Crystal varizonicity: fundamental and applied aspects.

A set of ideas about the homogeneous variable zone structure in the near-surface region of ionic crystals is presented. Its origin is shown using generalizations of the Seitz–Madelung scheme. A number of important consequences have been demonstrated: the peculiarity of local surface levels different from Tamm levels; increase in the critical temperature of superconductivity in a sandwich structure; a significant anti-degradation role of these levels in the processes of energy exchange at the interfaces. It is concluded that such homo varizonality is an excellent example of the implementation of the “Bonds and Bands” concept.


1.
Introduction.The history of the development of condensed matter science can be clearly divided into several stages.At the first (pre-quantum) stage, chemistry and physics in crystals dominated as a methodology, on the basis of which serious results related to the phenomenology of mechanics, thermodynamics and electromagnetism were quite successfully obtained.At the second (quantum) stage, huge success was achieved on the basis of the presentation of the band theory, and the analysis was based mainly on the microscopic approach.At the third stage, usually associated with the quantum ideology of elementary excitations, (but in conjunction with the previous ones) a very large set of studies was obtained, in terms of deeply fundamental concepts (in particular, dimension).However, it is of great interest to obtain a formulation of the concept common to all three stages, combining relative simplicity with efficiency as well.Apparently, the most significant one was the socalled concept of "Bonds and Bands"(B-B) [1].Indeed, it fully corresponds to A. Einstein's ideology ("simple, but not simpler") and it is the concept (B-B) supplemented by the ideology of disequilibrium (N) and since then designated as (B-B-N) and it has shown extraordinary efficiency, which increases from year to year.60 years ago, when studying the energy of the near-surface regions of ion crystals, Seitz combined the ideas of Modelung about the energy of the lattice with the ideology of electronic zones and built an energy scheme for near-surface regions.The most important result of this scheme was that the electronic band gap on the surface turned out to be smaller than the volume band gap by the value associated with the Modelung energy: E gb > E gs [2].In a series of our works, by generalizing the results in [3][4][5], we obtained an analytical expression of the dependence of the band gap in an ion crystal on X, where X is the distance from the crystal surface to the observation point inside the crystal: where Q ijk is the Madelung energy term defined by the indices i, j, k.
However, Seitz's reasoning was excessively complex and often led to confusion in understanding the variables used by Seitz (see [2]).At the same time, when using a threedimensional construction, the situation of the dependence of the width of the variable band gap on X and the fictitious interatomic distance of the scaled lattice (R) makes it easy to understand all the situations that arise («Figure 1»).

3.
Surface states in ionic crystals in the variable band gap.
After Tamm's work in 1932, where using the methods of quantum theory, he discovered local states on the surface (Tamm's levels), very significant results were obtained in the field of studies of the electronic structure of near-surface regions [2].Recently, in a series of works [3][4][5] it has been shown that the exit of the variable zone to the surface leads to a completely new situation radically different from all previous works.«Figure 2» demonstrates how varizonicity creates potential pits of a special type (namely Airy pits) in which a whole group of local near-surface states can be localized.A detailed theoretical analysis of this situation has shown that local levels in such Airy pits are described by expressions: where m is the electron mass, F is the strength of variation, i.e. the tangent of the slope angle of the zone in its graded-gap part which is the basic parameter of all graded-gap structures, where α n+1 0 are the roots of the equation for the Airy function (2.7; 4.09; 5.52…….)[6]; is a small negative additive that lowers the depth of the local level in the potential well; its permanent negative sign indicates a small permeability of the wave function Ψ II in regions I and III (because of the finiteness of U1 and U2).We believe that this condition is satisfied in the graded-gap part, where even the lowest level of electron energy is not absorbed in the "toothed well", which leads to zero absorption of light.Varizon coatings at small thicknesses do not have surface states and, therefore, do not absorb sunlight, being an ideal material for OSC encapsulation.So, this condition is («Figure» 2): where F is the slope of variation; 2,7 is the first root of the Airy function [6]; the value of U 2 can be seen from «Figure 2» and is easily obtained from data for graded-gap semiconductors.

4.
The role of the varizonicity of metal film plates in the superconducting sandwich structure.
In the broad problems of superconductivity, a special role is devoted to the search for recipes for both materials and principles (mechanisms) to increase the critical temperature of the high temperature of superconductivity (Т с ) [7].Among the proposed principles, such as a fundamental concept for the topological and fractal dimensions of an object undoubtedly plays a special role, and in this regard it is necessary to note the intuition of V.L.Ginzburg, who has been concentrating the attention of researchers on sandwich structures for many years (see [7] -«Figure 3»).The physics of increasing Т с in sandwiches in comparison with a separate metal film is due to a change in the potential well holding two fermion electrons and their transformation into a boson with further Bose-Einstein condensation.This occurs because of additional interactions with non-metallic gaskets and modification of the interface itself and the latter is due to an increase in binding by a polarization mechanism, as well as tunneling processes of electrons in a metal film [7].The specific value of the changed Т с can be consistently calculated in the ε(k, ω) -formalism, which was implemented in the form of a variety of variants ( [7][8]).The variant studied in this paper has not been considered before, and it is not due to the usually accepted flat zone structure, but to their varizonal type.It is essential that a special potential well (of the Airy type) appears on the surface, and this radically modifies the surface electronic structure, turning the Tamm's levels into something completely different [5] («Figure 4»).As our calculations show (in the same ε(k, ω) -formalism), this replacement actually modifies all components required for the calculation of Т с .In particular, even in a very rough approximation, using polarization mechanisms (tested in [8]), modified varizonicity leads to important relationship between the critical temperatures of superconductivity in variable zone and the planar one: In all these equalities, the values of ε i and Ω imply a fractional averaging.It is interesting to discuss the applicability of the described varizonicity concept to the recent shocking event of the possible discovery of superconductivity at above room temperature (LK-99) [9].Interesting considerations about a possible interpretation based on the previous model theory were presented by A.Kavokin and A.Zahidov [10].In the work of Korean researchers [9], considerations expressed the special role of superconductivity (LK-99) of quantum well aggregates obtained in the structure they studied.Moreover, they hypothesized about the shape of these potential wells and in the works [9-10], these potential pits were presented as Airy pits.We find these considerations interesting because in the cycle of our previous work [3][4][5], when studying the varizonicity of crystals with an ionic bond, we obtained some potential wells near the interface in the form of Airy.Because of this, we think it is interesting to combine the ideas of Airy pits and Airy electronic levels, expressed in this comment («Figure .4»),which play a basic role in the increase of Т с in the superconductivity of sandwiches for the case (LK-99).From our point of view, it may be as following.Around the axis passing through ions of the same sign, it is necessary to build a system of coaxial multilayer cylindrical capacitors, which being charged form a system of cylindrical sandwiches.Such a model, subjecting to the condition of mutatis mutandis, seems to us very useful, because it contains specific theoretical expressions linking Т с with the parameters of the material and structure.The influence of radiation on such a high-temperature superconducting sandwich scheme is also interesting but it has not been studied before, unlike other variants of the HTSC [12].In our case, it is particularly important, firstly, the rechargement of Airy levels, and, secondly, stimulation of atomic rearrangements by radiation which change the penetration lengths of metal atoms into the space of the plates (if we focus on the tunneling mechanism of the interface manifestation in the magnitude of Т с , see [7]).

5.
The role of varizonicity in the efficiency of the carbothermic method of hydrogen production in the Zn -ZnO Solar Furnace system.Economic and demographic studies carried out since the beginning of the XIX century have revealed a quadratic dependence of energy consumption on the number of people (the population of the Earth):  =  + 2 • , which indicates the inevitability of an energy crisis.The fight against this is currently taking place through large investments and with a drift from narrow technical solutions, but with the involvement of fundamental laws of physics, chemistry, biology and cybernetics.The beginning of such a convergence of natural sciences was laid back in 1977 in Santa Fe (USA) and designated as Complexity [13].The approach to solving the outlined problem, designated as "hydrogen energy", contains all the signs of complexity (due to its multi-step nature) and is quite optimistic.Phenomenological analysis.The scheme we have adopted contains two stages of the thermochemical cycle (Fig. 5) with the involvement of factors of influence of a Large Solar Furnace (LSF) [14]: Zinc is needed in the form of nanopowder and everything happens in the presence of concentrated solar energy. +  2  →  +  2 (∆2 = −62 kJ/mol) The reaction takes place on the surface of zinc nanoparticles, the ZnO product returns to the reactor, completing the thermochemical cycle.
Due to the multifactorial nature of LSF radiation, the Born-Haber energy cycle is completely satisfied, which corresponds to the law of conservation of energy, without disturbing the entire cycle.However, it is necessary to check the issue of coupling flows at interfaces where energy is transformed (satisfaction of the Umov-Poiting principle) [15].In general, the coupling of flows according to the Umov-Pointing principle looks like this Here   and   are the energy density and the velocity of the energy carrier on both sides of the interface;  12 → -is the heat outflow vector.With an ideal pairing, when  1 <  2 , there is no degradation of the interface but under the condition  1 >  2 , i.e.  > 0 degradation is possible.In the latter case, for the scheme we are discussing, it means that the case of degradation corresponds to the recrystallization of zinc nanoparticle powders with a sharp decrease in the catalytic activity of the zinc surface and inhibition of the process [16].In the light of the problem of varizonality discussed here, the presence of local levels in potential Airy pits at the interface can serve as a certain drain of the heat released.At the same time, the electrons in these potential wells, which serve as a certain type of hub, are excited by taking the excess energy on themselves.The movement of these electrons along the surfaces of the powders will result in the outflow of excess energy, which, in principle, will suppress the degradation process.Microscopic analysis.The identification of the mechanisms of processes at the stages that are the "narrow throat" of the entire hydrogen output is an absolutely necessary stage of general research.The concept of "Bonds and Bands", combining the ideas of quantum theory with chemistry, is a suitable basis for studying complex processes against the background of multifactorial irradiation from LSF. «Figure 6» shows the mechanism of a diatomic molecule decay in a basic singlet state S.  When exposed to a passing electron or in the presence of a paramagnetic ion, a reversal of any of the spins occurs, resulting in the transformation of a singlet → triplet (S → T), after which the unstable triplet state decays.The energy of this process is drawn from the absorbed photon; however, such a transformation violates the principle of spin symmetry, and therefore a third spin is necessary for its implementation.This third spin can be any spin from a nearby paramagnetic ion, or from a passing electron lingering in the field of a deformed singlet.The probability of such a three-spin process involving an exchange between a singlet spin and a third-party spin (so called flip-flop (ff)) is easily estimated in the second order of perturbation theory [18].In relation to our objects, this may be important for the decay of two Н-О bonds in a water molecule located on the surface of a zinc nanoparticle.However, a lot of other options are possible if we note that the zinc surface can become a drain or a source of phonons, which can be useful for adjusting the energy balance at the time of the f-f process.

6.
Conclusion.The varizonality discussed in the article takes place due to the long-range action of Coulomb forces and is associated with a decrease in the Modeling energy near the crystal surface.This is different from the standard varizonicity of semiconductors and because of the presence of an additional component is due to many new properties of the near-surface region of the crystal.The most important among them is the presence of an Airy pit leading to the appearance of Airy levels radically different from Tamm's levels.Among interesting consequences of this circumstance is the possibility of the temperature of the superconducting transition increase in a two-dimensional sandwich structure when the lining of the metal film is varizonal.Another effect is controlled optical absorbance in the area of varizonality, which can serve as coatings for optical devices.One more interesting consequence of the presence of Airy levels is also that they can serve as a hub of heat with an undesirable nature of Umov-Pointing flow at the interface.The studied type of homogeneous varizonicity is a characteristic example of the case in which the concept of "Bonds and Bands" successfully combines ionic and zone features of the structure.

Figure 1 .
Figure 1.The really occurring varizonality obtained by a simple cross-section of the three-dimensional relationship between E g , Х and R 0 (the latter means the real interatomic distance in the crystal).

Figure 2 .
Figure 2. Electronic structure in the near-surface region of the graded-gap design.

Figure 3 .
Figure 3. a) Sandwich structure and exciton mechanism.b) Two-dimensional surface structure.с) Calculation scheme for the Т с in the sandwich structure.

Figure 4 .
Figure 4. Sandwich structure with variable forbidden zone and Airy pits.

Figure. 5
Figure. 5 Diagram for a piece of equipment.

Figure 6 .
Figure 6.f -f scheme of the process leading to the reaction S → T followed by the decay of the molecule during photon absorption.