Phase-field method of phase transitions/domain structures in ferroelectric thin films: A review

Journal of the American Ceramic Society

Volumn 91, Issue 6, 2008, Pages 1835-1844

  Chen, Long Qing ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

(I ,J) CONDITIONS; (LIQUID + LIQUID) EQUILIBRIUM; (SKEW) FREE ENERGY; AMERICAN CERAMIC SOCIETY (ACERS); BULK SINGLE CRYSTALS; DOMAIN STRUCTURES; DOMAIN WALL ENERGY; DRIVING FORCES; ELASTIC ENERGIES; ELECTRO MECHANICAL SYSTEMS; ELECTROSTATIC ENERGIES; EVOLUTION (CO); FERROELECTRIC (BARIUM STRONTIUM TITANATE); FERROELECTRIC DOMAIN STRUCTURES; FERROELECTRIC PHASE TRANSITIONS; FERROELECTRIC SINGLE CRYSTALS; FERROELECTRIC TRANSITIONS; INHOMOGENEOUS SYSTEMS; PHASE FIELD METHOD (PFM); PHASE FIELDS; PHASE TRANSITION TEMPERATURE (TP); SPATIAL DISTRIBUTION OF; SPONTANEOUS POLARIZATIONS; STRAIN EFFECTS;

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; COATINGS; CRYSTALLOGRAPHY; CRYSTALS; ELECTROMECHANICAL DEVICES; FERROELECTRIC FILMS; FERROELECTRIC MATERIALS; FERROELECTRIC THIN FILMS; FERROELECTRICITY; FERROMAGNETISM; MAGNETIC BUBBLES; MAGNETIC DOMAINS; MAGNETISM; MATHEMATICAL TRANSFORMATIONS; MECHANICS; NUMERICAL METHODS; PHASE STABILITY; POWDERS; SINGLE CRYSTALS; SIZE DISTRIBUTION; SOLIDS; THERMODYNAMICS; THICK FILMS; THIN FILMS;

PHASE TRANSITIONS;

EID: 44649143775     PISSN: 00027820     EISSN: 15512916     Source Type: Journal    
DOI: 10.1111/j.1551-2916.2008.02413.x     Document Type: Article

References (74)

1. D. G. Schlom, L. Q. Chen, C. B. Eom, K. M. Rabe, S. K. Streiffer J. M. Triscone Strain Tuning of Ferroelectric Thin Films Ann. Rev. Mater. Res., 37, 589 626 (2007).
2. N. A. Pertsev, A. G. Zembilgotov A. K. Tagantsev Effect of Mechanical Boundary Conditions on Phase Diagrams of Epitaxial Ferroelectric Thin Films Phys. Rev. Lett., 80 [9] 1988 91 (1998).
3. 3 Thin Films Science, 306 [5698] 1005 9 (2004).
4. 3 Nature, 430 [7001] 758 61 (2004).
5. N. A. Pertsev V. G. Koukhar Polarization Instability in Polydomain Ferroelectric Epitaxial Thin Films and the Formation of Heterophase Structures Phys. Rev. Lett., 84 [16] 3722 5 (2000).
6. V. G. Koukhar, N. A. Pertsev R. Waser Thermodynamic Theory of Epitaxial Ferroelectric Thin Films with Dense Domain Structures Phys. Rev. B, 6421 214103 (2001).
7. A. Devonshire Phenomenological Theory of High Permittivity in Fine-Grained Barium Titanate Philos. Mag., 40, 1040 (1949).
8. M. J. Haun, E. Furman, S. J. Jang, H. A. Mckinstry L. E. Cross Thermodynamic Theory of Pbtio3 J. Appl. Phys., 62 [8] 3331 8 (1987).
9. D. D. Fong, C. Cionca, Y. Yacoby, G. B. Stephenson, J. A. Eastman, P. H. Fuoss, S. K. Streiffer, C. Thompson, R. Clarke, R. Pindak E. A. Stern Direct Structural Determination in Ultrathin Ferroelectric Films by Analysis of Synchrotron X-Ray Scattering Measurements Phy. Rev. B, 71, 144112 (2005).
10. J. Wang T. Y. Zhang Effects of Nonequally Biaxial Misfit Strains on the Phase Diagram and Dielectric Properties of Epitaxial Ferroelectric Thin Films Appl. Phys. Lett., 86, 192905 (2005).
11. A. G. Zembilgotov, N. A. Pertsev, U. Bottger R. Waser Effect of Anisotropic in-Plane Strains on Phase States and Dielectric Properties of Epitaxial Ferroelectric Thin Films Appl. Phys. Lett., 86, 052903 (2005).
12. S. Nambu D. A. Sagala Domain Formation and Elastic Long-Range Interaction in Ferroelectric Perovskites Phys. Rev. B, 50 [9] 5838 47 (1994).
13. W. Yang L. Q. Chen Computer-Simulation of the Dynamics of 180-Degrees Ferroelectric Domains J. Am. Ceram. Soc., 78 [9] 2554 6 (1995).
14. H. L. Hu L. Q. Chen Computer Simulation of 90 Degrees Ferroelectric Domain Formation in Two-Dimensions Mater. Sci. Eng.-Struct. Mater. Properties Microstruct. Proc., 238 [1] 182 91 (1997).
15. H. L. Hu L. Q. Chen Three-Dimensional Computer Simulation of Ferroelectric Domain Formation J. Am. Ceram. Soc., 81 [3] 492 500 (1998).
16. A. Kuroda, K. Ozawa, Y. Uesu Y. Yamada Simulation Study of Zigzag Domain Boundary Formation in Ferroelectric - Ferroelastics using the TDGL Equation Ferroelectrics, 219 [1-4] 851 60 (1998).
17. R. Ahluwalia W. W. Cao Effect of Surface Induced Nucleation of Ferroelastic Domains on Polarization Switching in Constrained Ferroelectrics J. Appl. Phys., 93 [1] 537 44 (2003).
18. J. Wang, S. Q. Shi, L. Q. Chen, Y. L. Li T. Y. Zhang Phase Field Simulations of Ferroelectric/Ferroelastic Polarization Switching Acta Materialia, 52 [3] 749 64 (2004).
19. R. Ahluwalia, T. Lookman, A. Saxena W. Cao Piezoelectric Response of Engineered Domains in Ferroelectrics Appl. Phys. Lett., 84 [18] 3450 2 (2004).
20. R. Ahluwalia, T. Lookman, A. Saxena W. W. Cao Domain-Size Dependence of Piezoelectric Properties of Ferroelectrics Phys. Rev. B, 72, 014112 (2005).
21. W. Zhang K. Bhattacharya A Computational Model of Ferroelectric Domains. Part I: Model Formulation and Domain Switching Acta Materialia, 53 [1] 185 98 (2005).
22. A. K. Soh, Y. C. Song Y. Ni Phase Field Simulations of Hysteresis and Butterfly Loops in Ferroelectrics Subjected to Electro-Mechanical Coupled Loading J. Am. Ceram. Soc., 89 [2] 652 61 (2006).
23. Y. Su C. M. Landis Continuum Thermodynamics of Ferroelectric domain Evolution: Theory, Finite Element Implementation, and Application to Domain Wall Pinning J. Mech. Phys. Solids, 55 [2] 280 305 (2007).
24. W. F. Rao Y. U. Wang Bridging Domain Mechanism for Phase Coexistence in Morphotropic Phase Boundary Ferroelectrics Appl. Phys. Lett., 90, 182906 (2007).
25. W. F. Rao Y. U. Wang Domain Wall Broadening Mechanism for Domain Size Effect of Enhanced Piezoelectricity in Crystallographically Engineered Ferroelectric Single Crystals Appl. Phys. Lett., 90 [4] (2007).
26. S. Choudhury, L. Q. Chen Y. L. Li Correlation Between Number of Ferroelectric Variants and Coercive Field of Lead Ziconate Titanate Single Crystals Appl. Phys. Lett., 91 [3] (2007).
27. S. Semenovskaya A. G. Khachaturyan Development of Ferroelectric Mixed States in a Random Field of Static Defects J. Appl. Phys., 83 [10] 5125 36 (1998).
28. S. Semenovskaya A. G. Khachaturyan Ferroelectric Transition in a Random Field: Possible Relation to Relaxor Ferroelectrics Ferroelectrics, 206 [1-4] 157 80 (1998).
29. Y. L. Li, S. Y. Hu, Z. K. Liu L. Q. Chen Phase-Field Model of Domain Structures in Ferroelectric Thin Films Appl. Phys. Lett., 78 [24] 3878 80 (2001).
30. Y. L. Li, S. Y. Hu, Z. K. Liu L. Q. Chen Effect of Substrate Constraint on the Stability and Evolution of Ferroelectric Domain Structures in Thin Films Acta Materialia, 50 [2] 395 411 (2002).
31. 3 Thin Films - Thermodynamic Calculations and Phase-Field Simulations Appl. Phys. Lett., 83 [8] 1608 10 (2003).
32. 3 Thin Films Phys. Rev. B, 69, 174101 (2004).
33. 3 Thin Films at the Bulk Morphotropic Boundary Composition J. Am. Ceram. Soc., 88 [6] 1669 72 (2005).
34. 3 Epitaxial Thin Films J. Appl. Phys., 97, 034112 (2005).
35. 3 Thin Films Appl. Phys. Lett., 88, 072905 (2006).
36. 3 Thin Films Phys. Rev. B, 73, 184112 (2006).
37. D. A. Tenne, A. Bruchhausen, N. D. Lanzillotti-Kimura, A. Fainstein, R. S. Katiyar, A. Cantarero, A. Soukiassian, V. Vaithyanathan, J. H. Haeni, W. Tian, D. G. Schlom, K. J. Choi, D. M. Kim, C. B. Eom, H. P. Sun, X. Q. Pan, Y. L. Li, L. Q. Chen, Q. X. Jia, S. M. Nakhmanson, K. M. Rabe X. X. Xi Probing Nanoscale Ferroelectricity by Ultraviolet Raman Spectroscopy Science, 313 [5793] 1614 6 (2006).
38. 3 Films on (001) Si J. Appl. Phys., 100, 024108 (2006).
39. A. G. Khachaturyan, Theory of Structural Transformations in Solids. John Wiley & Sons, New York, 1983.
40. 14 Precipitates in Ti-Ni Alloys Under an Applied Stress - A Computer Simulation Study Acta Materialia, 46 [2] 639 49 (1998).
41. A. G. Khachaturyan, S. Semenovskaya T. Tsakalakos Elastic Strain Energy of Inhomogeneous Solids Phys. Rev. B, 52, 1 11 (1995).
42. S. Y. Hu L. Q. Chen A Phase-Field Model for Evolving Microstructures with Strong Elastic Inhomogeneity Acta Materialia, 49 [11] 1879 90 (2001).
43. P. Yu, S. Y. Hu, L. Q. Chen Q. Du An Iterative-Perturbation Scheme for Treating Inhomogeneous Elasticity in Phase-Field Models J. Computational Phys., 208 [1] 34 50 (2005).
44. A. G. Khachaturyan G. A. Shatalov Theory of Macroscopic Periodicity for A Phase Transition in Solid State Sov. Phys. JETP (Engl. Transl.), 29, 557 (1969).
45. A. N. Stroh Steady State Problems in Anisotropic Elasticity J. Math. Phys., 41, 77 (1962).
46. Y. L. Li, S. Y. Hu, Z. K. Liu L. Q. Chen Effect of Electrical Boundary Conditions on Ferroelectric Domain Structures in Thin Films Appl. Phys. Lett., 81 [3] 427 9 (2002).
47. L. Q. Chen J. Shen Applications of Semi-Implicit Fourier-Spectral Method to Phase Field Equations Comp. Phys. Commun., 108 [2-3] 147 58 (1998).
48. 3 Single Crystals J. Appl. Phys., 98, 064101 (2005).
49. 3 Superlattices with Domains Appl. Phys. Lett., 91, 112914 (2007).
50. 3 Superlattices Probed by Ultraviolet Raman Spectroscopy Science, 313, 1614 (2006).
51. 3 Epitaxial Thin Films Phys. Rev. B, 61 [2] R825 (2000).
52. 3 Superlattices J. Phys. Condensed Matter, 15 [21] L305 9 (2003).
53. A. Vasudevarao, A. Kumar, L. Tian, J. H. Haeni, Y. L. Li, C. J. Eklund, Q. X. Jia, R. Uecker, P. Reiche, K. M. Rabe, L. Q. Chen, D. G. Schlom V. Gopalan Multiferroic Domain Dynamics in Strained Strontium Titanate Phys. Rev. Lett., 97, 257602 (2006).
54. 9 Epitaxial Thin Films: Electron Microscopy and Phase-Field Simulations J. Appl. Phys., 95 [11] 6332 40 (2004).
55. 3 Thin Films J. Appl. Phys., 101 [11] (2007).
56. 3 through Substrate Vicinality Adv. Mater., 19, 2662 6 (2007).
57. 3 Films Phys. Rev. Lett., 99, 217601 (2007).
58. J. Slutsker, I. Levin, J. H. Li, A. Artemev A. L. Roytburd Effect of Elastic Interactions on the Self-Assembly of Multiferroic Nanostructures in Epitaxial Films Phys. Rev. B, 73, 184127 (2006).
59. J. X. Zhang, Y. L. Li, D. G. Schlom, L. Q. Chen, F. Zavaliche, R. Ramesh Q. X. Jia Phase-Field Model for Epitaxial Ferroelectric and Magnetic Nanocomposite Thin Films Appl. Phys. Lett., 90, 052909 (2007).
60. B. J. Roriguez, S. V. Kalinin, S. Jesse, Y. H. Chu, T. Zhao, R. Ramesh, S. Choudhury, L. Q. Chen, E. A. Eliseev A. N. Morozovska Self-Consistent Spectroscopic Measurements of Single Domain Switching in Ferroelectric Materials: Nucleation Mechanism and Domain Growth Proceedings of the National Academy of Sciences, 2007. accepted.
61. S. Jesse, J. Rodriguez, A. P. Baddorf, I. Vrejoiu, D. Hesse, M. Alexe, E. A. Eliseev, A. N. Morozovska, J. X. Zhang, S. Choudhury, L. Q. Chen S. V. Kalinin Direct Imaging of Spatial and Energy Distribution of Nucleation Centers in Ferroelectric Materials: 50 Years After Landauer Nat. Mater., 7, 209 15 (2008).
62. L. Tian, N. Ogadawa, S. Choudhury, A. Vasudevarao, P. Capek, V. Dierolf, A. N. Morozovska, E. A. Eliseev, L. Q. Chen, Y. Cho, S. V. Kalinin V. Gopalan Domain Wall Width and Coercive Field in Ferroelectrics Phys. Rev. Lett. (2007 Submitted.
63. W. Zhang K. Bhattacharya A Computational Model of Ferroelectric Domains. Part II: Grain Boundaries and Defect Pinning Acta Materialia, 53 [1] 199 209 (2005).
64. S. Choudhury, Y. L. Li, C. Krill L. Q. Chen Effect of Grain Orientation and Grain Size on Ferroelectric Domain Switching and Evolution: Phase Field Simulations Acta Materialia, 55 [4] 1415 26 (2007).
65. S. Choudhury, Y. L. Li, C. E. Krill L. Q. Chen Phase-Field Simulation of Polarization Switching and Domain Evolution in Ferroelectric Polycrystals Acta Materialia, 53 [20] 5313 21 (2005).
66. S. Y. Hu, Y. L. Li L. Q. Chen Effect of Interfacial Dislocations on Ferroelectric Phase Stability and Domain Morphology in a Thin Film - a Phase-Field Model J. Appl. Phys., 94 [4] 2542 7 (2003).
67. Y. Zheng, B. Wang C. H. Woo Effects of Interface Dislocations on Properties of Ferroelectric Thin Films J. Mech. Phys. Solids, 55 [8] 1661 76 (2007).
68. H. L. Hu, Y. L. Li, S. Choudhury, A. Saxena, T. Lookman, M. Baskes, Q. X. Jia, D. G. Schlom L. Q. Chen Influence of Interfacial Dislocations on Hysteresis Loop of Ferroelectric Materials Appl. Phys. Lett. (2007 Submitted.
69. S. Choudhury, Y. L. Li L. Q. Chen Tailoring Domain Switching Behavior in Barium Titanate Thin Films Using Substrate Constraint Appl. Phys. Lett. (2007 in press.
70. Y. Xiao, V. B. Shenoy K. Bhattacharya Depletion Layers and Domain Walls in Semiconducting Ferroelectric Thin Films Phys. Rev. Lett., 95 [24] (2005).
71. J. X. Zhang, R. Wu, S. Choudhury L. Q. Chen Three-dimensional Phase-Field Simulations of Domain Structures in Ferroelectric Islands Appl. Phys. Lett., 2007, in press.
72. J. X. Zhang L. Q. Chen Piezoelectricity of Ferroelectric Islands, unpublished, 2007.
73. J. Wang T. Y. Zhang Phase Field Simulations of Polarization Switching-Induced Toughening in Ferroelectric Eramics Acta Materialia, 55 [7] 2465 77 (2007).
74. Y. C. Song, A. K. Soh Y. Ni Phase Field Simulation of Crack Tip Domain Switching in Ferroelectrics J. Phys. D-Appl. Phys., 40 [4] 1175 82 (2007).