Quantitative characterization and comparison of precipitate and grain shape in Nickel -base superalloys using moment invariants

A fundamental objective of materials science and engineering is to understand the structure-property-processing-performance relationship. We need to know the true 3-D microstructure of a material to understand certain geometric properties of a material, and thus fulfill this objective. Focused ion beam (FIB) serial sectioning allows us to find the true 3-D microstructure of Ni-base superalloys. Once the true 3-D microstructure is obtained, an accurate quantitative description and characterization of precipitate and/or grain shapes is needed to understand the microstructure and describe it in an unbiased way.;In this thesis, second order moment invariants, the shape quotient Q, a convexity measure relating the volume of an object to the volume of its convex hull, V/Vconv, and Gaussian curvature have been used to compare an experimentally observed polycrystalline IN100 microstructure to three synthetic microstructures. The three synthetic microstructures used different shape classes to produce starting grain shapes. The three shape classes are ellipsoids, superellipsoids, and the shapes generated when truncating a cube with an octahedron. The microstructures are compared using a distance measure, the Hellinger distance. The Hellinger distance is used to compare distributions of shape descriptors for the grains in each microstructure. The synthetic microstructure that has the smallest Hellinger distance, and so best matched the experimentally observed microstructure is the microstructure that used superellipsoids as a starting grain shape. While it has the smallest Hellinger distance, and is approaching realistic grain morphologies, the superellipsoidal microstructure is still not realistic.;Second order moment invariants, Q, and V/V conv have also been used to characterize the γ' precipitate shapes from four experimental Ru-containing Ni-base superalloys with differences in alloying additions. The superalloys are designated UM-F9, UM-F18, UM-F19, and UM-F22. The different alloying additions in each sample cause differences in lattice misfit and γ' precipitate shape morphology, varying from spherical, to cuboidal, to intermediate morphologies. 3-D datasets from each alloy were collected via automated Focused Ion Beam (FIB) serial sectioning. Digital image processing methods are used to register, clean, and segment the images in each of the datasets in order to digitally reconstruct the microstructures in 3-D. The distributions of the shape descriptors of the γ' precipitates from each microstructure are compared using the Hellinger distance. The Hellinger distance determines if there are quantitative differences in the γ' precipitate morphologies, or if they are the same. It was found that comparing distributions of the second order affine moment invariant Ω 3 with the Hellinger distance is sufficient for recognizing that alloys have different compositions.;The secondary γ' precipitate shapes in two Ni-based superalloys, one from a UM-F20 alloy with cuboidal precipitates, and one from a Rene-88 DT alloy with more complex dendritic precipitates, have been decomposed and reconstructed using 3-D Zernike functions, which are orthogonal over the unit ball; they can be used to decompose an arbitrary shape scaled to fit inside an embedding sphere into spherical harmonics. Relatively complex shapes can be decomposed into, and reconstructed from, 3-D Zernike functions. In this thesis we show the 3-D Zernike functions and a method to derive expressions for Zernike moments from the more familiar geometric moments. Then Zernike moment reconstructions up to order 20 of precipitates from the two Ni-base superalloys are presented. The Zernike moment reconstructions were characterized using second order moment invariants, and have yielded good reconstructions of cuboidal precipitates. More orders of Zernike moments may be needed to accurately reconstruct the dendritic precipitates.;We also introduce the concept of moment invariant density maps to describe 3-D shapes using 2-D moment invariants. To do this we characterize 2-D sections of a 3-D microstructure using 2-D moment invariants. The statistical distribution of 2-D moment invariants from the sections are compared to a library of density maps produced from different shapes. The sectioning plane is random so each group of particles produces a statistical distribution of 2-D moments that can represent a microstructure. Then we show three example applications: determination of a 3-D shape by computing the Hellinger distance between moment invariant density maps derived from random 2-D section micrographs and the density map database; automated detection and quantification of rafting in cuboidal microstructures; and quantitative comparison of pairs of microstructures.