Stereology of dense polycrystalline materials—from interface density and mean curvature integral density to Rayleigh distributions of grain sizes

Using transparent yttrium–aluminum garnet (YAG) as an example, the microstructure of dense polycrystalline ceramics is investigated by microscopic image analysis. The mean chord length and Jeffries grain size determined via stereological relations are 9.9–11.3 μm and 19.0–21.3 μm after 2 h and 16 h of firing at 1735 °C, respectively. Distributions of grain size sections are determined via image analysis and transformed via Saltykov, Cruz-Orive and Woodhead transformations. None of the weighted means or deciles of these distributions corresponds to the mean chord length or Jeffries size exactly, but the distributions of 2D grain size sections are almost identical to the 3D grain size distributions obtained after transformation, which is possible only for Rayleigh distributions. It is shown that the grain size distributions determined here are indeed close to Rayleigh distributions that evidently arise as a result of certain grain growth and ripening processes (Ostwald ripening).