The results of a statistical study of hard x-ray solar flares are presented in this dissertation. Two methods of analysis were used, the Diffusion Entropy (DE) method coupled with an analysis of the data distributions and the Rescaled Range (R/S) Method, sometimes referred to as "Hurst's method". Chapter one provides an introduction to hard x-ray flares within the context of the solar environment and a summary of the statistical paradigms solar astronomers currently work under. Chapter two presents the theory behind the DE and R/S methods. Chapter three presents the results of the two analysis methodologies: most notably important evidence of the conflicting results of the R/S and DE methods, evidence of a Levy statistical signature for the underlying dynamics of the hard x-ray flaring process and a possible separate memory signature for the waiting times. In addition, the stationary and nonstationary characteristics of the waiting times and peak intensities, are revealed. Chapter four provides a concise summary and discussion of the results.

In this work, we have utilized an ion beam process known as gettering to migrate implanted Ni ions much deeper into the bulk substrate than their initial projected end of the range. The projected mean depth is known as Rp. The gettering effect is the most crucial part of the fabrication and we have found that for an H fluence of 3x 1016 cm-2 there is a threshold fluence of approximately 7.5 x 1015 cm-2 that cannot be surpassed if the gettering process is to be completed along with the substrate recovered to the high crystalline quality. This hard threshold is due to the gettering process relaxation induced mechanism that is responsible for migrating the Ni to the Rp/2 location while the H is vacating during the thermal annealing process. If the total number of vacancies produced by the H dissociation is not substantially larger than the total number of implanted Ni atoms the Ni will migrate to the Rp location of the Ni implantation at the amorphous and crystalline interface and toward the surface. When the gettering condition is not met the resulting magnetic responses vary from an exceptionally weak ferromagnetic response to not exhibiting a magnetic response. Additionally, …