SpringerLink
Log in

Physical description of the monoclinic phase of zirconia based on the bond-order characteristic of the Tersoff potential

  • Research Article
  • Published:
Frontiers of Physics Aims and scope Submit manuscript

Abstract

Zirconia has many important phases with Zr coordination varying from six-fold in the orthorhombic phase to eight-fold in the cubic and tetragonal phases. Development of empirical potentials to describe these zirconia phases is an important but long-standing challenge, and it is a bottleneck for theoretical investigation of large zirconia structures. Here, instead of using the standard core—shell model, we developed a new potential for zirconia by combining the long-range Coulomb interaction and bond-order Tersoff model. The bond-order characteristic of the Tersoff potential enables it to be well suited to describe the zirconia phases with different coordination numbers. In particular, the complex monoclinic phase with two inequivalent oxygen atoms, which is difficult to describe with most existing empirical potentials, is well described by this newly developed potential. This potential provides reasonable predictions of most of the static and dynamic properties of various zirconia phases. Besides its clear physical essence, this potential is at least one order of magnitude faster than core—shell based potentials in molecular dynamics simulation. This is because it does not include an ultralight shell that requires an extremely small time step. We also provide potential scripts for the widely used simulation packages GULP and LAMMPS.

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 includes VAT (Canada)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. H. Kisi and C. J. Howard, Crystal structures of zirconia phases and their inter-relation, Key Eng. Mater. 153–154, 1 (1998)

    Article  Google Scholar 

  2. N. P. Padture, M. Gell, and E. H. Jordan, Thermal barrier coatings for gas-turbine engine applications, Science 296(5566), 280 (2002)

    Article  ADS  Google Scholar 

  3. E. H. Kisi and C. J. Howard, in: Zirconia Engineering Ceramics: Old Challenges-new Ideas, Netikon-Zurich: Trans Tech, 1998

    Google Scholar 

  4. H. J. F. Jansen and J. A. Gardner, Total energy calculations for ZrO2, Physica B 150(1–2), 10 (1988)

    Article  Google Scholar 

  5. K. Parlinski, Z. Q. Li, and Y. Kawazoe, First-principles determination of the soft mode in cubic ZrO2, Phys. Rev. Lett. 78(21), 4063 (1997)

    Article  ADS  Google Scholar 

  6. G. Jomard, T. Petit, A. Pasturel, L. Magaud, G. Kresse, and J. Hafner, First-principles calculations to describe zirconia pseudopolymorphs, Phys. Rev. B 59(6), 4044 (1999)

    Article  ADS  Google Scholar 

  7. A. Kuwabara, T. Tohei, T. Yamamoto, and I. Tanaka, Ab initio lattice dynamics and phase transformations of ZrO2, Phys. Rev. B 71(6), 064301 (2005)

    Article  ADS  Google Scholar 

  8. P. Souvatzis and S. P. Rudin, Dynamical stabilization of cubic ZrO2 by phonon-phonon interactions: Ab initio calculations, Phys. Rev. B 78(18), 184304 (2008)

    Article  ADS  Google Scholar 

  9. H. Wu, Y. Duan, K. Liu, D. Lv, L. Qin, L. Shi, and G. Tang, First-principles study of phase transition and band structure of ZrO2 under pressure, J. Alloys Compd. 645, 352 (2015)

    Article  Google Scholar 

  10. C. W. Li, H. L. Smith, T. Lan, J. L. Niedziela, J. A. Munoz, J. B. Keith, L. Mauger, D. L. Abernathy, and B. Fultz, Phonon anharmonicity of monoclinic zirconia and yttrium-stabilized zirconia, Phys. Rev. B 91(14), 144302 (2015)

    Article  ADS  Google Scholar 

  11. G. V. Lewis and C. R. A. Catlow, Potential models for ionic oxides, J. Phys. C 18(6), 1149 (1985)

    Article  ADS  Google Scholar 

  12. M. Born and K. Huang, Dynamical Theory of Crystal Lattices, Oxford: Oxford University Press, 1954

    MATH  Google Scholar 

  13. P. K. Schelling, S. R. Phillpot, and D. Wolf, Mechanism of the cubic-to-tetragonal phase transition in zirconia and yttria-stabilized zirconia by molecular-dynamics simulation, J. Am. Ceram. Soc. 84(7), 1609 (2001)

    Article  Google Scholar 

  14. M. Kilo, C. Argirusis, G. Borchardt, and R. A. Jackson, Oxygen diffusion in yttria stabilised zirconia — experimental results and molecular dynamics calculations, Phys. Chem. Chem. Phys. 5(11), 2219 (2003)

    Article  Google Scholar 

  15. C. Yang, K. Trachenko, S. Hull, I. T. Todorov, and M. T. Dove, Emergence of microstructure and oxygen diffusion in yttrium-stabilized cubic zirconia, Phys. Rev. B 97(18), 184107 (2018)

    Article  ADS  Google Scholar 

  16. J. B. G. Dick and A. W. Overhauser, Theory of the dielectric constants of alkali halide crystals, Phys. Rev. 112(1), 90 (1958)

    Article  ADS  Google Scholar 

  17. A. Dwivedi and A. N. Cormack, A computer simulation study of the defect structure of calcia-stabilized zirconia, Philos. Mag. A 61(1), 1 (1990)

    Article  ADS  Google Scholar 

  18. M. Wilson, U. Schonberger, and M. W. Finnis, Transferable atomistic model to describe the energetics of zirconia, Phys. Rev. B 54(13), 9147 (1996)

    Article  ADS  Google Scholar 

  19. K. C. Lau and B. I. Dunlap, Molecular dynamics simulation of yttria-stabilized zirconia (YSZ) crystalline and amorphous solids, J. Phys.: Condens. Matter 23(3), 035401 (2011)

    ADS  Google Scholar 

  20. F. Shimojo, T. Okabe, F. Tachibana, M. Kobayashi, and H. Okazaki, Molecular dynamics studies of yttria stabilized zirconia (I): Structure and oxygen diffusion, J. Phys. Soc. Jpn. 61(8), 2848 (1992)

    Article  ADS  Google Scholar 

  21. M. Smirnov, A. Mirgorodsky, and R. Guinebretiere, Phenomenological theory of lattice dynamics and polymorphism of ZrO2, Phys. Rev. B 68(10), 104106 (2003)

    Article  ADS  Google Scholar 

  22. S. Fabris, A. T. Paxton, and M. W. Finnis, Relative energetics and structural properties of zirconia using a self-consistent tight-binding model, Phys. Rev. B 61(10), 6617 (2000)

    Article  ADS  Google Scholar 

  23. A. C. T. van Duin, B. V. Merinov, S. S. Jang, and W. A. Goddard, The ReaxFF reactive force field for solid oxide fuel cell systems with application to oxygen ion transport in yttria-stabilized zirconia, J. Phys. Chem. A 112, 3133 (2008)

    Article  Google Scholar 

  24. C. Wang, A. Tharval, and J. R. Kitchin, A density functional theory parameterised neural network model of zirconia, Mol. Simul. 44(8), 623 (2018)

    Article  Google Scholar 

  25. J. Tersoff, New empirical model for the structural properties of silicon, Phys. Rev. Lett. 56(6), 632 (1986)

    Article  ADS  Google Scholar 

  26. O. Ohtaka, H. Fukui, T. Kunisada, T. Fujisawa, K. Funakoshi, W. Utsumi, T. Irifune, K. Kuroda, and T. Kikegawa, Phase relations and equations of state of ZrO2 under high temperature and high pressure, Phys. Rev. B 63(17), 174108 (2001)

    Article  ADS  Google Scholar 

  27. D. Wolf, P. Keblinski, S. R. Phillpot, and J. Eggebrecht, Exact method for the simulation of Coulombic systems by spherically truncated, pairwise r−1 summation, J. Chem. Phys. 110(17), 8254 (1999)

    Article  ADS  Google Scholar 

  28. C. J. Fennell and J. D. Gezelter, Is the Ewald summation still necessary? Pairwise alternatives to the accepted standard for long-range electrostatics, J. Chem. Phys. 124(23), 234104 (2006)

    Article  ADS  Google Scholar 

  29. S. Dai, M. Gharbi, P. Sharma, and H. S. Park, Surface piezoelectricity: Size effects in nanostructures and the emergence of piezoelectricity in non-piezoelectric materials, J. Appl. Phys. 110(10), 104305 (2011)

    Article  ADS  Google Scholar 

  30. R. Agrawal, B. Peng, E. E. Gdoutos, and H. D. Espinosa, Elasticity size effects in ZnO nanowires: A combined experimental-computational approach, Nano Lett. 8(11), 3668 (2008)

    Article  ADS  Google Scholar 

  31. J. Tersoff, New empirical approach for the structure and energy of covalent systems, Phys. Rev. B 37(12), 6991 (1988)

    Article  ADS  Google Scholar 

  32. J. Tersoff, Modeling solid-state chemistry: Interatomic potentials for multicomponent systems, Phys. Rev. B 39(8), 5566 (1989)

    Article  ADS  Google Scholar 

  33. P. M. Morse, Diatomic molecules according to the wave mechanics (II): Vibrational levels, Phys. Rev. 34(1), 57 (1929)

    Article  ADS  MATH  Google Scholar 

  34. W. A. Harrison, Elemetary Electronic Structure, Singapore: World Scientific, 2004

    Book  Google Scholar 

  35. J. D. Gale, GULP: A computer program for the symmetry-adapted simulation of solids, J. Chem. Soc. Faraday Trans. 93(4), 629 (1997)

    Article  Google Scholar 

  36. S. J. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys. 117(1), 1 (1995)

    Article  ADS  MATH  Google Scholar 

  37. A. Christensen and E. A. Carter, First-principles study of the surfaces of zirconia, Phys. Rev. B 58(12), 8050 (1998)

    Article  ADS  Google Scholar 

  38. A. Kokalj, Computer graphics and graphical user interfaces as tools in simulations of matter at the atomic scale, Comput. Mater. Sci. 28(2), 155 (2003)

    Article  Google Scholar 

  39. A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO — the Open Visualization Tool, Model. Simul. Mater. Sci. Eng. 18(1), 015012 (2010)

    Article  ADS  Google Scholar 

  40. A. Eichler and G. Kresse, First-principles calculations for the surface termination of pure and yttria-doped zirconia surfaces, Phys. Rev. B 69(4), 045402 (2004)

    Article  ADS  Google Scholar 

  41. G. Ballabio, M. Bernasconi, F. Pietrucci, and S. Serra, Ab initio study of yttria-stabilized cubic zirconia surfaces, Phys. Rev. B 70(7), 075417 (2004)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The work was supported by the National Natural Science Foundation of China (Grant Nos. 11822206 and 12072182) and Innovation Program of the Shanghai Municipal Education Commission (Grant No. 2017-01-07-00-09-E00019).

Author information

Authors and Affiliations

  1. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200072, China

    Run-Sen Zhang, Ji-Dong He & **-Wu Jiang

  2. State Key Laboratory of Semiconductor Superlattice and Microstructure and Institute of Semiconductor, Chinese Academy of Sciences, Bei**g, 100083, China

    Bing-Shen Wang

Authors
  1. Run-Sen Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ji-Dong He
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bing-Shen Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. **-Wu Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to **-Wu Jiang.

Additional information

ar**v: 2007.13947. This article can also be found at https://doi.org/10.1007/s11467-020-1044-7.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, RS., He, JD., Wang, BS. et al. Physical description of the monoclinic phase of zirconia based on the bond-order characteristic of the Tersoff potential. Front. Phys. 16, 33505 (2021). https://doi.org/10.1007/s11467-020-1044-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11467-020-1044-7

Keywords

Search

Navigation