**3. Mechanisms of Spherical Vaterite Formation**

The crystallization of calcium carbonate crystalline polymorphs often occurs via amorphous calcium carbonate (ACC), which is initially formed in the solution [42]. The structure of the ACC precursor consists of a porous calcium-rich nanoscale framework containing water and carbonate ions. ACC is transformed into vaterite due to the rapid dehydration and internal structure reorganization. It is suggested that the possibility of crystallization of the vaterite particles occurs, as the initially generated ACC exhibits proto-vaterite features. [43]. In the final stage, the slow transformation of vaterite into calcite takes place via a dissolution and recrystallization process [42].

There are two main concepts proposed for the explanation of spherical vaterite formation. The first one is based on the aggregation of nanoparticles and the second mechanism is a development of the classical theory of crystal growth [44]. According to the first concept, the production of polycrystalline vaterite particles is a result of the assembly of nano-sized crystals by oriented or not-oriented attachment [44,45]. The aggregation requires the production of many small particles at the beginning of the reaction, which is supported by a high supersaturation. The aggregation mechanisms were applied to interpret both the formation of core-shell microspheres [45] and hollow vaterite particles [46]. It was suggested that the core-shell vaterite structure was a result of a successive aggregation and coverage of formed spheres with hexagonal plates [45] in the presence of poly(styrene sulfonic acid) sodium salt, while the precipitation with the addition of ethylene glycol led to the formation of an initial shell structure from the primary nanoparticles and then hollow vaterite particles [46].

However, the spherulitic growth mechanism is based on the classical theory of crystal growth [44]. Spherulites are produced when a new nucleus arises on the surface of the growing crystal. Based on the experiments, two concepts of spherical growth are proposed: (i) Spherulites arise from a central precursor via multidirectional growth of crystalline fibers, and (ii) spherules grow from a precursor via low angle branching starting on the edges [44,47]. The spherulitic growth mechanism was used to explain the formation of vaterite particles with spherical and dumbbell morphology [47,48].
