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The development of analytical theories and numerical models that capture with realism the time evolution of polarization domains in polycrystalline lead-containing and lead-free ferroelectric materials is being pursued. Specifically, variational principles are being built based on Landau-like free energy formulations and by introducing the adequate kinetic laws to describe the switching dynamics for materials in thin film and bulk form. The focus lies on integrating simulation and experiments to provide research and development tools to the community (e.g., oof and piezos3D), as it has become a key national priority through the Materials Genome Initiative. Here, we determine the effect of texture of ferroelectric, ferroelastic, and piezoelectric materials to drive the simulation work. The models are being validated directly through coordinated experiments to test their predictions, leading to the development of material microstructures, textures and compositions that enhance its macroscopic  performance and reliability. Undergraduate, graduate and postdoctoral researchers we have established a thriving research community that extends to collaborations overseas and to open source applications that can be readily accessed through the nanoHUB.

Ferroelectric Thin Films

An innovative methodology was pioneered to utilize: 1) the experimental results of Electron Back Scattered Diffraction to map the crystallographic orientation of each grain, 2) the Finite Element method to simulate the local grain-grain interactions, and 3) Piezo-Force Microscopy to infer the local properties of polycrystalline ferroelectric materials by comparing the output of the numerical calculations with the experimental results. The combined integrated method resolves the local hysteretic and electromechanical interactions in polycrystalline ferroelectric films, thus quantifying the effects of grain corners and boundaries on the polycrystal's macroscopic response. 

Example results include the identification of a finite range of crystallographic orientations and epitaxial strains to enhance the out-of-plane electrical response of the film with respect to its single-crystal, stress-free counter part. Results show that {111} oriented grains parallel to the normal of the surface of the film yield the largest polarization magnitude enhancement, compressive stresses, and built-in electric fields, as well as an asymmetry in the quasistatic coercive field. In the absence of epitaxial strains, {001} oriented grains will be enhanced in their out-of-plane hysteretic response through the in-plane compressive stresses provided by the local neighboring grains. Grain corners and boundaries become favorable sites for pinning or nucleation of ferroelectric domains, depending on the local state of stress and polarization.

Current research (Sarah Leach, Logan Williams) focuses on the development of models that capture with realism the time evolution of domains in polycrystalline lead-free ferroelectric materials. Specifically, the development of models that describe the polarization switching kinetics in the vicinity of the morphotropic phase boundary is of particular interest. Here, we formulate phase field descriptions that simultaneously include the thermal, mechanical, and electric field contributions to the free energy from individual phases, e.g., for a two-phase system, fR(P, T), for the rhombohedral, and fT(P,T), for the tetragonal phase.The goal is to quantify the effects of microstructure to tailor the local and macroscopic hysteretic response for specific technological applications, such as actuators, mechanical sensors, and random access memories. 

Equilibrium Properties in Bulk Ferroelectrics

Computational and experimental methodologies have been integrated to define design criteria to maximize the properties of textured and untextured piezoelectric microstructures (Sukbin LeeThomas Key). Two-dimensional orientation maps measured through electron backscatter diffraction on sequential parallel layers, are used to reconstruct experimentally-determined three-dimensional samples and thus directly assess the properties and reliability of piezoelectric materials. Three-dimensionally reconstructed microstructures (see right) are used to generate detailed finite element models that realistically capture the shapes and crystallographic orientations of individual grains, and thus predict the macroscopic piezoelectric response and their associated mechanical and electrical reliability. Based on the knowledge acquired from experimentally analyzed samples, 3D computer-generated facsimiles (below) are assembled to explore the effects of accessible and inaccessible processing parameters on the macroscopic material properties. Thus, electrical shielding and stress field concentrations (bottom right) underscore locations where ferroelectric domains are pinned, nucleate, and grow, and also point to places where crack growth and arrest will be favored. Developed 3D models incorporate dielectric, elastic, as well as direct and converse piezoelectric effects. In addition, theories are developed to realistically capture the effects of processing, ferroelastic, and ferroelectric texture and thus propose optimal microstructures: grain sizes, poling fields, and textures.

Switching Kinetics in Bulk Ferroelectrics

In combination with the knowledge generated through the thin-film ferroelectric switching model (see Ferroelectric Thin Film Section), the multitude of grain-grain ferroelectric interactions that occur during poling in bulk ferroelectrics are being detailed in the present project (Eva-Maria Anton, Zizhao Zhao, and Sarah Leach). Here, switching mechanisms such as simple switching (where domains perform electrical work against the applied electric field) and domain pinning of domains are being quantified and experimentally demonstrated to understand the long-term large-field reliability of bulk ferroelectric materials.

As a recent application, the macroscopic hysteretic response associated with the underlying microscopic switching of domains of a polycrystalline ferroelectric was investigated for bipolar, sesquipolar, and unipolar electrical loadings. As a result of the intergranular interactions and physical electromechanical couplings, the statistical contribution from each of the self-stabilized interactions (see left) demonstrate that the asymmetric polarization distribution corresponds to the linear superposition of four Gaussian polarization distributions. Results show that in the sesquipolar regime, tensile stresses are minimized by 33% and compressive stress minimized by 38%. The maximum strain output decreases by only 1%, thus, making it a favorable fatigue-reduced actuation design. In this research a parameter to define asymmetric electric field loads, the electrical load ratio, RE, was defined. This description parallels the well- known mechanical load ratio, Rσ =σminmaxand is written as RE=Emin/Emax.