Compositions, methods, and systems related to multi-modal distribution of vaterite particles

A system comprising:

• (i) a calcining reactor configured to calcine limestone to form a mixture comprising lime and a gaseous stream comprising carbon dioxide;
• (ii) a dissolution reactor operably connected to the calcination reactor configured for dissolving the mixture comprising lime in an aqueous N-containing salt solution to produce an aqueous solution comprising calcium salt;
• and
• (iii) a treatment reactor operably connected to the dissolution reactor configured for treating the aqueous solution comprising calcium salt with the gaseous stream comprising carbon dioxide to form a composition comprising bimodal distribution of reactive vaterite cement comprising reactive vaterite cement A having an average particle size of between about 0.1-10 μm and reactive vaterite cement B having an average particle size of between about 11-50 μm.