This dissertation presents single crystal studies of Pd.213Cd.787 and Pd.235Cd765, synchrotron powder studies of Pd1-xCdx, 0.755 >= x >= 0.800, and LDA-DFT and extended Hueckel (eH) calculations on these or related phases. The two single crystal structures have a, b, and c axis lengths of respectively 9.9013, 14.0033, 37.063 and 9.9251, 14.0212, 60.181 angstroms. Their structures are in respectively Ccme and F2mm (solved as (3+1)-dimensional crystals their most convenient superspace group is Xmmm00gamma)s00). The structures have two different structural components each with their own separate axis parameters. Powder data shows that the ratio of these separate axes, S/L, varies from 1.615 to 1.64, values near the golden mean (1.618). For Pd.213Cd.787, different Pd and Cd site occupancies lead to variation in the R-factor from 2.6-3.6%. The site occupancy pattern with the lowest R-factor (among the 26,820 variants studied) is the exact site occupancy pattern predicted by LDA-DFT parameterized eH Mulliken charge populations. The phases can be understood through a chemical twinning principle found in gamma-brass, the parent structure for the above phases (a relation with the MgCu2 Laves phase is also noted). This twinning principle can be used to account for Cd and Pd site prefences. At the same time there is a clean separation among the Cd and Pd atoms for the two separate chain types at height b=0 and 1/2. These results indicate that Cd:Pd stoichiometry plays a role in phase stability.

The second chapter presents the single crystal structures of Pd.211Cd.789 and Pd.204Cd.796 in an abbreviated form. It explicitly details the results of the synchrotron powder diffraction study in chapter one as well as the 4-dimensional refinements of Pd.213Cd.787 and Pd.235Cd.765. In addition, a variable temperature, synchrotron powder x-ray diffraction study is given for Pd.210Cd.790.