Concrete, a mixture formed by mixing cement, water, and fine and coarse mineral aggregates is used in the construction of nuclear power plants (NPPs), e.g., to construct the reactor cavity concrete that encases the reactor pressure vessel, etc. In such environments, concrete may be exposed to radiation (e.g., neutrons) emanating from the reactor core. Until recently, concrete has been assumed relatively immune to radiation exposure. Direct evidence acquired on Ar$^+$-ion irradiated calcite and quartz indicates, on the contrary, that, such minerals, which constitute aggregates in concrete, may be significantly altered by irradiation. Specifically, while quartz undergoes disordering of its atomic structure resulting in a near complete lack of periodicity, i.e., similar to glassy silica, calcite only experiences random rotations, and distortions of its carbonate groups. As a result, irradiated quartz shows a reduction in density of around 15%, and an increase in chemical reactivity, described by its dissolution rate, similar to a glassy silica; i.e., an increase of around 3 orders of magnitude. Calcite however, shows little change in dissolution rates - although its density noted to reduce by around 9%. These differences are correlated with the nature of bonds in these minerals, i.e., being dominantly ionic or covalent, and the rigidity of the mineral's atomic network that is characterized by the number of topological constraints (n$_c$) that are imposed on the atoms in the network. The outcomes are discussed within the context of the durability of concrete structural elements formed with calcitic/quartzitic aggregates in nuclear power plants.