**6. Crystal-chemical symbolism and system theory**

Sulfur anions form cubic close packing with tetrahedral voids [65]. Half of them are filled in with zinc cations, while the second half is empty. When four tetrahedral voids are temporarily filled in due to photon excitement, the part of the solid (4ZnS) will lose the particles' placement

Comparing states (21) and (22), one can acknowledge that if the states

(Zn4S4)0and Zn4S4

are energetically identical, the predissociation of the crystal cell in Fig. 7b may be presented

(Zn4S4)\*→4 ZnS (non-crystal)→4 ZnS (quasi-gas)

between energetically identical states if ε=4Δ*H*subl/*N*A. So, in the cell Zn4S4 of sphalerite there are 2Z=8 tetrahedral voids, half of which is populated by 4 zinc atoms. Remaining 4 voids can provide their space to Zn atoms at the moment of pre-dissociation of no more than 4 chemical

**3.** Following this example, we consider the cell of wurtzite, Zn2S2, while *Z=*2. The cell can increase its potential energy through the resonance absorption of a photon with energy

(Zn2S2)0= (Zn2S2) \* +ε,

Sulfur anions form cubic close packing with tetrahedral voids [65]. Half of them are filled in with zinc cations, while the second half is empty. When four tetrahedral voids are temporarily filled in due to photon excitement, the part of the solid (4ZnS) will lose the particles' placement

(Zn2S2)\*→2 ZnS (non-crystal)→2 ZnS (quasi-gas)

between energetically identical states if ε=2Δ*H*subl/*N*A. Thus, in Zn2S2 of wurtzite there 2Z=4 tetrahedral voids half of which is populated by 2 atoms of zinc. Remaining 2 nanovoids can provide their space to Zn atoms at the moment of pre-dissociation of no more than 2 chemical

is the basic state of the cell and (Zn2S2)\* is an excited state.

Zn S sphalerite = 4 ZnS non-crystal + 4 / , 4 4 ( )( ) *H N*<sup>A</sup> D (22)

(crystal)

symmetry, and we will write

134 Solar Cells - New Approaches and Reviews

bonds Zn-S in spectral experiment.

ε. Then, according to Fig. 7b we can write

as a transition

where (Zn2S2)

0

symmetry, and we will write

bonds Zn-S in spectral experiment.

In the general theory of systems, the category of "emergence" is used as an effective tool for studying natural, economic, and social objects. The system has emergent properties, i.e. properties that are not inherent in its subsystems and modules as well as the ensemble of its elements without system-forming bounds. System properties are not reduced to the sum of the properties of its components. In solid-state physics, the emergence can be expressed as follows: one particle is not a body. For example, the symmetry of the body is not applicable to the individual particle. The photon is a particle that is not subjected to disassembling in elements or subsystems. The system consisting of photons has emergent properties. For example, the photon gas, unlike the unique photon, is characterized by its temperature and entropy. In the solar cell, the photon is one of the components of the system "crystal radiation". In this chapter, we consider one of the changes in the system emergence as an antenna process. In crystallography and crystal chemistry, the emergence is the appearance of new functional unities of crystal that are not reduced to a simple rearrangement of particles.

In the system classification, the emergence can be the basis of their systematics, representing the criterion feature of the system. Let us consider the single crystal as a set of interrelated atomic particles located in the respective specific order, i.e. as a system, and denote it with **S**. It has emergent properties. For example, a crystal system is characterized by the symmetry of the external shape as well as by the symmetry of the spatial location of atomic particles.

Authors of [9] define the crystal system **S** as a set of individuals belonging to a mineral species that are, in turn, present in the crystalline formations of the atoms of corresponding chemical elements; these sets of atoms can independently exist with further growth.

In crystalline systems, the crystallinity and size limit can serve as the unifying community feature. Work [9] describes the elements of such systems. Their reality makes it possible, for example, to measure the amount of substance in the initial stage of crystallization by the mole of seeds, the number of cosmic dust particles by the mole of dust, the amount of substance in real crystal by the mole of blocks that are broken by line and screw dislocations, nuclear, and other macroscopic defects. The substance of colloidal solutions may be measured by the mole of colloidal particles that they contain. Let us denote such elements with the letter **b**.

In this chapter we will consider the element **b** as a crystal system **S\*** and characterize it by the element that corresponds to the symmetry of the crystal. Note that this element is denoted as **a**. In the first approximation, the element **a** is formed in an ideal crystal environment and is defined as a set of atoms of chemical elements; the number of these elements is limited and is equal to the multiplicity of regular point systems. The element **a**, that keeps the chemical composition of the crystal does not exist independently.

In connection with the definition of the element **a**, the special procedure for defining the substance quantity of a crystal consists of disassembling systems **S** and **S\*** into new subsys‐ tems, i.e. into such systems where the internal laws correspond to the geometric theory of the structure of crystals. Such subsystems are identified by us with the element **a** and are identified as the structural elements of matter (elementary entity).

The practical value of disassembling such crystal systems is that for the first time we have an opportunity to relate the quantitatively geometrical properties of the crystal with the density of the matter and the mass of the atoms, and to describe other characteristics through these features.

This relation is based on the individuality of the ratio value of the regular points systems of crystalline space. That is why the ratio of the amount of element a present in relation to the crystal volume is its characteristic value. This value will be called the "density of substance quantity" with the measurement unit of a mole. It characterizes the number of structural elements of substance in the crystal volume. It is necessary to clarify that the other physical quantity, "density," is characterized not by quantity, but by weight. Therefore, it is obvious that the values of the "density of matter" and the "density of the amount of a substance" differ in terms of their physical nature.

The density of the amount of a substance was introduced into scientific practice only recently in [42] as a derived quantity stated in SI and marked with the letter σ. The unit σ represents the "moles per cubic meter." The crystal as a system is characterized by the ratio of the volume, ν, of the amount of a substance to its volume, V. Therefore, the equations defining and linking it with other physical values are the following:

$$\circ \circ \circ \text{/V =} \circ / \text{M}\_{\prime} \tag{23}$$

where M is the mass of a mole of a structural element of the substance or a structural element **a** of the subsystem **S\*** in the system **S**; *ρ* is the density of matter.

The values σ for gases do not depend on the chemical nature. For example, according to Avogadro's law, σ is a gas under normal conditions equal 44.6 moles of molecules per cubic meter. The values σ for crystals are individualized and are determined by the formula derived from Eq. (23)

$$\sigma \equiv \mathbb{Q} / \boldsymbol{\Sigma}^{\mathrm{n}}\_{\;\;\;\;\mathrm{i}} \left( k\_{\mathrm{i}} \mathbf{M}\_{\mathrm{i}} \right) . \tag{24}$$

where *k*<sup>i</sup> is the multiplicity of a regular points system for atoms of i-sort; Mi is the mass of moles for atoms of i-sort. For example, the denominator of the ratio (24) for СаF2 equals

In this chapter we will consider the element **b** as a crystal system **S\*** and characterize it by the element that corresponds to the symmetry of the crystal. Note that this element is denoted as **a**. In the first approximation, the element **a** is formed in an ideal crystal environment and is defined as a set of atoms of chemical elements; the number of these elements is limited and is equal to the multiplicity of regular point systems. The element **a**, that keeps the chemical

In connection with the definition of the element **a**, the special procedure for defining the substance quantity of a crystal consists of disassembling systems **S** and **S\*** into new subsys‐ tems, i.e. into such systems where the internal laws correspond to the geometric theory of the structure of crystals. Such subsystems are identified by us with the element **a** and are identified

The practical value of disassembling such crystal systems is that for the first time we have an opportunity to relate the quantitatively geometrical properties of the crystal with the density of the matter and the mass of the atoms, and to describe other characteristics through these

This relation is based on the individuality of the ratio value of the regular points systems of crystalline space. That is why the ratio of the amount of element a present in relation to the crystal volume is its characteristic value. This value will be called the "density of substance quantity" with the measurement unit of a mole. It characterizes the number of structural elements of substance in the crystal volume. It is necessary to clarify that the other physical quantity, "density," is characterized not by quantity, but by weight. Therefore, it is obvious that the values of the "density of matter" and the "density of the amount of a substance" differ

The density of the amount of a substance was introduced into scientific practice only recently in [42] as a derived quantity stated in SI and marked with the letter σ. The unit σ represents the "moles per cubic meter." The crystal as a system is characterized by the ratio of the volume, ν, of the amount of a substance to its volume, V. Therefore, the equations defining and linking

where M is the mass of a mole of a structural element of the substance or a structural element

The values σ for gases do not depend on the chemical nature. For example, according to Avogadro's law, σ is a gas under normal conditions equal 44.6 moles of molecules per cubic meter. The values σ for crystals are individualized and are determined by the formula derived

( ) <sup>n</sup>

σ=ν/ V =ρ/ M, (23)

i=1 i i σ=ρ/ Σ M , *k* (24)

composition of the crystal does not exist independently.

as the structural elements of matter (elementary entity).

features.

from Eq. (23)

in terms of their physical nature.

136 Solar Cells - New Approaches and Reviews

it with other physical values are the following:

**a** of the subsystem **S\*** in the system **S**; *ρ* is the density of matter.

$$4\text{M}\_{\text{Ca}} + 8\text{M}\_{\text{Fe}}$$

because the multiplicity of the regular points system for calcium atoms equals 4 and for fluorine atoms it equals 8. Taking into account the density of matter, the σ value for СаF2 equals 10.2 kmol of element **a** in a cubic meter, and the mole of element **a** corresponds to the mole of elementary Bravais cells in the crystal.

In this chapter, we calculated σ values for simple substances and chemical compounds that are crystallizing in differently spaced symmetry groups. The multiplicity of regular points systems may differ from each other under calculation, so that the amount of element **a** in a given crystal system may vary by the number of included atoms. In this case, a unit mass of a substance will contain a different number of elements **a**. In other words, we can say that the phenomenon of polymorphism is a reflection of the state of a unit mass of a crystal with a different number of substances. For example, the multiplicity of a regular points system of carbon-12 in a diamond equals 8 and in graphite it equals 2. Thus, 0.012 kg of carbon-12 corresponds to either an 1/8 mole of diamond or a 1/4 mole of graphite. Let us explain the value of a mole of graphite. There are two sorts of carbon atoms with the same multiplicity of regular points systems in graphite. Thus, the denominator of relation (24) equals

$$\text{2M}\_{\text{C1}} + \text{M}\_{\text{C2}} = \text{4M}\_{\text{graphite}}$$

because MC1=MC2. The values σ are equal to 36.6 and 47.0 moles of elements **a** in a cubic meter of diamond and graphite, respectively.

The use of a multiplicity of a regular points system in calculations of substance amounts in crystals allows us to reveal completely unexpected correlations in numerous known experi‐ mental data. For example, the enthalpy values of gas-crystal phase transitions related to the mole of elements **a** correlate to the wavelengths of the absorption of substances in the ultra‐ violet region of the electromagnetic spectrum. The description of this correlation is presented in the next section, in which the element **a** of the crystal system is presented through the Bravais cell.
