Light scattering models for describing the transmittance of transparent and translucent alumina and zirconia ceramics

Abstract

The original Apetz-van-Bruggen model for predicting the transmittance of dense polycrystalline ceramics with randomly oriented birefringent crystallites is shown to be incorrect. In a correct Apetz-van-Bruggen equivalent composite model (ECM) the volume fraction must be 1/3 instead of 1/2 and the factor 2/3 in front of the maximum birefringence must be abandoned. This ECM is in good agreement with the simplified version of Pecharromán’s dense polycrystalline model (DPM) and can be improved by replacing the Jobst approximation (i.e. the large-size limit of the Rayleigh-Gans approximation) by the van-de-Hulst approximation. Similarly, a new DPM is proposed that combines the van-de-Hulst approximation with Pecharromán’s texture function. However, all these models fail for small grains. Therefore two new models (infimum-supremum-based ECM and DPM) are proposed, which combine the full Rayleigh-Gans approximation (for small grains) with the van-de-Hulst approximation (for large grains) and provide (for all grain sizes) predictions almost identical to Mie theory.