Multiscale Modeling and Simulation of Ferroelectric Materials

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The state of the art in material modeling offers accurate simulation methods for specific length and time scales, spanning from electronic structure calculations and molecular mechanics at atomistic scales to continuum formulations at the macroscale. However, computational costs limit the length and time scales accessible to atomistic simulation techniques. As a noteworthy exception, the quasicontinuum (QC) method reduces computational costs without losing atomistic detail in regions where it is required. Thereby it reduces the number of degrees of freedom by introducing kinematic constraints, which interpolate lattice site positions from the positions of a reduced set of representative atoms. In addition to kinematic constraints, summation rules are introduced to efficiently reduce the number of lattice sites to be considered in the computation of energies and forces. The QC method has proven useful to study exemplary problems in multiscale material modeling such as nanoindentation, interaction of lattice defects with nanosized cracks and nanovoids, etc.However, the established QC method has two central limitations. First, it does not extend satisfactorily to multi-lattice crystals to capture non-uniform behavior within a unit cell or a molecule. Second, and more importantly, it does not extend to ionic crystals, since long-range Coulomb interactions present an additional challenge for the QC method. The QC summation rules take advantage of typical short-range interatomic potentials, which admit the local evaluation of quantities of interest. When long-range interactions gain importance, such a concept no longer applies. This restriction on the nature of atomic-level interactions for the conventional QC method excludes its application to a large class of materials; all dielectrics, polarizable solids, and ionic solids.The QC method, therefore, does not find application to study the rich dielectric behavior of typical functional materials that are central to modern technologies in energy storage, sensing/actuation, etc. Developing and extending the QC method for ionic crystals is thus a significant leap in broadening the applicability of the method. Therefore, through this project we propose a novel extended QC method that is applicable to multi-lattice crystals and ionic crystals thereby overcoming limitations of the established QC method. The preliminary work undertaken at LTM using a QC software developed and implemented in-house shows promising results and indicates that the proposed extended QC method will indeed apply effectively to ionic crystals. Thus in summary, the goals of this project are (i) extension of the QC method to multi-lattice crystalline materials, (ii) extension of the QC method to handle long-range Coulomb interactions, (iii) implementation of these extensions and providing the first open-source library for three-dimensional QC simulations, and (iv) the study of ferroelectric behavior using the extended QC method.