Ca

EAM Potential: Ca.lammps.eam

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Properties Predicted by EAM

Ref. 2.1    K.M. Andersson, R.L. Johnston, and J.N. Murrell, Empirical Potential-energy Function for Calcium Solids and Clusters, Phys. Rev. B 49, 3089 (1994)

Ref. 2.2    J.E. Hearn, R.L. Johnson, S.L. Leoni and J.N. Murrel, Global Potentials for Calcium and Strontium solids, J. Chem. Soc., Faraday Trans.,  92, 425 (1996) (postscript file)

Ref. 2.3    C. Stassis, J. Zaretsky, D.K. Misemer, H.L. Skriver, B.N. Harmon and R.M. Nicklow, Lattice Dynamics of fcc Ca, Phys. Rev. B 27, 3303 (1983)

Ref. 2.4    M. Heiroth, U. Buchenau, H.R. Schober and J. Evers, Lattice Dynamics of fcc and bcc Calcium,  Phys. Rev. B 34, 6681 (1986)

Ref. 2.5    M.S. Anderson, C.A. Swenson, and D.T. Peterson, Experimental Equations of State for Calcium, Strontium and Barium Metals to 20 kbar from 4 to 295 K, Phys. Rev. B 41, 3329 (1990)

Ref. 2.6    S.N. Vaidya and G.C. Kennedy, J. Phys. Chem. Solids 31, 2329 (1970)

Ref. 2.7    http://www.webelements.com/calcium/physics.html

Ref. 2.9    H.L. Skriver and N.M. Rosengaard, Surface energy and work function of elemental metals, Phys. Rev B 46, 7157 (1992)

Ref. 2.10  MD simulation of liquid-solid phase equilibrium with an NPH ensemble. 

Ref. 2.11  Ab initio calculation in the present work.

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.

     Elastic Constants

Ref. 4.1     G. Simons and H. Wang, Single Crystal Elastic Constants and Calculated Aggregate Properties (MIT Press, Cambridge, MA, 1977)

Ref. 4.2    The anomalous elastic constant behavior may contribute to the phase complexity of Ca under pressure.  

    Phonon Dispersion Curves

Ref. 5.1     C. Stassis, J. Zaretsky, D.K. Misemer, H.L. Skriver, B.N. Harmon and R.M. Nicklow, Lattice Dynamics of fcc Ca, Phys. Rev. B 27, 3303 (1983) 

Ref. 5.2     PWSCF calculation. Ultrasoft pseudopotential Ca.pw91-nsp-van.UPF has been used, with a kinetic energy cutoff ecutwfc = 50.0 Ry. Kpoint selection: 11x11x11. Energy minimization of fcc Ca yields a lattice parameter of a = 5.525 Å. 

Crystal Structures

Generalized Stacking Fault Energy

    Stacking fault along [101] and [121] directions

    Calcium gamma surface evaluated with the EAM potential

      Comparison of ab initio and EAM calculations of stacking fault energies (Ca, a = 5.5884 A )

Deformation Path

    The Bain path

    Engergy contours along the Bain path (EAM calculations, Ca)

    Comparison of ab intio and EAM calculations along the Bain path

Surface Relaxation 

Liquid Structure

    Liquid density: EAM vs. experiment

Ref. 8.1    S. Hiemstra, D. Prins, G. Gabrielse and J. B. Van Zytveld, Densities of liquid metals: calcium, strontium, barium,  Physics and Chemistry of Liquids, 6, 271 (1977)

Ref. 8.2    http://en.wikipedia.org/wiki/Calcium

    Pair correlation functions

    Structure factors

    Comparison of experimental structure factors and EAM calculations      

Ref. 8.2. Y. Waseda, The Structure of Non-Crystalline Materials (McGraw-Hill, New York, 1980).

Liquid Dynamics

    Diffusivity based on the Einstein relation

 Ref. 9.1. A.V. Gorshkov, Correlations of the self-diffusion coefficients and viscosity of elemental melts with properties of     elements,     Inorganic Materials, 2, 218 (2000) Doi: 10.1007/BF02758020

    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)