X-ray polycrystalline diffraction techniques are used to determined the defect structure in a commercial Cu-l1.55 at. %Be-O.23 at. %Co alloy during low temperature aging. The analysis of the X-ray diffraction patterns is aided by the computer modeling of the defects inside the crystals using an elastic model. The research is to provide more detailed understanding of the precipitate structures in the process of aging and the age hardening mechanism of the alloy. The diffraction profiles from samples aged for different times at 315°C are collected using a position sensitive proportional counter with eu 1(0:1 radiation. The hardness values of the samples are also measured. An elastic model for the coherent precipitates in anisotrpic matrix is developed according to Eshelby's treatment of transformed regions in an elastic continuum. The displacement fields generated by the precipitates in the surrounding matrix, obtained through the elastic model, are used to explain the (110) streaks near the Bragg reflection, and to calculate the powder diffraction patterns from the aged alloys. For the latter purpose, a general X-ray diffraction theory is developed, combining the work of Krivoglaz and Dederichs. The X-ray diffraction patterns are compared with existing TEM observations in the literature. The analysis of the diffraction patterns suggests that the precipitates in the early stage of aging (GP zones) can be the matrix constrained version of 7, the equilibrium phase, similar to an observation by Khatchaturyan and Laughlin on 7 and 7'. The quantitative calculation based on this model shows excellent agreement with experimental data for samples aged at 315°C. The averaged inter-precipitate spacing in the crystals for the optimally aged sample at 315°C is determined to be 200-300A. A simplified method of evaluating the thermal diffuse scattering and a method for calculating the diffuse scattering from polycrystalline materials with textures are also presented. / Ph. D.