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Based on spherical random bond-random field model, micro-macro domain mechanism under electric field, and the fuzzy domain boundary with fractal dimension of electric field, the mechanism of polarization effect is analyzed. The results show that the effect of electric field on polarization effect of increment of domain dipoles leads to an unsaturated electric hysteresis loop and its associated big electrostrictive effect. But the variation of binding energy, when dipole couples to the increment of domain dipoles induced by electric field, has a little influence on electric hysteresis loop in a low electric field, and has almost no influence in a high electric field. The initial size of the micro domain is very important for electric hysteresis loop: small micro domain can lead to a long electric hysteresis loop and better linear relationship between electric field and electrostriction.
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Keywords:
- relaxor ferroelectrics /
- polarization /
- electrostriction
[1] Chino K U 1986 Am. Ceram. Soc. Bull. 65 647
[2] Uchino K, Nomura S, Cross L E, Jang S J, Newnham R E 1980 J. Appl. Phys. 51 1142
[3] Cross L E, Jang S J, Newnham R E, Nomura S, Uchino K 1980 Ferroelectrics 23 187
[4] Park S E, Shrout T R 1997 J. Appl. Phys. 82 1804
[5] Zhang S T, Yan F, Yang B, Cao W W 2010 Appl. Phys. Lett. 97 122901
[6] Cao W Q, Chen W, Shang Y L, Shu M F 2012 Ferroelectr. Lett. 39 71
[7] Zhang Q M, Bharti V, Zhao X 1998 Science 280 2101
[8] Wu Z Q 2003 Ph. D. Dissertation (Beijing: Tsinghu University) (in Chinese) [吴忠庆 2003 博士学位论文 (北京: 清华大学)]
[9] Pirc R, Blinc R 1999 Phys. Rev. B 60 13470
[10] Blinc R, Dolinšek J, Gregorovič A, Zalar B, Filipic C, Kutnjak Z, Levstik A, Pirc R 1999 Phys. Rev. Lett. 83 424
[11] Blinc R, Gregorovic A, Zalar B, Pirc R 2000 Phys. Rev. B 61 253
[12] Yao X, Chen Z L, Cross L E 1983 J. Appl. Phys. 54 3399
[13] Wad S, Park S E, Cross L E, Shrout T R 1998 J. Korean Phys. Soc. 32 S1290
[14] Kutnjak Z, Petzelt J, Blinc R 2006 Nature 441 956
[15] Shang Y L, Shu M F, Chen W, Cao W Q 2012 Acta Phys. Sin. 61 197701 (in Chinese) [尚玉黎, 舒明飞, 陈威, 曹万强 2012 61 197701]
[16] Shang X Z, Chen W, Cao W Q 2012 Acta Phys. Sin. 61 217701 (in Chinese) [尚勋忠, 陈威, 曹万强 2012 61 217701]
[17] Cao W Q, Chen W 2012 Ferroelectr. Lett. 39 56
[18] Zhang X D, Rogers C A 1993 J. Intell. Mater. Syst. Struct. 4 307
[19] Gan Y C, Cao W Q 2013 Acta Phys. Sin. 62 127701 (in Chinese) [甘永超, 曹万强 2013 62 127701]
[20] Wang X S, Yamada H, Xu C N 2005 Appl. Phys. Lett. 86 022905
[21] Chen X F, Li H M, Li D J, Cao F, Dong X L 2008 Acta Phys. Sin. 57 7298 (in Chinese) [陈学锋, 李华梅, 李东杰, 曹菲, 董显林 2008 57 7298]
[22] Moura F, Simoes A Z, Stojanovic B D Zaghete M A, Longo E, Varela J A 2008 J. Alloys Compd. 462 129
[23] Wang Z J, Li X Z, Long X F, Ye Z G 2009 Scripta Mater 60 830
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[1] Chino K U 1986 Am. Ceram. Soc. Bull. 65 647
[2] Uchino K, Nomura S, Cross L E, Jang S J, Newnham R E 1980 J. Appl. Phys. 51 1142
[3] Cross L E, Jang S J, Newnham R E, Nomura S, Uchino K 1980 Ferroelectrics 23 187
[4] Park S E, Shrout T R 1997 J. Appl. Phys. 82 1804
[5] Zhang S T, Yan F, Yang B, Cao W W 2010 Appl. Phys. Lett. 97 122901
[6] Cao W Q, Chen W, Shang Y L, Shu M F 2012 Ferroelectr. Lett. 39 71
[7] Zhang Q M, Bharti V, Zhao X 1998 Science 280 2101
[8] Wu Z Q 2003 Ph. D. Dissertation (Beijing: Tsinghu University) (in Chinese) [吴忠庆 2003 博士学位论文 (北京: 清华大学)]
[9] Pirc R, Blinc R 1999 Phys. Rev. B 60 13470
[10] Blinc R, Dolinšek J, Gregorovič A, Zalar B, Filipic C, Kutnjak Z, Levstik A, Pirc R 1999 Phys. Rev. Lett. 83 424
[11] Blinc R, Gregorovic A, Zalar B, Pirc R 2000 Phys. Rev. B 61 253
[12] Yao X, Chen Z L, Cross L E 1983 J. Appl. Phys. 54 3399
[13] Wad S, Park S E, Cross L E, Shrout T R 1998 J. Korean Phys. Soc. 32 S1290
[14] Kutnjak Z, Petzelt J, Blinc R 2006 Nature 441 956
[15] Shang Y L, Shu M F, Chen W, Cao W Q 2012 Acta Phys. Sin. 61 197701 (in Chinese) [尚玉黎, 舒明飞, 陈威, 曹万强 2012 61 197701]
[16] Shang X Z, Chen W, Cao W Q 2012 Acta Phys. Sin. 61 217701 (in Chinese) [尚勋忠, 陈威, 曹万强 2012 61 217701]
[17] Cao W Q, Chen W 2012 Ferroelectr. Lett. 39 56
[18] Zhang X D, Rogers C A 1993 J. Intell. Mater. Syst. Struct. 4 307
[19] Gan Y C, Cao W Q 2013 Acta Phys. Sin. 62 127701 (in Chinese) [甘永超, 曹万强 2013 62 127701]
[20] Wang X S, Yamada H, Xu C N 2005 Appl. Phys. Lett. 86 022905
[21] Chen X F, Li H M, Li D J, Cao F, Dong X L 2008 Acta Phys. Sin. 57 7298 (in Chinese) [陈学锋, 李华梅, 李东杰, 曹菲, 董显林 2008 57 7298]
[22] Moura F, Simoes A Z, Stojanovic B D Zaghete M A, Longo E, Varela J A 2008 J. Alloys Compd. 462 129
[23] Wang Z J, Li X Z, Long X F, Ye Z G 2009 Scripta Mater 60 830
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