Computer simulation of 90 ° ferroelectric domain formation in two-dimensions

Continuum thermodynamics of ferroelectric domain evolution: Theory, finite element implementation, and application to domain wall pinning

“…This form of the free energy differs from that implemented previously (Cao and Cross, 1991;Nambu and Sagala, 1994;Hu and Chen, 1997;Cao, 2000, 2001;Li et al, 2001Li et al, , 2002and Zhang and Bhattacharya, 2005a,b) in the following ways. First, the eighth rank term on the second line was introduced by Zhang and Bhattacharya (2005a) in order to allow for adjustments of the dielectric properties and the energy barriers for 90° switching.…”

“…The theory falls into the class of phase-field or diffuse-interface modeling approaches (Cao and Cross, 1991;Nambu and Sagala, 1994;Hu and Chen, 1997;Cao, 2000, 2001;Li et al, 2001Li et al, , 2002and Zhang and Bhattacharya, 2005a,b), which has the potential to bridge atomistic calculations (Cohen and Krakauer, 1992;Meyer and Vanderbilt, 2002) and the larger scale phenomenological modeling approaches. In a departure from previous derivations of the phase-field equations, a set of micro-forces and governing balance laws are postulated and applied within the second law of thermodynamics to identify the appropriate material constitutive relationships, Gurtin, 1993, 1994;Gurtin, 1996).…”

Domain-size dependence of piezoelectric properties of ferroelectrics

“…The calculations are based on a time-dependent Ginzburg-Landau model 11,12,13 with long-range elastic and electrostatic effects. We restrict ourselves to a 2D ferroelectric transition to illustrate the basic principles and use parameters from a model for BaT iO 3 in our calculations 9 .…”

Phenomenological theory of a single domain wall in uniaxial trigonal ferroelectrics: Lithium niobate and lithium tantalate

“…However, while considering an inhomogeneous case, non-local (or long-range) electric dipole-dipole interaction must be included in principle. 11 Not including this interaction slightly changes the profile and energetics of the domain wall.…”