Multivariate Analysis on a Complex, Rare-Earth Doped Alumina Database with Fractal Dimension as a Microstructural Quantifier

Abstract

Alumina ceramics were obtained from three different alumina sources, A1–A3, with various rare-earth dopants (La₂O₃–La, Nd₂O₃–Nd, and Y₂O₃–Y), concentration levels (500 and 1000 ppm) and synthesizing routes (1500 °C, 1815 °C and cold plasma-P). Absorption (A) and density (ρ in text, rho in images) were measured, resulting in a complex, multivariate database. Principal Component Analysis (PCA) was run with the aim of deducing relationships between variables (alumina source, dopant level, thermal processing route, A and ρ), observations, and between variables and observations. A total of 206 Scanning Electron Microscopy (SEM) micrographs were recorded at various scales and the corresponding images were processed to quantify the microstructural features. Two techniques of edge detection were used; Fractal Dimension (FD) was calculated for each micrograph and results were compared. Various scales of the micrographs prevented us from using any other approach, such as simply measuring the grains or obtaining shape parameters. The initial database was extended by including FDs and PCA was run again. We found that plasma processing is positively correlated to A and negatively correlated to both temperature (T) and ρ; La ceramics have an opposite behavior to Y and Nd ceramics. FD successfully explained observations being correlated, mainly, to Y, Nd and, to a lesser extent, to La. FD proved that it is a reliable and simple approach to quantifying microstructural features when comparing highly different, noisy micrographs.