Skip to main content
Log in

Domain Engineered Relaxor Ferroelectric Single Crystals

  • Original Article
  • Published:
Continuum Mechanics and Thermodynamics Aims and scope Submit manuscript

Abstract

Single crystal relaxor ferroelectric materials exhibit extraordinary electromechanical properties. They are being applied in high performance sensors, actuators, and transducers. Field induced polarization switching and phase transitions of these crystals lead to complex nonlinear behavior. In recent years experimental investigations have been conducted to characterize the polarization switching and phase transition behavior as a function of crystallographic orientation, temperature, electric field, and stress. The results give insight into the mechanism underlying the observed large field hysteretic behavior. This review article describes the observed behavior and presents results of multiscale modeling that predicts the macroscopic behavior from the single domain single crystal behavior and evolution of crystal variants at the microscale.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Park S.E., Shrout T.R. (1997). Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals. J. Appl. Phys. 82(4):1804–1811

    Article  Google Scholar 

  2. Liu T., Lynch C.S. (2003). Ferroelectric properties of [110], [001] and [111] poled relaxor single crystals: measurements and modeling. Acta Mater. 51(2):407–416

    Article  Google Scholar 

  3. McLaughlin E.A., Liu T., Lynch C.S. (2004). Relaxor ferroelectric PMN-32%PT crystals under stress and electric field loading: I – 32 mode measurements. Acta Mater. 52(13):3849–3857

    Article  Google Scholar 

  4. Bell A.J. (2001). Phenomenologically derived electric field-temperature phase diagrams and piezoelectric coefficients for single crystal barium titanate under fields along different axes. J. Appl. Phys. 89(7):3907–3914

    Article  Google Scholar 

  5. Jiang Y.L., Dan L. (2004). On ferroelectric crystals with engineered domain configurations. J. Mech. Phys. Solids. 52(8):1719–1742

    Article  MathSciNet  MATH  Google Scholar 

  6. Dammak H., Renault A.E., Gaucher P., Thi M.P., Calvarin G. (2003). Origin of the Giant Piezoelectric Properties in the [001] Domain Engineered Relaxor Single Crystals. Jpn. J. Appl. Phys. Part 1 42(10):6477–6482

    Article  Google Scholar 

  7. Durbin M.K., Hicks J.C., Park E., Shrout T.R. (2000). X-ray diffraction and phenomenological studies of the engineered monoclinic crystal domains in single crystal relaxor ferroelectrics. J. Appl. Phys. 87(11):8159–8164

    Article  Google Scholar 

  8. Litvin D.B. (2003). Domain configurations and their symmetry in domain average engineered structures. J. Phys. Conden. Matter. 15(35):553–558

    Article  Google Scholar 

  9. Liu D., Li J. (2004). Energy minimization of domain engineered ferroelectric crystals. Proc. SPIE Int. Soc. Opt. Eng. 5387:366–370

    Google Scholar 

  10. Urenski, P.: Engineered ferroelectric domain configurations in 4 crystals for nonlinear optical converters. In: 21st IEEE convention of the electrical and electronic engineers in Israel. Proceedings (Cat. No.00EX377)., pp.472–475 (2000)

  11. Wada S., Tsurumi T. (2002). Domain switching properties in PZN-PT single crystals with engineered domain configurations. Key Eng. Mater. 214–215, 9–14

  12. Wada S., Seung-Eek P., Cross L.E., Shrout T.R. (1999). Engineered domain configuration in rhombohedral PZN-PT single crystals and their ferroelectric related properties. Ferroelectrics 221(1–4):147–155

    Google Scholar 

  13. Yin J., Cao W. (2001). Observation and analysis of domain configurations in domain engineered PZN-PT single crystals. Ferroelectrics 251:93–100

    Google Scholar 

  14. Yin J., Cao W. (2000). Domain configurations in domain engineered 0.955 Pb(Zn1/3Nb2/3)O3-0.045PbTiO3 single crystals. J. Appl. Phys. 87(10):7438

    Article  Google Scholar 

  15. Zhang R., Jiang B., Jiang W., Cao W. (2002). Anisotropy in domain engineered 0.92Pb(Zn1/3Nb2/3)PbTiO3-0.08PbTiO3 single crystal and analysis of its property fluctuations. IEEE T Ultrason. Ferr. 49(12):1622–1627

    Article  Google Scholar 

  16. Zhang R., Jiang B., Cao W., Amin A. (2002). Complete set of material constants of 0.93Pb(Zn1/3Nb2/3)PbTiO3-0.07PbTiO3 domain engineered single crystal. J. Mater. Sci. Lett. 21(23):1877–1879

    Article  Google Scholar 

  17. Uchino K. (1994). Relaxor ferroelectric devices. Ferroelectrics 151(1–4 pt 1):321–330

    Google Scholar 

  18. Uchino K. (1996). Piezoelectric Actuators and Ultrasonic Motors. Kluwer, Boston

    Google Scholar 

  19. Kuwata J., Uchino K., Nomura S. (1981). Phase transitions in the Pb(Zn1/3Nb2/3)O3-PbTiO3 system. Ferroelectrics 37(1–4):579–582

    Google Scholar 

  20. Kuwata J., Uchino K., Nomura S. (1982). Dielectric and piezoelectric properties of 0.91Pb(Zn1/3Nb2/3)O3-0.09PbTiO3 single crystals. Jpn. J. Appl. Phys. Part 1 21(9):1298–1302

    Article  Google Scholar 

  21. Uchino K. (1998). High electromechanical coupling piezoelectrics: relaxor and normal ferroelectric solid solutions. Solid State Ionics 108(1–4):43–52

    Article  Google Scholar 

  22. Park S.E., Shrout T.R. (1997). Characteristics of relaxor-based piezoelectric single crystals for ultrasonic transducers. IEEE T Ultrason. Ferr. 44(5):1140–1147

    Article  Google Scholar 

  23. Kobayashi, T., Saitoh, S., Harada, K., Shimanuki, S., Yamashita, Y.: Growth of large and homogeneous PZN-PT single crystals for medical ultrasonic array transducers. In: Proceedings of the 11th IEEE international symposium on applications of ferroelectrics (Cat. no. 98CH36245), 235–238 (1998)

  24. Hackenberger W., Rehrig P., Pan M.J., Shrout T. (2001). Single crystal piezoelectrics for advanced transducer and smart structures applications. Proc. SPIE Int. Soc. Opt. Eng. 4333:92–103

    Google Scholar 

  25. Powers J.M., Moffett M.B., Nussbaum F. (2000). Single crystal naval transducer development. IEEE Int. Sympos. Appl. Ferr. 1:351–354

    Google Scholar 

  26. Gururaja T.R., Panda R.K., Chen J., Beck H. (1999). Single crystal transducers for medical imaging applications. Proc. IEEE Ultrasonics Symp. 2:969–972

    Google Scholar 

  27. Hackenberger W., Rehrig P.W., Ritter T., Shrout T. (2001). Advanced piezoelectric materials for medical ultrasound transducers. IEEE Ultrason. Symp. (Cat. No.01CH37263) 2:1101–1104

    Article  Google Scholar 

  28. Harada K., Shimanuki S., Kobayashi T., Saitoh S., Yamashita Y. (2000). Growth of Pb[(Zn1/3Nb2/3)0.91TI0.09]O3 single crystal of ultrasonic transducer for medical application. J. Intell. Mater. Syst. Struct. 10(6):493–497

    Article  Google Scholar 

  29. Lu, Y., Jeong, D.Y., Cheng, Z.Y., Zhang, Q.M.: A new kind of ultrasonic transducer for medical imaging by combining electromechanical and optical properties of PZN-PT single crystal. In: Conference on lasers and electro-optics europe – technical digest, pp 309–310 (2001)

  30. Lopath P.D., Park S.E., Shung K.K, Shrout T.R. (1996). Ultrasonic transducers using piezoelectric single crystal perovskite. IEEE Inte. Symp. Appl. Ferr. 2:543–546

    Google Scholar 

  31. Damjanovic D. (2001). Piezoelectric properties of perovskite ferroelectrics: unsolved problems and future research. Ann. Chim. Sci. Mater. 26(1):99–106

    Article  Google Scholar 

  32. Saitoh S., Kobayashi T., Harada K., Shimanuki S., Yamashita Y. (1999). Forty-channel phased array ultrasonic probe using 0.91Pb(Zn1/3Nb2/3)PbTiO3-0.09PbTiO3 single crystal. IEEE T. Ultrason. Ferr. 46(1): 152–157

    Article  Google Scholar 

  33. Park S.E., Lopath P.D., Shung K.K., Shrout T.R. (1997). Relaxor-based single-crystal materials for ultrasonic transducer applications. Proc. SPIE Int. Soc. Opt. Eng. 3037:140–147

    Google Scholar 

  34. Bhattacharya K., Ravichandran G. (2003). Ferroelectric perovskites for electromechanical actuation. Acta Mater. 51(19):5941–5960

    Article  Google Scholar 

  35. Lines M.E., Glass A.M. (1977). Principles and Applications of Ferroelectrics and Related Materials. Oxford Clarendon Press, New York

    Google Scholar 

  36. Lynch C.S. (1996). The effect of uniaxial stress on the electro-mechanical response of 8/65/35 PLZT. Acta Mater. 44(10):4137–4148

    Article  Google Scholar 

  37. Chen W., Lynch C.S. (1999). Finite element analysis of cracks in ferroelectric ceramic materials. Eng. Fract. Mech. 64(5):539–562

    Article  Google Scholar 

  38. Lucato S.L.D.S., Lupascu D.C., Kamilah M., Rodel J., Lynch C.S. (2001). Constraint-induced crack initiation at electrode edges in piezoelectric ceramics. Acta Mater. 49(14):2751–2759

    Article  Google Scholar 

  39. Wan S., Lynch C. (2001). Crack growth of PZN crystals under cyclic electric field. Proc. SPIE Int. Soc. Opt. Eng. 4333:33–34

    Google Scholar 

  40. Priya S., Hyeoung W.K., Jungho R., Shujun Z., Shrout T.R., Uchino K. (2002). Modeling of fatigue behavior in relaxor piezocrystals: Improved characteristics by Mn substitution. J. Appl. Phys. 92(7):3923–3927

    Article  Google Scholar 

  41. Viehland D., Amin A., Li J.F. (2001). Piezoelectric instability in <011>-oriented Pb(B I1/3 B II2/3 )O3-PbTiO3 crystals. Appl. Phys. Lett. 79(7):1006–1008

    Article  Google Scholar 

  42. Zhao X., Fang B., Cao H., Guo Y., Luo H. (2002). Dielectric and piezoelectric performance of PMN-PT single crystals with compositions around the MPB: influence of composition, poling field and crystal orientation. Mat. Sci. Eng. B 96(3):254–262

    Article  Google Scholar 

  43. Nye J.F. (1967). Physcical properties of crystals: their representation by tensors and matrices. Oxford University Press, Oxford

    Google Scholar 

  44. Aizu K. (1970). Possible species of ferromagnetic, ferroelectric and ferroelastic crystals. Phys. Rev. B 2:754–772

    Article  Google Scholar 

  45. Ye Z.-G. (2002). Crystal chemistry and domain structure of relaxor piezocrystals. Curr. Opin. Solid State Mater. Sci. 6(1):35–44

    Article  Google Scholar 

  46. Lu Y., Jeong D.Y., Cheng Z.Y., Zhang Q.M., Luo H.S., Yin Z.-W., Viehland D. (2001). Phase transitional behavior and piezoelectric properties of the orthorhombic phase of Pb(Mg1/3Nb2/3)O3-PbTiO3 single crystals. Appl. Phys. Lett. 78(20):3109–3111

    Article  Google Scholar 

  47. La Orauttapong D., Noheda B., Ye G., Gehring P.M., Toulouse J., Cox D.E., Shirane G. (2002). Phase diagram of the relaxor ferroelectric (1 − x)Pb(Zn1/3Nb2/3)O3-xPbTiO3. Phys. Rev. B 65(14 eid = 144101), 144101

  48. Fujishiro K., Vlokh R., Uesu Y., Yamada Y., Kiat M., Dkhil B., Yamashita Y. (1998). Optical observation of heterophase and domain structures in relaxor ferroelectrics Pb(Zn1/3Nb2/3)O3-9%PbTiO3. Jpn. J. Appl. Phys. Part 1 37:5246–5248

    Article  Google Scholar 

  49. Uesu Y., Yamada Y., Fujishiro K., Tazawa H., Enokido S., Kiat J.M., Dkhil B. (1998). Structural and optical studies of development of the long-range order in ferroelectric relaxor Pb(Zn1/3Nb2/3)O3-9%PbTiO3. Ferroelectrics 217(1):319–325

    Google Scholar 

  50. Ye Z.-G., Dong M., Zhang L. (1999). Domain structure and phase transitions in relaxor-based piezo-/ferroelectric (1−x) Pb(Zn1/3Nb2/3)O3-xPbTiO3 single crystals. Ferroelectrics. 229:223–232

    Google Scholar 

  51. Zhang L., Dong M., Ye Z.-G. (2000). Flux growth and characterization of the relaxor-based Pb[(Zn1/3Nb2/3)1- x Ti x ]O3 [PZNT] piezocrystals. Mat. Sci. Eng. B 78(2–3):96–104

    Article  Google Scholar 

  52. Noheda B., Cox D.E., Shirane G., Park S.E., Cross L.E., Zhong Z. (2001). Polarization rotation via a monoclinic phase in the piezoelectric 92%Pb(Zn1/3Nb2/3)O3– 8%PbTiO3. Phys. Rev. Lett. 86 (17):3891–3894

    Article  PubMed  Google Scholar 

  53. Cox D.E., Noheda B., Shirane G., Uesu Y., Fujishiro K., Yamada Y. (2001). Universal phase diagram for high-piezoelectric perovskite systems. Appl. Phys. Lett. 79(3):400–402

    Article  Google Scholar 

  54. Noheda B., Cox D.E., Shirane G., Guo R., Jones B., Cross L.E. (2001). Stability of the monoclinic phase in the ferroelectric perovskite PbZr1- x Ti_xPbTiO3. Phys. Rev. B 63 (014103):1–6

    Article  Google Scholar 

  55. Ye, G., Noheda, B., Dong, M., Cox, D., Shirane, G.: Monoclinic phase in the relaxor-based piezoelectric/ferroelectric Pb(Mg1/3Nb2/3)O3– PbTiO3 system. Phys. Rev. B 64 (18 eid = 184114), 184114 (2001)

    Google Scholar 

  56. Noheda B. (2002). Structure and high-piezoelectricity in lead oxide solid solutions. Curr. Opin. Solid State Mater. Sci. 6(1):27–34

    Article  Google Scholar 

  57. Lima-Silva J.J., Guedes I., Mendes Filho J., Ayala A.P., Lente M.H., Eiras J.A., Garcia D. (2004). Phase diagram of the relaxor (1−x) Pb(Zn1/3Nb2/3)O3– xPbTiO3 investigated by dielectric and Raman pectroscopies. Solid State Commun. 131(2):111–114

    Article  Google Scholar 

  58. Noheda B., Cox D.E., Shirane G., Gao J., Ye G. (2002). Phase diagram of the ferroelectric relaxor (1 −x)Pb(Mg1/3Nb2/3)O3– xPbTiO3 crystals. Phys. Rev. B 66(5e):054104

    Article  Google Scholar 

  59. Akhilesh, K.S., Dhananjai, P., Oksana, Z.: Confirmation of B-type monoclinic phase in Pb[(Mg1/3Nb2/3)0.71Ti0. 29]O3: a powder neutron diffraction study. Phys. Rev. B 68(17 eid = 172103), 172103 (2003)

    Google Scholar 

  60. Akhilesh, K.S., Dhananjai, P.: Evidence for MB and MC phases in the morphotropic phase boundary region of (1 − x)Pb(Zn1/3Nb2/3)O3– xPbTiO3: a Rietveld study. Phys. Rev. B 67(6 eid = 064102), 064102 (2003)

    Google Scholar 

  61. Bai, F., Wang, N., Li, J., Viehland, D., Gehring, P.M., Xu, G., Shirane, G.: X-ray and neutron diffraction investigation of the structural phase transformation sequence under electric field in 0.7Pb(Mg1/3Nb2/3)O3–0.3PbTiO3 crystals. Cond-mat 0402296 (2004)

  62. Ye Z.-G., Dong M. (2000). Morphotropic domain structures and phase transitions in relaxor-based piezo-/ferroelectric (1−x)Pb(Zn1/3Nb2/3)O3–xPbTiO3 single crystals. J. Appl. Phys. 87(5):2312–2319

    Article  Google Scholar 

  63. Belegundu U., Du X.H., Cross L.E., Uchino K. (1999). In situ observation of domains in 0.9Pb(Zn1/3Nb 2/3)O3–0.1PbTiO3 single crystals. Ferroelectrics 221(1–4):67–71

    Google Scholar 

  64. Bertram R., Reck G., Uecker R. (2003). Growth and correlation between composition and structure of (1-x)Pb(Zn1/3Nb2/3)O3– xPbTiO3 crystals near the morphotropic phase boundary. J. Cryst. Growth 253(1–4):212–220

    Article  Google Scholar 

  65. Singh A.K., Pandey D. (2003). Evidence for M B and M C phases in the morphotropic phase boundary region of (1-x) [Pb(Mg1/3Nb2/3)O3]– xPbTiO3: a Rietveld study. Phys. Rev. B 67(6):064102

    Article  Google Scholar 

  66. Hooton J.A., Merz W.J. (1955). Etch patterns and ferroelectric domains in BaTiO3 single crystals. Phys. Rev. 98(2):409–413

    Article  Google Scholar 

  67. Shu Y.C., Bhattacharya, K.: Domain patterns and macroscopic behaviour of ferroelectric materials. Philo. Maga. B (Physics of Condensed Matter: Statistical Mechanics, Electronic, Optical and Magnetic Properties) 81(12), 2021–2054 (2001).

  68. Han J., Cao W. (2003). Interweaving domain configurations in [001]-poled rhombohedral phase 0.68 Pb(Mg1/3Nb2/3)O3–0.32PbTiO3 single crystals. Appl. Phys. Lett. 83(10):2040–2042

    Article  Google Scholar 

  69. Erhart J., Cao W. (2003). Permissible symmetries of multi-domain configurations in perovskite ferroelectric crystals. J. Appl. Phys. 94(5):3436–3445

    Article  Google Scholar 

  70. Shin M.C., Chung S.J., Lee S.G., Feigelson R.S. (2004). Growth and observation of domain structure of lead magnesium niobate-lead titanate single crystals. J. Cryst. Growth 263(1–4):412–420

    Article  Google Scholar 

  71. Abplanalp M., Barosova D., Bridenbaugh P., Erhart J., Fousek J., Gunter P., Nosek J., Sulc M. (2001). Ferroelectric domain structures in PZN-8%PT single crystals studied by scanning force microscopy. Solid State Commun. 119(1):7–12

    Article  Google Scholar 

  72. Yin J., Jiang B., Cao W. (2000). Elastic, piezoelectric, and dielectric properties of 0.955Pb(Zn1/3Nb2/3)O3–0.045PbTiO3 single crystal with designed multidomains. IEEE T. Ultrason. Ferr. 47(1):285–291

    Article  Google Scholar 

  73. Zhang R., Jiang B., Cao W. (2001). Elastic, piezoelectric, and dielectric properties of multidomain 0.67Pb(Mg1/3Nb2/3)O3–0.33PbTiO3 single crystals. J. Appl. Phys. 90(7):3471–3475

    Article  Google Scholar 

  74. Ozgul, M.: Polarization switching and fatigue anisotropy in relaxor-lead titanate ferroelectric single crystals. PhD Dissertation, The Pennsylvania State University (2003)

  75. Jiang W., Zhang R., Jiang B., Cao W. (2003). Characterization of piezoelectric materials with large piezoelectric and electromechanical coupling coefficients. Ultrasonics 41(2):55–63

    Article  PubMed  Google Scholar 

  76. Dammak H., Renault A.E., Gaucher P., Thi M.P., Calvarin G. (2003). Origin of the giant piezoelectric properties in the [001] domain engineered relaxor single crystals. Jpn. J. Appl. Phys. Part 1 42(10):6477–6482

    Article  Google Scholar 

  77. Zhao X., Wang J., Chew K.H., Chan H.L.-W., Choy C.L., Yin Z., Luo H. (2004). Composition dependence of piezoelectric constant and dielectric constant tunability in the <001>–oriented Pb(Zn1/3Nb2/3)O3- PbTiO3 single crystals. Mater. Lett. 58(14):2053–2056

    Article  Google Scholar 

  78. Chen, J., Panda, R., Beck, H., Gururaja, R.: New orientation cuts for enhanced electromechanical properties of PMN-PT and PZN-PT single crystals. The Tenth US-Japan Seminar on dielectric and piezoelectric ceramics, pp 233–236 (2001)

  79. Ujiie R., Uchino K. (1990). Dynamical domain observation in relaxor ferroelectrics. Ultrasonics Symp. Proc. 2:725–728

    Article  Google Scholar 

  80. Liu S.F., Park S.E., Shrout T.R., Cross L.E. (1999). Electric field dependence of piezoelectric properties for rhombohedral 0.955Pb(Zn1/3Nb2/3)O3–0.045PbTiO3 single crystals. J. Appl. Phys. 85(5):2810

    Article  Google Scholar 

  81. Cao H., Fang B., Xu H., Luo H. (2002). Crystal orientation dependence of dielectric and piezoelectric properties of tetragonal Pb(Zn1/3Nb2/3)O3–38%PbTiO3 single crystal. Mater. Res. Bull. 37(13):2135–2143

    Google Scholar 

  82. Takemura K., Ozgul M., Bornand V., Troller-McKinstry S., Randall C.A. (2000). Fatigue anisotropy in single crystal Pb(Zn1/3Nb2/3)O3–PbTiO3. J. Appl. Phys. 88(12):7272–7277

    Article  Google Scholar 

  83. Bornand V., Trolier-McKinstry S., Takemura K., Randall C.A. (2000). Orientation dependence of fatigue behavior in relaxor ferroelectric-PbTiO3 thin films. J. Appl. Phys. 87(8):3965–3972

    Article  Google Scholar 

  84. Ozgul M., Takemura K., Trolier-McKinstry S., Randall C.A. (2001). Polarization fatigue in Pb(Zn1/3Nb2/3)O3–PbTiO3 ferroelectric single crystals. J. Appl. Phys. 89(9):5100–5106

    Article  Google Scholar 

  85. Samara G.A., Venturini E.L., Schmidt V.H. (2000). Pressure-induced crossover from long-to-short-range order in [Pb(Zn1/3Nb2/3)O3]0.905– (PbTiO3)0.095 single crystal. Appl. Phys. Lett. 76(10):1327–1329

    Article  Google Scholar 

  86. Viehland D., Powers J. (2001). Electromechanical coupling coefficient of <001>-oriented Pb(Mg1/3Nb2/3)O3–PbTiO3 crystals: Stress and temperature independence. Appl. Phys. Lett. 78(20):3112–3114

    Article  Google Scholar 

  87. Shang J.K., Tan X. (2001). Indentation-induced domain switching in Pb(Mg1/3Nb2/3)O3– PbTiO3 crystal. Acta. Mater. 49(15):2993–2999

    Article  Google Scholar 

  88. Fang F., Yang W. (2002). Indentation-induced cracking and 90 degrees domain switching pattern in barium titanate ferroelectric single crystals under different poling. Mater. Lett. 57(1):198–202

    Article  Google Scholar 

  89. Viehland D., Powers J. (2001). Effect of uniaxial stress on the electromechanical properties of 0.7Pb(Mg1/3Nb2/3)O3–0.3PbTiO3 crystals and ceramics. J. Appl. Phys. 89(3):1820–1825

    Article  Google Scholar 

  90. Viehland D., Li J.F., Gittings K., Amin A. (2003). Electroacoustic properties of <110>-oriented Pb(Mg1/3Nb2/3)O3– PbTiO3 crystals under uniaxial stress. Appl. Phys. Lett. 83(1):132–134

    Article  Google Scholar 

  91. McLaughlin E.A., Liu T., Lynch C.S. (2005). Relaxor ferroelectric PMN-32%PT crystals under stress, electric field and temperature loading: II-33-mode measurements. Acta Mater. 53(14):4001–4008

    Article  Google Scholar 

  92. Tan X., Xu Z., Shang J.K., Han P. (2000). Direct observations of electric field-induced domain boundary cracking in <001> oriented piezoelectric Pb(Mg1/3Nb2/3)O3– PbTiO3 single crystal. Appl. Phys. Lett. 77(10):1529–1531

    Article  Google Scholar 

  93. Han J., Cao W. (2003). Electric field effects on the phase transitions in [001]-oriented (1−x)Pb(MG1/3Nb2/3)O3– xPbTiO3 single crystals with compositions near the morphotropic phase boundary. Phys. Rev. B 68(13):134102–134106

    Article  Google Scholar 

  94. Ren W., Liu S.F., Mukherjee B.K. (2002). Piezoelectric properties and phase transitions of <001>-oriented Pb(Zn1/3Nb2/3)O3– PbTiO3 single crystals. Appl. Phys. Lett. 80(17):3174

    Article  Google Scholar 

  95. Lu Y., Jeong D.Y., Cheng Z.Y., Shrout T., Zhang Q.M. (2002). Phase stabilities of "morphotropic" phases in Pb(Zn1/3Nb2/3)O3– PbTiO3 single crystals. Appl. Phys. Lett. 80(11):1918

    Article  Google Scholar 

  96. Viehland D., Li J.F. (2002). Anhysteretic field-induced rhombhohedral to orthorhombic transformation in <110>-oriented 0.7Pb(Mg1/3Nb2/3)O3–0.3PbTiO3 crystals. J. Appl. Phys. 92(12):7690–7692

    Article  Google Scholar 

  97. Feng Z., Luo H., Guo Y., He T., Xu H. (2003). Dependence of high electric-field-induced strain on the composition and orientation of Pb(Mg1/3Nb2/3)O3– PbTiO3 crystals. Solid State. Commun. 126(6):347–351

    Article  Google Scholar 

  98. Park S.E.E., Hackenberger W. (2002). High performance single crystal piezoelectrics: applications and issues. Curr. Opin. Solid State Mater. Sci. 6(1):11–18

    Article  Google Scholar 

  99. Viehland D. (2000). Symmetry-adaptive ferroelectric mesostates in oriented Pb(BI1/3BII2/3)O3– PbTiO3 crystals. J. Appl. Phys. 88(8):4794–4806

    Article  Google Scholar 

  100. Chen K.-P., Zhang X.-W., Luo H.-S. (2002). Electric-field-induced phase transition of <001> oriented Pb(Mg1/3Nb2/3)O3– PbTiO3 single crystals. J. Phys. Condens. Matter. 14:571–576

    Article  Google Scholar 

  101. Meeks S.W., Timme R.W. (1975). Effects of one-dimensional stress on piezoelectric ceramics. J. Appl. Phys. 46(10):4334–4338

    Article  Google Scholar 

  102. Schmidt V.H., Chien R., Shih I.C., Tu C.-S. (2003). Polarization rotation and monoclinic phase in relaxor ferroelectric PMN-PT crystal. AIP Conf. Proc. 677(1):160–167

    Article  Google Scholar 

  103. Tu C.-S., Huang L.W., Chien R., Schmidt V.H. (2003). E-field and temperature dependent transformation in <102>-cut PMN-PT crystal. AIP Conf. Proc. 677(1):152–159

    Article  Google Scholar 

  104. Damjanovic D., Budimir M., Davis M., Setter N. (2003). Monodomain versus polydomain piezoelectric response of 0.67Pb(Mg1/3Nb2/3)O3–0.33PbTiO3 single crystals along nonpolar directions. Appl. Phys. Lett. 83(3):527–529

    Article  Google Scholar 

  105. Shur, Vladimir Ya, Rumyantsev, Evgenii, Nikolaeva, Ekaterina, Shishkin, Eugene, Baturin, Ivan, Shur, Alevtina, Lupascu, Doru C., Randall, Clive, and Ozgul, Metin (2002). Fatigue effect in bulk ferroelectrics. Proc. SPIE Int. Soc. Opti. Eng. 4699:40–50

    Google Scholar 

  106. Priya S., Jungho R., Uchino K., Viehland D. (2001). Mechanical aging behavior of oriented Pb(Mg1/3Nb2/3)O3– PbTiO3 and Pb(Zn1/3Nb2/3)O3– PbTiO3 single crystals. Appl. Phys. Lett. 79(16):2624–2626

    Article  Google Scholar 

  107. Ozgul M., Trolier-McKinstry S., Randall C.A. (2004). Influence of electrical cycling on polarization reversal processes in Pb(Zn1/3Nb2/3)O3– PbTiO3 ferroelectric single crystals as a function of orientation. J. Appl. Phys. 95(8):4296–4302

    Article  Google Scholar 

  108. Jaffe B., Cook W.R., Jaffe H. (1971). Piezoelectric ceramics. Academic, London

    Google Scholar 

  109. Mauck, L.D.: The role of rate dependence and dissipation in the constitutive behavior of ferroelectric ceramics for high power applications PhD Dissertation, The Georgia Institute of Technology (2002)

  110. Yin J., Cao W. (2002). Coercive field of 0.955Pb(Zn1/3Nb2/3)O3–0.045PbTiO3 single crystal and its frequency dependence. Appl. Phys. Lett. 80(6):1043–1045

    Article  Google Scholar 

  111. Mukherjee B.K., Ren W., Liu S.F., Masys A.J., Yang G. (2001). Non-linear properties of piezoelectric ceramics. Proc. SPIE Int. Soc. Opt. Eng. 4333:41–54

    Google Scholar 

  112. Ozgul M., Furman E., Trolier-McKinstry S., Randall C.A. (2004). Polarization relaxation anisotropy in Pb(Zn1/3Nb2/3)O3– PbTiO3 single-crystal ferroelectrics as a function of fatigue history. J. Appl. Phys. 95(5):2631–2638

    Article  Google Scholar 

  113. Allen R.E. (1976). Structural phase transitions in solids with applied stresses and fields, and effect of isotopic impurities on the free energy. J. Chem. Phys. 64(2):552–553

    Article  Google Scholar 

  114. George A.M., Iniguez J., Bellaiche L. (2001). Anomalous properties in ferroelectrics induced by atomic ordering. Nature 413(6851):54–57

    Article  PubMed  Google Scholar 

  115. Fu H., Cohen R.E. (2000). Polarization rotation mechanism for ultrahigh electromechanical response in single-crystal piezoelectrics. Nature 403(6767):281–283

    Article  PubMed  Google Scholar 

  116. Tadmor E.B., Waghmare U.V., Smith G.S., Kaxiras E. (2002). Polarization switching in PbTiO3: an ab initio finite element simulation. Acta Mater. 50(11):2989–3002

    Article  Google Scholar 

  117. Landis C.M., Wang J., Sheng J. (2003). Micro-electromechanically informed phenomenological constitutive models for ferroelectrics. Proc. SPIE Int. Soc. Opt. Eng. 5053:335–346

    Google Scholar 

  118. Chen W., Lynch C.S. (1998). A micro-electro-mechanical model for polarization switching of ferroelectric materials. Acta Mater. 46 (15):5303–5311

    Article  Google Scholar 

  119. Chen W., Lynch C.S. (1998). Model for simulating polarization switching and AF-F phase changes in ferroelectric ceramics. J. Intell. Mater. Syst. Struct. 9(6):427–431

    Article  Google Scholar 

  120. Lynch C.S. (1998). On the development of multiaxial phenomenological constitutive laws for ferroelectric ceramics. J. Intell. Mater. Syst. Struct. 9(7):555–563

    Google Scholar 

  121. Kamlah M., Tsakmakis C. (1999). Phenomenological modeling of the non-linear electro-mechanical coupling in ferroelectrics. Int. J. Solids Struct. 36(5):669–695

    Article  MATH  Google Scholar 

  122. McMeeking R.M., Landis C.M. (2002). A phenomenological multi-axial constitutive law for switching in polycrystalline ferroelectric ceramics. Int. J. Eng. Sci. 40(14):1553–1577

    Article  MathSciNet  Google Scholar 

  123. Glinchuk M.D. (2004). Relaxor ferroelectrics: From cross superparaelectric model to random field theory. Br. Ceram. Trans. 103 (2):76–82

    Article  Google Scholar 

  124. Asamitsu A., Moritomo Y., Tomioka Y., Arima T., Tokura Y. (1995). A structural phase transition induced by an external magnetic field. Nature 373(6513):407–409

    Article  Google Scholar 

  125. Fiebig M., Lottermoser T., Frohlich D., Goltsev A.V., Pisarev R.V. (2002). Observation of coupled magnetic and electric domains. Nature 419(6909):818–820

    Article  PubMed  Google Scholar 

  126. Vanderbilt, D., Cohen, M.H.: Monoclinic and triclinic phases in higher–order Devonshire theory. Phys. Rev. B 63(9 eid = 094108), 094108 (2001)

  127. Li W., Guo S., Tang Y., Zhao X. (2003). Phase transition induced by thermal and electric fields in electron-irradiated poly (vinylidene fluoride–trifluoroethylene) copolymers. J. Phys. D. Appl. Phys. 36(19):2382–2385

    Article  Google Scholar 

  128. Su C., Vugmeister B., Khachaturyan A.G. (2001). Dielectric properties of material with random off-center defects: monte Carlo simulation of relaxor ferroelectrics. J. Appl. Phys. 90(12):6345–6356

    Article  Google Scholar 

  129. Wang X., Liu M., Chan L.W., Choy C.L. (2004). Monte Carlo simulation on dielectric and ferroelectric behaviors of relaxor ferroelectrics. J. Appl. Phys. 95(8):4282–4290

    Article  Google Scholar 

  130. Li Y.L., Hu S.Y., Liu Z.K., Chen L.Q. (2001). Phase-field simulation of domain structure evolution in ferroelectric thin films. Mater. Res. Soc. Symp. Pro. 652:421–4210

    Google Scholar 

  131. Yang W., Chen L.Q. (1995). Computer simulation of the dynamics of 180&deg; ferroelectric domains. J. Am. Ceram. Soc. 78(9):2554–2556

    Article  Google Scholar 

  132. Hu H.L., Chen L.Q. (1998). Three-dimensional computer simulation of ferroelectric domain formation. J. Am. Ceram. Soc. 81(3): 492–500

    Article  Google Scholar 

  133. Hu H.L., Chen L.Q. (1997). Computer simulation of 90° ferroelectric domain formation in two-dimensions. Mater. Sci. Eng. A A238(1):182–191

    Article  Google Scholar 

  134. Khachaturyan, A.G.: Prospects of 3-dimensional nanoscale modeling of engineering materials. In: Science of alloys for the 21st century. A Hume-Rothery symposium celebration. Proceedings of symposuim. TMS Fall Meeting 293–308 (2000)

  135. Hwang S.C., Lynch C.S., McMeeking R.M. (1995). Ferroelectric/ferroelastic interactions and a polarization switching model. Acta Metall. Mater. 43(5):2073–2084

    Article  Google Scholar 

  136. Huber J.E., Fleck N.A., Landis C.M., McMeeking R.M. (1999). Constitutive model for ferroelectric polycrystals. J. Mech. Phys. Solids 47(8):1663–1697

    Article  MATH  MathSciNet  Google Scholar 

  137. McMeeking R.M., Hwang S.C. (1997). On the potential energy of a piezoelectric inclusion and the criterion for ferroelectric switching. Ferroelectrics 200(1–4):151–173

    Google Scholar 

  138. Hom C.L., Shankar N. (1996). A finite element method for electrostrictive ceramic devices. Int. J. Solids Struct. 33(12):1757–1779

    Article  MATH  Google Scholar 

  139. Essig O., Wang P., Hartweg M., Janker P., Nafe H., Aldinger F. (1999). Uniaxial stress and temperature dependence of field induced strains in antiferroelectric lead zirconate titanate stannate ceramics. J. Eur. Ceram. Soc. 19(6–7):1223–1228

    Article  Google Scholar 

  140. Ghandi K., Hagood N.W. (1997). Hybrid finite element model for phase transitions in nonlinear electromechanically coupled material. Proc. SPIE Int. Soc. Opt. Eng. 3039:97–112

    MathSciNet  Google Scholar 

  141. Hwang S.C., McMeeking R.M. (2000). Finite element model of ferroelectric/ferroelastic polycrystals. Proc. SPIE Int. Soc. Opt. Eng. 3992:404–417

    Google Scholar 

  142. Kessler H., Kamlah M., Balke H. (2002). Constitutive and finite element modeling of ferroelectric repolarization. Proc. SPIE Int. Soc. Opt. Eng. 4699:21–30

    Google Scholar 

  143. ,Kim S.J. (2003). Polarization switching of ferroelectric polycrystals: finite element modeling and simulations. Proc. SPIE Int. Soc. Opt. Eng. 5053:387–394

    Google Scholar 

  144. Landis C.M. (2002). A new finite-element formulation for electromechanical boundary value problems. Int. J. Numer. Methods Eng. 55(5):613–628

    Article  MATH  Google Scholar 

  145. Li F., Fang D. (2004). Simulations of domain switching in ferroelectrics by a three-dimensional finite element model. Mech. Mater. 36(10):959–973

    Article  Google Scholar 

  146. Li J., Liu D. (2003). The effective electromechanical moduli of ferroelectric crystals with engineered domain configurations. Proc. SPIE Int. Soc. Opt. Eng. 5053:327–334

    Google Scholar 

  147. Davis M., Damjanovic D., Hayem D., Setter N. (2005). Domain engineering of the transverse piezoelectric coefficient in perovskite ferroelectrics. J. Appl. Phys. 98(1):014102

    Article  Google Scholar 

  148. Zhang R., Jiang B., Cao W. (2003). Orientation dependence of piezoelectric properties of single domain 0.67Pb(Mn1/3Nb2/3)O3–0.33PbTiO3 crystals. Appl. Phys. Lett. 82(21):3737–3739

    Article  Google Scholar 

  149. Yin J., Jiang B., Cao W. (1999). Determination of elastic, piezoelectric and dielectric properties of Pb(Zn1/3Nb2/3)O3– PbTiO3 single crystals. Proc. SPIE Int. Soc. Opt. Eng. 3664:239–246

    Google Scholar 

  150. Yin J., Jiang B., Cao W. (2000). Elastic, piezoelectric, and dielectric properties of 0.955Pb(Zn1/3Nb2/3)O3–0.045PbTiO3 single crystal with designed multidomains. IEEE T Ultrason. Ferr. 47(1):285–291

    Article  Google Scholar 

  151. Topolov V.Y. (2004). The remarkable orientation and concentration dependences of the electromechanical properties of 0.67Pb(Mg1/3Nb2/3)O3–0.33PbTiO3 single crystals. J. Phys. Condens. Matter (12),2115–2128

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to C. S. Lynch.

Additional information

Communicated by S. Seelecke

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, T., Lynch, C.S. Domain Engineered Relaxor Ferroelectric Single Crystals. Continuum Mech. Thermodyn. 18, 119–135 (2006). https://doi.org/10.1007/s00161-006-0017-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00161-006-0017-6

Keywords

PACS

Navigation