*3.3.3. Amorhous and dispersive bodies*

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

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

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

**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

on the type of syngony of a bulk crystal [48, 51, 52].

112 Solar Cells - New Approaches and Reviews

effects.

atom is not observed.

under normal conditions.

In extreme cases of aggregation of atoms or molecules the density of small particle can reach the density of solid phase, in particular, of the crystalline phase. When the aggregation of atoms is completed by formation of micro-particles, the formation of a massive body is possible, and Fig. 2a can be considered as an illustration of the mass distribution in amorphous body, which represents the fine system of ultramicroparticles. Chaotic arrangement of points disappears if the value of density of substance in each point of Fig. 2a will be divided by the mass of one mole of atoms. The result is presented in Fig. 2b.

The ordinate in Fig. 2brepresents the logarithm of the density of amount of substance, expressed per mole of molecules/m3 . It is seen that the lowest values of σ have alkaline and alkaline-earth metals; the highest values σ have boron, beryllium and carbon. Other solid substances have intermediate values of the density of amount of substance under specification of their structural elements as formula unit.

The dependence p/M0-Rat for gases can be shown in Fig. 2b by the horizontal line lg p/M0=1.65. Points between straight lines for gases and solids can be characterized the structure of small particles: from molecules, nano, nano-particles, small particle to microparticle, bulk liquid and solid body. Table 1 shows values of the density of amount σ for number of simple substances calculated by equation (2). Under calculating σ the structural element of the substance has corresponded to the chemical formula of the compound. In condensed phases the structural element in exceptional cases corresponds to a molecule or atom. The data show that the lowest values of σ have alkaline and alkaline-earth metals; the highest values of σ have boron, beryllium and carbon. It should be noted that the liquid hydrogen has maximum σ. Other solid and liquid substances have intermediate values of the density of the amount of substance under specification of their structural elements as formula unit.


**Table 1.** Values of density and density of amount of substance for some simple matters

According to Fig. 2b and Table 1, the points showing the density of amount of substance of liquids and radii of the atoms are arranged between straight lines for solids and gases. The position of these points allows giving a qualitative characteristic of the structure bodies. So that, liquid bromine and liquid mercury with their structure are similar to solids. In opposite, liquid helium and liquid nitrogen are maximally removed from the line of correlation. Absence of own correlation among them confirms the fact that liquids are the transitional state in condensation of gas to solid. Therefore, one should not expect the existence of a universal equationof state for liquids. These states should be described by special solutions of the equation of state of the real gas and solid body. An example is the equation of van der Waals describing condensation of gas to liquid, and a chain of equations by Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) which describes the melting of a solid body.
