Advertisement

Journal of Materials Science

, Volume 44, Issue 19, pp 5214–5224 | Cite as

Energetic analysis of ferroelectric domain patterns by equivalent inclusion method

  • Y. Y. LiuEmail author
  • J. Y. Li
Ferroelectrics

Abstract

The formation of domain configuration in ferroelectrics is a consequence of energy minimization, and critically depends on their transformation strain and spontaneous polarization. In this article, we develop an energetic analysis on ferroelectric domain patterns using equivalent inclusion method, treating ferroelectric domain as an ellipsoidal inhomogeneous inclusion in a ferroelectric matrix. The potential energy of the domain is calculated in terms of its orientation and shape, and the energy minimizing configurations have been identified. Both tetragonal and rhombohedral crystals have been analyzed, and the lamellar domain configurations as predicted by the compatibility analysis have been recovered. Additional energy minimizing states have also been revealed, including needle type of domains and charged domains. Different contributions of strain compatibility and polarization compatibility have also been analyzed.

Keywords

Domain Wall Spontaneous Polarization Transformation Strain Strain Compatibility Ferroelectric Crystal 

Notes

Acknowledgement

The work is partially supported by NSFC (Approval Nos. 10572124 and 10732100). Liu is also supported by China Scholarship Council Postgraduate Scholarship Program, and Li acknowledges support from NSF (OISE-0820583) and ARO (W911NF-07-1-0410).

References

  1. 1.
    Park SE, Shrout TR (1997) J Appl Phys 82:1804CrossRefGoogle Scholar
  2. 2.
    Park SE, Wada S, Cross LE, Shrout TR (1999) J Appl Phys 86:2746CrossRefGoogle Scholar
  3. 3.
    Wada S, Park SE, Cross LE, Shrout TR (1999) Ferroelectrics 221:147CrossRefGoogle Scholar
  4. 4.
    Wada S, Suzuki S, Noma T, Suzuki T, Osada M, Kakihana M, Park SE, Cross LE, Shrout TR (1999) Jpn J Appl Phys, Part 1 38:5505CrossRefGoogle Scholar
  5. 5.
    Liu D, Li JY (2003) Appl Phys Lett 83:1193CrossRefGoogle Scholar
  6. 6.
    Liu D, Li JY (2004) Appl Phys Lett 84:3930CrossRefGoogle Scholar
  7. 7.
    Liu JJ, Zhou YC, Soh AK, Li JY (2006) Appl Phys Lett 88:032904CrossRefGoogle Scholar
  8. 8.
    Wan Q, Chen C, Shen YP (2006) J Mater Sci 41:2993. doi: https://doi.org/10.1007/s10853-006-6766-6 CrossRefGoogle Scholar
  9. 9.
    Burcsu E, Ravichandran G, Bhattacharya K (2000) Appl Phys Lett 77:1698CrossRefGoogle Scholar
  10. 10.
    Ren XB (2004) Nat Mater 3:91CrossRefGoogle Scholar
  11. 11.
    Shu YC, Yen JH, Shieh J, Yeh JH (2007) Appl Phys Lett 90:172902CrossRefGoogle Scholar
  12. 12.
    Damjanovic D, Budimir M, Davis M, Setter N (2006) J Mater Sci 41:65. doi: https://doi.org/10.1007/s10853-005-5925-5 CrossRefGoogle Scholar
  13. 13.
    Shu YC, Bhattacharya K (2001) Philos Mag B 81:2021CrossRefGoogle Scholar
  14. 14.
    Sapriel J (1975) Phys Rev B 12:5128CrossRefGoogle Scholar
  15. 15.
    Li YL, Hu SY, Liu ZK, Chen LQ (2001) Appl Phys Lett 78:3878CrossRefGoogle Scholar
  16. 16.
    Wang J, Shi SQ, Chen LQ, Li YL, Zhang TY (2004) Acta Mater 52:749CrossRefGoogle Scholar
  17. 17.
    Zhang W, Bhattacharya K (2005) Acta Mater 53:185CrossRefGoogle Scholar
  18. 18.
    Dayal K, Bhattacharya K (2007) Acta Mater 55:1907CrossRefGoogle Scholar
  19. 19.
    Shu YC, Yen JH, Chen HZ, Li JY, Li LJ (2008) Appl Phys Lett 92:052909CrossRefGoogle Scholar
  20. 20.
    Yen JH, Shu YC, Shieh J, Yeh JH (2008) J Mech Phys Solids 56:2117CrossRefGoogle Scholar
  21. 21.
    Shur VY, Rumyantsev EL, Nikolaeva EV, Shishkin EI (2000) Appl Phys Lett 77:3636CrossRefGoogle Scholar
  22. 22.
    Eng LM, Guntherodt HJ (2000) Ferroelectrics 236:35CrossRefGoogle Scholar
  23. 23.
    Han JP, Cao WW (2003) Appl Phys Lett 83:2040CrossRefGoogle Scholar
  24. 24.
    Iwata M, Katsuraya K, Tachizaki S, Hlinka J, Suzuki I, Maeda M, Yasuda N, Ishibashi Y (2004) Jpn J Appl Phys, Part 1 43:6812CrossRefGoogle Scholar
  25. 25.
    Ledbetter H, Dunn ML (1999) Mater Sci Eng A 273–275:222CrossRefGoogle Scholar
  26. 26.
    Ledbetter H, Dunn ML (2000) Mater Sci Eng A 285:180CrossRefGoogle Scholar
  27. 27.
    Liu YY, Liu JJ, Xie SH, Li JY (2007) Appl Phys Lett 91:172910CrossRefGoogle Scholar
  28. 28.
    Wang BA (1992) Int J Solids Struct 29:293CrossRefGoogle Scholar
  29. 29.
    Dunn ML, Taya M (1993) Proc R Soc Lond Ser A 443:265CrossRefGoogle Scholar
  30. 30.
    Tang LP, Xie SH, Zheng XJ, Zhou YC, Li JY (2008) Mech Mater 40:362CrossRefGoogle Scholar
  31. 31.
    Li JY, Dunn ML (1999) Int J Eng Sci 37:665CrossRefGoogle Scholar
  32. 32.
    Zgonik M, Bernasconi P, Duelli M, Schlesser R, Gunter P, Garrett MH, Rytz D, Zhu Y, Wu X (1994) Phys Rev B 50:5941CrossRefGoogle Scholar
  33. 33.
    Mitsui T, Abe R, Furuhata Y, Gesi K, Ikeda T, Kawabe K, Makita Y, Marutake M, Nakamura E, Nomura S, Sawaguchi E, Shiozaki Y, Tatsuzaki I, Toyoda K (1969) Numerical data and fuctional relationships in sciences and technology. Springer, BerlinGoogle Scholar
  34. 34.
    Zhang R, Jiang B, Cao WW (2003) Appl Phys Lett 82:787CrossRefGoogle Scholar
  35. 35.
    Hane KF, Shield TW (2000) Mater Sci Eng A 291:147CrossRefGoogle Scholar
  36. 36.
    Miyazaki S, Kimura S, Otsuka K (1988) Philos Mag A 57:467CrossRefGoogle Scholar
  37. 37.
    Han JP, Cao WW (2003) Phys Rev B 68:134102CrossRefGoogle Scholar
  38. 38.
    Wasa K, Ito S, Nakamura K, Matsunaga T, Kanno I, Suzuki T, Okino H, Yamamoto T, Seo SH, Noh DY (2006) Appl Phys Lett 88:122903CrossRefGoogle Scholar
  39. 39.
    Lu Y, Jeong DY, Cheng ZY, Zhang QM, Luo HS, Yin ZW, Viehland D (2001) Appl Phys Lett 78:3109CrossRefGoogle Scholar
  40. 40.
    Shin MC, Chung SJ, Lee SG, Feigelson RS (2004) J Cryst Growth 263:412CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Key Laboratory of Low Dimensional Materials and Application Technology of Ministry of Education, Faculty of Materials, Optoelectronics and PhysicsXiangtan UniversityHunanChina
  2. 2.Department of Mechanical EngineeringUniversity of WashingtonSeattleUSA

Personalised recommendations