Calculation and Analysis of the Structure and Viscosity of B2O3- Regulated CaO-Al2O3-Based Mold Fluxes

*e high content of aluminum in the steel reacts with the CaO-Si2O-based mold fluxes, resulting in deterioration of the mold slag physical and chemical properties, which cannot be applied to the continuous casting molten slag casting process of high-Mn highAl steel Herein, the thermodynamic and structural properties of low-reactivity CaO-Al2O3-based mold fluxes were investigated. *e thermodynamic properties were studied based on the first principles of quantum mechanics. *e results show that the formation of stable structures of B-O and O-B-O in the mold fluxes was beneficial to reduce the probability of structural interconnection, degree of polymerization, and viscosity of the molten slag.*e increase in the ratio of CaO/Al2O3 � 0.88–2 led to an increase in the O concentration. O entered the [AlO4] structure to form a stable structure of [AlO6] and [AlO5], wherein [AlO6] was more stable than [AlO5], reducing the degree of polymerization of the network structure. When cosolvent content B2O3 � 2%–10%, a simple layered structure of [BO3] was formed, and the particle migration resistance, break temperature, and viscous activation energy of the mold fluxes were reduced, while the corrected optical basicity of mold fluxes was gradually increased.


Introduction
With the rapid industrialization of China, the demand for high value-added steel has gradually increased, especially for high-Mn-high-Al steel. e high-Mn-high-Al steel has excellent mechanics such as great strength, superb plasticity, and low density. is steel is widely used in several fields such as automotive, marine, and nonmagnetic steel [1][2][3][4][5][6][7]. e production of high-Mn-high-Al steel uses ingot casting technology. To improve the production efficiency and reduce costs, several steel industries use continuous casting technology in production. e reaction with traditional CaO-SiO 2 -based mold fluxes during continuous casting and pouring is as follows: e main component silica in CaO-SiO 2 -based mold fluxes reacts with Al and Mn in high-Mn-high-Al steel as shown in equations (1)- (3). e primary chemical reaction is presented in reaction formula (1). e high aluminum content in high-Mn-high-Al steel is the main reason for the deterioration of physical and chemical properties of traditional CaO-SiO 2 -based mold fluxes [8,9]. When the CaO-SiO 2 -based mold flux is in contact with the hightemperature high-Mn-high-Al steel, there is a significant pickup of alumina and dramatic reduction in silica in the spent mold flux. erefore, the low-reactivity CaO-Al 2 O 3based mold fluxes are replacing the traditional CaO-SiO 2based continuous casting mold powder [10][11][12][13]. A high amount of Al 2 O 3 and low content of SiO 2 in low-reactivity CaO-Al 2 O 3 -based mold fluxes are expected to lower the driving force for the reaction. Hence, the employment of low-reactivity CaO-Al 2 O 3 -based continuous casting mold fluxes can meet the technical requirements of the continuous casting process, ensuring a stable and efficient continuous casting production.
Researchers have conducted a systematic investigation on the physical and chemical properties of mold fluxes [14][15][16], while some studies [17][18][19][20] have been performed on the properties of aluminosilicate molten slag through MD (molecular dynamics) simulation. MD simulations can better analyze the molten slag network structure and associated physical and chemical properties. Wu et al. concluded that, as the content of Al 2 O 3 increases, the aluminosilicate network becomes more complex. Also, for a given Al 2 O 3 content in different systems, as the electronegativity of the metal cation increases, the disorder of the Al-O structure and network structure and the degree of polymerization increase [21]. Ting et al. [22] estimated the variation of viscosity and atomic selfdiffusion coefficient via MD simulations and compared it with mathematical models and experimental data. e results show that both Si-O and Al-O networks depolymerize into simple structures with higher basicity, self-diffusion coefficient increases, and viscosity decreases. Seo and Tsukihashi used MD simulations to calculate the structural properties of the CaO-SiO 2 -based molten slag, along with the phase diagram and liquid-phase physicochemical properties of CaO-SiO 2 -based mold fluxes [23]. Guillot and Sator analyzed the thermodynamic and structural properties of the silicate molten slag under different partial pressures via MD simulations, but due to some limitations in experiments, the properties of the silicate molten slag have not been well studied [24]. e macroscopic characteristics of the continuous casting mold fluxes are determined by the microstructure. In recent years, MD simulations have been widely used to analyze the microstructure of the continuous casting molten slag [25]. Some scholars have focused on the effect of CaO-Al 2 O 3 -based mold fluxes on the viscosity performance; however, most studies have focused on the impact of flux composition of mold fluxes on the physical and chemical properties. A little attention has been paid to the influence of the CaO/Al 2 O 3 ratio on the physical and chemical properties of mold fluxes [26], while some studies [27,28] have been performed on the computational modeling and prediction on viscosity of slags; computational modeling on viscosity of slags has been widely used to analyze the microstructure of continuous casting molten slag. Hence, this paper studies the structure and viscosity performance of mold fluxes based on molecular dynamics theory.
As discussed, it is necessary to extensively study the microstructure and macroscopic properties of the CaO-Al 2 O 3 -based mold fluxes. Herein, the basic structure and physicochemical properties of the mold fluxes were studied, and the network structure of CaO-Al 2 O 3 -based mold fluxes was obtained based on molecular dynamics and analyzed with experimental data. e results of this work can provide guidance for the design and optimization of CaO-Al 2 O 3based mold fluxes.

Computation Methods
DFT (density functional theory) calculations were performed to compute the structure of the mold fluxes and analyze the thermodynamic properties. e structure was obtained by using the statistical thermodynamics method based on the operating vibration frequency of the optimized structure. e stabilized structure was used as a reactant to explore the transition states via complete linear synchronous transit (LST) and quadratic synchronous transit (QST) methods. e self-consistent field (SCF) method was used with the total energy. e vibrational analysis evaluation was used to compute the temperature-dependent enthalpy (H), entropy (S), vibrational free energy (G V ), and constantpressure heat capacity (C P ). e heat capacity (C P ) can be given as [29] C P � C trans + C rot + C vib In formula (4), C trans is the translational heat capacity, C rot is the rotational heat capacity, C vib is the vibrational heat capacity, R is the gas constant (8.314 J/mol·k), K is the Boltzmann constant, h is Planck's constant, T is the absolute temperature, and H is the enthalpy. e enthalpy (H) can be given as In formula (5), H trans is the translational enthalpy, H rot is the rotational enthalpy, and H vib is the vibrational enthalpy. e entropy (S) can be given as In formula (6), S trans is the translational entropy, S rot is the rotational entropy, S vib is the vibrational entropy, p is the pressure, σ is the symmetry number, c is the molar concentration, and I A , I B , and I C represent the moment of inertia. G v can be given as In formulas (7)-(9), G v is the vibrational free energy, E (0k) is the total energy, G product is the vibrational free energy product, and G reaction is the vibrational free energy of the reaction.

Analysis of the Basic Structure.
e microstructure of the molten slag determines chemical properties. e stability of the basic network structure is the basis for stable physical and chemical properties of the molten slag. e structural diagram in Figure 1 shows For the poorly stable Na-O structure, it is easier to link with other structures to form a complex structure; therefore, the content of Na 2 O is controlled to reduce the probability of the formation of complex cluster structures. When the content of Na 2 O is controlled within 12%, the performance of the inner molten slag is stable [30].
In the anionic structure presented in Figure 2, O-B-O is the most stable. Hence, the addition of B 2 O 3 (which aids in the formation of the network) to the molten slag is beneficial for the stability of physical and chemical properties of the mold fluxes, and it also increases the probability of the formation of a [BO 3 ] 3− single-layer triangular structure. When the structure is simple, the viscosity of the mold fluxes is reduced so that the migration energy required by the particles is reduced, and the viscous activation energy is lowered. O-Si-O in the mold flux structure is relatively stable; therefore, O-Si-O in the mold fluxes helps to reduce the probability of structural interconnection. As the ratio of CaO/Al 2 O 3 rises and CaO increases, the free Ca + and O 2ions released by CaO can break the combination of the Al-O-Al structure and form a stable structure Ca-O-Al, and the structure depolymerizes into a simple structure. As presented in Figures 1 and 2 6 ], which mainly existed in the networks [32]. As shown in Figure 3, [AlO 6 ] is more stable than [AlO 5 ], and [AlO 6 ] is a network modifier. When the CaO/Al 2 O 3 ratio is increased, the main function of CaO is to release O 2− and destroy the structure of [AlO 4 ] aluminosilicate, reduce the degree of aggregation of the network structure, and weaken the mutual links in the structure. As the structure formation of [AlO 5 ] or [AlO 6 ] increases, [AlO 6 ] has a stable octahedral structure, demonstrating a layered isolated distribution, decreased viscosity, increased tendency of random movement of structural units, and reduced resistance to free migration of particles.
ere are three coordination numbers in mold flux aluminate: [AlO 4 ] 5− , [AlO 5 ] 7− , and [AlO 6 ] 9− ; their structural conversion causes the instability of the aluminate structure and interlinked structure to become complex and poorly stable. e mechanism of action in the molten slag has not yet been established, and hence, it is of great significance to study the aluminate structure of low-reactivity CaO-Al 2 O 3based mold fluxes. e O 2− content in the molten slag is increased to form an octahedral [AlO 6 ] stable structure.
ere are more octahedrons in slag structure [AlO 6 ], which are beneficial for the stability of physical and chemical properties of the molten slag. Figure 4 shows the change in ∆G of different structures with respect to temperature. e reaction that produces a tetrahedral [AlO 4 ] structure has the greatest ∆G trend, while the reaction that produces [AlO 5 ] and [AlO 6 ] structures has lesser ∆G tendency; therefore, it is easier to generate the [AlO 4 ] structure in the mold fluxes. As the [AlO 4 ] structure is easier to form, the molten slag forms a tetrahedral [AlO 4 ] structure which is not as stable as an octahedral structure [AlO 6 ].
e [AlO 4 ] increase in the structure is one of the main reasons for the increase in the viscosity of mold fluxes. e network structure [AlO 4 ] can reduce the tendency of irregular movement in the structure; the free migration resistance and shear force on particles increase, which is also one of the main factors for the increase in viscosity.

Sample Preparation and
Viscosity Measurement e chemical composition of the mold fluxes used in this study is listed in Table 1. e chemical reagents used were all pure reagents (>95.5%). CaO was calcined at 800°C in a muffle furnace for 8 h, and other powders were placed at 500°C, as shown in the schematic diagram of the rotary viscometer in Figure 5. A sample of 120 g mold flux was placed in a high-purity graphite crucible, and the viscosity of the molten slag was measured using the rotary viscometer.
e Pt/Rh thermocouple was placed directly below the bottom of the high-purity graphite crucible, and castor oil of known viscosity was used for the calibration measurements at room temperature. e heat furnace had the temperature of 1400°C, which was maintained for 8 min to stabilize under argon atmosphere (flow rate: 0.3 L/min). e purpose was to homogenize the temperature and molten slag. e Mo spindle rotated at a fixed speed of 15 r/min; when the signal Journal of Chemistry from the rotary viscometer stabilized, the furnace was cooled at a rate of 5°C/min, and the viscosity measurements were continued.

Effect of the CaO/Al 2 O 3 Ratio on Flux Viscosity.
Increasing the ratio of CaO/Al 2 O 3 in the mold fluxes tends to increase the concentration of free oxygen. e [AlO 4 ] tetrahedral structure depolymerized into simple and stable structure [AlO 6 ], the probability of structural interconnection was reduced, and the viscosity of the molten slag decreased. As shown in Figure 6, the mold flux samples A1, A2, A3, and A4 structure fractured with the increase in temperature. When the B 2 O 3 content was 2% to 10%, the viscosity of the mold fluxes gradually decreased, and the break temperature of the molten slag was reduced from 1193°C to 1108°C. With the increase in the CaO/Al 2 O 3 ratio, cosolvent B 2 O 3 mainly existed in a simple two-dimensional [BO 3 ] structure, and the degree of polymerization of mold fluxes decreased. As a result, the resistance to free migration of particles and the shear force were gradually reduced, the structure was depolymerized, and the viscosity was decreased.
As shown in Figure 7, when w (CaO)/w (Al 2 O 3 ) � 0.88-2, the viscosity of the mold flux and the degree of aggregation in the network structure were reduced. To lower the reactivity of aluminum in the high-Mn-high-Al steel and    SiO 2 in the mold fluxes, the Al 2 O 3 content was increased in the mold fluxes. e aluminate molten slag viscosity is inseparable from the microstructure. When the ratio of CaO/ Al 2 O 3 was increased, the content of CaO in the mold fluxes increased. As a result, the content of Ca 2+ ions increased and destroyed the aluminate melt structure. e basic structure O-Al-O was transformed into a stable structure Ca-Al-O; however, excessive addition of CaO or Al 2 O 3 can weaken this effect. e high-coordination structure with the high content of Al 2 O 3 in the mold fluxes can easily form a complex structure; therefore, the viscous flow mechanism of the coordination structure with different contents of Al 2 O 3 was different. As shown in schematic diagrams in Figure 8, [AlO 6 ] and [AlO 5 ] generated higher average coordination structures. e main function of CaO was to release O 2− to destroy the aluminate structure and form a high-coordination structure, reduce the particle migration resistance and shear force, and lower the viscosity.
As shown in Figure 1, the B-O structure is the most stable in the system; therefore, the addition of cosolvent B 2 O 3 to the mold fluxes is beneficial to stabilize the structure and performance. Figure 9 shows  Figure 10 shows the schematic diagram for the changes in the network. CaO provides O 2− for the depolymerization of complex structures, dissociates the complex structure, and forms a simple and stable structure.

Viscous Flow Activation Energy and Corrected Optical
Basicity. e molten slag temperature was higher than the break temperature, and the molten slag can be considered as a Newtonian fluid. Hence, the change of molten slag viscosity with temperature follows the Arrhenius equation: where T represents the absolute temperature, K; A is a constant; E a is the viscous flow activation energy, kJ/mol;   Journal of Chemistry 5 and R is the ideal gas constant, 8.314 J/mol·K. e viscous flow activation energy can be calculated using formulas (10) and (11). Figure 11 shows the linear relationship between lnη and 1/T in order to calculate the viscous flow activation energy. Figure 11    e molten slag is in a completely liquid state and is a Newtonian fluid, and the activation energy can be estimated using the Arrhenius equation. Table 2 shows the melting temperature (T m ), break temperature (T b ), and viscous activation energy of experimental slags. As the CaO/Al 2 O 3 ratio increased, the viscous flow activation energy and break temperature decreased, which were higher than those reported by Zhirong et al. [33]. e main reason is that the cosolvent was different in the experimental research of mold fluxes. Also, other research works have reported different mold flux network structures resulting in different viscous activation energies. As the ratio of CaO/Al 2 O 3 increased, the shear force on particles in free motion decreased, the ability of particles to move freely reduced, and the activation energy and viscosity decreased.
ese results are consistent with the law of activation energy and viscosity in the traditional mold fluxes.
e optical basicity (Λ) characterizes the 'availability' of providing free oxygen ions, which indicates the degree of polymerization of the melts. A corrected optical basicity (Λ corr ) was proposed by Mills to charge-balance the Al 3+ ions incorporated into the Si 4+ chain or ring [34]. In formula (12), Λ is the optical basicity, X is the mole fraction, n is the number of slag oxygen atoms in the component molecule, and Λ corr is the corrected optical basicity.
e Λ corr values of mold powders A1 to A4 are listed in Table 2. From A1 to A4, Λ corr of the mold powder increased, and the viscosity decreased. As the ratio of CaO/Al 2 O 3 increased from 0.88 to 2, the break temperature and activation energy decreased.
ese results are consistent with the law of alkalinity and viscosity in the traditional mold fluxes.   4 ] tetrahedral structure was reduced, which shows that the network structure was reformed, and the viscosity was reduced. e mold fluxes were mainly composed of the [AlO 6 ] octahedral structure, suggesting that the network structure was reformed, and the viscosity was reduced. e [AlO 6 ] structure is not conducive to the interconnection of the network structure. Figure 12 shows the  In the mold fluxes, the network structure is related to the relative displacement and the connection mode. At first, the microstructure of mold fluxes was investigated as the basic structure is directly related to the viscosity of the mold fluxes. Figure 2 shows the anion structure; the cation in the mold fluxes connects the anion structure through the bridge oxygen bond. e network structure changed from simple to a complex structure, and the complex structures needed to overcome viscous resistance. Another reason for the change in molten slag viscosity is temperature. e increase in temperature led to a decrease in the force between ions and depolymerized bridging oxygen in the melt into nonbridging oxygen. e particle ion migration is easier when the temperature rises, and the viscous resistance decreases. With the addition of cosolvent B 2 O 3 to the mold fluxes, the metal oxide formed a low-melting eutectic compound, thereby, reducing the viscosity of the mold flux system. B 3+ mainly forms the [BO 3 ] structural unit in this mold flux system, and the [BO 3 ] structural unit forms a two-dimensional, singlelayer simple structure. In this slag system, several factors compete with each other and, ultimately, affect the viscosity of the slag system.

Conclusions
Herein, the variations of the structure and viscosity of CaO-Al 2 O 3 -based mold fluxes were investigated. e following conclusions can be made: (  3 ] has a simple and stable structure, reducing the possibility of forming a complex structure. When CaO/Al 2 O 3 � 0.88-2, the viscosity and break temperature gradually decrease, and the particle migration resistance decreases.

Data Availability
All the data generated or analyzed during this study are included within the article.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.