On the question of using solid electrodes in the electrolysis of cryolite-alumina melts. Part 3. Electric field distribution on the electrodes

The aim of this work is to identify the theoretical limitations of molten salts electrolysis using solid electrodes to overcome these limitations in practice. We applied the theory of electric field distribution on the electrodes in aqueous solutions to predict the distribution of current density and potential on the polycrystalline surface of electrodes in molten salts. By combining the theoretical background of the current density distribution with the basic laws of potential formation on the surface of the electrodes, we determined and validated the sequence of numerical studies of electrolytic processes in the pole gap. The application of the method allowed the characteristics of the current concentration edge effect at the periphery of smooth electrodes and the distribution of current density and potential on the heterogeneous electrode surface to be determined. The functional relationship and development of the electrolysis parameters on the smooth and rough surfaces of electrodes were established by the different scenario simulations of their interaction. It was shown that it is possible to reduce the nonuniformity of the current and potential distribution on the initially rough surface of electrodes with an increase in the cathode polarisation, alumina concentration optimisation and melt circulation. It is, nonetheless, evident that with prolonged electrolysis, physical and chemical inhomogeneity can develop, nullifying all attempts to stabilise the process. We theoretically established a relationship between the edge effect and roughness and the distribution of the current density and potential on solid electrodes, which can act as a primary and generalising reason for their increased consumption, passivation and electrolytic process destabilisation in standard and low-melting electrolytes. This functional relationship can form a basis for developing the methods of flattening the electric field distribution over the anodes and cathodes area and, therefore, stabilising the electrolytic process. Literature overview, laboratory tests and theoretical calculations allowed the organising principle of a stable electrolytic process to be formulated -the combined application of elliptical electrodes and the electrochemical micro-borating of the cathodes. Practical verification of this assumption is one direction for further theoretical and laboratory research.


INTRODUCTION
Potential distribution and, to an even greater extent, current distribution are of great importance for the technical applications in electrochemistry. The uneven current distribution leads to an uneven thickness distribution of the deposited coating. Fig. 1 shows the crosssection of copper sediment on the metallic substrate (see). The thickness of the Cu coating increases from the recess uphill the pick and reaches the maximum on the crest of a serrated profile. Moreover, a large build-up of deposited copper is observed at the corner joint of the inclined and horizontal surfaces. This indicates an increasing current density towards the asperity tip and on the outer edges during the electrolytic process.

Fig. 2. Electrochemical local wear of the anodes along the edges around the perimeter Рис. 2. Электрохимический локальный износ анодов по ребрам периметра
Similar phenomena occur on the anode. For example, during the electrolytic production of aluminium, the carbon anodes are consumed at a higher rate on the edges around the perimeter ( fig. 2), resulting in the changes of actual integrated current density and interelectrode gap and increased electrode consumption. Similarly, for the inert anodes, the observed corrosion occurs more rapidly where current density localises.
In other words, without dwelling on the detail of the technological aspects, the electric field distribution theory is one of the fundamental principles of electrochemical engineering. Therefore, it is important to understand and predict the phenomena, which influence the current and potential distribution. The theory of these processes on the electrodes in the aqueous solutions is extensively discussed in the books of J. Newman, N. Ibl, Y. Gamburg, A. Baraboshkin [2][3][4][5]. Since the electrochemical laws are valid for the electrolysis of the molten salts, we will attempt, to the extent necessary, to use this theory to calculate the electric field distribution on the cathode as applied to the electrolysis of cryolite-alumina melts. The current and potential distribution on the anode follows the same laws (considering the corresponding processes, their kinetic parameters and polarisation effects) and will not be analytically considered here.

THEORETICAL JUSTIFICATION OF THE CALCULATIONS
The main factors influencing the electric field distribution in the electrode space are [2][3][4][5]: geometry and the hydrodynamic conditions of the system; electrical conductivity of electrolyte and electrodes; the profile characteristic and surface condition of electrodes; the degree of polarisation of the electrodes.
On the smooth or partially smooth surface of electrodes, for example, metallic one, the field and current density distribution is relatively uniform. However, there is a pronounced edge effect of current concentration at the edges, namely an increase in its density ( fig. 3).
The same applies to structural elements (edges, rods, peaks and joints) of perforated or grooved cathodes and anodes ( fig. 4). This is associated with the increasing electrolyte crosssection between the anode and the cathode in the direction of the edge surfaces and, accordingly, the decreasing electrical resistance at a distance of the pole gap.
The electric field distribution is strongly affected by the state of the electrode surface, including chemical heterogeneity (heterogeneous composition, impurities) and physical heterogeneity (roughness), inherent in all polycrystalline products, including hot-pressed and cast ones. On this kind of surface, the local current densities at the peaks and recesses are different, even if the macroscopic current distribution in a given area is entirely uniform. Since the electrical conductivity of the electrode is higher than that of the electrolyte, the electric field near the interface is non-uniform. The equipotential surfaces reproduce the topography of the interface, and the current lines are perpendicular to this surface ( fig. 5).
Therefore, the heterogeneity of the electric field leads to uneven current density distribution on the surface.
Integrating the mass and charge transport equation is the most general theoretical approach to solving the problem of current and potential distribution. The equation can rarely be solved with respect to the potential (or concentration) with all parameters considered. Therefore, the moderately simplified versions of this equation are used, resulting in the Laplace or Fick equations. The nature of the approximation depends on the type of the distribution (primary, secondary or tertiary).

Fig. 3. Equipotential lines and current lines
in the anode-cathode system Рис. 3

Fig. 5. Equipotential lines and current lines near the electrode Рис. 5. Эквипотенциальные линии и линии тока вблизи электрода
In the simplest case, one or both electrodes are non-polarisable, which corresponds to the primary field and current density distribution on this electrode. This distribution is the least uniform for the indicated geometry of the system. However, the surface of the melt next to the electrode is equipotential, and the current lines corresponding to the potential gradient are normal to the surface (see fig. 3 -5).
If one considers the electrode polarisationthe charge transfer overpotential , then the secondary field and current distribution takes place. The absence of the diffusion overpotential means that there are no noticeable concentration gradients or other mass transfer limitations in the solution. The charge transfer overpotential at the low current density (the electrode potential is near the equilibrium value) is determined by the equation: , where the polarisation at the secondary distribution is equal to [5]: (1) where n is the number of electrons involved in the reaction; R is the gas constant, J/mol·K; T is the temperature of the process, K; F is the Faraday constant, J/mol; i 0 is the exchange current density, A/сm 2.
The exchange current is the rate of an electrochemical process in the forward and reverse directions at the equilibrium potential. As follows from equation (1), with increasing i 0 the polarisation and charge transfer overpotential decrease. If i 0 >>i, the overpotential is close to zero, and the process is at equilibrium (reversible or non-polarisable). Usually, the cathodic exchange current values in the molten salts are highfrom one to hundreds of amperes per square centimetre (A/cm 2 ) owing to the process acceleration at high temperatures. For the electrolysis of the cryolite-alumina melts i 0 is approximately 20 A/cm 2 [6,7].
When the concentration field near the working electrode is considered, the corresponding solution to the problem results in a tertiary current distribution. Here, the metal deposition rate is determined by transport processes in the near-electrode diffusion layer. Tafel dependence between the current and the overpotential is introduced into the calculations to converge to the tertiary distribution: η = a + blgi, where the polarisation is approximately equivalent to the following value [4]: , (2) where i A is the integrated or geometric current density.
For the smooth electrodes constituting the hypothetical infinitely long plate with a width of 2B (-В < x < В), the solution of the twodimensional Laplace equation based on the conformal mapping method for the primary potential distribution reveals the dependence of local current density i S on the coordinate x [4]: According to equation (3), the current density i S , increases from the middle of the electrode to its periphery and tends to infinity at the edges. This owes to all the electric lines of force from an infinitely large area concentrated here |x| > B (see Fig. ).
For the secondary and tertiary current distribution on smooth electrodes, their polarisation β 2(3) , should be considered as well as the electrical resistance of the electrolyte ρ bath in the pole gap l x [4]: In this equation, the coefficient k characterises the dependence of l x on the coordinate x: k = dl/dx or in the first approximation k = dlnl/dx.
While discussing the electric field distribution on the rough surface, we will consider its profile described by the curve x S (y). The current distribution is set by the electric field between the electrode and the rough surface of the counter electrode with a sinuous profile with an amplitude less than the wavelength A<L ( fig. 6). The representation of the surface profile as a sine wave allows a variety of periodic shapes with different steps to be generated. In addition, the sine wave has no corner points, therefore the infinitely high current densities often observed at the corners are avoided.
In case of the constant polarisation β simultaneous solution of Laplace equation for the electrolyte and the cathodic surface profile x S = A· cos(2π/L) allows the local current density distribution to be calculated i S [2,4,5]: In this equation, i A is the integrated or geometric current density. This assumption is acceptable since we believe that the total current passes through the electrolyte cross-section in the pole gap with an electrical resistance ρ bath, Ω·cm. We also consider the electrical resistance of liquid aluminium ρ Al, Ω·cm; L is the sinuous wavelength or the elemental periodic physical defects, cm; A S is the current roughness amplitude varying during the period L in the limits from -A to +A, cm; y is the current coordinate on the «y» axis across the rough surface, cm.
The analysis of equation (5) shows that the value of polarisation β essentially affects the uniformity of current distribution over the initial or changing rough surface. The greater the polarisation of the surface of the electrode, the more uniform will be the current distribution on the electrode plane. Here it is important to address the term "polarisation". During the electrolysis, the current passes through the electrode and the potential deviates from the equilibrium values. A change in the electrode potential is called electrode polarisation and is expressed as the derivative of the overpotential on the current density: β = dη/di. This relation, i.e., polarisation, is technically the resistance per the square centimetre of the electrode area (Ω·cm 2 ). It can be determined as polarisation resistance R. If this resistance represents the slow charge transfer through the interface, it relates to the electrode kinetics and can be called charge transfer resistance R trans . When R is associated with the slow ion transport through the near-electrode layer, it can be called the diffusion resistance of the potential-determining components R D . Consequently, polarisation plays the role of a levelling additive in the electrolyte composition, widely used in electrometallurgy in aqueous media. These additives precipitate on the roughness crests, increasing the local surface resistance. Thus, the current distribution levelling over the cathode is achieved. Therefore, the polarisation of any kind (kinetic, transport, crystallisation and other) could be beneficial to some extent for the stabilisation of electrode processes and electrolysis. It is limited by maximum current density.
However, what happens when the maximum current density i P is achieved for aluminium? It is well known that without a change in the total current, the cathode potential shifts sharply to the electronegative side until the most electronegative impurities discharge. Their deficiency leads to the subsequent shift of the potential to the background decomposition values, i.e., electrolyte. However, the impurities discharge of and, what is more, the decomposition of aluminium or cryolite fluorides occur at higher cathodic polarisation, indicating the stable, gradual passivation process, i.e., the isolation of electrode. This unfavourable scenario can develop on the anode as well. However, in this case, the current density on the peaks and sharp edges of physical heterogeneity will lead to the fluorine ions discharge and the evolution of fluorocarbons on the carbon anode and of fluorine on the inert one (or to the electrochemical dissolution of the anode involving fluorine ions). In the first case, even with the stable electrolysis in the best-case scenario, an unfavourable environmental situation is created in the work area. In the other case, the chemical and electrochemical corrosion of the inert anode increases. These undesirable processes are highly probable when using polycrystalline or cast electrodes, anodes and cathodes, thus requiring practical and theoretical research. This study is the first attempt done in this direction.
The description of the potential distribution on a rough surface reduces to solving the Fick equation for concentration distribution of a substance in the diffusion layer. In the considerably diluted solutions, the diffusion equation can be represented as follows [2,4,5]: Since we examine the kinetics of the pro-cesses in the flat electrode systemthe melt, the diffusion can be considered linear, as follows: where x is the coordinate perpendicular to the electrode; the concentration gradient in the near-electrode layer of a certain thickness δ is constant (see fig. 6), i.e., the concentration changes linearly (Nernst assumption): Then the electrolysis rate is equal to the diffusion transport rate or the diffusion current [6]: , where D is the diffusion coefficient, cm 2 /s; δ is the thickness of the diffusion layer, cm; C 0 and C S are the ion concentration in the melt volume and at the surface of the electrode, respectively, mol/cm 3 . As the current density increases, C S decreases, and the highest possible current at C S →0 approaches the limiting diffusion : .
The concentration of the potentialdetermining ions on the surface does not reach zero and can be determined by solving the equation (9) for C S : The fractional expression on the right side of the equation (11) is the current ion concentration immediately at the sinuous surface (recesspeak). Hence, the cathode potential for the dilute solutions determined as: (12)  can be expressed as follows 1 : where is the standard decomposition voltage (equilibrium potential) of the saturated solution of the potential-determining ions in the electrolyte using carbon (-1,180 V) or inert (-2,180 V) anode at 965°C. Electrode potential E is the decomposition voltage at the current concentration gradient of potential-determining ions in the diffusion layer δ. If in equation (13) the current is equal to zero , then the entire system and the potential are equilibrium at the given concentration c 0: (14) Since in the actual system the same equilibrium potential establishes for all processes on the anode and cathode, the difference between the E and E r potentials represents the concentration overpotential of the current process on a specific electrode, cathode or anode : Equation (13) can be used to calculate the potential distribution depending on the actual current density i S and fixed values of the bulk concentration of the potential-determining ions С 0, the transfer coefficient D and diffusion layer thickness δ. For the electrolysis of the molten salts, δ usually ranges from 0.1 to 1 mm [6]. Convective stirring and gas generation at the anode and gas-lifting in the melt, in particular, reduce this value by an order of magnitude. On a rough surface with a defect height of H def = 2A>δ, the diffusion layer follows the profile equally ac cessible for diffusion everywhere (see fig. 6).
Thus, the sequence of analytical calculations is as follows: The calculation of current density distribution i S on a given surface profile according to equations (3)-(5).
The potential distribution E is calculated based on the current values of the current density i S on the surface according to equation (13).

CALCULATION RESULTS AND DISCUSSION
In the calculations, the standard characteristics of the NaF-AIF-AI 2 O 3 melts at a temperature of 965°C were used. It is important to note that the calculation results are not absolute at the given parameters and in the approximation of smooth and sinuous profiles, but adequately reflect trends in the current density and potential distribution on the surface of electrodes. This provides a better understanding of the work of electrodes under near-real conditions. Therefore, the first model at assumes the absence of the charge transfer overpotential and the alumina concentration in the electrolyte close to saturation. The other model suggests the standard operation of the electrolytic cell under the diffusion kinetics at β 3 . Here we stress again that the next section presents the calculation results for the cathode surface only. Nevertheless, they characterise qualitatively the electric field distribution on the anode as well.

Smooth electrodes
The current density i S and potential E are distributed relatively uniformly on the inner surface of smooth electrodes but increase sharply around the perimeter of the cathode (fig. 7).

Fig. 7. Distribution of iS (solid) and E (dashed) on smooth electrodes in the approximation of the primary distribution Рис. 7. Распределение iS (сплошная) и Е (пунктирная) на гладких электродах в приближении первичного распределения
At β 1 with the weakly polarised electrodes, the current density (solid line) on edges and peripheral surface exceeds the geometrical current density on the inner surface by several times and reaches 1,50÷3,6 A/cm 2 . The cathode potential (dashed lines) on the periphery can vary significantly depending on the conditions of the hydrodynamic stirring and the electroactive ions transfer. As the diffusion layer thickness δ increases and the transference number α сat decreases approximately by two-fold, the potential increases from 1.6 ÷ 2.0 V to 1.7 ÷ 2.8 V. For the cathode, this process acceleration leads to a transition from a local discharge of electronegative impurities, for example, calcium, to the passivation of peripheral regions by the electrolyte components. For the anode, the consequences of the edge effect involve the transition from the oxygen ions discharge to that of fluorine and accelerated chemical and electrochemical consumption.
These negative effects are mitigated by the diffusion control of electrolysis with tertiary β 3 electric field distribution ( fig. 8). With the same integrated current density of 0.8 A/cm 2 on the periphery, the current density increases by only two-fold. However, certain conditions can, to some extent, complicate the electrolysis process in the peripheral areas of the electrodes. For example, if the electrolyte viscosity increases or stirring conditions deteriorate and, hence, δ increases from 70 to 100 µm, the potential at the electrode edges can reach the level of impurity discharge at the cathode (see fig. 8) or selective dissolution of the anode components. The addressed particularities of the edge effect on solid electrodes are fully applicable to the perforated and grooved cathodes and anodes. The current and potential concentration on the edges, side surfaces of the openings and rods increases the cathode passivation or the anode consumption proportional to their total area.

Rough electrodes
Firstly, we compared the operating modes of a polycrystalline cathode without significant polarisation and under the diffusion control of cathode processes. The figure below shows the current density and potential distribution for a given cathode surface profile x S = Acos(2π/L) under the indicated parameters ( fig. 9). Under the diffusion control, β 3 , the current density distribution (solid lines) and the corresponding potential distribution (dashed lines) are within the limits that satisfy the stable aluminium reduction on a solid carbon cathode.
The distribution heterogeneity, the current density and potential values sharply increase without activation and diffusion overpotentials (sine wave β 1 on fig. 9). On the defect peaks, the actual current density is approximately 2 A/cm 2 , at which the cathode potential reaches and exceeds the ionic discharge values of calcium of 1.600÷1.890 V. The subsequent potential jumps up to the electrolyte components discharge occurs with the calcium deficit or its absence in the electrolyte.
The surface roughness of the solid electrodes significantly limits the electrolysis intensification. The slight increase in current density proportionally changes the potential distribution at fixed surface parameters. These changes manifest a pronounced tendency to shift the potential to the electronegative side with an increase in the current density at the electrode ( fig. 10). We fitted the alumina concentration and the stirring conditions (0 and δ) to the parameters of the cathode roughness in a way that the increase in the integral current density i A above 0.5 A/cm 2 led to an increase in the real current density i S at the defect peaks to the values close to the limiting values i lim . Under these conditions, a local potential jump creates conditions for the simultaneous discharge of the impurities that are more electronegative than aluminium. Fig. 11 shows the calculation results simulating the diffusion limitations of the cathode process with an increase in the integrated current density.

Fig. 10. Influence of the initial iA value on the distribution of iS (solid) and Е (dashed) Рис. 10. Влияние исходной iA на распределение iS (сплошная) и Е (пунктирная
At the roughness up to 600 µm, the current density i A = 0.5 A/cm 2 and the intensive melt stirring (δ = 75 m), the cathode process approaches limiting density only at the alumina concentration of 2 wt.%. However, at i A = 0.8 A/cm 2 electrolysis can be destabilised at the alumina concentration of 3 wt.%. Increasing the integral current density up to 1 A/cm 2 on a polycrystalline surface allows a stable process only with alumina concentrations above 4 wt.%. Indeed, the electrolysis conditions differ in highly soluble electrolytes (up to 10-15 wt.%) and low-melting electrolytes with the saturation of 4-5.5 wt.% of Al 2 O 3 . This difference is fundamental. In alumina-rich and particularly in suspended melts, the concentration component of polarisation is negligible. However, there is diffusion polarisation, which develops with an increase in the electrolyte viscosity and diffusion cathode layer thickness.
The alumina concentration c 0 and the diffusion layer thickness δ have the opposite effect on the maximum current density and cathode potential (equations (10) and (13)). When C 0 changes, δ changes, but not vice versa. In the standard melts, this one-way and indirect correlation through changes in the electrolyte viscosity becomes noticeable only in the hypereutectic region of the NaF-AlF 3 system and upon reaching the Al 2 O 3 concentrations of 9-10 mol.% [6]. On the other hand, the influence of δ on the electrolysis kinetics is stronger and depends on the hydrodynamic conditions in the interelectrode gap. These conditions, including the diffusion layer thickness, can differ throughout the electrode area. Negative consequences for cur-rent density distribution enhance with an increase in the electrolyte viscosity, a decrease of convective stirring, i.e., with an increase in the diffusion layer thickness δ (fig. 12).
The latter applies fully to the low-melting electrolytes of the KF-AlF 3 system with limited solubility of Al 2 O 3 and especially to the melts suspended in alumina. Furthermore, in these systems with relatively high viscosity, the extremely low diffusion currents do not permit the electrolysis with the current density higher than 0.5 A/cm 2 on the metal electrodes [8][9][10] and a fortiori on the polycrystalline surfaces. In the literature, there is an opinion that the inert anodes should operate at current densities of approximately 1.2 A/cm 2 [11] to maintain the heat balance of the electrolysis cells.
With a relatively low increase in δ from 60 to 75 and 85 µm, the overall voltage will increase to the discharge potentials of the impurities that are more electronegative than aluminium, i.e., sodium and calcium (see fig. 12). If the latter can passivate the electrode after interaction with the cathode material, its impurities and electrolyte, then Na will pollute aluminium (carbon cathode) or interact, for example, with the TiB 2 cathode surface to form the borates: TiB 2 + 8Na(g) + 4.5O 2 (g) → → Na 4 TiO 4 + Na 4 B 2 O 5 (l); (16) ΔG 0 T = -3528.4 J/ mol. The authors believe [12] that the products of this interaction can dissolve in the electrolyte, hence increasing the micro-defects and stimulating electrode corrosion.
In conclusion, we report the calculation results of the current density and potential distribution depending on the height of the physical defects ( fig. 13).
In the range of the roughness height from 0.1 to 1 mm (simulating the heterogeneity development) the current density on the defect peaks reaches limiting values, and potential approaches possible decomposition of the electrolyte components and cathode passivation. As expected, this trend has more pronounced negative effects on the cathode processes. To a certain extent, one can control the electrolysis parameters discussed above (i A , C 0, β, δ) and

. Impact of the height of the defect on the distribution of iS (continuous) and E (dashed) Рис. 13. Влияние высоты дефектов на распределение iS (сплошная) и Е (пунктирная)
select technologically and constructively the optimum conditions for the operation of the electrodes. Physical and chemical heterogeneity is more difficult to influence in the manufacture of electrodes by moulding or casting. Attempts to change/reduce initial roughness by mechanical methods, such as surface polishing, affect only the electrode start-up. The roughness parameters and the impurity profile of items change during the start-up and working cycle. More pre-cisely, the presence or propagation of chemical heterogeneity of the surface and/or bulk of the item leads to physical heterogeneity during the electrode working cycle.
Notably, aluminium can discharge on the entire surface, including the recesses (see fig.  9-13). However, kinetically, i.e., without current and overpotential in the recesses, this process barely occurs, more precisely, it proceeds under equilibrium conditions. When present in the melt, conditions for discharge in the cavities are more favourable for electropositive ions. This element is boron, which is almost twice as electropositive as aluminium. Boron, if reduced in a recess, reacts, for example, with titanium or titanium oxide, and the resulting titanium diboride will flatten any inhomogeneities.
Thus, the functional relationship among the following parameters was established by simulating different scenarios of the interaction of the cathode polarisation level, geometric current density, stirring intensity (by δ) and the alumina concentration in the electrolyte on the smooth and rough surface: The pronounced edge effect of current concentration, i.e., an increase in its density, is observed on the periphery of the nominally smooth electrodes and their internal perforated elements. The current and potential concentration on the edges, side surfaces of the openings and rods increases the cathode passivation or the anode consumption proportional to their total area.
An increase in the initial or acquired during the electrolysis surface defects of electrodes leads to the progressive heterogeneity of the current and potential distribution, increases the risk of the cathode passivation and/or electrochemical anode corrosion.
An elevation of the current alumina concentration in the electrolyte relative to its maximum content augments the limiting current density, but at the same time: deteriorates the scattering properties of the melt and the current micro-distribution on the micro-defects; increases the melt viscosity, diffusion nearcathode layer, consequently, gradually decreases the limiting current density.
The surface polarisation smooth out the cur-rent distribution on the smooth and polycrystalline electrodes. The intensification of the melt stirring, i.e., decreasing the diffusion layer thickness and levelling the concentration of the potentialdetermining ions in the electrolyte volume, increases maximum current density, equalises distribution and diminishes the absolute values of the electrode potential.
It is possible to reduce the heterogeneous current and potential distribution on the electrode surface with initial roughness by increasing the cathode polarisation, optimising the alumina concentration and melt circulation. However, initial physical heterogeneity can progress with the prolonged electrolysis in the presence of chemical heterogeneity, undermining all attempts to stabilise the process.

CONCLUSIONS
The above-discussed relationship between the edge effect and roughness and the current density and potential distribution over solid electrodes can act as a primary and unifying factor for their increased consumption, passivation and electrolytic process destabilisation in standard and low-melting electrolytes NaF(KF)-AlF 3 -Al 2 O 3 . Nevertheless, this functional relationship can form the basis for developing the methods of equalising the electric field distribution over the anodes and cathodes area and, therefore, stabilising the electrolytic process. Presumably, the reduction in the number of components, elements and units of the electrode with sharp or chamfered edges and joints is one important condition to diminish the negative effects of current density at the edges. Any bulging parts and perforations within the electrode geometry should be excluded. However, the current is distributed over the area of solid electrodes in such a manner that the current density increases from the centre to the perimeter with the accumulation at the edges of the cathode and anode ( fig.  7 and fig. 8). Possibly, a similar and adequate increase in resistance in the pole gap will minimise this effect on the periphery so that the current density does not change in width and over the area of electrodes. The elliptic form of electrodes with an acceptable increase in the pole gap from the centre to the periphery satisfies these conditions. When the electrodes are vertically positioned, both the anode and cathode should be shaped elliptical in cross-section, while with the horizontal arrangement of electrodes -only the inert anode. For example, in [13], the nature of the corrosion in the oxygenreleasing anodes was investigated in the NaF -53.6, AlF 3 -41.2, CaF 2 -4.0, MgF 2 -1.2 (wt.%) melts at the current density of 0.5 A/cm 2 and the temperature of 960°С for 50-150 hours. An aluminium layer on the bottom of the crucible was used as the cathode.
Regardless of the composition, the anode deterioration proceeded with a higher rate in the samples along the sharp peripheral edge (D). The samples with the elliptic side surface underwent uniform corrosion (E).
However, only a special shape is not sufficient to conduct a stable process using solid electrodes, polycrystalline and cast, singlephase and multiphase, which a priori have physical and chemical heterogeneity in their bulk and surface structure. In the work [14], electrochemical micro-borating of carbon cathodes containing refractory metals and their oxides was proposed as one method of surface homogenisation directly in the electrolysis process. The same method can be applied virtually to any reactive or inert cathodes with the surface heterogeneity smoothed by the chemical interaction of boron with the present impurities, hence equalising the surface physical state.
Thus, based on a relatively detailed examination and analysis of the problems of solidcathode electrolysis -literature review, laboratory practice and theoretical calculations -a simple procedure for the electrolysis process has been elaborated: combined application of elliptical electrodes and electrochemical microborating of the cathodes. The validation of this method is one of the possible areas of further theoretical and laboratory research. It could also be one of the last attempts at commercialising inert electrode technology. The latter relates to several factors: -The expectation of environmental and economic benefits from introducing inert electrode technology has been delayed. The closure of the project is stopped by huge funds that have not paid for themselves, invested in more than 70 years of technology development.
-Simple recommendations for process temperature reduction, electrode and electrolyte composition corrections [15][16][17][18][19][20] do not allow implementation in the industry; -Current technologies have come close to the technological and economic indicators expected from introducing the inert electrode technology. The urge to continue work on inert anodes is being questioned [21]; -Greenhouse gas capture and separation technologies such as carbon capture and sequestration are highly standardised and ready for use [22][23][24][25];

Fig. 14. Inert anode samples before (left) and after (right) the electrolysis [13] (D) NiFe2O4-NiO-Cu cermet and (E) the metal-cermet composite Рис. 14. Образцы инертных анодов до (слева) и после (справа) электролиза [13] (D) NiFe2O4-NiO-Cu металлокерамика и (E) металл-керметный композит
-New directions and methods of aluminium electrolytic production appear, associated with the utilization of "waste" energy, saving energy resources and increasing production per unit of working space of the cell [26]; -There is no complete understanding of the impact of the local excess of oxygen in the atmosphere on human and the environment, as well as of fire safety in the major oxygen source area, for example, the aluminium plant with inert anodes. With increasing the oxygen partial pressure in the atmosphere, the initial flash point, at which the vapours can ignite, lowers. In such an atmosphere, the fire can start with the spark generated by the friction of synthetic clothing with the human body [27].
However, in the near future, electrolysis of cryolite-alumina melts will remain the major industrial method of aluminium production. The ecology and electric power deficiency and their economic parameters encourage researchers to improve existing and develop new technologies. Potentially, we are at the turn of creating a new "Roadmap" of the development of the aluminium industry.