The electron energy loss spectrometer at Virginia Tech has been modified with new momentum deflectors and various other hardware improvements. In addition to some hardware changes all the software to run the spectrometer and analyze the data has been rewritten. It was suggested by Tsuei (1990) that a nested Fermi surface could be used to explain both the fact that these materials have high superconducting transition temperatures and have linear relaxation rates. It was suggested in that same paper that EELS might be able to confirm the presence of Fermi surface nesting. We have attempted to use transmission electron energy loss spectroscopy in a novel way to search for evidence of Fermi surface nesting in the high T_c superconductor Bi₂Sr₂Ca₁Cu₂O₈. High quality single crystal samples were obtained and thinned for use in the EELS. Data was taken at low energy (<1.0eV) and momentum was scanned along three different momentum transfer directions for |q| =0.0 to 3.0Å⁻¹. The data was scaled to be Im(-1/ε). A calculation of Im(-1/ε) was performed using a tight binding model and it was found that the features associated with the Fermi surface (from this TB calculation) were too small to be seen in our spectra. We interpret this problem to be associated with the presence of thermal diffuse scattering. / Ph. D.