Towards a universal embedded atom method interatomic potential for pure metals
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 8 (2015) no. 2, pp. 230-249.

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A new interatomic potential for metals based on the embedded atom method is proposed in this paper. Some approximation of electron density distribution is suggested from the basic principles of quantum mechanics. The functional form of the electron density distribution includes two adjustable parameters. The form of this distribution defines the pair potential and, in part, the form of embedding energy function. The parameters are determined empirically by fitting to the equilibrium lattice constant, cohesion energy, vacancy formation energy, low index surface energy and elastic constants. Potential parameters for 27 metals (10 fcc metals, 9 bcc metals and 8 hcp metals) are presented. Potential is expressed by simple functions and can be used in molecular dynamics simulations of large atomic systems. PACS: 34.20.Cf, 61.50.Ah
Keywords: interatomic potential, embedded atom method.
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Viktor E. Zalizniak; Oleg A. Zolotov. Towards a universal embedded atom method interatomic potential for pure metals. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 8 (2015) no. 2, pp. 230-249. http://geodesic.mathdoc.fr/item/JSFU_2015_8_2_a13/

[1] M. S. Daw, M. I. Baskes, “Semiempirical, quantum mechanical calculation of hydrogen embrittlement in metals”, Phys. Rev. Letters, 50:17 (1983), 1285 | DOI

[2] M. S. Daw, M. I. Baskes, “Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals”, Phys. Rev. B, 29 (1983), 6443 | DOI

[3] H. W. Sheng, M. J. Kramer, A. Cadien, T. Fujita, M. W. Chen, “Highly optimized embedded-atom-method potentials for fourteen fcc metals”, Phys. Rev. B, 83:13 (2011), 134118 | DOI

[4] I. A. Hijazi, Y. H. Park, “Consistent analytic embedded atom potential for face-centered cubic metals and alloys”, J. Mater. Sci. Technol., 25:6 (2009), 835–846

[5] X. D. Dai, Y. Kong, J. H. Li, B. X. Lin, “Extended Finnis-Sinclair potential for bss and fss metals and alloys”, J. Phys.: Condensed Metter, 18 (2006), 4527 | DOI

[6] B.-J. Lee, M. I. Baskes, H. Kim, Y. K. Cho, “Second nearest-neighbor modified embedded atom method potentials for bcc transition metals”, Phys. Rev. B, 64 (2001), 184102 | DOI

[7] S. J. Plimpton, A. P. Thompson, “Computational aspects of many-body potentials”, MRS Bulletin, 37:5 (2012), 513–521 | DOI

[8] R. B. Wilson, D. M. Riffe, “An embedded-atom-method model for alkali-metal vibrations”, J. Phys.: Condens. Matter, 24 (2012), 335401 | DOI

[9] R. Pasianot, E. J. Savino, “Embedded-atom-method interatomic potentials for hcp metals”, Phys. Rev. B, 45 (1992), 12704–12710 | DOI

[10] F. Cleri, V. Rosato, “Tight-binding potentials for transition metals and alloys”, Phys. Rev. B, 48 (1993), 22–33 | DOI

[11] S. Chen, J. Xu, H. Zhang, “A new scheme of many-body potentials for hcp metals”, Computational Materials Science, 29 (2004), 428–436 | DOI

[12] M. I. Baskes, R. A. Johnson, “Modified embedded atom potentials for hcp metals”, Model. Simul. Mater. Sci. Eng., 2 (1994), 147–163 | DOI

[13] L. D. Landau, E. M. Lifshitz, Course of Theoretical Physics, v. 3, Quantum Mechanics: Non-Relativistic Theory, Pergamon Press, Oxford, 1977

[14] S. M. Foiles, M. I. Baskes, M. S. Daw, “Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys”, Phys. Rev. B, 33:12 (1986), 7983 | DOI

[15] C. Kittel, Introduction to solid state physics, Wiley, New York, 1996

[16] F. R. de Boer, R. Boom, W. C. M. Mattens, A. R. Miedema, A. K. Niessen, Cohesion in metals, v. 1, North Holland, Amsterdam, 1988

[17] P. Ziesche, J. P. Perdew, C. Fiolhais, “Spherical voids in the stabilized jellium model: Rigorous theorems and Padé representation of the void-formation energy”, Phys. Rev. B, 49:12 (1994), 7916–7928 | DOI

[18] P. Ehrhart, P. Jung, H. Schultz, H. Ullmaier, Atomic defects in metals, Landolt–Bernstein — Group III, 25, ed. H. Ullmaier, Springer-Verlag, Berlin, 1991

[19] H-E. Schaefer, “Investigation of thermal equilibrium vacancies in metals by positron annihilation”, Phys. Status Solidi A, 102:1 (1987), 4–65

[20] H. Ledbetter, S. Kim, “Monocrystal elastic constants and derived properties of the cubic and the hexagonal elements”, Handbook of elastic properties of solids, liquids, and gases, v. 2, Academic Press, 2001

[21] P. Sisoda, M. P. Verma, “Shear moduli of polycrystalline cubic elements”, J. Phys. Chem. Solids, 50 (1989), 223–224 | DOI

[22] H. Ogi, H. Ledbetter, S. Kim, M. Hirao, “Contactless mode-selective resonance ultrasound spectroscopy: electromagnetic acoustic resonance”, J. Acoust. Soc. Am., 106 (1999), 660–665 | DOI

[23] R. O. Simmons, H. Wang, Single crystal elastic constants and calculated aggregate properties: a Handbook, MIT Press, Cambridge, MA, 1977

[24] W. Wycisk, M. Feller-Kniepmeier, “Quenching experiments in high purity Ni”, J. Nucl. Mater, 69/70 (1978), 616–619 | DOI

[25] R. W. Balluffi, “Vacancy defect mobilities and binding energies obtained from annealing studies”, J. Nucl. Mater, 69/70 (1978), 240–263 | DOI

[26] P. A. Korzhavyi, I. A. Abrikosov, B. Johansson, A. V. Ruban, H. L. Skriver, “First-principles calculations of the vacancy formation energy in transition and noble metals”, Phys. Rev. B, 59:18 (1999), 11693–11703 | DOI

[27] J. H. Rose, J. R. Smith, F. Guinea, J. Ferrante, “Universal features of the equation of state of metals”, Phys. Rev. B, 29 (1984), 2963–2969 | DOI

[28] R. Feder, “Equilibrium defect concentration in crystalline lithium”, Phys. Rev. B, 2:4 (1970), 828 | DOI | MR

[29] R. Feder, H. P. Charbnau, “Equilibrium defect concentration in crystalline sodium”, Phys. Rev., 149:2 (1966), 464 | DOI

[30] D. K. C. MacDonald, “Self diffusion in the alkali metals”, J. Chem. Phys., 21:1 (1953), 177 | DOI

[31] C. Janot, B. George, P. Delcroix, “Point defects in vanadium investigated by Mossbauer spectroscopy and positron annihilation”, J. Phys. F: Met. Phys., 12:1 (1982), 47 | DOI

[32] M. Puska, M. Nieminen, “Point defects in solids”, Density functional methods in chemistry and materials science, ed. M. Springborg, Wiley, New York, 1997

[33] K. Maier, M. Peo, B. Saile, S. H. Ehaefer, A. Seeger, “High-temperature positron annihilation and vacancy formation in refractory metals”, Phil. Mag. A, 40:5 (1979), 701 | DOI

[34] B. J. Lee, M. I. Baskes, H. Kim, Y. K. Cho, “Second nearest-neighbor modified embedded atom method potentials for bcc transition metals”, Phys. Rev. B, 64:18 (2001), 184102 | DOI

[35] R. A. Felice, J. Trivisonno, D. E. Shuele, “Temperature and pressure dependence of the single-crystal elastic constants of ${}^{6}Li$ and natural lithium”, Phys. Rev. B, 16:12 (1977), 5173 | DOI

[36] R. H. Martinson, “Variation of the elastic constants of sodium with temperature and pressure”, Phys. Rev., 178:3 (1969), 902 | DOI

[37] M. W. Rarquardt, J. Trivisonno, “Low temperature elastic constants of potassium”, J. Phys. and Chem. Solids, 26:2 (1965), 273 | DOI

[38] D. R. Lide, Handbook of chemistry and physics, CRC Press, Boca Raton, Fl, 2000

[39] D. K. C. MacDonald, “Self diffusion in the alkali metals”, J. Chem. Phys., 21 (1953), 177 | DOI

[40] W. Adlhart, G. Fritsch, E. Lüscher, “Equilibrium defect properties of sodium in the high temperature range”, J. Phys. and Chem. Solids, 36:12 (1975), 1405 | DOI

[41] J. N. Mundy, T. E. Miller, R. J. Porte, “Self-diffusion in potassium”, Phys. Rev. B, 3:8 (1971), 2445 | DOI

[42] M. Doyama, J. S. Koehler, “The relation between the formation energy of a vacancy and the nearest neighbor interactions in pure metals and liquid metals”, Acta Metall, 24:9 (1976), 871–879 | DOI

[43] E. Hashimoto, E. A. Smirnov, T. Kino, “Temperature dependence of the Doppler-broadened lineshape of positron annihilation in $\alpha$-Ti”, J. Phys. F: Met. Phys., 14:10 (1984), L215 | DOI

[44] V. O. Shestopal, “Specific heat and vacancy formation in titanium at high temperatures”, Sov. Phys. Solid State, 7 (1966), 2798–2800

[45] G. M. Hood, R. J. Schultz, N. Matsuura, “A positron annihilation spectroscopy study of Fe-free $\alpha$-Zr: Thermal equilibrium and irradiation effects”, J. Nucl. Mater, 226:1–2 (1995), 260–262 | DOI

[46] O. Le Bacq, F. Willaime, A. Pasturel, “Unrelaxed vacancy formation energies in group-IV elements calculated by the full-potential linear muffin-tin orbital method: Invariance with crystal structure”, Phys. Rev. B, 59:13 (1999), 8508–8515 | DOI

[47] G. M. Hood, R. J. Schultz, “Temperature dependence of positron annihilation in $\alpha$-Hf”, Materials Science Forum (Beijing, China, 1995), AECL (Series), 175–178, 375–378

[48] I. K. Mackenzie, J. Fabian, “Evidence from positron annihilation of anomalously low vacancy density in some metals with low melting points”, Can. J. Phys., 58:11 (1980), 1635–1639

[49] E. A. Brandes, G. B. Brook, Smithells metal reference book, Butterworths, Oxford, 1992, 15–16

[50] H. Ogi, S. Kai, H. Ledbetter, R. Tarumi, M. Hirao, K. Takashima, “Titanium high-temperature elastic constants through the hcp-bcc phase transformation”, Acta Materialia, 52 (2004), 2075–2080 | DOI

[51] J. F. Smith, J. A. Gjevre, “Elastic constants of yttrium single crystals in the temperature range 4.2–400K”, J. Appl. Phys., 31 (1960), 645–647 | DOI

[52] E. Fisher, C. Renken, “Adiabatic elastic moduli of single crystal alpha zirconium”, J. Nucl. Mater., 4 (1961), 311–316 | DOI

[53] R. W. Ferris, M. L. Shepard, J. F. Smith, “Elastic constants of thallium single crystals in the temperature range 4.2–300K”, J. Appl. Phys., 34 (1963), 768–770 | DOI

[54] W. R. Tyson, W. A. Miller, “Surface free energies of solid metals: Estimation from liquid surface tension measurements”, Surface Science, 62:1 (1977), 267 | DOI

[55] V. Y. Gankin, Y. V. Gankin, General Chemistry Textbook. Chapter 11. Physical and chemical properties of substances/Theory of Metallic Bonding, , Institute of the Theoretical Chemistry http://itchem.com/theory_of_metallic_bonding