Moment invariants for two-dimensional and three-dimensional characterization of the morphology of gamma-prime precipitates in nickel-base superalloys

The relation between microstructural features and a material's properties is central to materials science. Certain morphological features of a microstructure can only be determined by 3-D characterization techniques, e.g. the connectivity of precipitates, and the true precipitate shape; others require geometric assumptions for stereological estimates, e.g. precipitate size distribution and the number of precipitates. When these inherently 3-D features affect the properties of a specific material, experimental techniques are necessary to investigate the 3-D nature of the microstructure, and to provide a more complete microstructural characterization.;The quantitative description of 2-D and 3-D shapes is of fundamental importance to microstructural characterization. One approach to describing a microstructure is to characterize the shapes of individual precipitates. This characterization has typically been limited to particle size, aspect-ratio, and other qualitative descriptors. In general, these are insufficient and do not provide an adequate characterization in a way that allows for a direct comparison between different microstructures. This is evident during microstructure evolution when changes in precipitate morphology occur or when precipitates exhibit complex shapes. In this thesis, we show how moment invariants (combinations of second order moments that are invariant w.r.t. affine or similarity transformations) can be used as sensitive shape discriminators in 2-D and 3-D.;This work focuses on the characterization of the two phase microstructure of nickel base superalloys and specically the gamma-prime (Ni3Al) precipitate morphology. Experimental data is collected by means of automated Focused-Ion Beam (FIB) based serial sectioning. Techniques for automated image processing and segmentation are developed which allow for direct conversion of raw serial-sectioning data to 3-D microstructural data. The gamma-prime precipitate morphology is characterized using second order moment invariants in conjunction with other shape parameters such as volume and surface area. This provides a quantitative description of the gamma-prime precipitate morphology and allows for variations in morphology to be identified.