Microstructural modeling of ferroelectric materials: State of the art, challenges and opportunities

Materials Science Forum

Volumn 606, Issue , 2009, Pages 119-134

  Leach, Sarah ^a   García, R Edwin ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Ferroelectrics; Microstructures; Modeling; Texture effects

Indexed keywords

CERAMIC MATERIALS; FERROELECTRIC CERAMICS; FERROELECTRICITY; GRAIN BOUNDARIES; MICROSTRUCTURE; MODELS; SINGLE CRYSTALS; TEXTURES;

FERROELECTRIC FATIGUE; MESOSCOPIC INTERACTIONS; MICROSTRUCTURAL MODELING; NUMERICAL IMPLEMENTATION; PHENOMENOLOGICAL DESCRIPTION; POLYCRYSTALLINE FERROELECTRIC CERAMICS; TECHNOLOGICAL CHALLENGES; TEXTURE EFFECTS;

FERROELECTRIC MATERIALS;

EID: 67649109774     PISSN: 02555476     EISSN: 16629752     Source Type: Book Series    
DOI: None     Document Type: Article

References (107)

1. Scott, J. F. 2007. Applications of Modern Ferroelectrics. Science 315, 954-959.
2. Jona, F. and Shirane, G. 1962. Ferroelectric Crystals. Pergamon Press, MacMillan Company, New York.
3. Sheikholeslami, A., and Gulak, P.G. 2000. A survey of circuit innovations in ferroelectric random-access memories. Proceedings of the IEEE, Vol. 88, No. 5. pp 667-689
4. Bell, A.J. 2008. Ferroelectrics: the role of ceramic science and engineering. Journal of the European Ceramic Society (in press).
5. Cohen, R.E. 2000. Theory of ferroelectrics: a vision for the next decade and beyond. Journal of Physics and Chemistry of Solids 61, pp 139-146.
6. Damjanovic, D. 2005. Contributions to the piezoelectric effect in ferroelectric single crystals and ceramics. Journal of the American Ceramic Society 88 [10] 2663-2676.
7. 3. Physical Review B, Vol. 65
8. Diéguez, O., and Vanderbilt, D. 2006. First-principles calculations for insulators at constant polarization. Physical Review Lett. 96, 056401.
9. Diéguez, O., and Vanderbilt, D. 2007. Theoretical study of ferroelectric potassium nitrate. Physical Review B 76.
10. Grigalaitis, R. Banys, J., Lapinskas, S., Erdem, E., Böttcher, R., Gläsel, H-J., and Hartmann, E. 2006. Dielectric investigations and theoretical calculation of size effect in lead titanate nanocrystals. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control. Vol. 53, No. 12, pp. 2270-2274.
11. 3. Computational Materials Science 41, 242-246.
12. Rayleigh, J.W.S. 1892. On the influence of obstacles arranged in rectangular order upon the properties of the medium. Philos. Mag., 34, 481-502.
13. Eshelby, J.D. 1957. The determination of the field of an ellipsoidal inclusion and related problems. Proc. Roy. Soc. London A, 241, 376-396.
14. Hill, R. 1965. A self-consistent mechanics of composite materials. J. Mech. Phys. Solids, 13, 213-222.
15. Budiansky, B. 1965. On the elastic moduli of some heterogeneous materials. J. Mech. Phys. Solids, 13, 223-227.
16. Hashin, Z. 1983. Analysis of composite materials. J. Appl. Mech., 50, 481-505.
17. Deeg, W.F.J. 1980. The analysis of dislocation, crack, and inclusion problems in piezoelectric solids. Department of Materials Science and Engineering, Stanford University, PhD Thesis.
18. Marutake, M. 1956. A calculation of physical constants of ceramic barium titanate. J. Phys. Soc. Japan, 11 [8] 807-814.
19. Pertsev, N.A., Zembilgotov, A.G., and Waser, R. 1998. Aggregate linear properties of ferroelectric ceramics and polycrystalline thin films: calculation by the method of effective piezoelectric medium. Journal of Applied Physics 84 [3] 1524-1529.
20. Pertsev, N.A., Zembilgotov, A.G., and Waser, R. 1998. Effective dielectric and piezoelectric constants of thin polycrystalline ferroelectric films. Physics of the Solid State 40 [12] 2002-2008.
21. Hwang, S., Huber, J.E., McMeeking, R.E., and Fleck, N.A. 1998. The simulation of switching in polycrystalline ferroelectric ceramics. Journal of Applied Physics 84 [3] 1530-1540.
22. Kreher, W. and Rodel, J. 1998. Ferroelectric ceramics and composites: statistical models for effective piezoelectric and pyroelectric properties. Applications of Ferroelectrics, 1998, IASF 98, Proceedings of the Eleventh IEEE International Symposium of Ferroelectrics, Edited by E. Colla, D. Damjanovic, and N. Setter. pp 455-458.
23. Olson, T., and Avellaneda, M. 1992. Effective dielectric and elastic constants of piezoelectric polycrystals. Journal of Applied Physics 71 [9] 4455-4464.
24. Dunn, M.L. 1995. Effects of grain shape anisotropy, porosity, and microcracks on the elastic and dielectric constants of polycrystalline piezoelectric ceramics. Journal of Applied Physics 78 [3] 1533-1541.
25. Aleshin, V. 2000. Properties of anisotropic piezoactive polycrystals. Journal of Applied Physics 88 6] 3587-3591.
26. Li, J.Y. 2000. The effective electroelastic moduli of textured piezoelectric polycrystalline aggregates. Journal of the Mechanics and Physics of Solids 48, 529-552.
27. Nan, C.W., and Clarke, D.R. 1997. Effective properties of ferroelectric and/or ferromagnetic composites: a unified approach and its applications. Journal of the American Ceramics Society 80, 1333-1340.
28. Huang, L. and Tiersten, H.F. 1998. Electroelastic equations describing slow hysteresis in polarized ferroelectric ceramic plates. Journal of Applied Physics Vol. 83 No. 11, 6126-6139.
29. Haertling, G.H. 1999. Ferroelectric Ceramics: History and Technology, J. Am. Ceram. Soc. 82 [4] 797-818.
30. Kamlah, M. 2001. Ferroelectric and ferroeleastic piezoceramics-modeling of electromechanical hysteresis phenomena. Continuum Mech. Thermody. 13: 219-268.
31. Bolten, D., Böttger, U., Waser, R. 2004. Reversible and irreversible piezoelectric and ferroelectric response in ferroelectric ceramics and thin films. Journal of the European Ceramic Society 24, 725-732.
32. Kamlah, M. 2001. Ferroelectric and ferroeleastic piezoceramics-modeling of electromechanical hysteresis phenomena. Continuum Mech. Thermodynamics 13: 219-268
33. Kamlah, M. and Tsakmakis, C. 1999. Phenomenological modeling of the non-linear electromechanical coupling in ferroelectrics. International Journal of Solids and Structures 36: 669-695.
34. Kamlah, M. and Böhle, U. 2001. Finite element analysis of piezoceramic components taking into account ferroelectric hysteresis behavior. International Journal of Solids and Structures 38, 605-633.
35. Shur, V. 2004. Correlated nucleation and self-organied kinetics of ferroelectric domains., in Nucleation Theory and Applications. Schmelzer, J.W.P., Editor. Wiley-VCH. Ch. 6, pp. 178-214.
36. th ISAF, Piscataway, NJ: IEEE, pp 233-240.
37. Shur, V., Rumyantsev, E., Batchko, R, MIller, G, Fejer, M., and Byer, R. 1999. Physical basis of the domain engineering in the bulk ferroelecrics. Ferroelectrics, [221] pp. 157-167.
38. Shur, V., Rumyantsev, E. Nikolaeva, E., Shishkin, E., and Baturin, I. 2001. Kinetic approach to fatigue phenomenom in ferroelectrics. Journal of Applied Physics. Vol. 90, No. 12 pp. 6312-6315.
39. Shur, V., Rumyantsev, E., Nikolaeva, E., Shishkin, E., Baturin, I., Lupascu, D., Nuffer, J., Randall, C., and Ozgul, M. 2002. Kinetics of fatigue in bulk ferroelectrics. SPIE Proc. V. 80, N. 6, pp. 1037-1039.
40. Shur, V., Rumyantsev, E., Nikolaeva, E., and Shishkin, E. 2003. Fast and superfast motion of ferroelectric domain boundaries. Integrated Ferroelectrics, 59: 1439-1503.
41. Shur, V. 2006. Domain engineering in lithium niobate and lithium tantalate: domain wall motion. Ferroelectrics, 340: 3-16.
42. 3. Journal of Materials Science 41, pp. 199-210.
43. 3. Ferroelectrics, 341:1, 109-116.
44. Fousek, J., Cross, L.E., and Nosek, J. 2003. Domain phenomena in single crystalline and ceramic ferroics: unresolved and attractive problems. Microelectronic Engineering 66, pp 574-583.
45. Smith, R.C, and Hom, C. L. 1999. Domain wall theory for ferroelectric hysteresis. Journal of Intellegent Material Systems and Structures, 10 (3) pp. 195-213.
46. Huber, J.E., Fleck, N.A., Landis, C.M. and McMeeking, R.M. 1999. A constitutive model for ferroelectric polycrystals. Journal of the Mechanics and Physics of Solids 47: 1663-1697.
47. Davi, F. and Mariano, P.M. 2001. Evolution of domain walls in ferroelectric solids. Journal of the Mechanics and Phusics of Solids 49: 1701-1726.
48. Su, Y. and Landis, C.M. 2006. Continuum thermodynamics of ferroelectric domain evolution: theory, finite element implementation, and application to domain wall pinning. Journal of the Mechanics and Phusics of Solids, 55, pp. 280-305.
49. Zhang, Z.K., Fang, D.N., Soh, A.K. 2006. A new criterion for domain-switching in ferroelectric materials. Mechanics of Materials 38, pp. 25-32.
50. Sun, C-T. and Achuthan, A. 2004. Domain-switching criteria for ferroelectric materials subjected to electrical and mechanical loads. Journal of the American Ceramic Society, 87 [3] 395-400.
51. Shaikh, M.G., Phanish, S., and Sivakumar, S.M. 2006. Domain switching criteria for ferroelectrics. Computational Materials Science 37, pp. 178-186.
52. Li, F.X, and Rajapakse, R.K.N.D. 2007. A constrained domain-switching model for polycrystalline ferroelectric ceramics. Part I: Model formulation and application to tetragonal materials. Acta Materialia 55, 6472-6480.
53. Li, F.S., and Rajapakse, R.K.N.D. 207.A constrained domain-switching model for polycrystalline ferroelecric ceramics. Part II: Combined switching and application to rhombohedral materials. Acta Materialia 55, 6481-6488.
54. Landis, C.M. 2002. A new finite-element formulation for electromechanical boundary value problems. International Journal for Numerical Methods in Engineering 55, 613-628.
55. Landis, C.M. 2002b. Fully coupled, multi-axial, symmetric constitutive laws for polycrystalline ferroelectric ceramics. Journal of the Mechanics and Physics of Solids 50, 127-152.
56. Landis, C.M. 2004. Energetically consistent boundary conditions for electromechanical fracture. International Journal of Solids and Structures 41, 6291-6315.
57. Huber, J.E. 2005. Micromechanical modeling of ferroelectrics. Current Opinion in solid State and Materials Science 9, pp. 10-106.
58. Setter, N. and Waser, R. 2000. Electroceramic materials. Acta Materialia 48, 151-178.
59. Bhattacharya, K. and Ravichandran, G. 2003. Ferroelectric perovskites for electromechanical actuation. Acta Materialia 51, 5941-5960.
60. Zhang, W. and Bhattacharya, K. 2005a. A computational model of ferroelectric domains. Part I: model formulation and domain switching. Acta Materialia 53, 185-198.
61. Zhang, W. and Bhattacharya, K. 2005b. A computational model of ferroelectric domains. Part II: grain boundaries and defect pinning. Acta Materialia 53, 199-209.
62. Li, J. and Bhattacharya, K. 2002. A mesoscopic electromechanical theory of ferroelectric films and ceramics. Fundamental Physics of Ferroelectrics, R.E. Cohen, ed. AIP.
63. Dayal, K, and Bhattacharya, K. 2006, A real-space non-local phase-field model of ferroelectric domain patterns in complex geometries., submitted to Acta Materialia.
64. Devonshire, A.F. 1949. Theory of barium titanate. Part 1. Philos. Mag. 40:1040-1063.
65. Devonshire, A.F. 1951, Theory of barium titanate. Part 2. Philos. Mag. 42: 1065-1079
66. Devonshire, A.F. 1954. Theory of ferroelectrics. Philos. Mag. (Supplement) 3(10) pp. 1010-4.
67. Cahn, J.W, and Hilliard, J.E. 1958. Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28:258-267.
68. Cahn, J.W., 1959. Free energy of a nonuniform system. II. Thermodynamics basis. J. Chem. Phys. 30:1121-1124.
69. Landau, L.D, and Lifshitz E.M. 1980. Statistical physics. Pergamon Press, Oxford.
70. Li, L.Y., Hu, S.Y., Liu, Z.K. and Chen, L.Q. 2001. Phase-field model of domain structures in ferroelectric thin films. Applied Physics Letters. Vol 78 No 24: 3878-3880.
71. Li, Y.L., Hu, S.Y., Liu, Z.K. and Chen, L.Q. 2002. Effect of electrical boundary conditions on ferroelectric domain structures in thin films. Applied Physics Letters. Vol 81 No 3: 427-429.
72. Zhang, W. and Bhattacharya, K. 2005. A computational model of ferroelectric domains. Part I: model formulation and domain switching. Acta Materialia 53 185-198.
73. Dayal, K. and Bhattacharya, K. 2007. A real-space non-local phase-field model of ferroelectric domain patterns incomplex geometries. Acta Materialia 55 1907-1917.
74. Chew, K.-H., Ishibashi, Y., Shin, F.G., and Chan, H.L.W. 2003. Effective Landau-Devonshiretype theory of phase transitions in ferroelectric thin films based on the Tilley-Zeks Model. Journal of the Physical Society of Japan Vol 72, No 11 pp. 2972-2978.
75. Li, J., and Weng, G.J. 1999. A theory of domain switch for the nonlinear behaviour of ferroelectrics. Proceedings: Mathematical, Physical and Engineering Sciences, Vol. 455, No. 1989, pp. 3493-3511.
76. Damjanovic, D. 2005. Contributions to the piezoelectric effect in ferroelectric single crystals and ceramics. Journal of the American Ceramic Society 88 [10] 2663-2676.
77. Soh, A.K., Song, Y.C., and Ni, Y. 2006. Phase field simulations of hysteresis and butterfly loops in ferroelectrics subjected to electro-mechanical coupled loading. Journal of the American Ceramic Society 89[2] 652-661.
78. Xiao, Y., Shenoy, V. B., and Bhattacharya, K. 2005. Depletion layers and domain walls in semiconducting ferroelectric thin films. Physical Review Letters 95, 247603.
79. Su, Y., and Landis, C. M. 2007. Continuum thermodynamics of ferroelectric domain evolution: Theory, finite element implementation, and application to domain wall pinning. Journal of the Mechanics and Physics of Solids 55, 280-305.
80. García, R. E., Bishop, C. M., and Carter, W.C. 2003. Thermodynamically consistent variational principles with applications to electrically and magnetically active systems. Acta Materialia 52, 11-21.
81. García, R.E., Carter, W.C., and Langer, S.A. 2005. Finite element implementation of a thermodynamic description of piezoelectric microstructures. Journal of the American Ceramic Society, 88 [3] 42-749.
82. García, R.E., Langer, S.A. and Carter, W.C., 2005. The effect of texture and microstructure on the macroscopic properties of polycrystalline piezoelectrics: application to BaTiO3 and PZN-PT, Journal of the American Ceramic Society. 88[3] 750-757.
83. García, R.E., Huey, B.D., and Blendell, J.E. 2006. Virtual piezoforce microscopy of polycrystalline ferroelectric films. J. of App. Phys. 100, 064105.
84. Lupascu, D.D., Genenko, Y. A., Balke, N. 2006. Aging in ferroelectrics. Journal of the American Ceramic Society 89[1] 224-29.
85. 3. Computational Materials Science 39 pp, 896-902.
86. Wolny, W.W. 2004. European approach to development of new environmentally sustainable electroceramics. Ceramics International 30 pp 1079-1083.
87. Takenaka, T., and Nagata, H. 2005. Current status and prospects of lead-free piezoelectric ceramics. Journal of the European Ceramic Society 25, pp 2693-2700.
88. Shvartsman, V.V., Kholkin, A.L., Verdier, C., Yong, Z., and Lupascu. D.C. 2005. Investigation of fatigue mechanism in ferroelectric ceramic via piezoresponse force microscopy. Journal of the European Ceramic Society 25, pp 2559-2561.
89. 3+-doped SrBi2Ta2O9 Thin Films. Journal of the American Ceramic Society 88[1] 85-88.
90. Fiebig, M. 2005. Revival of the magnetoelectric effect. J. Phys. D: Appl. Phys. 38, R123-R152.
91. Hill, N.A. 2000. First principles study of multiferroic magnetoelectric manganites. J. Phys. Chem. B 104 pp 6694-
92. Spaldin, N.A., and Fiebig, M. 2005. The renaissance of magnetoelectric multiferroics. Science Vol. 309. pp. 391-392.
93. Ederer, C., and Spaldin, N.A. 2005. Recent progress in first-principles studies of magnetoelectric multiferroics. Current Opinion in Solid State and Materials Science 9, pp 128-139.
94. Spaldin, N. A., and Pickett, W.E. 2003. Computational design of multifunctional materials. Journal of Solid State Chemistry 176, pp. 615-632.
95. 3. Physical Review B 71, 014113.
96. Singh, M.P., Prellier, W., Mechin, L., Simon, Ch. and Raveau, B. 2007. Can multiferroics be synthesized by superlattice approach? Thin Solid Films 515, pp 6526-6531.
97. Feng, H.J., and Liu, F.M. 2007. First-principles prediction of coexistence of magnetism and ferroelectricity in rhombohedral Bi2FeTiO6. Physics Letters A (in press)
98. Srinivasan, G. Laletsin, V.M., Hayes, R., Puddubnaya, N., Rasmussen, E.T., and Fekel, D.J. 2002. Giant magnetoelectric effects in layered composites of nickel zinc ferrite and lead zirconate titanate. Solid State Communications 124, pp. 373-378.
99. Li, J., Levin, I., Slutsker, J., Provenzano, V., Schenck, P.K., Ramesh, R, Ouyang, J., and Roytburd, A.L. 2005. Self-assembled multiferroic nanostructures in the CoFe2O4-PbTiO3 system. Applied Physics Letters 87, 072909.
100. Tokura, Y. 2006. Multiferroics as quantum electromagnets. Science Vol. 312 pp. 1481-1482.
101. Kuwahara, H., Noda, K., Nagayama, H., and Nakamura, S. 2005. Magnetic field and external pressure control of ferroelectricity in multiferroic manganites. Physica B pp 359-361.
102. Cheong, S.W., and Mostovoy, M. 2007. Multiferroics: a magnetic twist ofr ferroelectricity. Nature Materials Vol. 6. pp. 13-20.
103. Ramesh, R. and Spaldin, N.A. 2007. Multiferroics: progress and prospects in thin films. Nature Materials Vol. 6 pp. 21-29.
104. Tsymbal, E.Y., and Kohlstedt, H. 2006. Tunneling across a ferroelectric. Science Vol. 313, pp 181-183.
105. He, Y., and Fan, J. 2005. Multiscale modeling methodology for layered composites of polymer-ferroelectric ceramics. Journal of Intelligent Material Systems and Structures 16: 603.
106. Trimper, S., Michael, T., and Wesselinowa, J. Ferroelectric soft modes and Gilbert damping. Physical Review B 76.
107. Wan, S., and Bowman, K. 2001. Modeling of electric field induced texture in lead zirconate titanate ceramics. Journal of Materials Research, Vol. 16 No. 8.