*3.3.2. Small particles*

Atomic structure of bodies in general theory of systems supposes availability of atomic aggregates between gases and condensed bodies with properties which are fundamentally differ or are intermediate between the properties of isolated atoms of gas and bounded atoms of bulks. Usually aggregates from two to several hundred atoms are called clusters, and the larger aggregates are called small or microparticles [13]. The clusters as well as particles can have linear size more than 1 nm. At present time they are called nano-clusters and nanopar‐ ticles that expect different dimension effects. There are no general criteria for type definition of small particles on the number of atoms. In paragraph X of this chapter we propose to consider crystalline nanoparticles the particles which have no translation in the atomic arrangement. These groups contain from 27 to 63 atoms of one chemical element, depending on the type of syngony of a bulk crystal [48, 51, 52].

It is seemed to be reasonable to identify the structural element as the formula unit in calcula‐ tions of the number of substances of small particles. In the case of simple substances the mass of mole of formula units is equal to the mass of the mole of atoms; in the case of chemical compounds it is equal to the mass of the mole of molecules. Characters of these molar quantities are marked with lower index "0". Therefore, the values σ<sup>0</sup> may describe the density of amount of substance of nanoscaled bodies and they will be useful in examining features of dimension effects.

The principle of construction of physical quantities "density of matter and density of amount of the substance" is the same for all bodies: the ratio of the corresponding main unit to the volume as a value derived from the length. However, their functional relationships principally differ from the linear dimension. For example, the density of the bodies ρ depends on the chemical composition. The diversity of chemical composition can be expressed through the radius of the atom. In Fig. 2a these densities p of chemical elements are compared with the radius of the atom: any correlation between the density of small particles and the radius of the atom is not observed.

**Figure 2.** (a)-uncorrelative density ρ and radius of the atom in crystals of simple solids: metals, semiconductors, dielec‐ trics. Points of gases densities are coinciding with abscissa axes; (b)-correlation between the density of amount of sub‐ stance σ or ratio ρ/M<sup>0</sup> of the density to the mole weight and the radius of atom in simple solid. lg ρ/M=1.65 for all gases under normal conditions.

If we take into account the chemical identity of atoms through the mass of the mole, there is a linear correlation of the amount of substance σ of the small particle from the radius of the atom. For example, the density of the amount σ of any gaseous substances under the same conditions is constant. Therefore, the boundary between the molecule, nanocluster, nanoparticle and a bulk of the given substance can be found according to the nature of the dependence of the density of amount σ0 of the substance on the radius of atom or molecule. Let's consider a simple example.

The sizes of the atoms are in a periodic dependence on the number of the chemical element in the Periodic system. The density of amount σ0 of gaseous substance does not depend on the size of atom or molecule. For example, for all gases under normal conditions lgσ<sup>0</sup> is equal to 1.65. If lgσ<sup>0</sup> of the gaseous system exceeds this value, one should consider a body consisting of small particles. The more lgσ0 differs from 1.65, the smaller particle differs from the molecule. Molecular associates in gases can be an example. The density of small particles in aerosols and gels is higher; the deviation lgσ0 from 1.65 will be significant.
