Mr. Nien-Ti Tsou Profile

Nien-Ti Tsou

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Proceedings Article | 31 March 2010 Paper

A variational model of ferroelectric rank-2 laminate domain structures

N. T. Tsou, J. Huber

Proceedings Volume 7644, 76440B (2010) https://doi.org/10.1117/12.847131

KEYWORDS: Crystals, Systems modeling, Protactinium, Polarization, Interfaces, Switching, Ferroelectric materials, Thermodynamics, Dielectrics, Electroluminescence

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The equilibrium domain arrangements of ferroelectric single crystals are significantly affected by loads and boundary conditions. Domain structures evolve towards a minimum energy state. In this paper, a variational method, which minimizes a functional based on free energy and dissipation, is developed to model the evolution of several typical rank-2 laminate domain patterns in the tetragonal crystal system. Periodic laminates which satisfy compatibility at every domain wall are studied. These domain patterns include herringbone and vortex array structures. The unit cells for both types of domain pattern dictate a set of domain walls whose positions may vary while maintaining the same topology. The positions of domain walls are treated as thermodynamic variables in the formulation, and the total dissipation rate is then a function of the velocities of the domain walls. By using this model, many features normally observed in ferroelectric single crystals can be reproduced, such as the dielectric hysteresis loop and butterfly loop. The characteristics of the hysteresis loop for different topologies, as well as under different applied loads and boundary conditions are discussed. The model can readily be extended to higher rank laminate structures and other crystal systems.

Proceedings Article | 1 April 2009 Paper

Construction of compatible microstructures for tetragonal ferroelectric single crystals

N. Tsou, J. Huber

Proceedings Volume 7289, 72890B (2009) https://doi.org/10.1117/12.815478

KEYWORDS: Crystals, Polarization, Lithium, Dielectric polarization, Solid modeling, Mechanics, Interfaces, Physics, Solids, Crystallography

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The microstructure of ferroelectric single crystals is a crucial factor that determines macroscopic properties and poling behaviour. Recent models of domain configuration, (such as that of Li & Liu, Journal of Mechanics and Physics of Solids, 2004) employ multi-rank laminate structures that satisfy compatibility in an average sense. In general, these models result in high-rank structures, corresponding to fine microstructure. However, minimum energy structures may be expected to have low rank and to satisfy compatibility requirements at every domain wall exactly. In this paper, the criteria of exact compatibility and average compatibility are defined and then used to determine energy minimizing microstructure in the tetragonal crystal system. In addition, the lowest rank construction of compatible laminate structure for a given macroscopic state of strain and polarization is found. Based on this, poling paths from unpoled to the fully-poled state in the tetragonal system are found, which allow the structure to stay in the lowest possible rank while maintaining exact compatibility. The application of the theory to a broader class of crystal structures is discussed.

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