**2.1 Evolutionary route of solid formation**

Heterogeneity is the main feature of all hardening systems; therefore, when analyzing an evolutionary model, one should consider a heterogeneous composition consisting of different dispersion of solid particles placed in a liquid or gaseous medium (internal medium of the system) and in contact with the external environment space from which matter, thermal, mechanical energy, etc. can be introduced into the hardening system. When considering the processes of evolution of a solid substance in a heterogeneous system, a microvolume can be distinguished at a certain homogeneity. In this conditionally homogeneous system, the nucleation of a solid phase occurs.

In the chemical technology of homogeneous system substances, three determining methods for the synthesis and nucleation of solid particles (including nanoparticles) are distinguished: the ones leading to the formation of a new phase; the method based on the high-temperature reactions of interaction of two or more substances, leading to the formation of an insoluble product; and the method of condensation from the gas phase, when, as a result of redox reactions or hydrolysis reactions occurring in the gas phase, the solid phase is released.

In disclosing and analyzing a general evolutionary model of the formation of a solid, one can follow the interpretations of Melikhova [3]. In accordance with modern concepts applicable to systems of any composition, the following main stages

in the evolution of a substance can be distinguished in the formation of a solid: the nucleation of a solid phase, particle growth, agglomeration, and spontaneous transformation in time (**Figure 1**). In this case, it is necessary to speak of three evolutionary transitions between the stages and, accordingly, the phenomena of molecular, topological, and morphological selection. In the evolution of solids, two branches of the process development could be implemented: the left, corresponding to small (pre-foreign) supersaturations, and the right, corresponding to large (super-foreign) supersaturations of the phase-forming macrocomponent.

It is important to emphasize that each stage corresponds to a certain range of sizes of solid particles based on them. The size scale shown in **Figure 1** illustrates dimensional and geometric boundaries and limits. It is clear that we can use the "arsenal of nano" most significantly at the stages of nucleation of the phase and growth of particles; at other stages, other physicochemical methods of technological impact, affecting the micro- and macroscale of the evolutionary process, become priorities. This should be taken into account when developing methods of influence on each of the considered stages and transitions of the evolutionary route. Based on this, a detailed discussion of the determining stages of the evolutionary route and transitions between them should be carried out, bearing in mind the rationale and formation of "nanotools" but not only "nano" in the technology of building materials, if we take into account the problem of modifying the structure on all its scale levels.

#### **Figure 1.**

*The evolutionary path of formation of solid substances and "dimensional scale" of their structural components.*
