This proposal is concerned with understanding the properties of materials used in important applications in catalysis and energy, such as in molecular transformations of exhaust gases for environmental remediation. We will study the local atomic structure of a set of mixed cerium-zirconium oxides to examine the issue of phase separation on the nanoscale. We need to understand why materials with the same chemical composition can have very different properties, thus by measuring the distribution of atoms on the local to medium-range length scale we will uniquely determine a signature of atomic structure. We will also investigate the early stages of chemical synthesis by making a study of gel precursors of the same materials. Then we can understand both which structural characteristics are important for optimum materials, and which synthesis conditions are needed to achieve this.