Nien-Ti Tsou

A Review of Domain Modelling and Domain Imaging Techniques in Ferroelectric Crystals

The present paper reviews models of domain structure in ferroelectric crystals, thin films and bulk materials. Common crystal structures in ferroelectric materials are described and the theory of compatible domain patterns is introduced. Applications to multi-rank laminates are presented. Alternative models employing phase-field and related techniques are reviewed. The paper then presents methods of observing ferroelectric domain structure, including optical, polarized light, scanning electron microscopy, X-ray and neutron diffraction, atomic force microscopy and piezo-force microscopy. Use of more than one technique for unambiguous identification of the domain structure is also described.

Domain evolution processes during poling of a near-morphotropic Pb(Zr, Ti)O3 ceramic

Domain wall motion during the poling of near-morphotropic Pb(Zr,Ti)O3 PZT was observed using Piezoresponse Force Microscopy (PFM). Poling was conducted on bulk polycrystalline PZT in a series of steps, interrupted by vertical PFM scans, which were used to identify the domain evolution processes. The mechanisms of evolution in complex domain patterns such as herringbone and checkerboard structures are revealed. Of interest, in the case of a herringbone pattern consisting of two sets of lamellae angled to each other, one set of lamellae expands and is observed to overwrite the other, transforming the herringbone structure into a single lamination. Also, lengthening without broadening, and simultaneous lengthening and broadening of lamellar domain bands in checkerboard structures are observed. The observations show that 180° and non-180° domain switching can occur simultaneously in complex domain patterns. Methods are developed for identifying the polarization directions of the individual domains in near-mor...

Relationships among the structural topology, bond strength, and mechanical properties of single-walled aluminosilicate nanotubes

Carbon nanotubes (CNTs) are regarded as small but strong due to their nanoscale microstructure and high mechanical strength (Youngs modulus exceeds 1000 GPa). A longstanding question has been whether there exist other nanotube materials with mechanical properties as good as those of CNTs. In this study, we investigated the mechanical properties of single-walled aluminosilicate nanotubes (AlSiNTs) using a multiscale computational method and then conducted a comparison with single-walled carbon nanotubes (SWCNTs). By comparing the potential energy estimated from molecular and macroscopic material mechanics, we were able to model the chemical bonds as beam elements for the nanoscale continuum modeling. This method allowed for simulated mechanical tests (tensile, bending, and torsion) with minimum computational resources for deducing their Youngs modulus and shear modulus. The proposed approach also enabled the creation of hypothetical nanotubes to elucidate the relative contributions of bond strength and nanotube structural topology to overall nanotube mechanical strength. Our results indicated that it is the structural topology rather than bond strength that dominates the mechanical properties of the nanotubes. Finally, we investigated the relationship between the structural topology and the mechanical properties by analyzing the von Mises stress distribution in the nanotubes. The proposed methodology proved effective in rationalizing differences in the mechanical properties of AlSiNTs and SWCNTs. Furthermore, this approach could be applied to the exploration of new high-strength nanotube materials.

Numerical Method for the Design of Healing Chamber in Additive-Manufactured Dental Implants

The inclusion of a healing chamber in dental implants has been shown to promote biological healing. In this paper, a novel numerical approach to the design of the healing chamber for additive-manufactured dental implants is proposed. This study developed an algorithm for the modeling of bone growth and employed finite element method in ANSYS to facilitate the design of healing chambers with a highly complex configuration. The model was then applied to the design of dental implants for insertion into the posterior maxillary bones. Two types of ITI® solid cylindrical screwed implant with extra rectangular-shaped healing chamber as an initial design are adopted, with which to evaluate the proposed system. This resulted in several configurations for the healing chamber, which were then evaluated based on the corresponding volume fraction of healthy surrounding bone. The best of these implants resulted in a healing chamber surrounded by around 9.2% more healthy bone than that obtained from the original design. The optimal design increased the contact area between the bone and implant by around 52.9%, which is expected to have a significant effect on osseointegration. The proposed approach is highly efficient which typically completes the optimization of each implant within 3–5 days on an ordinary personal computer. It is also sufficiently general to permit extension to various loading conditions.

A sharp interface model of compatible twin patterns in shape memory alloys

The cubic–orthorhombic shape memory alloy system is studied using a sharp interface model based on the linear theory of compatible laminates. A computational method is developed to generate all possible compatible laminates for a given state of strain, and check whether these laminates satisfy exact compatibility conditions. The type of austenite–martensite interface that can form is dependent upon the detail of the martensite structure; the formation of flat and wedge-like austenite–martensite interfaces is explored. A full search is used to reveal the routes in strain space along which the two-phase structure can continuously evolve. A variety of laminate structures, some well known and some new, are reported. The methods developed are readily applied to other crystal systems, such as the tetragonal crystal system, in shape memory alloys or related materials.

Construction of compatible microstructures for tetragonal ferroelectric single crystals

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.

Theory of Compatible Domain Arrangements in Ferroelectric Thin Films

Thin films of single crystal ferroelectric material are constrained by their substrate to a fixed state of macroscopic in-plane strain. Domain structures can form to minimize the overall energy of the system by matching the imposed strain conditions in an average sense. We study low-energy equilibrium states of ferroelectric thin films using the theory of domain compatibility. In a thin film with a given state of average strain, periodic laminate microstructures can be predicted or designed using compatibility theory and the condition that domain wall orientations parallel to the substrate are prohibited by the reduction to 2-dimensions. The theory is applied to [001] , [011] and [111] oriented single crystal films of tetragonal ferroelectric materials. Compatible configurations are generated and the ability of such films to be poled by electric field is then explored.Copyright

Strain actuation of barium titanate single crystals under electromechanical loading in the non-polar [110] direction

The switching characteristics of BaTiO3 single crystals subjected to uniaxial electromechanical loading in the non-polar [110] direction at room temperature and 55 C were investigated. Polarization and strain hysteresis measurements in the [110] direction revealed that under the combination of large in-plane switching coercivities and a strong out-of-plane depolarization field (induced by the shape irregularity and large unshielded surfaces of the crystal sample), strain-inducing 90 in-plane to out-of-plane (or vice versa) switching was the dominant switching behavior even in the absence of mechanical bias. By lowering the in-plane switching coercivities, which was achieved by increasing the loading temperature from room temperature to 55 C, a contrasting non-strain-inducing switching behavior characterized by 90 and/or 180 switches between the in-plane variants was observed instead. The contrasting switching behavior at two different temperatures indicates that apart from the bias stress magnitude, the combined effect of the depolarization field and switching coercivity is another critical factor governing the strain actuation of BaTiO3 single crystals. The [110] electromechanical loading responses reveal the possibility of increasing the strain capacity of BaTiO3 single crystals by introducing accompanying depolarization fields which promote strain-inducing 90 switching. Such an approach could be potentially useful when bias stress-activated ferroelastic switching is not attainable. (Some figures may appear in colour only in the online journal)

Low Energy Periodic Microstructure in Ferroelectric Single Crystals

Two distinct modelling approaches are used to find minimum energy (equilibrium) microstructural states in tetragonal ferroelectric single crystals. The first approach treats domain walls as sharp interfaces and uses analytical solutions of the compatibility conditions at domain walls to identify multi-rank laminate microstructures that are free of residual stress and electric field. The second method treats domain walls as diffuse interfaces, using a phase-field model in 3-dimensions. This is computationally intensive, but takes the full field equations into account and allows a more general class of periodic microstructure to be explored. By searching for minimum energy configurations of a cube of tetragonal material, candidate unit cells of a periodic microstructure are identified. Adding periodic boundary conditions allows the assembly of the unit cells into a macro-structure of low energy. A noteworthy structure identified in this way is a “hexadomain” vortex consisting of six tetragonal domains meeting along the major diagonal of a cube. Several of the structures identified by the phase-field model are found to be special cases of multi-rank laminate structure. Thus the analytical approach offers a fast method for finding equilibrium microstructures, while the phase-field model provides a validation of these solutions.

A Model of Compatible Twin Patterns in Shape Memory Alloys

A sharp interface model is developed to allow rapid discovery of exactly compatible or averagely compatible laminate twin patterns in a cubic-orthorhombic shape memory alloy system. Given an imposed strain state, the method finds a corresponding exactly compatible twin structure if one exists; otherwise, the method produces an averagely compatible solution. Two cases are considered: The first case allows austenite and martensite phases to be arbitrarily mixed. The second is an essentially flat austenite-martensite phase boundary, with an exactly compatible martensite laminate on one side. The results show several well-known configurations and also many new structures. A full search reveals the routes in strain space along which the two-phase structure can continuously evolve. The influence of the middle eigenvalue of the martensite transformation strain on twin patterns is explored.Copyright