**6.1. The photon and the crystal cell as elementary entities of matter**

The mole is a unit of measure of an amount of substance, i.e. the number of atoms, molecules, ions, or other elementary entities of a substance (EES). We are adopting a definition of the mole that was presented at the 14th General Conference on Measures and Weights in 1971: "mole is equal to the amount of substance of a system containing in carbon-12 with a mass of 0.012 kg. In application of the mole, the elementary entities must be specified: they may be atoms, molecules, ions, electrons, or other particles or specified groups of particles" [12, 67], IUPC, 1988).

The mole is applied to a gas without any difficulty. In a liquid, the specification of elementary entities often creates difficulties. In the application of the mole to a crystal, we propose specifying the elementary entities in accordance with the basic indicator of a crystal—its threedimensional periodic structure.

The elementary cell will correspond to such an elementary entity. In this case, the elementary entity will be characterized by the number of formula units *Z*. For example, the formula of the elementary entity of fluorite is written as Ca4F8; *Z* will be equal to 4. Here it has been shown that the elementary entity corresponding to an elementary cell of the crystal is an object that is capable of absorbing a quantum of energy.

Let us examine this in the example of copper, for which the formula of the elementary entity is written as Cu4. Through the symbol Δ*Ε* we will denote the change in the energy of the crystal upon the dissociation of a mole of Cu4 into an ideal atomic gas. The value of Δ*Ε* can be calculated based on Hess' law:

> Cu4 (crystal)↔4 Cu (gas).

Under isobaric conditions, the heat of this reaction is equal to the enthalpy change Δ*H*. Then Δ*Ε* will be equal to the product of *Z* and the Δ*H* of the sublimation of copper:

$$
\Delta E = Z \,\,\Delta \mathbf{H}\_{\text{subl}}
$$

For copper at 1 atm and 250 C, according to [70], Δ*Ε*=4·80.7=323 kcal/mol.

Let us assume that one of the mechanisms of radiation absorption by a crystal is resonance absorption by an elementary entity of a quantum of energy, *ε*=Δ*Ε*/NA, where NA is the Avogadro number. After resonance absorption, the transition of the elementary entity from a stable electronic state to an unstable state is possible without any change in energy. Such a transition is called "predissociation." It may also end in the dissociation of an elementary entity.

If the probability of absorption of an energy quantum *ε* makes it possible for the intensity of absorption to exceed the background level, an individual peak in the absorption spectrum of the crystal, or possibly a shelf, wing, or shoulder on a peak of a different nature can occur. Their positions on the absorption curve can be calculated from the generally known relation‐ ship between the wavelength and the energy of the quantum. In the present case, it is written as

$$
\lambda = \text{chN}\_{\text{A}} / \Delta E\_{\text{A}} \tag{25}
$$

where *h* is the Planck constant and *c* is the speed of light. For copper, the value of λ is 887 Å. In the absorption spectrum of copper [56], this wavelength corresponds to a shelf in the 885– 950 Å interval (Fig. 8).

From this standpoint, let us examine graphite, for which there are two modifications with the number of formula units *Z*: 4 and 6. Calculations of λ are 418 Å for *Z=*4 and 219 Å for *Z=*6. Since natural graphite is a concretion of these two modifications, the absorption curve of graphite should have two maximums corresponding to the values of Δ*Ε* for these two kinds of elementary entities. In fact, in spectrum [28] there are two such peaks that are not observed on amorphous samples of carbon (see Fig. 8).

The mole is applied to a gas without any difficulty. In a liquid, the specification of elementary entities often creates difficulties. In the application of the mole to a crystal, we propose specifying the elementary entities in accordance with the basic indicator of a crystal—its three-

The elementary cell will correspond to such an elementary entity. In this case, the elementary entity will be characterized by the number of formula units *Z*. For example, the formula of the elementary entity of fluorite is written as Ca4F8; *Z* will be equal to 4. Here it has been shown that the elementary entity corresponding to an elementary cell of the crystal is an object that

Let us examine this in the example of copper, for which the formula of the elementary entity is written as Cu4. Through the symbol Δ*Ε* we will denote the change in the energy of the crystal upon the dissociation of a mole of Cu4 into an ideal atomic gas. The value of Δ*Ε* can be

(crystal)↔4 Cu (gas).

Under isobaric conditions, the heat of this reaction is equal to the enthalpy change Δ*H*. Then

Δ*E*= *Z* ΔHsubl

Let us assume that one of the mechanisms of radiation absorption by a crystal is resonance absorption by an elementary entity of a quantum of energy, *ε*=Δ*Ε*/NA, where NA is the Avogadro number. After resonance absorption, the transition of the elementary entity from a stable electronic state to an unstable state is possible without any change in energy. Such a transition is called "predissociation." It may also end in the dissociation of an elementary

If the probability of absorption of an energy quantum *ε* makes it possible for the intensity of absorption to exceed the background level, an individual peak in the absorption spectrum of the crystal, or possibly a shelf, wing, or shoulder on a peak of a different nature can occur. Their positions on the absorption curve can be calculated from the generally known relation‐ ship between the wavelength and the energy of the quantum. In the present case, it is written

where *h* is the Planck constant and *c* is the speed of light. For copper, the value of λ is 887 Å. In the absorption spectrum of copper [56], this wavelength corresponds to a shelf in the 885–

<sup>A</sup> λ = chN /Δ , *E* (25)

C, according to [70], Δ*Ε*=4·80.7=323 kcal/mol.

Cu4

Δ*Ε* will be equal to the product of *Z* and the Δ*H* of the sublimation of copper:

dimensional periodic structure.

138 Solar Cells - New Approaches and Reviews

calculated based on Hess' law:

For copper at 1 atm and 250

entity.

as

950 Å interval (Fig. 8).

is capable of absorbing a quantum of energy.

Eq. (24) and (25) offer a means for predicting the positions of the absorption peak maximum for another modification of carbon, namely diamond, the structure of which, according to [27, 70], is characterized by a single Z=8 and Δ*H*atom of atomization 1364 kcal/mol. The maximum of the sought peak should lie in the 210 Å region. This absorption band of diamond has not been investigated [56], but it can be obtained in principle. Germanium and silicon have a structure analogous to that of diamond. The values of λ calculated for these elementary entities, 395 and 331 Å, respectively, practically coincide with the maximum at 395 Å on the germanium absorption curve and the wing at 330 Å for the silicon [56].

**Figure 8.** Absorption spectra (the absorptivity to the wavelength) of copper, graphite, and amorphous carbon [28, 56].
