Abstract
Although the space charge model is commonly used to explain the high grain boundary resistance in proton conducting yttrium-substituted BaZrO3, it fails in its simplest forms with factors 10–40 to fit experimental data with respect to the characteristic frequency of the grain boundary impedance. We suggest modifications to the model, somewhat improving its fit. Including trapping effects of protons near yttrium substituents reduces the error only by factors less than 1.6. Increasing the width of the grain boundary core reduces the error with factors of 1.5–3. Discretizing the space charge layer, such that protons can only reside on specific, discrete sites, reduces the error with another factor of around 2. Considering reduced proton mobility in the GB by reducing its effective area may give a reduction in the fitting error of a factor of 2. Varying the dielectric constant in the GB does not affect the error considerably. Neither each single modification, nor their combined effect, can, however, account for the majority of the discrepancy between the space charge model and experimental data.
Highlights
Introduction to transmission electron microscope (TEM)Figure 8 shows a simplified schematic of the TEM column, highlighting the parts most relevant for electron holography
In the (2 1 0) Grain boundaries (GBs), the CPU cost is reduced by around 75% compared to the brute force method; in the (1 1 1) GB, the CPU cost is reduced by around 85%
This stems from the assumption that the GB core is positively charged with an excess of segregated oxygen vacancies and protons, and that the GB resistance is a result of the depletion of these charge carriers in the adjacent space charge layers
Summary
Introduction to TEMFigure 8 shows a simplified schematic of the TEM column, highlighting the parts most relevant for electron holography. A major drawback is the low grain boundary (GB) conductivity, typically orders of magnitude lower than the bulk conductivity [2,3,4,5,6]. This is usually explained by strongly proton-depleted and highly resistive space charge layers. These are induced by positively charged defects segregating to the GB core to lower lattice mismatch strain there [4], generating a net electrostatic potential. Since the area of interest around the GB is in the range of only a few nanometers, direct experimental observation of the GB potential is challenging
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