**2.2. State-of-the-art of the problem**

In this chapter the formula unit of the crystal is a group of atomic particles corresponding to the molecule of the substance. The formula unit gives information about chemical elements and their relationship in the crystal. Thus writing the formula unit of the crystal as a set of chemical elements' symbols coincides with an analogical denote of chemical molecule. In crystal of organic compounds the formula unit of the crystal corresponds to the molecule, but its elemental cell may be formed by different molecules. The formula unit of the inorganic crystal may correspond to the real object, namely, to the molecule of substance, but its elemental cell can also not correspond to the formula unit or molecule of the substance.

Despite the evidences of ionic structure of minerals they were further called "molecules". Thus, the crystal was called "a giant molecule" [21], p.128, which is not correct. In 50th years of XX century the international crystal-chemistry literature started using the category "formula unit" as an alternative to the category "molecule". Authors [7] have critically analyzed the situation. At present time the category "formula unit" is practically usable in crystal-chemistry literature regardless the absence of its official formulation.

A long discussion how is the ionic crystal to be presented: single macromolecule or a set of any structural units was ended by separation of categories "formula unit, cell, individuum, and crystal habitus" and establishment of hierarchical relationships between them.

If using categories "formula unit" and "cell of the crystal structure" is now doubtless, the category "individual of crystal" is still attractive for researchers. This topic is almost completely

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

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

Vcell= M0Z / (ρNA),

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

In this chapter the formula unit of the crystal is a group of atomic particles corresponding to the molecule of the substance. The formula unit gives information about chemical elements and their relationship in the crystal. Thus writing the formula unit of the crystal as a set of chemical elements' symbols coincides with an analogical denote of chemical molecule. In crystal of organic compounds the formula unit of the crystal corresponds to the molecule, but its elemental cell may be formed by different molecules. The formula unit of the inorganic crystal may correspond to the real object, namely, to the molecule of substance, but its elemental cell can also not correspond to the formula unit or molecule of the substance.

Despite the evidences of ionic structure of minerals they were further called "molecules". Thus, the crystal was called "a giant molecule" [21], p.128, which is not correct. In 50th years of XX century the international crystal-chemistry literature started using the category "formula unit" as an alternative to the category "molecule". Authors [7] have critically analyzed the situation. At present time the category "formula unit" is practically usable in crystal-chemistry literature

A long discussion how is the ionic crystal to be presented: single macromolecule or a set of any structural units was ended by separation of categories "formula unit, cell, individuum,

If using categories "formula unit" and "cell of the crystal structure" is now doubtless, the category "individual of crystal" is still attractive for researchers. This topic is almost completely

and crystal habitus" and establishment of hierarchical relationships between them.

structure cell Vcell and density of crystal *ρ* is as follows:

structure.

106 Solar Cells - New Approaches and Reviews

formula units.

**2.2. State-of-the-art of the problem**

regardless the absence of its official formulation.

**Figure 1.** Kathodoluminescence image (a) of polished diamond surface (size 300 μm2 ) [32, 41];.auger-electron image (b) of polycrystalline lead sulphide surface [60] and the map (c) of isolines of concentration of Fe2+ions in the wafer of oli‐ vine [2].

worked-out by G. B. Bokii with using an example of individuals in mineralogy [9]. Vesnin Yu. I. wrote in his preprint [73] about "elemental unit of the crystal" principally corresponding to the category of individual. At present time one considers a monograin or monocrystal with a surface of phase separation as an individual. A separate crystal block with sizes of 10-5 ÷ 10-6 сm is called sub-individual if dangle chemical bonds, linear and screw dislocation, and other defects of crystalline structure are concentrated along the boundaries of this crystalline block. These blocks are relatively disoriented in 1 – 3<sup>о</sup>, sometimes up to 5о. Namely, the sub-individ‐ uals of the crystal are regions of coherent X-ray dispersion [9].

The crystal sub-individuals may be identified by tunnel electron microscopy. Fig. 1a shows an electron image of diamond surface obtained in mode of the cathodoluminescence of the sample [32, 41]. White fields can be considered as images of sub-individuals, and the black ones are images of their boundary regions. Fig. 1b plots Auger-electron image of the polycrystalline PbS film [60]. The seed of the crystal is also may be considered as its sub-individual.

Results [2] are also present identification of olivine sub-individual by method of optical spectroscopy. Fig. 1c illustrates a map of isolines built for distribution of arbitrary concentra‐ tion of Fe2+ions in the wafer of olivine crystal.

The distance between the closest isolines is significantly larger than the measurement error. Points show regions of photometry. Authors [2] suppose microblock-like structure of the olivine crystal. The blocks are of submicron sizes but they have practically same crystallo‐ graphic orientation which is highlighted by simultaneous turning-off of the entire crystal in crossed Nicole prisms under microscopic examination. These properties of olivine and absence of interruptions in isolines are allowing to assume that identificated blocks of the crystal are sub-individuals of olivine.

Modern X-ray analysis has no difficulties in giving principal information about geometry of crystal cells. There is a big data set on numbers and multiplicity of regular point systems, and on numbers of formula units in cells of many crystal structures. There is no doubt that these properties are affecting the facets of the crystal. Many outside forms of crystals are studied and identified. As an example one can use Fedorov's crystal-chemical analysis allowing determination of the crystal formula unit from its macro-and microsymmetry.

Habitus (facets working-out) is a visual level of structure organization of any crystal. It was found out that the facets are to be described by simple forms: by a single form or by a combi‐ nation. The simple form is a set of facets defining by elements of symmetry of point group satisfying the Hauyi law. If the crystal visuallyoutside presents the same and symmetrical facets, it can be described by a simple form. If the facets are differing by shape and size the crystal habitus may be presented by a combination of simple forms. Now we know47 geo‐ metrically different simple forms, 146 physically different simple forms [5], and 1403 struc‐ tural-cry stallographic differentiations [68]. The number of facets is not countable. For example, in [23, 24] are presented more than 30000 images of the crystals.

Atoms coordination in the crystal is caused by their spatial localization. The complex of symmetry location elements does not multiply the symmetry. However, the plane out of this location will be cloned and will create one of the simple forms (shapes) depending on its placement relative to the elements of symmetry for a chosen location. When all peaks of the simple form or part of them will belong to equivalent positions relative to the chosen one, the symmetry of the simple form should be bound with symmetry of coordination polyhedron [51, 52].
