The combinatorial approach to materials research is based on the synthesis of hundreds or thousands of related materials in a single experiment. The popularity of this approach has created a demand for new tools to rapidly characterize these materials libraries and new techniques to analyze the resulting data. The research presented here is intended to make a contribution towards meeting this demand, and thereby advance the pace of materials research.

The first part of the dissertation discusses the development of a materials characterization tool called a near field microwave microscope (NFMM). We focus on one particular NFMM topology, the open ended coaxial resonator. The traditional application of this NFMM topology is the characterization of the dielectric properties of materials at GHz frequencies. With the goal of expanding the capabilities of the NFMM beyond this role, we explore two non-traditional modes of operation. The first mode is scanning ferromagnetic resonance spectroscopy. Using this technique, we map the magnetostatic spin wave modes of a single crystal gallium doped yttrium iron garnet disk. The second mode of operation entails combining near field microscopy with scanning tunneling microscopy (STM). Operating in this mode, we show that the NFMM is capable of obtaining atomic resolution images by coupling microwaves through an atomic scale tunnel junction.

The second part of the dissertation discusses the analysis of X-Ray Diffraction (XRD) data from combinatorial libraries. We focus on two techniques that are designed to simultaneously analyze all of the XRD spectra from a given experiment, providing a faster method than the traditional one-at-a-time approach. First, we discuss agglomerative hierarchical cluster analysis, which is used to identify regions of composition space that have similar crystal structures. Second, we discuss non-negative matrix factorization (NMF). NFM is used to decompose many experimental diffraction patterns into a smaller number of constituent patterns; ideally, these constituent patterns represent the unique crystal structures present in the samples. Compared to hierarchical clustering, NMF has the advantage of identifying multi-phase regions within the composition space. These techniques are also applicable to other types of spectral data, such as FTIR, Raman spectroscopy, XPS, and mass spectrometry.