SpringerLink
Log in

Computer Experiments on Self-diffusion Coefficients of Some Liquid Metals

  • Published:
Journal of Phase Equilibria and Diffusion Aims and scope Submit manuscript

Abstract

The available experimental self-diffusion coefficients of twenty-two liquid elements near their melting temperatures are compared with the calculated data by the first-principal dynamics simulation. The holistic evaluation shows that the calculated self-diffusion coefficients are in reasonable agreement with the experimental data. For liquid metals with loose-packed structure, the self-diffusion coefficient decreases in general with the increase of packing fraction. For liquid metals with close-packed structure in which the coordination number is larger than 11.5, the self-diffusion coefficient fluctuates around 2.0×10-9 m2s-1, except for liquid Al, Ti and Li of which the self-diffusion coefficients are anomalously large. The packing fraction can only partially account for the self-diffusion coefficient of liquid metals.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Reference

  1. G. Kaptay, G. Kaptay, A new theoretical equation for temperature dependent self-diffusion coefficients of pure liquid metals, Int. J. Mater. Res., 2008, 99, p 14–17

    Article  Google Scholar 

  2. M. Asta, C. Beckermann, A. Karma, W. Kurz, R. Napolitano, M. Plapp, G. Purdy, M. Rappaz, and R. Trivedi, M. Asta, C. Beckermann, A. Karma, W. Kurz, R. Napolitano, M. Plapp, G. Purdy, M. Rappaz, and R. Trivedi, Solidification microstructures and solid-state parallels: Recent developments, future directions, Acta Mater., 2009, 57, p 941–971

    Article  ADS  Google Scholar 

  3. W.H. Sun, L.J. Zhang, M. Wei, Y. Du, and B.Y. Huang, W.H. Sun, L.J. Zhang, M. Wei, Y. Du, and B.Y. Huang, Effect of liquid diffusion coefficients on microstructure evolution during solidification of Al356.1 alloy, Trans. Nonferrous Met. Soc. China, 2013, 23, p 3722–3728

    Article  Google Scholar 

  4. M.H. Avazkonandeh-Gharavol, M. Haddad-Sabzevar, and H. Fredriksson, M.H. Avazkonandeh-Gharavol, M. Haddad-Sabzevar, and H. Fredriksson, Analysis of phase diagram and diffusion coefficient for modeling of microsegregation, J. Mater. Sci., 2017, 52, p 1446–1460

    Article  ADS  Google Scholar 

  5. H. Cheng, Y.J. Lue, and M. Chen, H. Cheng, Y.J. Lue, and M. Chen, Interdiffusion in liquid Al-Cu and Ni-Cu alloys, J. Chem. Phys., 2009, 131, p 38

    Article  Google Scholar 

  6. E.L. Cussler, Diffusion: Mass Transfer in Fluid Systems, Vol. 3. Cambridge University Press, Cambridge, 2009.

    Book  Google Scholar 

  7. S.M. Chathoth, B. Damaschke, T. Unruh, and K. Samwer, S.M. Chathoth, B. Damaschke, T. Unruh, and K. Samwer, Influence of structural changes on diffusion in liquid germanium, Appl. Phys. Lett., 2009, 94, p 339

    Article  Google Scholar 

  8. F. Demmel, L. Hennet, S. Brassamin, D.R. Neuville, J. Kozaily, and M.M. Koza, F. Demmel, L. Hennet, S. Brassamin, D.R. Neuville, J. Kozaily, and M.M. Koza, Nickel self-diffusion in a liquid and undercooled NiSi alloy, Phys. Rev. B, 2016, 94, p 014206

    Article  ADS  Google Scholar 

  9. P. Ascarelli, and A. Paskin, P. Ascarelli, and A. Paskin, Dense-gas formulation of self-diffusion of liquid metals, Phys. Rev, 1968, 165(1), p 222–224

    Article  ADS  Google Scholar 

  10. V.G. Postovalov, I.Z. Sattybaev, E.P. Romanov, On the Theory of the Thermophysical Properties of Liquid Nontransition Metals, Russ. Metall. pp. 153-161 (2015)

  11. P. Protopapas, H.C. Andersen, and N.A.D. Parlee, P. Protopapas, H.C. Andersen, and N.A.D. Parlee, Theory of transport in liquid metals. I. Calculation of self-diffusion coefficients, J. Chem. Phys., 1973, 59, p 15–25

    Article  ADS  Google Scholar 

  12. A.S. Chauhan, R. Ravi, and R.P. Chhabra, A.S. Chauhan, R. Ravi, and R.P. Chhabra, Self-diffusion in liquid metals, Chem. Phys., 2000, 252, p 227–236

    Article  Google Scholar 

  13. L.W. Wang, L.W. Wang, Atomistics of self-diffusion in liquid metals, EPJ Web of Conf, 2017, 151, p 02004

    Article  Google Scholar 

  14. J.H. Lee, S. Liu, H. Miyahara, and R. Trivedi, J.H. Lee, S. Liu, H. Miyahara, and R. Trivedi, Diffusion-coefficient measurements in liquid metallic alloys, Metall. Mater. Trans. B, 2004, 35, p 909–917

    Article  Google Scholar 

  15. T. Scopigno, G. Ruocco, and F. Sette, T. Scopigno, G. Ruocco, and F. Sette, Microscopic dynamics in liquid metals: The experimental point of view, Rev. Mod. Phys., 2005, 77, p 881–933

    Article  ADS  Google Scholar 

  16. E.V. Levchenko, and A.V. Evteev, E.V. Levchenko, and A.V. Evteev, Insight into interrelation between single-particle and collective diffusion in binary melts, Phys. A, 2018, 490, p 1446–1453

    Article  MathSciNet  Google Scholar 

  17. Y.J. Lv, and M. Chen, Y.J. Lv, and M. Chen, Thermophysical properties of undercooled alloys: an overview of the molecular simulation approaches, Int. J. Mol. Sci., 2011, 12, p 278–316

    Article  ADS  Google Scholar 

  18. Meyer, The measurement of self-diffusion coefficients in liquid metals with quasielastic neutron scattering, in: B. Frick, M.M. Koza, M. Boehm, H. Mutka (Eds.) Qens/Wins 2014 - 11th International Conference on Inelastic Neutron Spectrometers.

  19. T. Iida, and R.I.L. Guthrie, The Physical Properties of Liquid Metals. Clarendon Press, Oxford, 1988.

    Google Scholar 

  20. C.A. Zhu, Y. Geng, and B. Zhang, C.A. Zhu, Y. Geng, and B. Zhang, Diffusion in liquid metals, Sci. China Ser. A, 2012, 42, p 619–630

    Google Scholar 

  21. Y. Han, C. Ban, Q. Ba, and J. Cui, Y. Han, C. Ban, Q. Ba, and J. Cui, Developments on measuring methods and theoretical studies of diffusion in liquid metals, Mater. Rev., 2004, 18, p 10–13

    Google Scholar 

  22. A. Rahman, A. Rahman, Liquid structure and self-diffusion, J. Chem. Phys., 1966, 45, p 2585–2592

    Article  ADS  Google Scholar 

  23. B.J. Alder, and T.E. Wainwright, B.J. Alder, and T.E. Wainwright, Velocity autocorrelations for hard spheres, Phys. Rev. Lett., 1967, 18, p 988–990

    Article  ADS  Google Scholar 

  24. L. Verlet, L. Verlet, Computer “Experiments” on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules, Phys. Rev., 1967, 159, p 98–103

    Article  ADS  Google Scholar 

  25. T. Gaskell, T. Gaskell, Self-diffusion in liquid metals: A generalized Stokes-Einstein equation, J. Non-Cryst. Solids, 1984, 61–2, p 913–918

    Article  ADS  Google Scholar 

  26. B.J. Alder, and W.E. Alley, B.J. Alder, and W.E. Alley, Long-Time correlation effects on displacement distributions, J. Statist. Phys., 1978, 19, p 341–347

    Article  ADS  Google Scholar 

  27. A.C. Wright, A.C. Wright, Can a periodic boundary model reproduce the longer-range density fluctuations in a real amorphous material?, J. Non-Cryst. Solids, 2017, 461, p 113–128

    Article  ADS  Google Scholar 

  28. F.J. Alexander, A.L. Garcia, and B.J. Alder, F.J. Alexander, A.L. Garcia, and B.J. Alder, Cell size dependence of transport coefficients in stochastic particle algorithms, Phys. Fluids, 1998, 10, p 1540–1542

    Article  ADS  Google Scholar 

  29. R.L. McGreevy, and L. Pusztai, R.L. McGreevy, and L. Pusztai, Reverse Monte Carlo simulation: a new technique for the determination of disordered structures, Mol. Simulat., 1988, 1, p 359–367

    Article  Google Scholar 

  30. T. Iida, R. Guthrie, and N. Tripathi, T. Iida, R. Guthrie, and N. Tripathi, A model for accurate predictions of self-diffusivities in liquid metals, semimetals, and semiconductors, Metall. Mater. Trans. B, 2006, 37, p 559–564

    Article  Google Scholar 

  31. P.G. Sanders, and M.J. Aziz, P.G. Sanders, and M.J. Aziz, Self-diffusivity of liquid silicon measured by pulsed laser melting, J. Appl. Phys., 1999, 86, p 4258–4261

    Article  ADS  Google Scholar 

  32. G. Kresse, and J. Hafner, G. Kresse, and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B, 1993, 47, p 558–561

    Article  ADS  Google Scholar 

  33. G. Kresse, and D. Joubert, G. Kresse, and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B, 1999, 59, p 1758–1775

    Article  ADS  Google Scholar 

  34. P.E. Blöchl, P.E. Blöchl, Projector augmented-wave method, Phys. Rev. B, 1994, 50, p 17953–17979

    Article  ADS  Google Scholar 

  35. J.P. Perdew, and Y. Wang, J.P. Perdew, and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B, 1992, 45, p 13244–13249

    Article  ADS  Google Scholar 

  36. D. Keffer, The working man’s guide to obtaining self diffusion coefficients from molecular dynamics simulations, Department of Chemical Engineering. University of Tennessee, Knoxville, 2001.

    Google Scholar 

  37. A. Bogicevic, L.B. Hansen, and B.I. Lundqvist, A. Bogicevic, L.B. Hansen, and B.I. Lundqvist, Simulations of atomic structure, dynamics, and self-diffusion in liquid Au, Phys. Rev. E, 1997, 55(5), p 5535–5545

    Article  ADS  Google Scholar 

  38. S. Munejiri, F. Shimojo, K. Hoshino, and T. Itami, S. Munejiri, F. Shimojo, K. Hoshino, and T. Itami, Structure and self-diffusion of liquid germanium studied by a first-principles molecular-dynamics simulation, J. Non. Cryst. Solids, 2002, 312–314, p 182–186

    Article  ADS  Google Scholar 

  39. W. Yu, Z.Q. Wang, and D. Stroud, W. Yu, Z.Q. Wang, and D. Stroud, Empirical molecular-dynamics study of diffusion in liquid semiconductors, Phys. Rev. B, 1996, 54, p 13946–13954

    Article  ADS  Google Scholar 

  40. J.R. Chelikowsky, N. Troullier, and N. Binggeli, J.R. Chelikowsky, N. Troullier, and N. Binggeli, First-principles simulation of liquid silicon using Langevin dynamics with quantum interatomic forces, Phys. Rev. B, 1994, 49, p 114–119

    Article  ADS  Google Scholar 

  41. I. Stich, R. Car, and M. Parrinello, I. Stich, R. Car, and M. Parrinello, Structural, bonding, dynamical, and electronic properties of liquid silicon: An ab initio molecular-dynamics study, Phys. Rev. B, 1991, 44, p 4262–4274

    Article  ADS  Google Scholar 

  42. N. Jakse, and A. Pasturel, N. Jakse, and A. Pasturel, Liquid Aluminum: Atomic diffusion and viscosity from ab initio molecular dynamics, Sci. Rep., 2013, 3, p 1–8

    Article  MATH  Google Scholar 

  43. J.S. Murday, and R.M. Cotts, J.S. Murday, and R.M. Cotts, Self-diffusion coefficient of liquid lithium, J. Chem. Phys., 1968, 48, p 4938

    Article  ADS  Google Scholar 

  44. R.E. Meyer, and N.H. Nachtrieb, R.E. Meyer, and N.H. Nachtrieb, Self-diffusion of liquid sodium, J. Chem. Phys., 1955, 23, p 1851

    Article  ADS  Google Scholar 

  45. F. Demmel, D. Szubrin, W.-C. Pilgrim, and C. Morkel, F. Demmel, D. Szubrin, W.-C. Pilgrim, and C. Morkel, Diffusion in liquid aluminium probed by quasielastic neutron scattering, Phys. Rev. B, 2011, 84, p 014307

    Article  ADS  Google Scholar 

  46. J. Rohlin, and A. Lodding, J. Rohlin, and A. Lodding, Selbstdiffusion in geschmolzenem Kaliummetall, Zeitschrift Für Naturforschung A, 1962, 17(12), p 1081–1085

    Article  ADS  Google Scholar 

  47. A. Meyer, J. Horbach, O. Heinen, D. Holland-Moritz, and T. Unruh, A. Meyer, J. Horbach, O. Heinen, D. Holland-Moritz, and T. Unruh, Self diffusion in liquid titanium: quasielastic neutron scattering and molecular dynamics simulation, Defect Diff. Forum, 2009, 289–292, p 609–614

    Article  Google Scholar 

  48. A. Meyer, S. Stüber, D. Holland-Moritz, O. Heinen, and T. Unruh, A. Meyer, S. Stüber, D. Holland-Moritz, O. Heinen, and T. Unruh, Determination of self-diffusion coefficients by quasielastic neutron scattering measurements of levitated Ni droplets, Phys. Rev. B, 2008, 77, p 092201

    Article  ADS  Google Scholar 

  49. A. Meyer, A. Meyer, Self-diffusion in liquid copper as seen by quasielastic neutron scattering, Phys. Rev. B, 2010, 81, p 012102

    Article  ADS  Google Scholar 

  50. N.H. Nachtrieb, E. Fraga, and C. Wahl, N.H. Nachtrieb, E. Fraga, and C. Wahl, Self-diffusion of liquid zinc, J. Phys. Chem., 1963, 67, p 2353

    Article  Google Scholar 

  51. J. Petit, and N.H. Nachtrieb, J. Petit, and N.H. Nachtrieb, Self-diffusion in liquid gallium, J. Chem. Phys., 1956, 24, p 1027

    Article  ADS  Google Scholar 

  52. S.M. Chathoth, B. Damaschke, T. Unruh, and K. Samwer, S.M. Chathoth, B. Damaschke, T. Unruh, and K. Samwer, Influence of structural changes on diffusion in liquid germanium, Appl. Phys. Lett., 2009, 94, p 221906

    Article  ADS  Google Scholar 

  53. A. Lodding, A. Lodding, Selbstdiffusion in geschmolzenem Indiummetall, Zeitschrift Für Naturforschung A, 1956, 11, p 200–203

    Article  ADS  Google Scholar 

  54. A. Bruson, and M. Gerl, A. Bruson, and M. Gerl, Diffusion coefficient of 113Sn, 124Sb, 110mAg, and 195Au in liquid Sn, Phys. Rev. B, 1980, 21, p 5447–5454

    Article  ADS  Google Scholar 

  55. N.H. Nachtrieb, and J. Petit, N.H. Nachtrieb, and J. Petit, Self-diffusion in liquid mercury, J. Chem. Phys., 1956, 24, p 746

    Article  ADS  Google Scholar 

  56. R.E. Barras, H.A. Walls, and A.L. Hines, R.E. Barras, H.A. Walls, and A.L. Hines, Liquid thallium self-diffusion measurements, Metall. Trans. B, 1975, 6, p 347–348

    Article  Google Scholar 

  57. G. Mathiak, A. Griesche, K.H. Kraatz, and G. Frohberg, G. Mathiak, A. Griesche, K.H. Kraatz, and G. Frohberg, Diffusion in liquid metals, J. Non. Cryst. Solids, 1996, 205, p 412–416

    Article  ADS  Google Scholar 

  58. F. Kargl, E. Sondermann, H. Weis, and A. Meyer, F. Kargl, E. Sondermann, H. Weis, and A. Meyer, Impact of convective flow on long-capillary chemical diffusion studies of liquid binary alloys, High Temp. High Press., 2013, 42, p 3–21

    Google Scholar 

  59. R.J. Reynik, R.J. Reynik, Self-diffusion in liquid metals, Appl. Phys. Lett., 1966, 9, p 239

    Article  ADS  Google Scholar 

  60. G. Mathiak, A. Griesche, K.H. Kraatz, and G. Frohberg, G. Mathiak, A. Griesche, K.H. Kraatz, and G. Frohberg, Diffusion in liquid metals, J. Non Cryst. Solids, 1996, 205–207, p 412–416

    Article  ADS  Google Scholar 

  61. Y.Y. Ju, Q.M. Zhang, Z.Z. Gong, and G.F. Ji, Y.Y. Ju, Q.M. Zhang, Z.Z. Gong, and G.F. Ji, Molecular dynamics simulation of self-diffusion coefficients for liquid metals, Chin. Phys. B, 2013, 22, p 083101

    Article  ADS  Google Scholar 

  62. A. De Santis, A. Ercoli, and D. Rocca, A. De Santis, A. Ercoli, and D. Rocca, Negative tails in the velocity correlation function of supercooled liquids, J. Chem. Phys., 2003, 119, p 9661–9666

    Article  ADS  Google Scholar 

  63. D.C. Wallace, D.C. Wallace, Liquid dynamics theory of the velocity autocorrelation function and self-diffusion, Phys. Rev. E, 1998, 58, p 538–545

    Article  ADS  Google Scholar 

  64. X.G. Gong, G.L. Chiarotti, M. Parrinello, and E. Tosatti, X.G. Gong, G.L. Chiarotti, M. Parrinello, and E. Tosatti, Coexistence of monatomic and diatomic molecular fluid character in liquid gallium, Europhysics Lett., 1993, 21, p 469–475

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work is financially supported by the National Natural Science Foundation of China (Grant Nos. 51571132, 51731007, 51701135, 51901117).

Author information

Authors and Affiliations

  1. Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials (Ministry of Education), Shandong University, **an, 250061, China

    Qiqi Sun & **gyu Qin

  2. School of Materials Science and Engineering, Liaocheng University, Liaocheng, 252000, China

    **nxin Li

  3. Shandong Provincial Key Laboratory of High Strength Lightweight Metallic Materials, Advanced Materials Institute, Qilu University of Technology (Shandong Academy of Sciences), **an, 250014, China

    ** Wang

  4. College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan, 030024, People’s Republic of China

    Shaopeng Pan

Authors
  1. Qiqi Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. **gyu Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. **nxin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. ** Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shaopeng Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to **gyu Qin.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, Q., Qin, J., Li, X. et al. Computer Experiments on Self-diffusion Coefficients of Some Liquid Metals. J. Phase Equilib. Diffus. 42, 166–174 (2021). https://doi.org/10.1007/s11669-021-00868-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11669-021-00868-y

Keywords

Search

Navigation