Thermodynamics and Agglomeration Behavior on Spinel Inclusion in Al-Deoxidized Steel Coupling with Mg Treatment

: There are many types of non-metallic MgAl 2 O 4 inclusions observed in Al-deoxidized steel coupling with Mg treatment, including single-particle MgAl 2 O 4 , agglomerated MgAl 2 O 4 , and MgAl 2 O 4 -MnS. Thermodynamic calculation shows that MgAl 2 O 4 precipitates in the liquid phase. The phase transformation follows liquid + Al 2 O 3 + MgAl 2 O 4 → liquid + MgAl 2 O 4 → liquid + MgO + MgAl 2 O 4 → liquid + MgO with the Mg content increasing when the Al content is a constant in molten steel, and it is in agreement with the experimental results for the formation of MgAl 2 O 4 in molten steel. The calculation results of various attractive forces between two particles show that the cavity bridge force plays a dominant role in the agglomeration process and results in the agglomerated MgAl 2 O 4 . The lattice mismatch calculation result shows that MgAl 2 O 4 can provide e ﬀ ective sites for MnS nucleating in


Introduction
Non-metallic inclusion has a great influence on the microstructure and performance of steel materials. Although many large-size inclusion particles can be removed into slag from molten steel in the steelmaking process, a small amount of inclusion with a wide size range remains unavoidable in steel products. In the process of steelmaking, aluminum is often used for deep deoxidation for liquid steel. However, solid alumina inclusions with a wide size range partially retained in the steel products destroy the microstructure and properties of the steel with their aggregation size and hard brittleness. Thus, controlling the chemistry, morphology, and size distribution of Al-deoxidation inclusion in steel is a key problem to improve the Al-killed steel performance.
Recently, magnesium is being widely used to disperse and refine inclusion, as it has strong agglomeration characteristics, such as Al 2 O 3 particles in molten steel [1][2][3][4][5][6]. In those published works, after the magnesium addition, the large-sized and irregularly shaped Al 2 O 3 inclusion in the steel were modified into small-sized and approximately spherical MgAl 2 O 4 inclusion. Meanwhile, the average diameter of MgAl 2 O 4 inclusion gradually decreases, while the number density of inclusion increases with the increase of magnesium content [7][8][9]. Yang [10] and Takata et al. [11] found that the total oxygen content drops to 15 ppm via Mg vapor deoxidation. The fine Mg-treated inclusion could be utilized to exert the "oxide metallurgy" to enhance the microstructures of steel products. However, some studies have found that fine MgAl 2 O 4 inclusion particles after magnesium treatment partially agglomerate in the molten steel. The agglomeration of MgAl 2 O 4 inclusions was also observed in our experiments. Wang et al. [7] and Du et al. [12] found that the attractive force of MgAl 2 O 4 inclusion has a certain relationship with inclusion radius by Newton's second law. Kimura et al. [13] thought that the aggregation of two MgAl 2 O 4 particles based on the general expression of thermodynamic potential by the capillary force. However, a comparison of the effects of various attractive forces between MgAl 2 O 4 particles leading to inclusion agglomeration in molten steel has not been reported. Therefore, we calculated various forces between MgAl 2 O 4 particles in molten steel and determined the main factors. In addition, complex MgAl 2 O 4 -MnS inclusions were observed in the current experiment. Wen et al. [3], Li et al. [14], and Isobe et al. [15] used two-dimensional mismatch to calculate the lattice mismatch between MgAl 2 O 4 between α-Fe, γ-Fe, and δ-Fe; however, a two-dimensional mismatch between MgAl 2 O 4 and MnS has rarely been reported to explain the formation mechanism of MgAl 2 O 4 -MnS inclusions. We calculated the two-dimensional mismatch between MgAl 2 O 4 and MnS to characterize the heterogeneous nucleation ability of MnS on MgAl 2 O 4 inclusion.
The current work carried out a deoxidation for molten steel by Al coupling with Ni-Mg alloy and observed the two-dimensional (2D) and the three-dimensional (3D) morphologies of inclusions in the deoxidized solid steel samples. Based on these observations, the thermodynamics of Fe-Mg-Al-O melt were studied by FactSage, various attractive forces between MgAl 2 O 4 particles in molten steel were calculated for clarifying the agglomeration of MgAl 2 O 4 inclusion, and then the misfit degree between MgAl 2 O 4 and MnS was calculated to reveal the formation mechanism of MgAl 2 O 4 -MnS inclusion.

Materials and Processes
The compositions and quantities of experimental raw materials are as follows. Pure iron powder 500 g, ferrous oxalate 1.125 g (99 mass pct), Ni-Mg alloy 7.5 g, and the high purity aluminum 0.5 g (99.99 mass pct Al). The compositions of raw materials containing pure iron, Al wires, and Ni-Mg alloy are shown in Table 1. A tubular resistance furnace was used to smelt and deoxidize for molten steel. First, the pure iron powder and ferrous oxalate were placed into the alumina crucible (the oxygen content is almost 200 ppm in the melt) and then the alumina crucible was placed into the tubular resistance furnace. The temperature was raised to 1873 K (1600 • C) and held for 30 min to ensure complete melting of the pure iron in the crucible. Then, Al particles wrapped with high-purity iron were added into the melt, and then Ni-Mg alloy was immediately added into the melt. After 5 s, the molten steel was cooled down to room temperature in the furnace chamber at a rate of 4 K/min. The whole experimental process was protected by high-purity argon gas with an argon flow rate of 1 L/min.

Chemical Composition Analysis
The chemical compositions of the steel samples were analyzed by the chemical methods. The total oxygen T.O was measured using a nitrogen-oxygen analyzer (Model: TC600, LECO Corporation, St. Joseph, MI, USA). The total content of aluminum Al(t) was measured by the inductively coupled plasma-mass spectrometry (ICP-MS, Shimadzu Europa GmbH, Duisburg, Germany). The acid-soluble aluminum Al(s) content was measured by the chromazurol-s spectrophotometric method. The Mg content was measured by the inductively coupled plasma atomic emission spectrometry (ICP-AES, Spectro Analytical Instrument GmbH, Kleve, Germany).

Inclusion Samples Preparation
The solidified steel was cut into two semicircle steel samples (63 mm × 31.5 mm × 22 mm) as shown in Figure 1a by a wire electric discharge machine. Taking a rectangular sample (10 mm × 10 mm × 22 mm) from the center of the semicircles, as shown in Figure 1b,c. The rectangular sample was cut into two small rectangular samples, and the sample was polished by metallographic sandpaper with different particle sizes ranging from 60 mesh to 5000 mesh, and then the surface of the sample was polished to a mirror surface with surface area of 10 mm × 10 mm, as shown in Figure 1d. The Mg content was measured by the inductively coupled plasma atomic emission spectrometry (ICP-AES, Spectro Analytical Instrument GmbH, Kleve, Germany).

Inclusion Samples Preparation
The solidified steel was cut into two semicircle steel samples (63 mm × 31.5 mm × 22 mm) as shown in Figure 1a by a wire electric discharge machine. Taking a rectangular sample (10 mm × 10 mm × 22 mm) from the center of the semicircles, as shown in Figure 1b,c. The rectangular sample was cut into two small rectangular samples, and the sample was polished by metallographic sandpaper with different particle sizes ranging from 60 mesh to 5000 mesh, and then the surface of the sample was polished to a mirror surface with surface area of 10 mm × 10 mm, as shown in Figure 1d. The electrolysis set-up is shown in Figure 2. The steel sample as the anode, the copper plate as the cathode, and the electrolyte consists of 1 pct 4-methyl ammonium chloride, 5 pct tri-ethanolamine, 5 pct glycerol, and 89 pct methyl alcohol (in volume fraction). During the electrolysis process, the current density was controlled for 40 to 60 mA/cm 2 via a DC regulated power supply. The electrolyte was stirred with nitrogen gas to improve the kinetic conditions. After the electrolysis process, the sample was placed in ethanol for ultrasonic cleaning to obtain all particles. The carbide was separated by the ferromagnet from all particles in ethanol, and the residual inclusion particles were collected and placed on a double-sided conductive carbon tape for the electron microscope observation.
The samples prepared by the above two methods were placed in the field emission scanning electron microscope (FESEM, model: ZEISS ∑IGMA HD, Carl Zeiss, Oberkochen, Germany) for observation and energy dispersive spectroscopy (EDS, model: Oxford-X-Max 50 mm 2 , Carl Zeiss, Oberkochen, Germany) analysis. The electrolysis set-up is shown in Figure 2. The steel sample as the anode, the copper plate as the cathode, and the electrolyte consists of 1 pct 4-methyl ammonium chloride, 5 pct tri-ethanolamine, 5 pct glycerol, and 89 pct methyl alcohol (in volume fraction). During the electrolysis process, the current density was controlled for 40 to 60 mA/cm 2 via a DC regulated power supply. The electrolyte was stirred with nitrogen gas to improve the kinetic conditions. After the electrolysis process, the sample was placed in ethanol for ultrasonic cleaning to obtain all particles. The carbide was separated by the ferromagnet from all particles in ethanol, and the residual inclusion particles were collected and placed on a double-sided conductive carbon tape for the electron microscope observation.  Table 2 shows the chemical compositions of the experimental steel sample. The experimental steel can be considered as ultra-low-carbon steel. The silicon content is 30 ppm, which is lower than the production of general steel, the main source is raw materials and Ni-Mg alloys. The content of total Al (Al(t)) is 0.003 mass percent higher than the content of acid-soluble Al (Al(s)) in the steel sample. The samples prepared by the above two methods were placed in the field emission scanning electron microscope (FESEM, model: ZEISS IGMA HD, Carl Zeiss, Oberkochen, Germany) for observation and energy dispersive spectroscopy (EDS, model: Oxford-X-Max 50 mm 2 , Carl Zeiss, Oberkochen, Germany) analysis. Table 2 shows the chemical compositions of the experimental steel sample. The experimental steel can be considered as ultra-low-carbon steel. The silicon content is 30 ppm, which is lower than the production of general steel, the main source is raw materials and Ni-Mg alloys. The content of total Al (Al (t) ) is 0.003 mass percent higher than the content of acid-soluble Al (Al (s) ) in the steel sample. The content of Mg in the steel sample is 8 ppm. Since the surface of the molten steel is not covered with slag during the laboratory experiment, few inclusions leave the molten steel, so the total oxygen (T.O) content is 107 ppm.  Figure 3 shows the 2D and 3D morphologies of single-particle MgAl 2 O 4 inclusion by FESEM-EDS observation. Figure 3a-d shows the 2D morphologies of MgAl 2 O 4 inclusion in the metallographic specimens, and these inclusion particles are long-strip, elliptical, and trapezoidal shape with a size of less than 4 µm in steel. Figure 3e-h shows the 3D morphologies of single-particle MgAl 2 O 4 inclusion extracted from the steel specimens by the non-aqueous electrolysis method, and the 3D morphologies of MgAl 2 O 4 inclusion particles are regular crystalline octahedron or approximate regular octahedron with a size range of 2-6 µm.    inclusion are formed by the aggregation of several small-sized MgAl2O4 particles. It can be seen from the 3D morphologies that the contact interface between the two MgAl2O4 inclusion is very obvious. The contact between them is different from the phenomenon in which the reaction causes the aggregation of inclusions, which are bonded together by different surfaces of two MgAl2O4 inclusions. It can be found from the binding sites that the two MgAl2O4 inclusions are tightly packed and there is no trace of occurrence of breakage.

Thermodynamics of the Formation of MgAl 2 O 4 Inclusion
The liquidus temperature and solidus temperature of the experimental steel were calculated to be 1807 K (1534 • C) and 1805 K (1532 • C) using Equations (1) and (2) Because the experiment is carried out by adding Mg alloy immediately after adding Al, the chemical reactions for the formation of MgAl 2 O 4 can be expressed by Equation (3): where a ( (5) can be simplified to Equation (6): The iron content in molten steel is extremely high, and the second-order interaction coefficient is negligible. Combining Table 2

Mechanism on the Agglomeration of MgAl2O4 Inclusions
In this experiment, single particle octahedral MgAl2O4 and agglomerated MgAl2O4 were observed. In order to understand the aggregation mechanism of octahedral spinel particles, we calculated the van der Waals force, capillary force, and cavity bridge force that may occur between spinel particles. It is a regular octahedron model. Assuming that a regular octahedron has a side length of a, and the regular octahedron and the sphere have the same volume, then When two MgAl2O4 inclusion particles are close in molten steel, the van der Waals force for attraction can be expressed by Equation (7) [22]: where A121 represents the Hamaker constant of particles, 0.45 × 10 −20 J [23]. a is assumed as 1 to 50 μm; In the calculation of this paper, A = 0.1, 0.14, 0.3. A = 0.14 is used in the literature [24], so this calculation covers this value. The calculation results of FV are shown in Figure 7. As the side length of the two inclusions increases, the van der Waals force will gradually decrease. According to Paunov et al. [25], when two solid particles with poor wettability are close to each other in liquid steel, the surface of the molten steel is deformed, and then the capillary force is generated in a horizontal direction by two close MgAl2O4 inclusions in molten steel. The capillary force can be expressed by Equation (8): where Q is the capillary charge (based on 26] is the surface tension of molten steel, N/m. Since capillary charge has little dependence on the distance between surface particles, Q is approximately equivalent to Q  . The capillary charge between two solid particles, Q  can be expressed by Equation (9)

Mechanism on the Agglomeration of MgAl 2 O 4 Inclusions
In this experiment, single particle octahedral MgAl 2 O 4 and agglomerated MgAl 2 O 4 were observed. In order to understand the aggregation mechanism of octahedral spinel particles, we calculated the van der Waals force, capillary force, and cavity bridge force that may occur between spinel particles. It is a regular octahedron model. Assuming that a regular octahedron has a side length of a, and the regular octahedron and the sphere have the same volume, then d = a 2 · A (A is a constant). When two MgAl 2 O 4 inclusion particles are close in molten steel, the van der Waals force for attraction can be expressed by Equation (7) [22]: where A 121 represents the Hamaker constant of particles, 0.45 × 10 −20 J [23]. a is assumed as 1 to 50 µm; In the calculation of this paper, A = 0.1, 0.14, 0.3. A = 0.14 is used in the literature [24], so this calculation covers this value. The calculation results of F V are shown in Figure 7. As the side length of the two inclusions increases, the van der Waals force will gradually decrease. According to Paunov et al. [25], when two solid particles with poor wettability are close to each other in liquid steel, the surface of the molten steel is deformed, and then the capillary force is generated in a horizontal direction by two close MgAl 2 O 4 inclusions in molten steel. The capillary force can be expressed by Equation (8): where Q is the capillary charge (based on J = N · m, the unit of Q is m). σ Fe [26] is the surface tension of molten steel, N/m. Since capillary charge has little dependence on the distance between surface particles, Q is approximately equivalent to Q ∞ . The capillary charge between two solid particles, Q ∞ can be expressed by Equation (9) [27]: where q is the capillary constant, m −1 . q is expressed by (ρ Fe × g/σ Fe ) 0.5 . ρ Fe represents the density of iron, 7000 kg/m 3 [28]. ρ MgAl 2 O 4 represents the density of MgAl 2 O 4 inclusion, 3578 kg/m 3 [28].
g represents the acceleration of gravity, 9.8 m/s 2 . θ represents the angle between the inclusion of MgAl 2 O 4 and the molten iron, 105 • [29]. [24]: The calculation result of FCB is shown in Figure 7. Comparing the calculated value of three attracting forces of FV, FC, and FCB, it can be found that the cavity bridge could be the main force between two particles leading to inclusion aggregation, while the capillary force could be little affection for inclusion aggregation in the steel melt.  The calculation result of F C is shown in Figure 7. The capillary force between the two MgAl 2 O 4 inclusion increases as the particle side length increases, but the F C value is less than the van der Waals force. Furthermore, according to the theory of cavity bridges [24], for two unwetted inclusion particles in contact with molten steel, a cavity bridge is formed between the two particles when two MgAl 2 O 4 inclusions are close together, as shown in Figure 8. As the radius of curvature of the cavity bridge is reduced, a cavity bridge force is generated. F CB can be expressed by Equations (10) and (11) [24]:

Mechanism on the Formation of MgAl2O4-MnS Inclusion
The MgAl2O4-MnS inclusion is a common complex inclusion in the current experimental steel. However, whether MgAl2O4 can be used as a MnS heterogeneous nucleation site is rarely reported. In this study, the equilibrium concentration product curve of MnS in molten steel was calculated The calculation result of F CB is shown in Figure 7. Comparing the calculated value of three attracting forces of F V , F C , and F CB , it can be found that the cavity bridge could be the main force between two particles leading to inclusion aggregation, while the capillary force could be little affection for inclusion aggregation in the steel melt.

Mechanism on the Formation of MgAl 2 O 4 -MnS Inclusion
The MgAl 2 O 4 -MnS inclusion is a common complex inclusion in the current experimental steel. However, whether MgAl 2 O 4 can be used as a MnS heterogeneous nucleation site is rarely reported. In this study, the equilibrium concentration product curve of MnS in molten steel was calculated according to Equations (12) and (13) [30].
where a MnS , a Mn , a S represent the activity of MnS, Mn, S, respectively. The precipitation temperature of MnS is 1656 K (1383 • C), the liquidus temperature 1807 K (1534 • C) and solidus temperature 1805 K (1532 • C) During the solidification process of the molten steel, it is assumed that the S element can diffuse completely. Therefore, the actual concentration of Mn and S can be obtained by Equations (14) and (15) [31]: where C Mn L and C S L represent the concentration of Mn and S at the solidification front, respectively; C Mn 0 and C S 0 denote the initial concentration of Mn, S in the molten steel, respectively; f s is the solid fraction; k Mn and k S are the equilibrium distribution coefficients of Mn and S, respectively; k Mn = 0.78 and k S = 0.035 [32].
The actual concentration product Q MnS during solidification can be expressed by Equation (16): The relationship between the solid fraction and the temperature during solidification can be expressed by Equation (17) [16]: where T is the temperature of the liquid phase during solidification. The relationship (log KMnS and log QMnS) between the theoretical and actual concentration of MnS and the solidification fraction is calculated as shown in Figure 9. The equilibrium constant of MnS is equal to the theoretical concentration product of Mn and S (KMnS = [pct Mn] × [pct S]), it can be calculated by Equation (13) and the actual concentration product QMnS is calculated by Equation (16), respectively. Precipitation of a solid phase will occur if the actual concentration reaches the equilibrium concentration (QMnS = KMnS). There is no intersection point between log KMnS and log QMnS in Figure 9. It indicates that the precipitation temperature of MnS is lower than the solidus temperature. MgAl2O4 precipitates in the liquid phase, and then MgAl2O4 inclusion can be wrapped by the MnS inclusion, forming the MgAl2O4-MnS inclusion.   Table 3. [33,34] Bramfitt [35] proposed the lattice mismatch to characterize the ability of compound substrates to promote heterogeneous nucleation. The mismatch can be expressed by Equation (18) (18) where (hkl)s is a low-index crystal face on the substrate; (uvw)s is a low-index direction on the crystal plane (hkl)s; (hkl)n is a low-index crystal plane on the nucleation phase; (uvw)n is a low-index direction on the (hkl)n crystal plane; d [uvw]s is the spacing of atoms in the (uvw)s direction; d [uvw]n is the spacing of atoms along the (uvw)n direction; θ is the angle between (uvw)s and (uvw)n.    Table 3 [33,34]. Bramfitt [35] proposed the lattice mismatch to characterize the ability of compound substrates to promote heterogeneous nucleation. The mismatch can be expressed by Equation (18): where (hkl) s is a low-index crystal face on the substrate; (uvw) s is a low-index direction on the crystal plane (hkl) s ; (hkl) n is a low-index crystal plane on the nucleation phase; (uvw) n is a low-index direction on the (hkl) n crystal plane; d[uvw] s is the spacing of atoms in the (uvw) s direction; d[uvw] n is the spacing of atoms along the (uvw) n direction; θ is the angle between (uvw) s and (uvw) n .