Calculated substantiation of isolation of boron and sodium cations from molten working and heating medium during hardening of restored parts

Scientific and technological research in the development of the technical process for the restoration and strengthening of worn parts using calculated justification allowed us to make an optimal technical decision on the development of a method for surfacing and electrolysis borating of parts to increase their service life. The working medium for strengthening the restored tillage organs of agricultural aggregates is substantiated theoretically using the developed mathematical model describing the working medium as a thermodynamic system consisting of boron cations, sodium and oxygen anions. The creation of a potential difference in this medium will provide a process in which boron and sodium ions are discharged at the cathode, and oxygen ions at the anode. For this, it is necessary to theoretically determine the electromotive forces of polarization of electrolytic cells and compare them. The solution to this problem requires an assessment of the change in the Gibbs energy during the decomposition of sodium oxide and boric anhydride for the temperature of the borating process, taking into account its change under standard conditions, the chemical potentials of the reacting components and phase transitions, the melting of substances and their sublimation. The order in which boron and sodium are separated at the cathode is determined by comparing the electromotive forces of polarization of boric anhydride and sodium oxide. It was found that sodium oxide is more stable than boric anhydride. Consequently, boron atoms are reduced on the cathode surface, and calculations have confirmed the possibility of its use.


Introduction
The adoption of an optimal technical solution in the development of a technological process for the restoration and hardening of worn parts requires its computational verification. As a result of scientific and technological research, methods were developed for surfacing and electrolysis boriding of these parts to increase their technical resource [1,2,4,11].
The possibility of using the developed composition as a working and heating medium for strengthening the restored tillage organs of agricultural aggregates must be established theoretically [11]. This requires a mathematical model describing the working and heating medium as a thermodynamic system.
The molten working and heating medium is thermodynamically considered as a system consisting of boron, sodium and oxygen anions [1,6,8,7]. The creation of a potential difference in the molten working and heating medium will provide a process in which boron and sodium ions are discharged at

The object and method of research
For a quantitative assessment of the sequence of isolation of sodium and boron from the developed borate-sodium melt [10], it is necessary to theoretically determine electromotive forces of polarization of electrolytic cells and compare them.
In electrolytic cells, decomposition reactions of sodium oxide and boric anhydride take place. The change in the Gibbs energy during the decomposition of sodium oxide is determined for the temperature of the borating process, taking into account the change in this energy under standard conditions, as well as the chemical potentials of the reacting components [3,5,6,10]. It is also necessary to consider phase transitions, melting of substances and their sublimation. Therefore, this change is determined taking into account the Van't Hoff equation as follows: The enthalpy of the decomposition reaction of sodium oxide at the process temperature is determined by the formula (3): where Р 1 С -the specific heat of the decomposition reaction of sodium oxide at the process temperature, J/(ºС mol); pt1 Н ∆ -the enthalpy of phase transitions of sodium oxide (at the corresponding temperatures pt1 T ), J/mol. The entropy of the decomposition reaction of sodium oxide at operating temperature is determined by the formula (4): The electromotive force of polarization is calculated, taking into account the expressions of Nernst and changes in the Gibbs energy [3,11], according to the formula (5): where F -Faraday constant, C/mol. The change in the Gibbs energy of the decomposition of boric anhydride is determined for the temperature at which boration is carried out, taking into account the change in this energy under standard conditions and the chemical potentials of the reacting substances, as well as the resulting phase transitions and sublimation. This change in the Gibbs energy is determined taking into account the Van't Hoff equation [4,7,10] by formula (6)  The change in the Gibbs energy under standard conditions is calculated taking into account the enthalpy and entropy of the decomposition reaction of boric anhydride [3,4,5,6,7,10] according to formula (7): The enthalpy of the decomposition reaction of boric anhydride at the borating temperature is determined by formula (8): where Р 2 С -the specific heat capacity for the decomposition reaction of boric anhydride, J/ºС• mol; -the enthalpy of phase transitions of boric anhydride (at the corresponding temperatures pt 2 T ), J/mol. The entropy of the decomposition reaction of boric anhydride at operating temperature is determined by the formula (9): The electromotive force of polarization of boric anhydride in this case is calculated, taking into account the expression for determining the change in the Gibbs energy and the Nernst formula [3,4,5,6,7,10] by the formula (10): The sequence of the release of boron and sodium at the cathode is determined by a quantitative comparison of the electromotive forces of polarization of boric anhydride and sodium oxide (11): Based on the anionic and cationic composition of the molten working and heating medium, the energy of chemical bonds between them and the structure model, a mathematical model is formulated. It is based on the determination of the Gibbs free energy using the theory of regular solutions, which takes into account the interaction of boron and sodium cations with the oxygen anion, as well as their energy and entropy change.
The average bond energy of sodium cations with oxygen ions, in accordance with the mixing rule, is described by expression (12): Chemical bonds between all ions of one mole of a molten working and heating medium have an energy that is determined by expression (14): This energy depends on the mutual arrangement of cations and anions and is the sum of the energies of all boron and sodium cations, as well as oxygen anions [3,4,5,6,7,10].
As a result, we get the expression (15): U -the energy of sodium oxide and boric anhydride, respectively, J; d Q -the displacement energy, J.
Taking into account the Boltzmann equation and Stirling's formula [9], the entropy of the system is determined by the formula (16): (16) The Gibbs free energy of one mole of the molten working and heating medium is determined by the formula (17): where n1 and n2 -the number of moles of sodium oxide and boric anhydride in the composition of the working and heating medium, respectively. The chemical potentials of sodium oxide and boric anhydride are actually the free energies of one mole of each substance in the working and heating medium. To determine them, it is necessary to take the partial derivatives of expression (18), first by n1 (19), and then by n2 (20): The value of the energy of mixing of ions is carried out taking into account the thermal effect of the formation of sodium tetraborate from oxides. The enthalpy of this reaction is determined for the borating temperature [3,4,5,6,7,10] taking into account the enthalpy of phase transitions from the crystalline to the molten state of oxides and sodium tetraborate itself during its formation (23):

Results
The calculation results according to the formulas (1) -(27) are summarized in the following table.

Conclusion
As a result of the calculation, it turns out that sodium oxide is more stable than boric anhydride (Е1 -Е2 > 0). In the case of electrolysis of such melts, when a higher decomposition voltage of boric anhydride and a lower decomposition voltage of sodium oxide are applied to the cell, active boron atoms are reduced from cations on the cathode surface. Consequently, the calculated substantiation of the application of the proposed composition for strengthening and restoring parts confirmed the possibility of its use.