This dissertation essentially consists of three related studies concerned with quantifying the structure and micromechanical state of bulk polycrystalline materials. They are contained in Chapters 1, 2 and 3, which may be read independently. The emphasis is on the development of new methods for the analysis and interpretation of generalized pole figure data.

Chapter 1 contains an expanded version of a manuscript my coauthors and I have submitted for review [3]. In it, a robust method for obtaining an orientation distribu- tion function (ODF) from pole density functions (PDFs) is presented. The method uses the gradient norm of the ODF for conditional control of the solution in the context of a constrained minimization problem. The introduction has been expanded to include a detailed definition of the ODF and PDF. Several additional sample applications of the method have also been included, as well as several appendices that elaborate on the mathematical formalism of orientations and other technical aspects of the implementation.

Chapter 2 is largely similar to a second manuscript that has been provisionally accepted for publication in the Journal of Applied Crystallography [5]. In it, the methods developed in Chapter 1 have been adapted to obtain a lattice strain distribution function (LSDF) from strain pole figures (SPFs). The proposed SPF inversion method utilizes conditional control formulated independently of any kinematic linking assumptions.

In Chapter 3, a methodology is presented for extracting generalized pole figure data from 2-d powder diffraction images. An example application of this analysis, along with the methods presented in Chapters 1 and 2, is provided using data obtained via an in situ loading/diffraction experiment performed at the Cornell High Energy Synchrotron Source.

The fourth and final chapter provides a summary of the salient scientific contributions of this dissertation, along with proposed extensions of the research. Together, the 3 methods presented in this dissertation provide a set of tools for characterizing the structure and micro-mechanical state of polycrystalline materials at the bulk scale. Most importantly, the resulting distributions are suitable for direct comparison to the predictions of structure-based models of polycrystalline materials.