- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Phase-field model of oxidation: Equilibrium

Q. C. Sherman and P. W. Voorhees

  • Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA

PDF

Phys. Rev. E 95, 032801 – Published 2 March, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.032801

Abstract

A phase-field model of an oxide relevant to corrosion resistant alloys for film thicknesses below the Debye length LD, where charge neutrality in the oxide does not occur, is formulated. The phase-field model is validated in the Wagner limit using a sharp interface Gouy-Chapman model for the electrostatic double layer. The phase-field simulations show that equilibrium oxide films below the Wagner limit are charged throughout due to their inability to electrostatically screen charge over the length of the film, L. The character of the defect and charge distribution profiles in the oxide vary depending on whether reduced oxygen adatoms are present on the gas-oxide interface. The Fermi level in the oxide increases for thinner films, approaching the Fermi level of the metal in the limit L/LD→0, which increases the driving force for adsorbed oxygen reduction at the gas-oxide interface.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (53)

  1. R. Mévrel, Mater. Sci. Eng. A 120-121, 13 (1989).
  2. G. Meetham, J. Mater. Sci. 26, 853 (1991).
  3. F. Pettit and G. Meier, in Superalloys, edited by M. Gell, C. Kartovich, R. Bricknel, W. Kent, and J. Radovich (The Metal Society AIME, Warrendale, PA, 1984), p. 651.
  4. A. Velon and I. Olefjord, Oxid. Met. 56, 425 (2001).
  5. C. S. Giggins and F. S. Pettit, J. Electrochem. Soc. 118, 1782 (1971).
  6. T. J. Nijdam, N. M. van der Pers, and W. G. Sloof, Mater. Corros. 57, 269 (2006).
  7. P. Saltykov, O. Fabrichnaya, J. Golczewski, and F. Aldinger, J. Alloys Compd. 381, 99 (2004).
  8. R. T. Wu, R. Zhu, L. T. Wu, Y. M. Nie, R. C. Reed, K. Kawagishi, and H. Harada, Can. Metall. Q. 50, 291 (2011).
  9. B. E. Deal and A. S. Grove, J. Appl. Phys. 36, 3770 (1965).
  10. C. Wagner, Corros. Sci. 13, 23 (1973).
  11. A. Atkinson, Rev. Mod. Phys. 57, 437 (1985).
  12. Z. Xu, K. M. Rosso, and S. Bruemmer, Phys. Chem. Chem. Phys. 14, 14534 (2012).
  13. N. Cabrera and N. F. Mott, Rep. Prog. Phys. 12, 163 (1949).
  14. C. Wagner, Z. Physik. Chem. (B) 21, 25 (1933).
  15. V. Battaglia, J. Electrochem. Soc. 142, 1423 (1995).
  16. N. Provatas and K. Elder, Phase-Field Methods in Materials Science and Engineering, 1st ed. (Wiley-VCH, Weinheim, Germany, 2010).
  17. S. G. Kim, W. T. Kim, and T. Suzuki, Phys. Rev. E 60, 7186 (1999).
  18. I. Steinbach, F. Pezzolla, B. Nestler, M. Seeßelberg, R. Prieler, G. Schmitz, and J. Rezende, Phys. D (Amsterdam, Neth.) 94, 135 (1996).
  19. R. Kobayashi, J. A. Warren, and W. C. Carter, Phys. D (Amsterdam, Neth.) 119, 415 (1998).
  20. M. Asle Zaeem and H. El Kadiri, Comput. Mater. Sci. 89, 122 (2014).
  21. A. T. Fromhold, Oxid. Met. 13, 475 (1979).
  22. J. E. Guyer, W. J. Boettinger, J. A. Warren, and G. B. McFadden, Phys. Rev. E 69, 021603 (2004).
  23. J. E. Guyer, W. J. Boettinger, J. A. Warren, and G. B. McFadden, Phys. Rev. E 69, 021604 (2004).
  24. T.-l. Cheng, Y.-h. Wen, and A. Hawk, J. Phys. Chem. C 118, 1269 (2014).
  25. L. Hong, J.-M. Hu, K. Gerdes, and L.-Q. Chen, J. Power Sources 287, 396 (2015).
  26. K. R. Lawless, Rep. Prog. Phys. 37, 231 (1974).
  27. K. Kliewer and J. Koehler, Phys. Rev. 140, A1226 (1965).
  28. U. Aschauer, P. Bowen, and S. C. Parker, Acta Mater. 57, 4765 (2009).
  29. J. Maier, J. Am. Ceram. Soc. 76, 1212 (1993).
  30. M. H. R. Lankhorst, H. J. M. Bouwmeester, and H. Verweij, J. Am. Ceram. Soc. 80, 2175 (1997).
  31. S. K. Mohapatra and F. A. Kröger, J. Am. Ceram. Soc. 61, 106 (1978).
  32. A. Heuer, T. Nakagawa, M. Azar, D. Hovis, J. Smialek, B. Gleeson, N. Hine, H. Guhl, H.-S. Lee, P. Tangney, W. Foulkes, and M. Finnis, Acta Mater. 61, 6670 (2013).
  33. F. Zhou, T. Maxisch, and G. Ceder, Phys. Rev. Lett. 97, 155704 (2006).
  34. J. Honig, J. Chem. Educ. 43, 76 (1966).
  35. J. J. Quinn and K.-S. Yi, in Solid State Physics: Principles and Modern Applications (Springer, Berlin, 2009), pp. 79–107.
  36. S. Mrowec and Z. Grzesik, J. Phys. Chem. Solids 65, 1651 (2004).
  37. L. B. Loeb, in Static Electrification (Springer, Berlin, 1958), pp. 32–58.
  38. J. Maier, Solid State Ionics 23, 59 (1987).
  39. T. Robert, M. Bartel, and G. Offergeld, Surf. Sci. 33, 123 (1972).
  40. L. Mulay and L. Keys, J. Am. Chem. Soc. 87, 1192 (1965).
  41. A. T. Dinsdale, CALPHAD 15, 317 (1991).
  42. M. Z. Bazant, Acc. Chem. Res. 46, 1144 (2013).
  43. E. Gongadze, S. Petersen, U. Beck, and U. V. Rienen, COMSOL Conference 2009 (Milan) (COMSOL, Milan, Italy, 2009).
  44. D. C. Grahame, Chem. Rev. 41, 441 (1947).
  45. S. L. Wang, R. F. Sekerka, A. A. Wheeler, B. T. Murray, S. R. Coriell, R. J. Braun, and G. B. McFadden, Phys. D (Amsterdam, Neth.) 69, 189 (1993).
  46. J. Eiken, B. Böttger, and I. Steinbach, Phys. Rev. E 73, 066122 (2006).
  47. N. Moelans, Acta Mater. 59, 1077 (2011).
  48. A. A. Wheeler, W. J. Boettinger, and G. B. McFadden, Phys. Rev. A 45, 7424 (1992).
  49. M. Stengel and N. A. Spaldin, Nature (London) 443, 679 (2006).
  50. J. Antula, Phys. Lett. 25, 308 (1967).
  51. L. Y. Chen, 8th Int. Conf. Electron. Packag. Tech. (IEEE, Shanghai, China, 2007).
  52. N. Ashcroft and N. Mermin, Solid State Physics (Saunders College, Philadelphia, PA, 1976).
  53. D. D. MacDonald, Electrochim. Acta 56, 1761 (2011).

Outline

Information

Phys. Rev. E 95, 032801– Published 2 March, 2017
  • Received 2 December 2016
Article part of CHORUS

©2017 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation