Session: 12-22-01: Multiscale Models and Experimental Techniques for Composite Materials and Structures

Paper Number: 150556

150556 - Nonuniqueness in Defining the Polarization: Nonlocal Surface Charges and the Electrostatic, Energetic, and Transport Perspectives 

Ionic crystals, ranging from dielectrics to solid electrolytes to complex oxides, play a central role in the development of modern technologies for energy storage, sensing, actuation, and other functional applications. Mesoscale descriptions of these crystals are based on the continuum polarization density field to represent the effective physics of charge distribution at the scale of the atomic lattice. However, a long-standing difficulty is that the classical electrostatic definition of the macroscopic polarization — as the dipole or first moment of the charge density in a unit cell — is not unique; rather, it is sensitive to translations of the unit cell in an infinite periodic system. 
As a simple example to drive home the issue, consider a 1D line of point charges consisting of alternating positive and negative charges. The polarization, defined as the dipole moment per unit cell can be thought of as an arrow going from the negative charge to the positive charge. However, every negative charge has two neighboring positive charges. The choices result in completely opposite sign for the polarization density, which explains the non-uniqueness.

This unphysical non-uniqueness has been shown to arise from starting directly with an infinite system — wherein the boundaries are ill-defined — rather than starting with a finite body and taking appropriate limits. This limit process shows that the electrostatic description requires not only the bulk polarization density, but also the surface charge density, as the effective macroscopic descriptors; that is, a nonlocal effective description. Other approaches to resolve this difficulty include the popular modern theory of polarization that completely sets aside the polarization as a fundamental quantity in favor of the change in polarization from an arbitrary reference value and then relates the change in polarization to the transport of charge (the “transport” definition); or, in the spirit of classical continuum mechanics, to define the polarization as the energy-conjugate to the electric field (the “energetic” definition).

This work examines the relation between the classical electrostatic definition of polarization, and the transport and energy-conjugate definitions of polarization. We show the following: (1) The transport of charge does not correspond to the change in polarization in general; instead, one requires additional simplifying assumptions on the electrostatic definition of polarization for these approaches to give rise to the same macroscopic electric fields. Thus, the electrostatic definition encompasses the transport definition as a special case. (2) The energy-conjugate definition has both bulk and surface contributions; while traditional approaches neglect the surface contribution, we find that accounting for the nonlocal surface contributions is essential to be consistent with the classical definition and obtain the correct macroscopic electric fields.

Presenting Author: Shoham Sen University of Houston

Presenting Author Biography: Shoham Sen got his undergraduate degree in Mechanical Engineering from Jadavpur University in Kolkata, West Bengal. He then went to the Indian Institute of Science (IISc Bangalore) to receive a Masters of Research in Engineering (locally described as a mini PhD) in the field of structural acoustics from the Mechanical Engineering department. Being a lover of Mathematics and Physics, and wanting to broaden his horizon, he went on to pursue a PhD in Computational Mechanics from the Department of Civil and Environmental Engineering at Carnegie Mellon University. Under the tutelage of Kaushik Dayal, he focused on the abinitio modeling of Quantum Mechanical Phenomenon. Here he honed his advanced physics and mathematics skills. His thesis was titled "Nonlocal Dipolar Interactions in Complex Geometries for Quantum Embedding". In this thesis, he analyzed the non-uniqueness in the dipole definition of polarization and presented a real space approach to counter the non-uniqueness. This is in contrast to the Fourier space approach usually presented as counter to the non-uniqueness. After completing his PhD at CMU, he went to the University of Minnesota as a Postdoctoral associate working with Dr. Richard D James on superconductivity. Superconductivity has been described as a second-order phase transition (the thermodynamic variables change continuously across the transition). Shoham's focus at the University of Minnesota was to find a superconductor that achieves superconductivity via a first-order phase transition (thermodynamic variables change discontinuously across the transition). His job was to analyze the literature on superconductors to find materials that might have been incorrectly categorized as a 2nd-order phase transforming superconductor. He presented models (respecting first-order phase transformation) that matched the experimental response. He then went on to make predictions that could be validated by experiments. He then decided to do another postdoc, this time at the University of Houston under the tutelage of Dr. Pradeep Sharma. His research interest here was also on superconductivity, but he looked at modification to the Ginzburg Landau model of superconductivity due to Gurtin. Gurtin's model had extra terms that were missing from the traditional model of superconductivity. Have made progress on the scalar version of the problem, mapping it via a series of transformations into the original Ginzburg Landau problem, he is analyzing the tensorial version of the same problem.

Authors:

Shoham Sen University of Houston
Yang Wang Pittsburgh Supercomputing Centre
Kaushik Dayal Carnegie Mellon University