Hafnium-silicate capacitors with 4.5-nm equivalent oxide thickness gate insulators were irradiated with 10-keV X-rays. The midgap and flatband voltage shifts in these devices increase linearly with dose and are significantly larger than the shifts seen in high quality, thermal SiO2 gate oxides of similar electrical thickness. The standard trapping efficiency equation is adapted for calculating effective trapping efficiencies in alternative dielectrics and used to compare the radiation response of hafnium silicate to SiO2 from several manufacturers. The effects of common reliability screens such as "burn-in" and bias stress tests are also discussed. It is shown that baking these devices can degrade their capacitance-voltage characteristics, and large applied voltages inject excess charge into the dielectric, which can lead to a misinterpretation of the radiation results. However, the radiation responses of these devices, coupled with the demonstrated resistance of these films to heavy-ion induced gate rupture in previous studies, suggest that alternative dielectrics to SiO2 potentially could be integrated into future electronics technologies for many low-power space applications.