Investigation of Thermophysical and Physicochemical Characteristics of Al2O3-SiO2- CaO - Na3AlF6 Flux for SMAW Electrode Coating

This study investigated the thermophysical, physicochemical, and electrical characteristics of electrode coatings developed for application in the weld joint of nuclear power plants (NPPs). The extreme vertices design technique has been used in this work to develop the Al2O3-SiO2-CaO-Na3AlF6-based Shielded metal arc welding (SMAW) electrodes. Twenty-six electrode coating compositions were formulated, and flux coatings were milled into a fine powder for further characterization. X-ray diffraction (XRD) technique was utilized to investigate the structure and phases of the coating composition, and the Fourier transform infrared (FTIR) analysis technique was employed to determine the nature of bonds. The coating's thermal characteristics, including conductivity, diffusivity, and specific heat, were evaluated using hot disk equipment. Enthalpy change and thermal stability of flux coating were determined using the Differential thermal analysis(DTA)/ differential scanning calorimetry (DSC) technique.. The precision inductance (L), capacitance (C), and resistance (R) (LCR) instrument was used further to examine the electrical characteristics of the flux coatings. In addition, a regression model has been developed for each coating property using statistical analysis and investigated a correlation between the properties and mineral interactions. Results reveal that the individual elements and their binary and tertiary interaction significantly influence the physicochemical, thermophysical, and electrical properties of the flux coatings.


Introduction
The global energy supply and demand are increased by economic growth and industry development. Coal-based fossil fuels are used in industry and power plants to generate electricity. Coal combustion produced a significant amount of Carbon dioxide (CO 2 ) gas, accounting for 60% of the enhanced greenhouse impact [1,2]. The CO 2 gas produced affects the atmosphere globally and contributes to climate change. Many countries have shifted towards alternate energy resources to counter this effect. Renewable energy sources are presently the main emphasis in order to meet future energy demands and counteract the effects of global warming [3][4][5]. As a substitute for CO 2 -emitting electric power generating technologies, nuclear energy has once again become significant in the modern world due to rising energy demand. According to the literature, nuclear energy contributes only 10% of the electrical energy produced worldwide. Nuclear power plants have reduced annual emissions of greenhouse gases by 1.5 to 2 billion tonnes since 1990 [6][7][8][9][10]. High-temperature applications in nuclear power reactors mainly rely on austenitic and ferritic steel.
Nuclear power plants (NPPs) parts such as steam generators and pressure vessels are typically manufactured of ferritic steel SA508 or SA533 grade low alloy steel (LAS) due to economic reasons. While austenitic steel is often used in the primary heat-transfer pipe system because it offers better corrosion resistance and the required strength. The primary pipe system made of austenitic steel must be connected to the ferritic steel components using a dissimilar metal weld (DMW) connection [11,12]. The safety of the plant's operation and lifespan depends on the integrity of the weld joints. There have been several cases of DMW joint failures reported, including Three Mile Island 1 in the USA (2003), Calvert Cliffs 2 in the USA (2005), Tsuruga 2 in Japan (2003), Ringhals 3 and 4 in Sweden (2000), Tihange 2 in Belgium (2002), and Biblis-A in Germany (2000) for leaks and breakages [13]. Welding of dissimilar metals is challenging due to several issues such as carbon migration, formation of residual stresses, cyclic thermal stresses, stress corrosion cracking (SCC), etc. In addition, mechanical characteristics mismatch and metallurgical degradation are significant weld joint problems that shorten the Weld's design life. Weld joint failure is caused by carbon migration, which creates a soft zone on the ferritic side and a carbonrich zone on the austenitic side. Cyclical thermal stresses are generated by variations in the coefficients of thermal expansion (CTE) of austenitic and ferritic steel throughout the weld joint. Across the weld joints, these joints exhibit different mechanical and metallurgical characteristics. The desired weld joint strength and durability depend significantly on selecting the most appropriate welding techniques and filler materials. Gas tungsten arc welding (GTAW) and shielded metal arc welding (SMAW) technologies are the most extensively utilized welding technologies due to their high productivity, good weld quality, and consistency in providing good weld quality during multi-pass welding [14][15][16][17][18][19][20]. Austenitic steel-based fillers such as SS309L/ SS308L and nickel-based fillers such as IN82/IN52/IN182/ IN152 are widely used in NPPs applications. Nickel-based fillers are chosen over austenitic fillers because their CTE is between austenitic and ferritic steel and exhibits improved weld integrity. Studies reveal that nickel-based welding consumables outperform stainless steel consumables in NPPs [21,22].
Coated filler consumables have been utilized in the shielded metal arc welding (SMAW) process to combine dissimilar materials. The coating in the filler consumables significantly impacts the integrity of the weld joint. The coating of filler consumables functions as an arc stabilizer, a deoxidizer, and a shield against outside contaminants for the weld pool. Coating components also transferred to the weld fusion zone and changed the chemistry of the weldment by controlling element transfer. The composition of the weldment is determined by the base metal and filler consumables, as well as dilution ratios and elemental migration across the joint during quick slag-metal reactions. The electrode flux coating mixture's thermophysical and physicochemical characteristics significantly impact the weld deposits [23][24][25]. The influence of the electrode coating composition on the mechanical and chemical characteristics of welded joints was explored by a number of researchers. The coating melts prior to the filler wire during welding, forming a gas and acting as a shield for the weld pool from outside contaminants and gases. This also helps to preserve the stability of the arc [25][26][27][28][29][30][31][32][33][34]. Calcium oxide (CaO) addition lowers the hydrogen concentration of the weld metal and raises the basicity of the flux. Additionally, it helps to stabilize the arc and minimizes the viscosity, enhancing the Weld's mechanical properties and quality [35][36][37][38][39][40]. The viscosity, surface finish, and slag detachability of the welding fluxes are improved by the inclusion of silica (SiO 2 ). The use of aluminium oxide (Al 2 O 3 ) enhances the viscosity and the appearance of beads and encourages the formation of acicular ferrite and grain refinement. The addition of cryolite (Na 3 AlF 6 ) improves the cleanliness of the weld joint and provides better slag detachability. The inclusion of rutile (TiO 2 ) enhances slag detachability by transferring titanium from TiO 2 to the molten weld pool [41].
There is a lack of literature on the fluxes and electrode coating's thermophysical and physicochemical characteristics [36,37]. The extreme vertices design technique has been used in this research work to design and develop the Al 2 O 3 -SiO2-CaO-Na 3 AlF 6 -based SMAW electrodes. The thermophysical, electrical, and physicochemical properties of an electrode coating developed for austenitic and ferritic steel dissimilar weld joints using the Al 2 O 3 -SiO 2 -CaO-Na 3 AlF 6 system are investigated in this paper. The coating was milled and formed into powder samples. These powder coating samples were tested for dielectric constant, density, thermal conductivity, specific heat, weight loss upon heating, thermal diffusivity, and enthalpy change. Various characterization techniques were used, including hot disk, differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA). The electrical properties of the flux coatings were investigated using inductance (L), capacitance (C), and resistance (R) (LCR) instruments. Coating structural analysis was carried out using X-ray diffraction (XRD) and Fourier transform infrared (FTIR). Additionally, for each coating property, a regression model has been developed using statistical analysis, along with investigating a correlation between the properties and mineral interactions. The developed model was also validated by examining the difference between actual and predicted values. Multi-response optimization was used to determine the most appropriate flux composition that meets the desired target range for all response values. The chemistry-based discussion has also provided evidence for the influence of component minerals and their interactions.

Materials
Calcite (CaO), aluminium oxide (Al 2 O 3 ), rutile (TiO 2 ), silica (SiO 2 ), and cryolite (Na 3 AlF 6 ) are the minerals employed 1 3 in the study to develop the flux coating. The compositional analysis of flux elements is shown in Table 1.

Design of Experiments
The extreme vertices design model developed by Anderson and McLean [42] was used to analyze the electrode coating formulation. Equation (1) and (2) [43] describes the design for a confined n component between the minimum and maximum range.
where i = 1, 2, 3, 4,…………., n, X i, and Y i are the minimum and maximum range of the constraints on Z i. It represents the mixture element percentage of the ith constituent. The minimum composite melting temperatures of the coating element (1222 °C) and their related design spaces were determined using the Al 2 O 3 -SiO 2 -CaO based ternary phase diagram shown in Fig. 1.
The ternary phase diagram establishes the minimum and maximum bounds of the constituents of Al 2 O 3 , CaO, Na 3 AlF 6 , and SiO 2 electrode coating. The coating flux prediction estimates are reduced to a total of 65%. The 15% TiO 2 was added to stabilize the arc, and the remaining 20% binder (potassium silicate) was then included by weight. TiO 2 and binder percentages were constant for all the coating samples. Equations (3) and (4) indicate the minimum and maximum range of the constituents used to construct the 26 various compositions of flux coatings. It is essential that the electrode coating in the SMAW 1 3 process melts before the wire and continues to remain in the molten state even after the weld metal has solidified. Therefore, the combination of flux composition is produced after considering this information. Consequently, the composite melting temperature of the wire and base metal is higher than the melting temperature of the flux coating. Table 2 represents the 26 alternative formulations of flux coating compositions using the design matrix. Figure 2 depicts the three-dimensional space image of flux coatings, which has 10 vertices, 15 edge centers of edges, and 1 centroid.

Development of Electrode and Characterization
Flux mineral powders are appropriately blended by manual mixing, followed by equipment-based motorized mixing, in accordance with the design matrix. Manual mixing was required to ensure homogenous dry mixing of mineral powders. China clay and potassium silicate (K 2 SiO 3 ) were added in the appropriate proportions to create a wet mixture to improve bonding and extrudability. The binder-added wet mixture was placed in a motorized mixer for 30 min to ensure adequate mixing. The mixed composition was put in the top head of the laboratory-scale extruder, where it was fed with core filler wire size 3.15 mm in diameter and 350 mm in length. The developed electrode was left out in the open air for 24 h before being baked in an oven at 200 °C for 2 h to eliminate the moisture thoroughly. The developed electrode's covering was removed from the core wire and ground into particles smaller than 300 μm using a multi-pass grain refinement sieve. These fine coating powder samples have now been used in several advanced characterization methods. X-ray diffraction (XRD) techniques were utilized to investigate the structure and phases of the coating composition, and Fourier Transform Infrared Spectroscopy (FTIR) analysis techniques were employed to determine absorption bonds. The pellet for the FTIR measurement was created by mixing 2 mg of coated powder sample with 10 mg of potassium bromide (KBr) in an agate mortar. A pellet measuring 2 mm in thickness and 10 mm in diameter was produced using the hydraulic press. The FTIR characteristic plots were formed by scanning the produced pellets in the 400-4000 cm −1 wavenumber region with a resolution of 2 cm −1 . The flux coatings' apparent density was estimated by weighing the coating samples using the 10 ml volume in a cylindrical flask. The enthalpy of fusion and thermal stability of the coated composition was determined using Perkin Elmer STA6000 Differential thermal analysis(DTA)/ differential scanning calorimetry (DSC) technique. In this experiment, a platinum crucible was filled with 10-15 mg of coating sample, and controlled thermal scanning was done at a rate of 20 ͦ C/min while the temperature ranged between 30℃-900℃. The experimentally determined area under the heat flow curve estimates the enthalpy involved in heating coating formulations. The coating's thermal characteristics, including conductivity, diffusivity, and specific heat, were evaluated. The coating powder was used to completely enclose a 3.415 mm Kapton sensor, and subsequent thermal scanning in the controlled environment provided an accurate assessment of the thermal characteristics. The Agilent E4980A precision inductance (L), capacitance (C), and resistance (R) (LCR) instruments were used to examine the electrical characteristics of the flux coatings. Experiments were performed in a voltage 1 V, frequency of 100 kHz at room temperature. Pellet samples dimensions were 7.5 mm in thickness and 10 mm in diameter. The capacitance of the flux coatings was measured, and using the mathematical expression shown in Eq. (9), the dielectric constant of all flux coating samples was calculated. Figure 3 depicts the sample preparation, characterization, and experimentation processes.

Characterization of Coatings
The bulk density of the coating flux was performed using a 10 ml volume cylindrical flask filled with the fine powder coating flux, and it functions as a coating volume representation. The filled coating fluxes were then measured using a weighing balance. All flux coating composition was evaluated three times for a precise result, and the mean bulk density result was reported. The mathematical formula for calculating bulk density is represented by Eq. 5. The reported mean density values for each flux coating are shown in Table 3.
whereas mass (m) is measured in grams (g), displaced volume (V) in a cubic centimeter (cm 3 ), and density (ρ) in grams per cubic centimeter (g/cc). Figure 4 shows the variation in the mean density of each flux coating.  where temperature change (∆T) is measured in Kelvin (k), contact area (A) in square meters, and length (L) is measured in meters (m). Equation (7) was used to determine thermal diffusivity and represent the heat transmission rate between a substance and its surroundings.  where C p is specific heat capacity measured in J/kg K, K is thermal conductivity in W/mk, and density (ρ) is measured in kg/m 3 . Equation (8) represents specific heat (C), which is the amount of heat provided to raise the coating temperature by 1℃.
Where Q is the energy added in watts (W), dT is the temperature change in Kelvins (K), and m is the unit mass (g).
The percentage weight change, enthalpy change, and weight loss in the flux composition samples following exposure to the high-temperature range were all evaluated utilizing thermogravimetric Analysis (TGA). The coating sample weight reduction for the flux coating is shown in Table 5. The optimum coating for filler wire is one with the lowest weight loss percentage at the specified temperature range because it is more thermally stable than others. The results demonstrate that coating sample 12 shows the least weight loss percentage, 14.194%, while coating sample 26 shows the highest weight loss percentage, 22.948%. As the CaO component increases, greater weight loss is observed in the coating samples, which is influenced by the hygroscopic nature of the CaO material. Moisture concentration on coating samples has a significant impact due to the presence of basic oxides. So higher percentages of CaO show higher weight loss while acidic fluxes such as TiO 2 and Al 2 O 3 influence thermal stability synergistically [24,32]. The weight loss of coating flux samples is shown in Fig. 5. Enthalpy is the quantity of heat associated with the process. Table 6 shows the values of enthalpy change in the flux coating samples. The weight loss curve shows three distinct phases: dehydration, high volatility, and decomposition. Figure 5b depicts a dehydration phase at temperatures ranging from 30 °C to 150 °C, during which moisture within the flux coating samples is vaporized. During the second phase, the volatile substances were evaporated at temperatures ranging from 150 °C to 350 °C. The third stage is decomposition, in which chemical bonds between minerals are broken. The decomposition stage was present at temperatures ranging from 350 °C to 650 °C. The CaCO 3 mineral in the flux coating decomposed into the CaO, producing carbon dioxide (CO 2 ).
Weight loss in coating flux samples should be kept to a minimum because the dehydration and volatility stages are undesirable for the coating. The hydrogen and moisture present in electrode coatings are the primary sources of hydrogen added to the metal during the metallurgical and welding processes. Hydrogen is removed from the compounds during the heating process. Moisture and hydrogen in the coating affect its mechanical properties. The decomposition stage is advantageous for the welding electrode coating because it produces shielding gases that protect the joint from atmospheric oxygen and nitrogen gases, improving weld joint integrity and producing a defect-free weld joint. Experimental results reveal that coating sample 16 shows a minimum enthalpy change of -2150.039 J/g, while coating number 13 indicates a maximum enthalpy change of -10,271.190 J/g. Supplementary Fig. 6 represents the graph plot between the heat flow and temperature of various flux compositions. The enthalpy value is represented by the region inside the heat flow curve. XRD graph shows the prominent phases of TiO 2 , Al 2 O 3 , CaCO 3 , Na 3 AlF 6 , and SiO 2 . In addition to this, Ti is found to bond with [O] in different molar ratios. Peaks of Ti 8 O 15 and TiO 2 were present in the graph separately. The peaks of all the coating samples were almost similar due to the presence of the same mineral coating constituents. Supplementary Fig. 7 represents the peak of three different coating samples. The type of absorption bonds that exist between the components is revealed by FTIR analysis. Results indicate that the nature of bonds significantly impacts the thermophysical and physicochemical characteristics of the electrode coatings. Silica ions (SiO 4 4− ) present in the flux coating samples have a network-forming nature, so it increases the thermal conductivity of flux coatings. The concentration of these anions depends mainly on the nonbridging oxygen available. As a result, several bonds were examined using their corresponding bond positions from the IR spectra. Previous literature [23,[44][45][46] investigated the characteristics of various bonds that correspond to specific peaks. Numerous peaks could be seen across the whole range of wave number span, as shown in Supplementary Fig. 8.
The FTIR curve indicates the type of bond present in the fluxes. The prior literature has been utilized to determine the FTIR peaks. Supplementary Fig. 8 demonstrates due to the presence of CaCO 3 , the broad absorption peak at 1470 cm-1 (range of 1400 to 1500 cm-1) and a sharp peak at 875 cm-1 of internal vibrations mode of [CO 3 ] 2− . The presence of absorption bands between 600 and 800 cm-1 may be formed by the Al-O bond in The presence of silicates permits the Si-O stretching and bending vibrations between 1200-800 cm-1 and 600-400 cm-1 to be observed in the spectra. The quartz exhibits the Si-O-Si inter-tetrahedral bridging bonds between 798 and 780 cm-1 [47]. TiO 2 could be the reason for the Ti-O-Ti peak stretching at 600 cm-1 [48] By combining with network modifiers, including Ti 3+ , K + , Li 2+ , and, Al 3+ by electrostatic attraction, the silicate anion (SiO 4 4− ) forms an ionic bridge between two different forms of non-bridging oxygen. Small wavenumber peaks between 1500 and 1750 cm-1 and 3500 and 3750 cm-1, which correspond to the H-OH bonding and OH vibration modes, respectively, are mostly brought on by the moisture content of the pellets.
The dielectric constant of all flux coating samples was examined using the mathematical formulation [49] shown in Eq. 9. The calculated values of the dielectric constant are given in Supplementary Table 7. where ε � is dielectric constant, c is capacitance, d is sample

Regression Analysis
The design expert software was employed to construct the regression analysis model and statistical correlation [25,31,34,53], and formulations of each attribute were generated, as illustrated in Eqs. (10)(11)(12)(13)(14)(15)(16). The error percentage was determined to assess how closely the obtained results matched those predicted by the developed models.
( ∕ ) = +1.84753 × CaO + 11.63908 × Al 2 O 3 + 0.596568 × Na 3 AlF 6 + 3.90598×  A F test was conducted on the constructed model to determine its feasibility. The F test, commonly referred to as a statistical test, uses the F distribution to examine the equality of variances between two samples. Comparing statistical models that have been fitted to a set of data is the common usage for it. Equation 17 is used to determine the F values, which are expressed as a ratio of the variances of the two samples, using the analysis of variance technique or ANOVA method.
where σ 12 and σ 22 are the variance of the first and second samples, respectively. The statistical method known as (12) ( ∕ ) = −6.55613 × CaO + 8.43974 × Al 2 O 3 + 0.265049 × Na 3 AlF 6 + 3.45784 × SiO 2 − 0.091474 × CaO × Al 2 O 3 + 0.181584 × CaO × Na 3 AlF 6 + 0.125636 × CaO× analysis of variance (ANOVA) is used to investigate the significance of the mean differences between more than two samples. Typically, two alternative ANOVA techniques are utilized. One-way ANOVA is a method in which one independent variable affects the various sample groups. In the two-way ANOVA technique, the same sample group is impacted by 2 distinct factors. In this investigation, a one-way ANOVA method was employed. The comprehensive range of regression models, such as quadratic, linear, cubic, special cubic, etc., with forward and backward interpolations having a 95% acceptance p-value, was examined using the design expert technique. The regression model that was generated using ANOVA approaches is shown in Supplementary Table 8. The impact of the elements of the mineral flux on the obtained responses was examined using the ANOVA technique. Based on the data, outcomes are determined as significant, non-significant, decreasing, or increasing effects. P-values below 0.05 indicate significant model values for the individual, binary, and tertiary components, whereas those above 0.05 indicate no significant results. Supplementary Table 9 summarizes the effects of the flux coating compositions on the thermophysical and physicochemical characteristics. A predicted-actual value plot for all the attributes of the flux coating samples is shown in Supplementary Fig. 9. The best fit line indicates that the estimated equation's value is adequate. According to the constructed regression model analysis, coating components significantly impact thermophysical, electrical, and physicochemical characteristics. The coating undergoes several chemical reactions as it is heated up during the welding process. The coating melts and is combined with the base metal, liquid weld pool, and consumable during the fusion process. The developed regression model reveals that the individual flux coating elements significantly affect the density and binary coating interaction of Al 2 O 3 . SiO 2 shows a significant increasing effect while other shows decreased effect on density. Ternary component of CaO. Al 2 O 3 .Na 3 AlF 6 and CaO.Na 3 AlF 6 .SiO 2 shows an increasing effect and enhances weld cleanliness and slag detachability. The complex tetrahedral structured silicate ion, SiO 4 4− , decreases the fluidity of the molten weld pool. The decreased fluidity of the molten weld pool ensures a good density of the flux coating samples. As a result, the density is greatly improved. The presence of cryolite in the composition enhances density and slag detachability by reacting with silica to produce Al 2 O 3 [54]. Density values should not be very high since they might cause serious welding problems. In order to ensure excellent weld quality while welding at higher temperatures, the thermal stability of the coating samples is a crucial factor. Enthalpy refers to the heat evolved during the welding process, whether it is emitted or absorbed owing to a chemical reaction. The outcomes of the enthalpy analysis indicate negative values, revealing that the process is exothermic. Enthalpy values should not be excessively high because they represent more heat generation, affecting the base metal, heat-affected zone (HAZ), and weld metal. In addition to this, it also promotes various welding defects. According to regression analysis, the model has a significant p-value of 0.0066. The enthalpy change was significantly positively impacted by the individual element,binary interaction of CaO.Na 3 AlF 6 and the ternary interaction of CaO. Al 2 O 3 .SiO 2 , CaO.Na 3 AlF 6 .SiO 2 , and Al 2 O 3 .Na 3 AlF 6 .SiO 2 , while negatively impacted by other elements. The generated regression analysis of weight loss revealed that it was strongly impacted by the binary element interaction of Al 2 O 3 . SiO 2 , CaO.Al 2 O 3 , CaO.Na 3 AlF 6 , CaO.SiO 2 , and Na 3 AlF 6 . SiO 2 exhibits an increasing effect which improves thermal stability, while the individual components have no significant effect. Sample number 12 of the flux coating has superior thermal stability compared to other samples, whereas sample number 26 exhibits the lowest thermal stability. The presence of CaO, which is hygroscopic by nature, accounts for the coating sample's increased weight loss. Due to its hygroscopic nature, it is quickly contaminated by air or moisture, reducing the slag's viscosity. The coating mixture made of fluorides and chlorides is significantly impacted by moisture. Thermal conductivity analysis reveals the individual flux element Al 2 O 3 and binary element interaction of Al 2 O 3 .SiO 2 , CaO.SiO 2 , CaO.Na 3 AlF 6 , Na 3 AlF 6 .SiO 2 , and Al 2 O 3 .Na 3 AlF 6 shows an increasing effect on the thermal conductivity of the coating samples. The presence of network-forming chains influences the conductivity of the flux coating samples, and conductivity increases as the SiO 2 content increases and the presence of Si4 + covalently bonded ions in the network chains [24,32,[55][56][57]. Previous literature also reveals that the presence of cations and non-bridging oxygen (NBO) in the flux composition significantly influences thermal and physical properties. The thermophysical properties of alumina silicate-based glasses, such as density, thermal expansion, thermal conductivity, and thermal diffusivity, are significantly influenced by alkaline ions. Regression model analysis of thermal diffusivity reveals the individual elements SiO 2 , Al 2 O 3 , Na 3 AlF 6 , and the binary interaction of CaO. Na 3 AlF 6 , CaO.SiO 2 and ternary interaction of CaO.Al 2 O 3 . Na 3 AlF 6 , CaO.Al 2 O 3 .SiO 2 , and Al 2 O 3 .Na 3 AlF 6 .SiO 2 indicates a significant effect on the coating samples. The regression model of thermal diffusivity was observed as a significant model with a p-value of 0.0299. similarly, the regression model of specific heat shows the individual element CaO, Na 3 AlF 6 , SiO 2 , and binary interaction of CaO.Al 2 O 3 , Al 2 O 3 . Na 3 AlF 6 , Al 2 O 3 .SiO 2 and ternary interaction of CaO. Na 3 AlF 6 .SiO 2 shows a significant and increasing effect on specific heat. Welding electrodes require a lot of heat to provide for melting and fusion, so the specific heat of the flux coating should not be very high. While low specific heat will produce a rise in temperature from a meager heat input and consequently increase in a pretty high temperature. This chemically reacts generates a significant amount of heat and degrades the weld joint. The regression model analysis of the dielectric constant reveals that the individual element shows an increasing effect, and the model is significant with a p-value of 0.0468. The binary interaction of all the components shows a decreasing impact on the dielectric constant. The substitution of alumina in place of silica decreases the value of the dielectric constant. The dielectric constant of the flux coating samples was impacted due to the presence of moisture in the composition. Electrical capacitance was crucial to investigating the moisture content in a welding flux. The capacitance employed to monitor the moisture content in electrodes has been mentioned in the literature to have potential utility. The capacitance value reveals the condition of the electrode and changes in the flux composition. The capacitance calculation is essential to achieve the electrode quality, moisture content, and consistency criteria. Additionally, the capacitance value is employed to comprehend chemical differences, particularly in rutile content and particle size variations. Additionally, it prevents moisture accumulation during storage and guarantees the quality of each developed electrode. Using the mathematical formulation dielectric constant of the flux coating samples was investigated. The fundamental cause of electrical conduction is the cation migration of flux composition. Basic oxides like CaO are considered to be present as Ca 2+ . In the flux coating system, alumina (Al 2 O 3 ) either modifies the network for low basicity or forms the network for high basicity. According to research, Al 2 O 3 can exist as the tetrahedral structure AlO 4 5− , which is relatively similar to the structure of SiO 4 4− .one mole Al 2 O 3 has the potential to form two tetrahedral at high basicity; as a result, in a flux system, replacing one mole of SiO 2 with one mole of Al 2 O 3 will result in an increase in the number of tetrahedral. So it reduces the dielectric constant of flux coating samples [49,[58][59][60]. The addition of the TiO 2 element results in the formation of CaTiO 3 with dendritic morphology. The TiO 2 /SiO 2 of the composition lowers the viscosity; increasing the ratio slightly increases the free oxygen while decreasing the non-bridged oxygen and the bridged oxygen. Al 3+ ions only reveal network former behaviour and act as [AlO 4 ]-tetrahedral units. The amount of non-bridging oxygen decreases as Al 2 O 3 content rises. The degree of polymerization of the flux system increases with increasing Al 2 O 3 content. Basic oxides depolymerize the complex structure formed by [AlO 4 ] 5− and [SiO 4 ] 4− tetrahedral structures, altering the network structure and thus influencing the variation of the heat transfer phenomenon. The alloying element transfer behaviors are also affected by Al-related structure, so Al 3+ can substitute Si 4+ in the silicate structure to permit sufficient Si to be transferred to the weld metal [61][62][63][64][65][66][67][68][69][70]

Contour Plots
Contour graphs indicate anticipated values for various physicochemical characteristic responses for different coating mixture concentrations. The contour curve's various colors represent the multiple ranges of output obtained. Lines crossing the plot are another way to depict the constant response value change in the mixture. Supplementary Fig. 10 indicates the contour plot for various acquired attributes.

Model Verification
By selecting three alternative compositions randomly, the regression models verified the actual and anticipated results. Supplementary Table 10 provides verification for error percentages of density, weight loss, and enthalpy along with their respective average error percentages. Supplementary Table 11 provides validation for error percentages of thermal properties and Supplementary Table 12 represents dielectric constant and their respective error percentages.

Conclusion
Electrode flux coating formulations were developed using extreme vertices techniques by combining different proportions of CaO, Al 2 O 3 , SiO 2 , and Na 3 AlF 6 welding fluxes. The physicochemical, thermophysical, and electrical characteristics of all twenty-six coating compositions were investigated. Conclusions from these investigations are as follows: • The SiO 2 -Al 2 O 3 -CaO-Na 3 AlF 6 system was developed utilizing extreme vertices design techniques for the twentysix flux coating compositions. • Investigations were carried out on the composition of the developed flux coating, including its structural characteristics, thermophysical, physicochemical, and electrical characteristics. Regression models have been developed for each analyzed property. • Individual elements, binary interaction Al 2 O 3 .SiO 2 and ternary interaction of CaO.Al 2 O 3 .Na 3 AlF 6 and CaO. Na 3 AlF 6 .SiO 2 shows an increasing effect on coatings density because of the well-known network-forming characteristics of Al 2 O 3 and SiO 2 . • The tetrahedral silicate ions (SiO 4 4− ) increase the coatings' density (ρ) while decreasing the weld pools fluidity. Cryolite also reacted with SiO 2 to form Al 2 O 3 , improving the density of the coated sample samples. • Individual element, binary interaction of CaO.Na 3 AlF 6 and the ternary interaction of Al 2 O 3 .Na 3 AlF 6 .SiO 2 , Al 2 O 3 .CaO.SiO 2 , and CaO.Na 3 AlF 6 .SiO 2 shows a positive impact on the enthalpy change. • Binary interaction of Al 2 O 3 .SiO 2 , CaO.Na 3 AlF 6 , CaO.SiO 2 , CaO.Al 2 O 3 and Na 3 AlF 6 . SiO 2 enhances flux coating thermal stability, and these interactions considerably influence weight loss. The mixture's moisture content causes weight loss.