Domain evolution in ferroelectric materials: A continuum phase field model and finite element implementation

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 41-44, 2007, Pages 4365-4374

  Schrade, D ^a   Mueller, R ^a   Xu, B X ^a   Gross, D ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Configurational forces; Ferroelectrics; Finite elements; Micromechanics; Phase field model

Indexed keywords

COMPUTER SIMULATION; CONTINUUM MECHANICS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; MICROMECHANICS; NONLINEAR EQUATIONS; POLARIZATION;

CONFIGURATIONAL FORCES; PHASE FIELD MODEL; POLARIZATION DISTRIBUTION;

FERROELECTRIC MATERIALS;

COMPUTER SIMULATION; CONTINUUM MECHANICS; FERROELECTRIC MATERIALS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; MICROMECHANICS; NONLINEAR EQUATIONS; POLARIZATION;

EID: 34547676608     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.05.010     Document Type: Article

References (22)

1. Ahluwalja R., and Cao W. Influence of dipolar defects on switching behavior in ferroelectrics. Phys. Rev. B 63 (2000) 012103
2. Ahluwalja R., and Cao W. Size dependence of domain patterns in a constrained ferroelectric system. J. Appl. Phys. 89 12 (2001) 8105-8109
3. Bhattacharya K., and Ravichandran G. Ferroelectric perovskites for electromechanical actuation. Acta Mater. 51 (2003) 5941-5960
4. Cao W., and Cross L. Theory of tetragonal twin structures in ferroelectric perovskites with a first-order phase transition. Phys. Rev. B 44 1 (1991) 5-12
5. Flippen R. Domain wall dynamics in ferroelectric/ferroelastic molybdates. J. Appl. Phys. 46 3 (1975) 1068-1071
6. Gross D., Kolling S., Mueller R., and Schmidt I. Configurational forces and their application in solid mechanics. Eur. J. Mech. A/Solids 22 (2003) 669-692
7. Hughes T. The Finite Element Method (2000), Dover, Mineola, New York
8. Kamlah M. Ferroelectric and ferroelastic piezoceramics - modeling of electromechanical hysteresis phenomena. Continuum Mech. Thermodyn. 13 (2001) 219-268
9. McCormack M., Khachaturyan A.G., and Morris J.W. A two-dimensional analysis of the evolution of coherent precipitate in elastic media. Acta Metall. Mater. 40 2 (1992) 325-336
10. Mueller R., Gross D., and Lupascu D. Driving forces on domain walls in ferroelectric materials and interaction with defects. Comp. Mater. Sci. 35 (2006) 42-52
11. W.H. Müller, Zur Simulation des Mikroverhaltens thermo-mechanisch fehlgepasster Verbundwerkstoffe, Fortschritt-Berichte VDI, Reihe 18, Nr.234, Düsseldorf, 1998.
12. Schrade D., Mueller R., Gross D., Utschig T., Shur V., and Lupascu D. Interaction of domain walls with defects in ferroelectric materials. Mech. Mater. 39 (2007) 161-174
13. Soh A., Song Y., and Ni Y. Phase field simulations of hysteresis and butterfly loops in ferroelectrics subjected to electro-mechanical coupled loading. J. Am. Ceram. Soc. 89 (2006) 652-661
14. Y. Su, C. Landis, A non-equilibrium thermodynamics framework for domain evolution; phase field models and finite element implementation, in: Proceeding to the SPIE, 2006.
15. Su Y., and Landis C. Continuum thermodynamics of ferroelectric domain evolution: theory, finite element implementation, and application to domain wall pinning. J. Mech. Phys. Sol. 55 (2007) 280-305
16. Wang J., Shi S.-Q., Chen L.-Q., Li Y., and Zhang T.-Y. Phase field simulations of ferroelectric/ferroelastic polarization switching. Acta Mater. 52 (2004) 749-764
17. Wang J., and Zhang T.-Y. Effect of long-range elastic interactions on the toroidal moment of polarization in a ferroelectric nanoparticle. Appl. Phys. Lett. 88 (2006) 182904
18. Wang J., and Zhang T.-Y. Size effects in epitaxial ferroelectric islands and thin films. Phys. Rev. B 73 (2006) 144107
19. Wang Y., Chen L., and Khachaturyan A.G. Kinetics of strain-induced morphological transformation in cubic alloys with a miscibility gap. Acta Metall. Mater. 41 1 (1993) 279-296
20. Xiao Y., Shenoy V., and Bhattacharya K. Depletion layers and domain walls in semiconducting ferroelectric thin films. Phys. Rev. Lett. 95 (2005) 247603
21. Zhang W., and Bhattacharya K. A computational model of ferroelectric domains. Part II: grain boundaries and defect pinning. Acta Mater. 53 (2005) 199-209
22. Zhang W., and Bhattacharya K. A computational model of ferroelectric domains. Part I: model formulation and domain switching. Acta Mater. 53 (2005) 185-198