Ferroelectric Materials by Design at the Mesoscale: Thermodynamic and Phase-Field Modeling
Restricted (Penn State Only)
- Author:
- Zorn, Jacob
- Graduate Program:
- Materials Science and Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 17, 2022
- Committee Members:
- John Mauro, Program Head/Chair
Venkatraman Gopalan, Major Field Member
Ismaila Dabo, Major Field Member
Jinchao Xu, Outside Unit & Field Member
Long-Qing Chen, Chair & Dissertation Advisor
Roman Engel-Herbert, Major Field Member - Keywords:
- phase-field
thermodynamic
ferroelectric
landau theory
TDGL
Cahn-Hilliard
Allen-Cahn - Abstract:
- Ferroelectric materials are characterized by the presence of a macroscopic polarization that can be reoriented under sufficiently high external forces, such as electrical fields. The coupling of ferroelectric materials and various external fields, such as mechanical or electrical, allow for a wide variety of applications, such as transducers, capacitors, and detectors, along with emerging applications such as neuromorphic computing and random-access memories. The device architecture of ferroelectric materials has a large effect on the properties of the material system. Therefore, it is critical to understand how various external conditions, fields, and device architectures can be tuned to optimize the performance of ferroelectrics for next generation applications. While traditionally this optimization has taken place using lab experiments, which be both time-consuming and monetarily prohibitive, the computer age has given researchers the opportunity to conduct “virtual experiments” toward the optimizing these properties and materials. This dissertation is motivated by the Materials by Design paradigm which exists to help speed-up the process of creating new materials and within which we apply this paradigm to the mesoscale level via thermodynamic and phase-field modeling. Motivated by a need to speed-up materials calculations and expand current material models, this dissertation seeks to address both within the context of ferroelectric materials while providing critical connections to other fields and applications. We seek to improve and hasten phase-field models by way of a novel adaptive time-stepping schemes, while introducing new solvers and models to accompany thermodynamic models of ferroelectrics. Through the incorporation of these two synergetic computational models, we demonstrate a pipeline toward faster material design and therefore property optimization. The goal of this dissertation will be to introduce new software tools, novel solvers, and innovative models for the modeling of ferroelectric materials while simultaneously applying these advanced techniques to present research problems to expand materials knowledge. The main content of this dissertation is split into three main parts. Firstly, three new schemes will be introduced for the modeling, simulation, and processing of ferroelectric materials. A novel evolutionary solver is described and tested for a host of materials science problems as we seek to solve complex extrema problems. Then an energy-based adaptive time stepping scheme is proposed for speeding up phase-field simulations while maintaining highly accurate solutions. Finally, to wrap up the first section, we describe the use of vector decompositions and computational fluid dynamics applied to polarization distributions. We demonstrate that using these methods it is possible to programmatically identify vortices in a vector field to aid in the analysis of high-throughput datasets, like what is possible to generate in today’s high performance computing space. The second section sees the application of these new novel tools and models to research problems. Specifically, we utilize the adaptive time-stepping in each of the works due to the thousands of phase-field simulations that were performed. First, we demonstrate the existence of exotic polarization vortices and skyrmions in lead-free Barium Titanate/Strontium Titanate superlattices, while presenting evidence for the control and manipulation of these exotic structures. By manipulating the mechanical boundary conditions by adjusting the underlying rare-earth substrate, while simultaneously controlling the thicknesses of the ferroelectric layers, polar vortices can be stabilized in a variety of cases providing needed guidance toward the construction of lead-free superlattices with exotic polar states. Combining the phase-field methods with thermodynamic models we study the polydomain states of the lead-free ferroelectric (Ba1-x, Cax)TiO3 and how the domain stability diagrams change for different levels of doping in the system. Lastly, we study the effect of electrical boundary conditions on the domain structures of the common lead titanate (PbTiO3) system toward controlling the growth of ferroelectric superdomains. Unlocking the mechanisms behind the formation of these superdomains as well as understanding how to manipulate the superdomain structures, it is demonstrated that the electrical boundary conditions play a large role in the construction of these superdomains. Using electrical fields we are able to tune and change the morphology of these superdomains toward developing curated domain structures. The final section of this dissertation is dedicated to the discussion of a novel software, termed Q-POP-Thermo, which can be used to identify the stable ferroelectric monodomain states and their properties in both bulk single crystals and thin-film architectures. It is expected that the software will be helpful toward providing a unified framework for the thermodynamic modeling of not just ferroelectrics but also many other systems as the software continues to grow as an open-source platform. In addition, a novel thermodynamic polydomain model is introduced that a priori predicts the domain structure and the domain wall orientations of ferroelectric systems. The model is shown to accurately predict the domain variants, domain fractions, and domain wall orientations when compared to phase-field models but in a fraction of the computing time. Through the combination of accurate thermodynamic modeling alongside efficient phase-field modeling codes the opportunities for effective materials modeling are endless.