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.

尽管通常使用空间电荷模型来解释质子传导钇取代的BaZrO _3中的高晶界电阻，它无法以最简单的形式使用10–40的系数来拟合晶界阻抗特征频率的实验数据。我们建议对模型进行修改，以提高其拟合度。包括钇取代基附近的质子的俘获效应仅将误差减小了小于1.6的因子。增加晶界核的宽度可将误差减小1.5-3倍。离散化空间电荷层，使质子只能驻留在特定的离散位置上，从而将误差降低了约2倍。考虑到通过减小GB的有效面积来降低其在GB中的质子迁移率，可能会降低GB的拟合误差。系数为2。改变GB中的介电常数不会显着影响误差。每种修改或其组合效果都不能，