Aspects of the invention include a method of producing a cement material comprising step of: first reacting a calcium-bearing starting material with a first acid to produce an aqueous first calcium salt; second reacting the aqueous first calcium salt with a second acid to produce a solid second calcium salt; wherein the second acid is different from the first acid and the second calcium salt is different from the first calcium salt; and thermally treating the second calcium salt to produce a first cement material. Preferably, but not necessarily, during the second reacting step, reaction between the first calcium salt and the second acid regenerates the first acid.