**2.1. History of the problem**

Atomic-molecular theory of matter structure is a basis of our understanding various properties of substances. Laws of Kirchhoff, Win, Stephan-Boltzmann and the Planck formula build a simplest model of optical, structural, thermal and chemical characteristics of substances: these laws are valid for any solids, liquids, gases, plasmas and radiation in the state of absolute black body. Our interest is focused on unity of these properties as a tool for introducing Formula Units or preventing a movement of solids to the state of black body.

This chapter presents a crystal-chemical model of unity of structural and optical properties and chemical and thermal characteristics for real solids. Self-consistence of their actions causes various departures of solid from the black body. Knowledge of these departures is necessary for proper choice of the object of investigation and working body under solving sciencetechnological tasks, in particular, for predicting and calculating efficiency of transformation solar heat → useful work.

The simplest Kirchhoff-Planck model gives identity of the optical properties of solids. Other‐ wise, the optical properties of real solids may belong to two groups according to sensing their atomic structure. Structural sensitivity of optical properties depends on atomic structure of the solid; absence of this sensitivity depends principally on electronic structure of the atom, ion, and other atomic particles. The fundamental absorption of UV-radiation is an example for the first case. The own color of solids and absorption of visual and IR-radiation are an example for the second case.

The first set of optical properties is defined by chemical composition of the light absorber; the second one is defined by mechanism of interaction between light and matter. A number of original works and reference editions summarize data on optical properties of solids in various aggregate and structural states. Here we will use one of them [30, 31, 56, 61].

Thermal properties of solids are characterized by melting heat, evaporation heat, sublimation heat, and by the energy of decaying chemical bonds. They are not so sensible to atomic structure as the optical properties. Sensing optical properties to structural changes is negligible in some cases.

Thermal and chemical properties of substances are subjected to the thermo-chemistry exami‐ nations. They are defined by the laws of thermodynamics and are studied well enough. Numerous data are reported in many reference books, for example, in [70]. Correlations of thermal and chemical properties of substances are considered in chemical thermodynamics. We should note the general theory of comparative calculating thermal properties proposed by Karapetjanz M.Ch. and Kireev V.A. in [37].

Crystals are presenting the limit case of regular and periodic locations of atomic particles in space. In non-crystalline solids there are micro-and nano-parts where the regular (partially periodical or completely crystal-like) distribution of atomic particles is also realized. Thus we will below consider the crystal as an ideal case of regular and periodical location of atomic particles.

**2. StructuI and formula units of crystalline substance**

Units or preventing a movement of solids to the state of black body.

Atomic-molecular theory of matter structure is a basis of our understanding various properties of substances. Laws of Kirchhoff, Win, Stephan-Boltzmann and the Planck formula build a simplest model of optical, structural, thermal and chemical characteristics of substances: these laws are valid for any solids, liquids, gases, plasmas and radiation in the state of absolute black body. Our interest is focused on unity of these properties as a tool for introducing Formula

This chapter presents a crystal-chemical model of unity of structural and optical properties and chemical and thermal characteristics for real solids. Self-consistence of their actions causes various departures of solid from the black body. Knowledge of these departures is necessary for proper choice of the object of investigation and working body under solving sciencetechnological tasks, in particular, for predicting and calculating efficiency of transformation

The simplest Kirchhoff-Planck model gives identity of the optical properties of solids. Other‐ wise, the optical properties of real solids may belong to two groups according to sensing their atomic structure. Structural sensitivity of optical properties depends on atomic structure of the solid; absence of this sensitivity depends principally on electronic structure of the atom, ion, and other atomic particles. The fundamental absorption of UV-radiation is an example for the first case. The own color of solids and absorption of visual and IR-radiation are an example

The first set of optical properties is defined by chemical composition of the light absorber; the second one is defined by mechanism of interaction between light and matter. A number of original works and reference editions summarize data on optical properties of solids in various

Thermal properties of solids are characterized by melting heat, evaporation heat, sublimation heat, and by the energy of decaying chemical bonds. They are not so sensible to atomic structure as the optical properties. Sensing optical properties to structural changes is negligible

Thermal and chemical properties of substances are subjected to the thermo-chemistry exami‐ nations. They are defined by the laws of thermodynamics and are studied well enough. Numerous data are reported in many reference books, for example, in [70]. Correlations of thermal and chemical properties of substances are considered in chemical thermodynamics. We should note the general theory of comparative calculating thermal properties proposed by

Crystals are presenting the limit case of regular and periodic locations of atomic particles in space. In non-crystalline solids there are micro-and nano-parts where the regular (partially periodical or completely crystal-like) distribution of atomic particles is also realized. Thus we

aggregate and structural states. Here we will use one of them [30, 31, 56, 61].

**2.1. History of the problem**

104 Solar Cells - New Approaches and Reviews

solar heat → useful work.

for the second case.

in some cases.

Karapetjanz M.Ch. and Kireev V.A. in [37].

After finding chemical individuality the crystal becomes a formula unit. The formula unit (FU is identical to the molecular unit of the substance in symbols of chemical elements. In a period for the X-ray analysis the mineralogy had a false opinion that the minerals are built from molecules, therefore, the mathematical crystallography did not need separating categories "structural unit of the crystal" and "formula unit of the crystal". Fedorov's crystallographic analysis made it possible to define the type of crystal lattice and, using his tables of mutual arrangement of the crystal facets gave a possibility to find out the chemical composition of the mineral, i.e. the formula unit [1]. However, the Fedorov's crystal-chemical analysis did not allow determining the particles which are to be located in the sites of the crystal lattice.

Invention of X-ray analysis made it possible to highlight the formula unit from the set of many structural units of the crystal. The modern crystallography and crystal chemistry consider atoms, ions, and their groups located at the sites of the crystal lattice as structural units. The contemporary X-ray structural analysis revealed a great number of structural units of the crystal which build a hierarchy. These data are described in various publications.

We have to note here that the first separation of categories "structural unit" and "formula unit" took place not in mineralogy, but in molecular theory worked out by Avogadro. It was appeared as a tool for describing chemical interaction of gases. At beginning of 50th years of 19th century it was further developed by A. M. Butlerov in theories of chemical structure, valence and coordination compounds. At the same time Kirchhoff investigations led to optical identification of structural units of the substance-to the atom and molecule.

Spectral analysis is not a decisive tool for determining structural unit and formula unit of the crystal. For example, in the crystal of magnium oxide (periclas) one can differ atoms' groups Mg, O, Mg4O4, MgO6, Mg6O, and many others. The first two ones are filling in the primitive crystal cell. The third structural unit symbolizes a formula unit of the substance; the next ones present the content of the elementary cell and coordination groups of atoms. All these units are the most important parts of crystal structure of periclas. Optical identification of the crystal does not consider its formula unit as one of the structural units. Modern hierarchy of these categories had been formed in crystallography and mineralogy as a consequence of neutron, electron, X-ray, and other structural analytical methods only.

Laue M., Friedrich W. and Knipping P. in 1913 made it possible to find out a function between experimentally observed diffraction patterns from dark points at one side and real locations of atoms in crystals and X-ray wave length from the other side. Scientific achievements of Bragg W. G. and Bragg W. L. reduced the analysis of simple crystals to the standard technique. It was a beginning of a new method of crystallographic analysis called X-ray crystallography. Laue M., Bragg W. G. and Bragg W. L. were awarded by Nobel Preis (1914, 1915).

Fedorov E.S. understood for the first time that only the atoms but not molecules are to be located periodically in the space at the sites of crystal lattice [17]. It was his explanation of false attempting to connect the molecule geometry with the form of crystal [16]. Further Fedorov E. S. carefully analyzed and discussed [18] works of Bragg W. G. and Bragg W. L. [11] and had found out that in chemical sense inorganic crystals are not built from separate atomic groups [18], he has correctly assumed existence of molecules in crystals of organic compounds [118].

[23, 36, 71] showed that the crystal structure is determined not only by the energy of particles interaction, relationship of their dimensions, polarization, but also by their number. So that the choice and numbering structural units of the crystal are of special importance for describing correlations between optical and thermal properties of crystal in dependence on the atomic structure.

X-ray structural analysis of simple crystals and complex chemically crystals allowed finding out geometric parameters of elementary cell, i.e. there is a cell of minimal dimension which keeps symmetry of atomic structure of the crystal. The relation between the volume of the structure cell Vcell and density of crystal *ρ* is as follows:

$$\mathbf{V}\_{\text{cell}} = \mathbf{M}\_0 \mathbf{Z} \,/\,\text{(çN}\_{\text{A}}\text{)}\_{\prime}$$

where M0 is mass of one mole of molecules, and NA is the Avogadro constant. Letter Z denotes a number of formula units in the cell of the crystal. After substituting a picknometry density of the crystal in this relation it became clear that the parameter Z is a rational constant of the crystal structure and elemental cells of various crystals can have one, two, three, or more formula units.
