and Sb,  J. Phys.: Condens. Matter 15 777 (2003) (10.635 g/cm3)

Ref. 8.2     http://en.wikipedia.org/wiki/Lead (liquid density at M.P. 10.66 g/cm3)

    Pair correlation functions

    Structure factors

    Comparison of experimental structure factors and EAM calculations      

Ref. 8.1. Y. Waseda, The Structure of Non-Crystalline Materials (McGraw-Hill, New York, 1980).

Liquid Dynamics

    Diffusivity based on the Einstein relation

    Diffusivity based on the Green-Kubo relation

    van Hove self-correlation functions at different temperatures

    Intermediate scattering functions F(q,t)  and dynamic structure factors S(q,w)