Transmittance predictions for transparent alumina ceramics based on the complete grain size distribution or a single mean grain size replacing the whole distribution

Abstract

A simple method, based on the equivalent composite model or the dense polycrystalline model, is proposed for predicting the in-line transmittance in ceramics with a grain size distribution of birefringent crystallites. It is shown that the transmittance predictions based on the Rayleigh-Gans approximation are indistinguishable from those based on Mie theory, so that the latter can be replaced by the former. Based on normal distributions of different position and width it is shown that size distributions with smaller mean sizes lead to higher transmittance, whereas the effect of the distribution width on the transmittance is comparatively weak (with the narrowest distribution being the most favorable for high transmittance). The key result of this paper is the fact that for the distributions investigated (normal and log-normal) the transmittance prediction based the whole grain size distribution can be replaced by a transmittance prediction based on the geometric mean of the intensity-weighted distribution.