Domain engineered relaxor ferroelectric single crystals

Continuum Mechanics and Thermodynamics

Volumn 18, Issue 1-2, 2006, Pages 119-135

  Liu, T ^a   Lynch, C S ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Domain engineering; Ferroelectric; Phase transition; Piezoelectric; Relaxor single crystals

Indexed keywords

ACTUATORS; CONTROL NONLINEARITIES; CRYSTAL ORIENTATION; ELECTRIC FIELD EFFECTS; FERROELECTRIC MATERIALS; PHASE TRANSITIONS; PIEZOELECTRIC MATERIALS; POLARIZATION; SENSORS; TRANSDUCERS;

DOMAIN ENGINEERING; ELECTROMECHANICAL; HYSTERETIC BEHAVIOR; RELAXOR SINGLE CRYSTALS;

SINGLE CRYSTALS;

EID: 33746055745     PISSN: 09351175     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00161-006-0017-6     Document Type: Article

References (151)

1. Park, S.E., Shrout. T.R.: Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals. J. Appl. Phys. 82(4), 1804-1811 (1997)
2. Liu, T., Lynch, C.S.: Ferroelectric properties of [110], [001] and [111] poled relaxor single crystals: measurements and modeling. Acta Mater. 51(2), 407-416 (2003)
3. McLaughlin, E.A., Liu, T., Lynch, C.S.: Relaxor ferroelectric PMN-32%PT crystals under stress and electric field loading: I-32 mode measurements. Acta Mater. 52(13), 3849-3857 (2004)
4. Bell, A.J.: 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 (2001)
5. Jiang. Y.L., Dan, L.: On ferroelectric crystals with engineered domain configurations. J. Mech. Phys. Solids. 52(8), 1719-1742 (2004)
6. Dammak, H., Renault, A.E., Gaucher, P., Thi, M.P., Calvarin, G.: Origin of the Giant Piezoelectric Properties in the [001] Domain Engineered Relaxor Single Crystals. Jpn. J. Appl. Phys. Part 1 42(10), 6477-6482 (2003)
7. Durbin, M.K., Hicks, J.C., Park, E., Shrout, T.R.: X-ray diffraction and phenomenological studies of the engineered monoclinic crystal domains in single crystal relaxor ferroelectrics. J. Appl. Phys. 87(11), 8159-8164 (2000)
8. Litvin, D.B.: Domain configurations and their symmetry in domain average engineered structures. J. Phys. Conden. Matter. 15(35), 553-558 (2003)
9. Liu, D., Li, J.: Energy minimization of domain engineered ferroelectric crystals. Proc. SPIE Int. Soc. Opt. Eng. 5387, 366-370 (2004)
10. 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.: Domain switching properties in PZN-PT single crystals with engineered domain configurations. Key Eng. Mater. 214-215, 9-14 (2002)
12. Wada, S., Seung-Eek, P., Cross, L.E., Shrout, T.R.: Engineered domain configuration in rhombohedral PZN-PT single crystals and their ferroelectric related properties. Ferroelectrics 221(1-4), 147-155 (1999)
13. Yin, J., Cao, W.: Observation and analysis of domain configurations in domain engineered PZN-PT single crystals. Ferroelectrics 251, 93-100 (2001)
14. 3 single crystals. J. Appl. Phys. 87(10), 7438 (2000)
15. 3 single crystal and analysis of its property fluctuations. IEEE T Ultrason. Ferr. 49(12), 1622-1627 (2002)
16. 3 domain engineered single crystal. J. Mater. Sci. Lett. 21(23), 1877-1879 (2002)
17. Uchino, K.: Relaxor ferroelectric devices. Ferroelectrics 151 (1-4 pt 1), 321-330 (1994)
18. Uchino, K.: Piezoelectric Actuators and Ultrasonic Motors. Kluwer, Boston (1996)
19. 3 system. Ferroelectrics 37(1-4), 579-582 (1981)
20. 3 single crystals. Jpn. J. Appl. Phys. Part 1 21(9), 1298-1302 (1982)
21. Uchino, K.: High electromechanical coupling piezoelectrics: relaxor and normal ferroelectric solid solutions. Solid State Ionics 108(1-4), 43-52 (1998)
22. Park, S.E., Shrout, T.R.: Characteristics of relaxor-based piezoelectric single crystals for ultrasonic transducers. IEEE T Ultrason. Ferr. 44(5), 1140-1147 (1997)
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.: Single crystal piezoelectrics for advanced transducer and smart structures applications. Proc. SPIE Int. Soc. Opt. Eng., 4333, 92-103 (2001)
25. Powers, J.M., Moffett, M.B., Nussbaum, F.: Single crystal naval transducer development. IEEE Int. Sympos. Appl. Ferr. 1, 351-354 (2000)
26. Gururaja, T.R., Panda, R.K., Chen, J., Beck, H.: Single crystal transducers for medical imaging applications. Proc. IEEE Ultrasonics Symp. 2, 969-972 (1999)
27. Hackenberger, W., Rehrig, P. W., Ritter, T., Shrout. T.: Advanced piezoelectric materials for medical ultrasound transducers. IEEE Ultrason. Symp. (Cat. No.01CH37263) 2, 1101-1104 (2001)
28. 3 single crystal of ultrasonic transducer for medical application. J. Intell. Mater. Syst. Struct. 10(6), 493-497 (2000)
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.: Ultrasonic transducers using piezoelectric single crystal perovskite. IEEE Inte. Symp. Appl. Ferr. 2, 543-546 (1996)
31. Damjanovic, D.: Piezoelectric properties of perovskite ferroelectrics: unsolved problems and future research. Ann. Chim. Sci. Mater. 26(1), 99-106 (2001)
32. 3 single crystal. IEEE T. Ultrason. Ferr. 46(1), 152-157 (1999)
33. Park, S.E., Lopath. P.D., Shung, K.K., Shrout, T.R.: Relaxor-based single-crystal materials for ultrasonic transducer applications. Proc. SPIE Int. Soc. Opt. Eng. 3037, pp 140-147 (1997)
34. Bhattacharya, K., Ravichandran, G.: Ferroelectric perovskites for electromechanical actuation. Acta Mater. 51(19), 5941-5960 (2003)
35. Lines, M.E., Glass, A.M.: Principles and Applications of Ferroelectrics and Related Materials. Oxford Clarendon Press (New York 1977)
36. Lynch, C.S.: The effect of uniaxial stress on the electro-mechanical response of 8/65/35 PLZT. Acta Mater. 44(10), 4137-4148 (1996)
37. Chen, W., Lynch, C.S.: Finite element analysis of cracks in ferroelectric ceramic materials. Eng. Fract. Mech. 64(5), 539-562 (1999)
38. Lucato, S.L.D.S., Lupascu, D.C., Kamilah, M., Rodel, J., Lynch, C.S.: Constraint-induced crack initiation at electrode edges in piezoelectric ceramics. Acta Mater. 49(14), 2751-2759 (2001)
39. Wan, S., Lynch, C.: Crack growth of PZN crystals under cyclic electric field. Proc. SPIE Int. Soc. Opt. Eng. 4333, 33-34 (2001)
40. Priya, S., Hyeoung, W.K., Jungho, R., Shujun, Z., Shrout, T.R., Uchino, K.: Modeling of fatigue behavior in relaxor piezocrystals: Improved characteristics by Mn substitution. J. Appl. Phys. 92(7), 3923-3927 (2002)
41. 3 crystals. Appl. Phys. Lett. 79(7), 1006-1008 (2001)
42. Zhao, X., Fang, B., Cao, H., Guo, Y., Luo, H.: 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 (2002)
43. Nye, J.F.: Physcical properties of crystals: their representation by tensors and matrices. Oxford: University Press, Oxford 1967
44. Aizu. K.: Possible species of ferromagnetic, ferroelectric and ferroelastic crystals. Phys. Rev. B 2, 754-772 (1970)
45. Ye, Z.-G.: Crystal chemistry and domain structure of relaxor piezocrystals. Curr. Opin. Solid State Mater. Sci. 6(1), 35-44 (2002)
46. 3 single crystals. Appl. Phys. Lett. 78(20). 3109-3111 (2001)
47. 3. Phys. Rev. B 65(14 eid = 144101), 144101 (2002)
48. 3. Jpn. J. Appl. Phys. Part 137, 5246-5248 (1998)
49. 3. Ferroelectrics 217(1), 319-325 (1998)
50. 3 single crystals. Ferroelectrics. 229, 223-232 (1999)
51. 3 [PZNT] piezocrystals. Mat. Sci. Eng. B 78(2-3), 96-104 (2000)
52. 3. Phys. Rev. Lett. 86 (17), 3891-3894 (2001)
53. Cox, D.E., Noheda, B., Shirane, G., Uesu, Y., Fujishiro, K., Yamada, Y.: Universal phase diagram for high-piezoelectric perovskite systems. Appl. Phys. Lett. 79(3), 400-402 (2001)
54. 3. Phys. Rev. B 63 (014103), 1-6 (2001)
55. 3 system. Phys. Rev. B 64 (18 eid = 184114), 184114 (2001)
56. Noheda, B.: Structure and high-piezoelectricity in lead oxide solid solutions. Curr. Opin. Solid State Mater. Sci. 6(1), 27-34 (2002)
57. 3 investigated by dielectric and Raman spectroscopies. Solid State Commun. 131(2), 111-114 (2004)
58. 3 crystals. Phys. Rev. B 66(5e), 054104 (2002)
59. 3: a powder neutron diffraction study. Phys. Rev. B 68(17 eid = 172103), 172103 (2003)
60. 3: a Rietveld study. Phys. Rev. B 67(6 eid = 064102), 064102 (2003)
61. 3 crystals. Cond-mat 0402296(2004)
62. 3 single crystals. J. Appl. Phys. 87(5), 2312-2319 (2000)
63. 3 single crystals. Ferroelectrics 221 (1-4), 67-71 (1999)
64. 3 crystals near the morphotropic phase boundary. J. Cryst. Growth 253(1-4), 212-220 (2003)
65. 3: a Rietveld study. Phys. Rev. B 67(6), 064102 (2003)
66. 3 single crystals. Phys. Rev. 98(2), 409-413 (1955)
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. 3 single crystals. Appl. Phys. Lett. 83(10), 2040-2042 (2003)
69. Erhart, J., Cao, W.: Permissible symmetries of multi-domain configurations in perovskite ferroelectric crystals. J. Appl. Phys. 94(5), 3436-3445 (2003)
70. Shin, M.C., Chung, S.J., Lee, S.G., Feigelson, R.S.: Growth and observation of domain structure of lead magnesium niobate-lead titanate single crystals. J. Cryst. Growth 263(1-4), 412-420 (2004)
71. Abplanalp, M., Barosova. D., Bridenbaugh, P., Erhart, J., Fousek, J.. Gunter, P., Nosek. J., Sulc, M.: Ferroelectric domain structures in PZN-8%PT single crystals studied by scanning force microscopy. Solid State Commun. 119(1), 7-12 (2001)
72. 3 single crystal with designed multidomains. IEEE T. Ultrason. Ferr. 47(1), 285-291 (2000)
73. 3 single crystals. J. Appl. Phys. 90(7), 3471-3475 (2001)
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.: Characterization of piezoelectric materials with large piezoelectric and electromechanical coupling coefficients. Ultrasonics 41(2), 55-63 (2003)
76. Dammak, H., Renault, A.E., Gaucher, P., Thi. M.P., Calvarin, G.: Origin of the giant piezoelectric properties in the [001] domain engineered relaxor single crystals. Jpn. J. Appl. Phys. Part 1 42(10), 6477-6482 (2003)
77. 3 single crystals. Mater. Lett. 58(14), 2053-2056 (2004)
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.: Dynamical domain observation in relaxor ferroelectrics. Ultrasonics Symp. Proc. 2. 725-728 (1990)
80. 3 single crystals. J. Appl. Phys. 85(5), 2810 (1999)
81. 3 single crystal. Mater. Res. Bull. 37(13), 2135-2143 (2002)
82. 3. J. Appl. Phys. 88(12), 7272-7277 (2000)
83. Bornand, V., Trolier-McKinstry, S., Takemura, K., Randall, C.A.: Orientation dependence of fatigue behavior in relaxor ferroelectric-PbTiO3 thin films. J. Appl. Phys. 87(8), 3965-3972 (2000)
84. 3 ferroelectric single crystals. J. Appl. Phys. 89(9), 5100-5106 (2001)
85. 3)0.095 single crystal. Appl. Phys. Lett. 76(10), 1327-1329 (2000)
86. 3 crystals: Stress and temperature independence. Appl. Phys. Lett. 78(20), 3112-3114 (2001)
87. 3 crystal. Acta. Mater. 49(15), 2993-2999(2001)
88. Fang, F., Yang, W.: Indentation-induced cracking and 90 degrees domain switching pattern in barium titanate ferroelectric single crystals under different poling. Mater. Lett. 57(1), 198-202 (2002)
89. 3 crystals and ceramics. J. Appl. Phys. 89(3). 1820-1825 (2001)
90. 3 crystals under uniaxial stress. Appl. Phys. Lett. 83(1), 132-134 (2003)
91. McLaughlin, E.A., Liu, T., Lynch, C.S.: Relaxor ferroelectric PMN-32%PT crystals under stress, electric field and temperature loading: II-33-mode measurements. Acta Mater. 53(14), 4001-4008 (2005)
92. 3 single crystal. Appl. Phys. Lett. 77(10), 1529-1531 (2000)
93. 3 single crystals with compositions near the morphotropic phase boundary. Phys. Rev. B 68(13), 134102-134106 (2003)
94. 3 single crystals. Appl. Phys. Lett. 80(17), 3174 (2002)
95. 3 single crystals. Appl. Phys. Lett. 80(11), 1918 (2002)
96. 3 crystals. J. Appl. Phys. 92(12), 7690-7692 (2002)
97. 3 crystals. Solid State. Commun. 126(6), 347-351 (2003)
98. Park, S.E.E., Hackenberger, W.: High performance single crystal piezoelectrics: applications and issues. Curr. Opin. Solid State Mater. Sci. 6(1), 11-18 (2002)
99. 3 crystals. J. Appl. Phys. 88(8), 4794-4806 (2000)
100. 3 single crystals. J. Phys. Condens. Matter. 14, 571-576 (2002)
101. Meeks. S.W., Timme, R.W.: Effects of one-dimensional stress on piezoelectric ceramics. J. Appl. Phys. 46(10), 4334-4338 (1975)
102. Schmidt, V.H., Chien, R.. Shih, I.C., Tu, C.-S.: Polarization rotation and monoclinic phase in relaxor ferroelectric PMN-PT crystal. AIP Conf. Proc. 677(1), 160-167 (2003)
103. Tu, C.-S., Huang, L.W., Chien, R., Schmidt, V.H.: E-field and temperature dependent transformation in 〈102〉-cut PMN-PT crystal. AIP Conf. Proc. 677(1), 152-159 (2003)
104. 3 single crystals along nonpolar directions. Appl. Phys. Lett. 83(3), 527-529 (2003)
105. Shur, Vladimir Ya, Rumyantsev, Evgenii, Nikolaeva, Ekaterina, Shishkin, Eugene, Baturin, Ivan, Shur, Alevtina, Lupascu, Doru C., Randall, Clive, and Ozgul, Metin: Fatigue effect in bulk ferroelectrics. Proc. SPIE Int. Soc. Opti. Eng. 4699, 40-50 (2002)
106. 3 single crystals. Appl. Phys. Lett. 79(16), 2624-2626 (2001)
107. 3 ferroelectric single crystals as a function of orientation. J. Appl. Phys. 95(8), 4296-4302 (2004)
108. Jaffe, B., Cook, W.R., Jaffe, H.: Piezoelectric ceramics. Academic, London (1971)
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. 3 single crystal and its frequency dependence. Appl. Phys. Lett. 80(6), 1043-1045 (2002)
111. Mukherjee, B.K., Ren, W., Liu, S.F., Masys, A.J., Yang, G.: Non-linear properties of piezoelectric ceramics. Proc. SPIE Int. Soc. Opt. Eng. 4333, 41-54 (2001)
112. 3 single-crystal ferroelectrics as a function of fatigue history. J. Appl. Phys. 95(5), 2631-2638 (2004)
113. Allen, R.E.: 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 (1976)
114. George, A.M., Iniguez, J., Bellaiche, L.: Anomalous properties in ferroelectrics induced by atomic ordering. Nature 413(6851), 54-57 (2001)
115. Fu, H., Cohen, R.E.: Polarization rotation mechanism for ultrahigh electromechanical response in single-crystal piezoelectrics. Nature 403(6767), 281-283 (2000)
116. Tadmor, E.B., Waghmare, U.V., Smith, G.S., Kaxiras, E.: Polarization switching in PbTiO3: an ab initio finite element simulation. Acta Mater. 50(11), 2989-3002 (2002)
117. Landis, C.M., Wang, J., Sheng, J.: Micro-electromechanically informed phenomenological constitutive models for ferroelectrics. Proc. SPIE Int. Soc. Opt. Eng. 5053, 335-346 (2003)
118. Chen, W., Lynch, C.S.: A micro-electro-mechanical model for polarization switching of ferroelectric materials. Acta Mater. 46(15), 5303-5311 (1998)
119. Chen, W., Lynch, C.S.: Model for simulating polarization switching and AF-F phase changes in ferroelectric ceramics. J. Intell. Mater. Syst. Struct. 9(6), 427-431 (1998)
120. Lynch, C.S.: On the development of multiaxial phenomenological constitutive laws for ferroelectric ceramics. J. Intell. Mater. Syst. Struct. 9(7), 555-563 (1998)
121. Kamlah, M., Tsakmakis, C.: Phenomenological modeling of the non-linear electro-mechanical coupling in ferroelectrics. Int. J. Solids Struct. 36(5), 669-695 (1999)
122. McMeeking, R.M., Landis, C.M.: A phenomenological multi-axial constitutive law for switching in polycrystalline ferroelectric ceramics. Int. J. Eng. Sci. 40 (14), 1553-1577 (2002)
123. Glinchuk, M.D.: Relaxor ferroelectrics: From cross superparaelectric model to random field theory. Br. Ceram. Trans. 103 (2), 76-82 (2004)
124. Asamitsu, A., Moritomo, Y., Tomioka, Y., Arima, T., Tokura, Y.: A structural phase transition induced by an external magnetic field. Nature 373(6513), 407-409 (1995)
125. Fiebig, M., Lottermoser, T., Frohlich, D., Goltsev, A.V., Pisarev, R.V.: Observation of coupled magnetic and electric domains. Nature 419(6909), 818-820 (2002)
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.: Phase transition induced by thermal and electric fields in electron-irradiated poly (vinylidene fluoride- trifiuoroethylene) copolymers. J. Phys. D. Appl. Phys. 36(19), 2382-2385 (2003)
128. Su, C., Vugmeister, B., Khachaturyan, A.G.: Dielectric properties of material with random off-center defects: monte Carlo simulation of relaxor ferroelectrics. J. Appl. Phys. 90(12), 6345-6356 (2001)
129. Wang, X., Liu, M., Chan, L.W., Choy, C.L.: Monte Carlo simulation on dielectric and ferroelectric behaviors of relaxor ferroelectrics. J. Appl. Phys. 95(8), 4282-4290 (2004)
130. Li, Y.L., Hu, S.Y, Liu, Z.K., Chen, L.Q.: Phase-field simulation of domain structure evolution in ferroelectric thin films. Mater. Res. Soc. Symp. Pro. 652, 421-4210 (2001)
131. Yang, W., Chen. L.Q.: Computer simulation of the dynamics of 180° ferroelectric domains. J. Am. Ceram. Soc. 78(9), 2554-2556(1995)
132. Hu, H.L., Chen, L.Q.: Three-dimensional computer simulation of ferroelectric domain formation. J. Am. Ceram. Soc. 81(3), 492-500 (1998)
133. Hu, H.L., Chen, L.Q.: Computer simulation of 90° ferroelectric domain formation in two-dimensions. Mater. Sci. Eng. A A238(1), 182-191(1997)
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.: Ferroelectric/ferroelastic interactions and a polarization switching model. Acta Metall. Mater. 43(5), 2073-2084 (1995)
136. Huber, J.E., Fleck. N.A., Landis, C.M., McMeeking. R.M.: Constitutive model for ferroelectric polycrystals. J. Mech. Phys. Solids 47(8), 1663-1697 (1999)
137. McMeeking, R.M., Hwang, S.C.: On the potential energy of a piezoelectric inclusion and the criterion for ferroelectric switching. Ferroelectrics 200(1-4), 151-173 (1997)
138. Horn, C.L., Shankar, N.: A finite element method for electrostrictive ceramic devices. Int. J. Solids Struct. 33(12), 1757-1779 (1996)
139. Essig, O., Wang, P., Hartweg, M., Janker, P., Nafe, H., Aldinger, F.: 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 (1999)
140. Ghandi, K., Hagood, N.W.: Hybrid finite element model for phase transitions in nonlinear electromechanically coupled material. Proc. SP1E Int. Soc. Opt. Eng. 3039, 97-112 (1997)
141. Hwang. S.C.. McMeeking, R.M.: Finite element model of ferroelectric/ferroelastic polycrystals. Proc. SPIE Int. Soc. Opt. Eng. 3992, 404-417 (2000)
142. Kessler, H., Kamlah. M., Balke, H.: Constitutive and finite element modeling of ferroelectric repolarization. Proc. SPIE Int. Soc. Opt. Eng. 4699, 21-30 (2002)
143. Kim, S.J.: Polarization switching of ferroelectric polycrystals: finite element modeling and simulations. Proc. SPIE Int. Soc. Opt. Eng. 5053, 387-394 (2003)
144. Landis, C.M.: A new finite-element formulation for electromechanical boundary value problems. Int. J. Numer. Methods Eng. 55(5), 613-628 (2002)
145. Li, F., Fang, D.: Simulations of domain switching in ferroelectrics by a three-dimensional finite element model. Mech. Mater. 36(10), 959-973 (2004)
146. Li, J., Liu, D.: The effective electromechanical moduli of ferroelectric crystals with engineered domain configurations. Proc. SPIE Int. Soc. Opt. Eng. 5053, 327-334 (2003)
147. Davis, M., Damjanovic, D., Hayem. D.. Setter. N.: Domain engineering of the transverse piezoelectric coefficient in perovskite ferroelectrics. J. Appl. Phys. 98(1), 014102 (2005)
148. 3 crystals. Appl. Phys. Lett. 82(21), 3737-3739 (2003)
149. 3 single crystals. Proc. SPIE Int. Soc. Opt. Eng. 3664, 239-246 (1999)
150. 3 single crystal with designed multidomains. IEEE T Ultrason. Ferr. 47(1), 285-291 (2000)
151. 3 single crystals. J. Phys. Condens. Matter (12), 2115-2128 (2004)