X-ray diffraction and transmission electron microscopy have been used to examine the microstructures of thin films of pure ZrO₂ - SiO₂ films formed by e-beam coevaporation. The results suggest that films composed of 100% ZrO₂ grow by the formation of tapered polycrystalline columns. Near the substrate the columns are small in diameter and consist of a single crystalline phase, but at increasing distances from the substrate the column diameters increase and material with two polycrystalline phases appears. At a given distance from the substrate, small additions of SiO₂ to the film composition result in a smaller column diameter. Films with 25 mole% SiO₂ show an amorphous electron diffraction pattern, a result consistent with previously observed x-ray diffraction patterns. The surfaces of the amorphous films appear nearly featureless and are significantly smoother than the surfaces of the pure ZrO₂ films.