Introduction -- Theory of Supercooled Liquids and Glasses -- Experimental Techniques -- Rare Earth Doped Barium Titanate Glass -- Liquid-Liquid Transitions in Y2O3-Al2O3 -- Liquid Invar -- Indium Selenide -- Conclusions.

This thesis presents neutron scattering data that contribute to the understanding of four distinct areas of condensed matter physics, including iso-compositional liquid-liquid phase transitions and the glass formation in rare earth doped BaTi2O5. In situ aerodynamic levitation with laser heating was combined with neutron scattering in order to study both liquid-liquid phase transitions in (Y2O3)x(Al2O3)1-x, and the atomic and magnetic ordering in liquid Invar. Among several significant results, obtained in this case from small angle neutron scattering, was the absence of a phase transition across a range of temperatures and compositions in the yttria aluminates.  As these are a principal system in which liquid-liquid phase transitions have been hypothesized, this is an important contribution in a contentious area.