Andrea M. Jokisaari

Topological phase transformations and intrinsic size effects in ferroelectric nanoparticles

Composite materials comprised of ferroelectric nanoparticles in a dielectric matrix are being actively investigated for a variety of functional properties attractive for a wide range of novel electronic and energy harvesting devices. However, the dependence of these functionalities on shapes, sizes, orientation and mutual arrangement of ferroelectric particles is currently not fully understood. In this study, we utilize a time-dependent Ginzburg-Landau approach combined with coupled-physics finite-element-method based simulations to elucidate the behavior of polarization in isolated spherical PbTiO3 or BaTiO3 nanoparticles embedded in a dielectric medium, including air. The equilibrium polarization topology is strongly affected by particle diameter, as well as the choice of inclusion and matrix materials, with monodomain, vortex-like and multidomain patterns emerging for various combinations of size and materials parameters. This leads to radically different polarization vs. electric field responses, resulting in highly tunable size-dependent dielectric properties that should be possible to observe experimentally. Our calculations show that there is a critical particle size below which ferroelectricity vanishes. For the PbTiO3 particle, this size is 2 and 3.4 nm, respectively, for high- and low-permittivity media. For the BaTiO3 particle, it is ∼3.6 nm regardless of the medium dielectric strength.

Benchmark problems for numerical implementations of phase field models

Abstract We present the first set of benchmark problems for phase field models that are being developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST). While many scientific research areas use a limited set of well-established software, the growing phase field community continues to develop a wide variety of codes and lacks benchmark problems to consistently evaluate the numerical performance of new implementations. Phase field modeling has become significantly more popular as computational power has increased and is now becoming mainstream, driving the need for benchmark problems to validate and verify new implementations. We follow the example set by the micromagnetics community to develop an evolving set of benchmark problems that test the usability, computational resources, numerical capabilities and physical scope of phase field simulation codes. In this paper, we propose two benchmark problems that cover the physics of solute diffusion and growth and coarsening of a second phase via a simple spinodal decomposition model and a more complex Ostwald ripening model. We demonstrate the utility of benchmark problems by comparing the results of simulations performed with two different adaptive time stepping techniques, and we discuss the needs of future benchmark problems. The development of benchmark problems will enable the results of quantitative phase field models to be confidently incorporated into integrated computational materials science and engineering (ICME), an important goal of the Materials Genome Initiative.

Phase field benchmark problems for dendritic growth and linear elasticity

Abstract We present the second set of benchmark problems for phase field models that are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input from other members in the phase field community. As the integrated computational materials engineering (ICME) approach to materials design has gained traction, there is an increasing need for quantitative phase field results. New algorithms and numerical implementations increase computational capabilities, necessitating standard problems to evaluate their impact on simulated microstructure evolution as well as their computational performance. We propose one benchmark problem for solidification and dendritic growth in a single-component system, and one problem for linear elasticity via the shape evolution of an elastically constrained precipitate. We demonstrate the utility and sensitivity of the benchmark problems by comparing the results of (1) dendritic growth simulations performed with different time integrators and (2) elastically constrained precipitate simulations with different precipitate sizes, initial conditions, and elastic moduli. These numerical benchmark problems will provide a consistent basis for evaluating different algorithms, both existing and those to be developed in the future, for accuracy and computational efficiency when applied to simulate physics often incorporated in phase field models.