No abstract

We apply inline electron holography to investigate the electrostatic potential across an individual BaZr 0.9 Y 0.1 O 3 grain boundary. With holography, we measure a grain boundary potential of -1.3 V.Electron energy loss spectroscopy analyses indicate that barium vacancies at the grain boundary are the main contributors to the potential well in this sample. Furthermore, geometric phase analysis and density functional theory calculations suggest that reduced atomic density at the grain boundary also contributes to the experimentally measured potential well.

Metamaterial effective parameters may exhibit freedom from typical dispersion constraints. For instance, the emergence of a magnetic response in arrays of split-ring resonators for long wavelengths cannot be attained in a passive continuous system obeying the Kramers-Kronig relations. We characterize such freedom by identifying the three possible asymptotes which effective parameters can approach when analytically continued. Apart from their dispersion freedom, we also demonstrate that the effective parameters may be redefined in such a way that they have a certain physical meaning for all frequencies. There exists several possible definitions for the effective permittivity and permeability whereby this is achieved, thereby giving several possible frequency variations for high frequencies, while nevertheless converging to the same dispersion for long wavelengths.

Common approximations used in space charge modelling are assessed on a BaZrO3 grain boundary.

A selective sampling procedure is applied to reduce the number of density functional theory calculations needed to find energetically favorable grain boundary structures. The procedure is based on a machine learning algorithm involving a Gaussian process, and uses statistical modelling to map the energies of the all grain boundaries. Using the procedure, energetically favorable grain boundaries in BaZrO 3 are identified with up to 85% lower computational cost than the brute force alternative of calculating all possible structures. Furthermore, our results suggest that using a grid size of 0.3 Å in each dimension is sufficient when creating grain boundary structures using such sampling procedures.