Skip to main content
SpringerLink
Log in

Development of physics based analytical interatomic potential for palladium-hydride

  • Original Paper
  • Published:
Journal of Molecular Modeling Aims and scope Submit manuscript

Abstract

Palladium hydrides (Pd-H) research is an important topic in materials research with many practical industrial applications. The complex behavior of the Pd-H alloy system such as phase miscibility gap, however, presents a huge challenge for developing reliable computational models. The embedded atom method (EAM) offers an advantage of computational efficiency and being suited to the metal-hydride system. We propose a new EAM interatomic potential for the complete mathematical modeling of palladium hydride. The present interatomic potential well predicts the lattice constant, cohesive energy, bulk modulus, other elastic constants, and stable alloy crystal structures during molecular dynamics simulations. The phase miscibility gap is also accurately predicted for the Pd-H system using the present potential. To our knowledge, only two Pd-H EAM potentials were used for predicting the phase miscibility gap for the PdH system. The predicted values from these works, however, considerably deviated from the experimental result, which hinders further application to the palladium hydride system. The present potential is reliably accurate and can be used to study the Pd-H system with its compete description of the mathematical formalism.

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

Access this article

Log in via an institution

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
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Graham T (1866) On the absorption and dialytic separation of gases by colloid septa. Philos Trans R Soc London 156:399–439

    Article  Google Scholar 

  2. Mueller WM, Blackledge JP, Libowitz GG (1968) Metal hydrides. Academic Press, New York

    Google Scholar 

  3. Povel R, Feucht K, Gelse W, Withalm G (1989) Hydrogen fuel for motorcars. Interdiscip Sci Rev 14:365

    Article  Google Scholar 

  4. Johnson JW as quoted by Troiano AR (1974) Bernstein IM, Thompson AW (eds.) Hydrogen in metals. American Society of Metals, pp 3–5

  5. Anisimkin VI, Kotelyanskii IM, Verardi P, Verona E (1995) Elastic properties of thin film palladium for surface-acoustic-wave (SAW) sensors. Sens Actuators B 23:203–208

    Article  CAS  Google Scholar 

  6. Nygren LA, Leisure RG (1988) Elastic constants of α-phase over the temperature range 4–300 K. Phys Rev B 37:6482

    Article  CAS  Google Scholar 

  7. Hsu DK, Leisure RG (1979) Elastic constants of palladium and ρ-phase palladium hydride between 4 and 300 K. Phys Rev B 20:1339

    Article  CAS  Google Scholar 

  8. Frieske H, Wicke E (1973) Magnetic susceptibility and equilibrium diagram of PdHn Ber. Bunsenges Phys Chem 77:48–52

    Article  CAS  Google Scholar 

  9. Wicke E, Nernst GH (1964) Phase diagram and thermodynamic behavior of the palladium-hydrogen and of the palladium-deuterium system at normal temperature; H/D separation effect. Ber Bunsenges Phys Chem 68:224–235

    Article  CAS  Google Scholar 

  10. Lässer R, Klatt KH (1983) Solubility of hydrogen isotopes in palladium 1983. Phys Rev 28:748

    Article  Google Scholar 

  11. Wicke E, Blaurock J (1987) New experiments on and interpretations of hysteresis effects of Pd-D2 and Pd-H2. J Less-Common Met 130:351–363

    Article  CAS  Google Scholar 

  12. Lässer R, Powell GL (1986) Solubility of H, D, and T in Pd at low concentrations. Phys Rev B 34:578

    Article  Google Scholar 

  13. Chen WC, Heuser BJ (2000) Solubility and kinetic properties of deuterium in single crystal Pd. J Alloys Comp 312:176–180

    Article  CAS  Google Scholar 

  14. McNicholl E-A, Lewis FA (1990) The hydride phase miscibility gap in palladium-rare earth alloys, Platin. Met Rev 34:81–84

    CAS  Google Scholar 

  15. Zhou XW, Zimmerman JA, Wong BM, Hoyt JJ (2008) An embedded-atom method interatomic potential for Pd-H alloy. J Mater Res 23:704–718

    Article  CAS  Google Scholar 

  16. Wolf RJ, Lee MW, Davis RC, Fay PJ, Ray JR (1993) Pressure–composition isotherms for palladium hydride. Phys Rev B 48:12415

    Article  CAS  Google Scholar 

  17. Daw MS, Baskes MI (1983) Semiempirical, quantum mechanical calculation of hydrogen embrittlement in metals. Phys Rev Lett 50:1285

    Article  CAS  Google Scholar 

  18. Foiles SM, Baskes MI, Daw MS (1986) Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys Rev B 33(12):7983

    Article  CAS  Google Scholar 

  19. Hijazi IA, Park YH (2009) Consistent analytic embedded atom potential for face-centered cubic metals and alloys. J Matter Sci Technol 25:835–846

    CAS  Google Scholar 

  20. Foiles S.M. and Hoyt J.J. 2001. Computer simulation of bubble growth in metals due to He (Sandia National Laboratories)

  21. Rose JH, Smith JR, Guinea F, Ferrante J (1984) Universal features of the equation of state of metals. Phys Rev B 29(6):2963

    Article  CAS  Google Scholar 

  22. Morse P (1929) Diatomic molecules according to the wave mechanics. II. Vibrational levels. Phys Rev 34:57–64

    Article  CAS  Google Scholar 

  23. Matsubara T, Matsushita E (1984) Further comment on isotope effect in hydrogen bonded crystal. Progr Theor Phys 67:209–211

    Article  Google Scholar 

  24. Zaluzniak V, Zolotov O (2015) Towards a universal embedded atom method interatomic potential for pure metals. Math Phys 8:230–249

    Google Scholar 

  25. Puska J, Nieminen RM, Manninen M (1981) Atoms embedded in an electron gas: immersion energies. Phys Rev B 24:3037

    Article  CAS  Google Scholar 

  26. Bambakidis G (1981) Metal hydrides. Plenum, New York

    Book  Google Scholar 

  27. Ilawe NV, Zimmerman JA, Wong BM (2015) Breaking badly: DFT-D2 gives sizeable errors for tensile strengths in palladium-hydride solids. J Chem Theory Comput 11:5426–5435

    Article  CAS  Google Scholar 

  28. Schwarz RB, Bach HT, Harms U, Tuggle D (2005) Elastic properties of Pd–hydrogen, Pd–deuterium, and Pd–tritium single crystals. Acta Mater 53:569–580

    Article  CAS  Google Scholar 

  29. Schirber JE, Morosin B (1975) Lattice constants of b-PdHx and b-PdDx with x near 1.0. Phys Rev B 12:117

    Article  CAS  Google Scholar 

  30. Sakamoto Y, Yuwasa K, Hirayama K (1982) X-ray investigation of the absorption of hydrogen by several palladium and nickel solid solution alloys. J Less-Comm Metals 88:115

    Article  CAS  Google Scholar 

  31. Jacobs MHG, Oonk HAJ (2006) The calculation of ternary miscibility gaps using linear contributions method: problems, benchmark systems and an application to (K, Li, Na)Br. Comput Coupling Phase Diag Thermochem 30:185–190

    Article  CAS  Google Scholar 

  32. Emelianko M, Liu Z-K, Dy Q (2006) A new algorithm for the automation of phase diagram calculation. Comput Mater Sci 35:61–74

    Article  Google Scholar 

  33. Lewis FA (1967) The palladium-hydrogen system. Academic, New York

    Google Scholar 

  34. Alefeld G, Völkl J (1978) Hydrogen in metals. Springer, Heidelberg

  35. Antonov VE (2008) Phase transformations, crystal and magnetic structures of high-pressure. J All Comp 330–332:110–116

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical & Aerospace Engineering Department, New Mexico State University, Las Cruces, New Mexico, 88003, USA

    Young Ho Park

  2. Mechanical Engineering Department, Marshal University, Huntington, WV, 25755, USA

    Iyad Hijazi

Authors
  1. Young Ho Park
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Iyad Hijazi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Young Ho Park.

Appendix: EAM potential functions for palladium

Appendix: EAM potential functions for palladium

$$ {\phi}_{Pd}(r)={\displaystyle \sum_{n=1}^{18}{a}_n{\left( r-{r}_0\right)}^n} $$
(A1)

Note the pair potential function is truncated at r cut = 5.35 Å

Table 7 The coefficients for palladium pair potential
Full size table
$$ {f}_{Pd}(r)={r}^8{e}^{-3.16413 r}+{2}^{11}{r}^8{e}^{-6.32826 r} $$
(A2)

The density function f Pd is also truncated at r cut = 5.35 Å. A function of distance g(r) is then modified to

$$ g(r)= g(r)- g\left({r}_{cut}\right)+\frac{r_{cut}}{n}\left(1-{\left(\frac{r}{r_{cut}}\right)}^n\right)\;{g}^{\prime}\left({r}_{r cut}\right) $$
(A3)

with n = 20.

The embedding function F is fitted as follows:

$$ F\left(\rho \right)={\displaystyle \sum_{n=1}^{14}{b}_n{\left(\frac{\rho}{\rho_0}-1\right)}^n} $$
(A4)
Table 8 The coefficients for palladium embedding function
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Park, Y.H., Hijazi, I. Development of physics based analytical interatomic potential for palladium-hydride. J Mol Model 23, 108 (2017). https://doi.org/10.1007/s00894-017-3288-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00894-017-3288-x

Keywords

Search

Navigation