Numerical Simulations of the Impact of CaO/Al₂O₃ on the Structure and Crystallization Behavior of Red Mud

Abstract

The problem of large stockpiles of red mud needs to be solved, and the use of red mud to prepare inorganic fibers is a new way of applying red mud on a large scale. The role of CaO/Al₂O₃ in the melting point and melt structure of red mud was investigated by molecular dynamics simulations and thermodynamic calculations. Liquid phase line temperatures for different CaO/Al₂O₃ systems were calculated using the Factsage program. The radial distribution function and the type of oxygen bonding were used to characterize the effect of different CaO/Al₂O₃ on the structure of the red mud melt. The melting point of MgAl₂O₄ is lower than that of CaTiO₃ due to the fact that the type of oxygen bonding in MgAl₂O₄ is predominantly bridging oxygen bonds. When the red mud system has a low SiO₂ content and CaO/Al₂O₃ is between 0.3 and 3.9, the melting point temperature increases significantly, which is not conducive to the fibrillation of the red mud melt.

1. Introduction

Red mud is a common type of non-ferrous metal industrial solid waste, typically referred to as waste slag generated during the alumina production process using the Bayer method [1,2,3,4]. Due to its complex composition and high alkalinity, as well as limited recycling research, red mud has not been effectively recycled, resulting in large-scale accumulation in landfills [5,6,7]. To recover the iron content from red mud, a process involving a rotary hearth furnace can yield low iron-containing red mud via extraction [8]. The resulting silicate substance mainly consists of SiO₂, Al₂O₃, CaO, and Na₂O, and can be used to produce mineral wool fibers. The research, development, and industrialization of mineral wool fiber products can serve as an effective strategy to utilize solid waste, such as red mud melt, on a large scale [9,10,11]. However, because the Al₂O₃ content in red mud melt exceeds the composition requirements of mineral wool fibers [12], with insufficient CaO and SiO₂ content, modulators with high silicon and low aluminum are needed to modify red mud melts.

Crystallization will occur during the fiberizing process of red mud slag. These crystals can potentially cause the fibers to break and affect the overall quality of mineral wool fibers [13,14,15]. In recent years, FactSage 7.1 thermodynamic calculation software has been commonly used to study the crystalline phases of high-temperature slag, to help elucidate the impact of slag composition on crystalline phase transition [16,17,18]. Unfortunately, thermodynamic calculations can only provide information such as crystalline phase precipitation and transformation, which may not provide suitable results for describing or explaining the evolution of ordered crystalline phase structures during the cooling process. Materials Studio 2017 (MS) simulation software serves as a powerful tool to study the crystal phase network structure at the molecular level, and has been widely used to uncover the fundamental physical properties of microstructure evolution [19,20]. Using molecular dynamics simulations, Bi et al. [21] found that changes in the Al₂O₃ content in SiO₂-CaO melts cause Al₂O₃ to exhibit amphoteric behavior and affect the bridging oxygen content and degree of polymerization in the system. In terms of slag crystallization behavior, MS simulations can offer insight into the continuous changes in the structure and properties of slag at different cooling temperatures [22]. The radial distribution function, mean coordination number, and bridging oxygen distribution results can be used to analyze the role of each component in the system, providing a correlation between crystal phase structure evolution and performance.

Al₂O₃ is an amphoteric oxide with different coordination forms in different acid–base systems, and can be used as a network former and modifier [23,24,25]. In silicate systems, CaO is a major source of free oxygen supply, and differences in the CaO content of the system affect the amphoteric behavior of Al₂O₃. Due to the high Al₂O₃ content in red mud melt, and considering the modification direction of mineral wool fiber and the difficulty of obtaining conditioners, in this study, we used CaO as the alkaline modifier. We also explored the impact of increasing calcium and reducing aluminum on the crystallization behavior of the red mud melt. Combined thermodynamic calculations and molecular dynamic simulations were used to analyze the impact of the CaO/Al₂O₃ mass percentage ratio on the crystallization phase during the red mud slag cooling process, particularly focusing on the primary phase at high temperatures. This study revealed how CaO/Al₂O₃ impacted the network structure of the red mud melt slag system from a microscopic perspective, providing theoretical guidance for improving the crystallization behavior of the red mud melt slag fibrillation process.

2. Materials and Methods

2.1. Simulation Method

The red mud raw material comes from an aluminum plant in Shandong Province, China. The pre-treatment process flow for iron extraction from red mud is red mud mixing after balling treatment into the rotary hearth furnace for roasting, and then heating by the electric arc furnace and reduction; to obtain the fused slag and molten iron, this process can be used directly for the production of steelmaking iron. The chemical composition of the red mud after iron extraction is shown in

Table 1. Chemical composition of red mud (mass percentage, %).

Red Mud Composition	SiO2	CaO	Al2O3	MgO	Na2O	Fe2O3	TiO2	K2O	MnO	Other
Mass/%	27.26	10.62	32.31	2.14	11.16	7.56	7.23	0.30	0.13	1.29

. In this study, due to the pre-treatment, during which most of the Fe²⁺ was oxidized to Fe³⁺, iron is only represented as Fe₂O₃ in this paper. Based on the main compositions of red mud in Table 1, seven main components were selected for the design of the simulation scheme.

Table 2. Red mud slag system simulation schemes under different CaO/Al₂O₃ ratios (mass percentage, %).

Scheme	CaO/Al2O3	Red Mud Composition/Mass Percentage, %
		CaO	Al2O3	SiO2	Na2O	Fe2O3	TiO2	MgO	Total
A1	0.3	10.80	32.89	27.75	11.36	7.69	7.36	2.17	100
A2	0.9	20.70	22.99	27.75	11.36	7.69	7.36	2.17	100
A3	1.5	26.20	17.49	27.75	11.36	7.69	7.36	2.17	100
A4	2.1	29.6	14.09	27.75	11.36	7.69	7.36	2.17	100
A5	2.7	31.9	11.79	27.75	11.36	7.69	7.36	2.17	100
A6	3.3	33.5	10.19	27.75	11.36	7.69	7.36	2.17	100
A7	3.9	34.8	8.89	27.75	11.36	7.69	7.36	2.17	100

presents the design method used in this study, where CaO/Al₂O₃ was increased from 0.3 to 3.9, and all other components remained constant.

2.2. Thermodynamics Calculations

The thermodynamic calculations in this study were conducted using the FactPS and FToxid databases in the FactSage 8.1 software package [13]. In addition, the Equilb module was used to calculate the liquidus temperature of the melted red mud system at equilibrium, as well as the type and content of the initial crystallization phase during the cooling process. The calculations were carried out in the temperature range of 1200 to 1600 °C at standard atmospheric pressure.

2.3. Molecular Dynamics Simulations

The Garofalini potential function in MS 2021 software was used in the molecular dynamics simulations of the red mud melt slag, to describe the interactions between the particles in the silicate melt [26]. Under this potential field, oxygen and metal atoms were imported into the three-dimensional periodic model as a single particle, and the number of atoms in the system was not limited. These assumptions met the requirements of random atom distribution in the red mud melt system. The Garofalini potential function contained a modified BMH potential function and a three-body potential function including the Coulomb potential, repulsive potential, and attractive potential, with the following expression:

$${\mathrm{V}}_{\mathrm{i}\mathrm{j}}=\frac{{\mathrm{q}}_{\mathrm{i}}{\mathrm{q}}_{\mathrm{j}}}{4\mathrm{\pi }{\mathrm{\epsilon }}_0{\mathrm{r}}_{\mathrm{i}\mathrm{j}}}+{\mathrm{A}}_{\mathrm{i}\mathrm{j}}\exp \left(-{\mathrm{B}}_{\mathrm{i}\mathrm{j}}{\mathrm{r}}_{\mathrm{i}\mathrm{j}}\right)-\frac{{\mathrm{C}}_{\mathrm{i}\mathrm{j}}}{{\mathrm{r}}_{\mathrm{i}\mathrm{j}}^6}-\frac{{\mathrm{D}}_{\mathrm{i}\mathrm{j}}}{{\mathrm{r}}^8}$$

(1)

where V_ij is the interaction potential between atoms i and j, q_iq_j denotes the charge of atoms i and j, ɛ₀ is the dielectric constant of the free space, r_ij is the distance between atoms i and j, and A_ij, B_ij, C_ij, and D_ij denote the potential constants between the atom couples.

Table 3. The BMH potential constant of the electron pairs in the red mud slag system.

i	j	Aij/eV	Bij/(Å−1)	Cij/(eV·Å6)
O	O	1.18 × 105	7.31	0
O	Si	1.98 × 105	5.77	0
O	Ca	1.52 × 105	4.93	0
O	Fe	2.74 × 105	6.08	0
O	Mg	1.06 × 105	4.95	0
Al	O	1.95 × 103	3.55	0
Ti	O	2.40 × 105	6.06	0
Na	O	1.99 × 103	6.25	0
Ca	Al	3.68 × 104	6.25	0
Al	Mg	1.72 × 102	6.25	0

lists all potential constants used in this study.

When using MS to simulate the microstructure of the red mud melt slag, the initial model required an amorphous state, with the atoms in a disordered and randomly distributed state. The atom number and density in the system, the calculation time, and the algorithm were critical to the accuracy and validity of the simulation results. In this study, the total number of atoms in the seven sample groups varied between 2121 and 2278, and the system density was in the range of 3.31 and 3.17 g/cm³, as shown in

Table 4. The density of the red mud slag system and the number of atoms.

Sample	Density	Number of Atoms
		Ca	Si	Al	Ti	Mg	Fe	Na	O	Total
A1	3.31	96	231	322	46	27	48	184	1324	2278
A2	3.26	185	231	226	46	27	48	184	1269	2216
A3	3.23	234	231	172	46	27	48	184	1237	2179
A4	3.21	264	231	138	46	27	48	184	1216	2154
A5	3.19	284	231	116	46	27	48	184	1203	2139
A6	3.18	299	231	100	46	27	48	184	1194	2129
A7	3.17	310	231	88	46	27	48	184	1187	2121

. The atoms in each group were randomly placed in the model box, where the side length of the simulation box was 32.5 Å. Periodic boundary conditions were applied around the model box to form a boundaryless infinite system, to make the calculation results more realistic.

Because the BMH potential energy assumed that the red mud melt slag system was completely molten during the simulation, the simulation had to be conducted at the temperature of complete melting. According to the thermodynamic calculation results, the liquid phase regions of the different CaO/Al₂O₃ samples were all below 1873 K. To ensure that the atoms in the melt system were uniformly mixed and in a molten state, the micro-canonical ensemble (NVE) was used to describe the relaxation process, and the canonical ensemble with a Nosé–Hoover thermal bath (NVT) was used to describe the cooling process when the system temperature was lowered to 1873 K. The entire cooling process could be divided into five stages, as shown in Figure 1. (1) The initial temperature was set as 5000 K and the relaxation time was set to 30 ps. (2) After 30 ps, the system was cooled down to 2000 K, and the cooling rate was 1 × 10¹⁴ K/s. (3) The system was relaxed at 2000 K for 30 ps. (4) The system was cooled down to 1873 K after 12.7 ps, and the cooling rate was 1 × 10¹³ K/s. (5) The system was finally relaxed at 1873 K for 30 ps. Based on the microstructural information obtained after the fifth relaxation stage, we assessed the bond length, bond angle, mean square displacement (MSD), bridge oxygen, and $Q_m^n$ distribution in the system with different CaO/Al₂O₃ ratios.

3. Results

3.1. Calculation of Red Mud Melting Point (Liquidus Temperature)

Above the liquidus temperature, the system was entirely in a liquid phase, while below this temperature, crystals started to precipitate as primary crystals. In order to investigate the influence law of CaO/Al₂O₃ on the melting point of red mud, calculations were carried out using the Scheil–Gulliver cooling model in the Equlib module of FactSage 8.1 thermodynamic software. The liquid phase line temperature of the red mud system was predicted and the data are shown in Figure 2.

At lower CaO/Al₂O₃ (0.3 to 1.5), the melting points calculated by FactSage increase rapidly as CaO/Al₂O₃ increases. Then, after CaO/Al₂O₃ is greater than 1.5, the melting point tends to decrease slowly. When CaO/Al₂O₃ increased from 0.3 to 1.5, the melting point of the feedstock increased by 132 °C, indicating that high melting point substances were generated in the system at lower CaO/Al₂O₃. This shows that when the SiO₂ content in the red mud is low, a small increase in CaO/Al₂O₃ will cause a significant increase in the melting point of the red mud, in which it is difficult for CaO to play the role of fluxing, but instead plays the role of nucleation. When CaO/Al₂O₃ increased from 1.5 to 3.9, the melting point of the raw material decreased by 45 °C, indicating that the effectiveness fluxing of CaO gradually began to appear at higher CaO/Al₂O₃.

The stable phases first formed by the melt under different CaO/Al₂O₃ conditions were also analyzed using the Equilib module of FactSage, as shown in Figure 3. When CaO/Al₂O₃ is 0.3, the first and most stable phase is Spinel, and after CaO/Al₂O₃ reaches 1.5, the first stable phase is CaTiO₃. There is a significant change in the liquidus temperature with increasing CaO/Al₂O₃, which may be attributed to the microstructural transition between Spinel and CaTiO₃. The liquidus temperature is above 1480 °C, when CaTiO₃ is the first stable phase to appear in the red mud melt. In this range, the flow behavior of the melt is not suitable for the preparation of inorganic fibers. Therefore, it is necessary to analyze the microstructural features provided by the MS results, such as the radial distribution function (RDF) and oxygen bonding species, in order to reveal the influence of CaO/Al₂O₃ on the melting point in the following calculations.

3.2. Analysis of the Red Mud Melt Structure

3.2.1. Radial Distribution Function

The radial distribution function (RDF) was used to describe the nearest neighbor distribution between atoms in the melt, as well as the distribution of other surrounding particles [27]. The RDF curve when CaO/Al₂O₃ increased from 0.3 to 3.9 is shown in Figure 4. The abscissa value of the first peak in (a)–(h) consisted of the bond length of the corresponding ion pairs. Due to the similarity in chemical bonds, the bond length positions of Si–O and Al–O in the different slag systems were the same. The abscissa value of the first peak in the radial distribution function of the corresponding iron pair was represented by r1, indicating the bond length between the corresponding ion pair. The length of each bond in the melt is shown in

Table 5. The mean position (r1) of the first peak in different samples.

	Si–O	Al–O	Ca–O	Mg–O	Ti–O	O–O	Fe–O	Na–O	Mg–Al	Ca–Al
	r1 (Å)
A1	1.59	1.77	2.29	2.37	2.45	2.63	2.59	2.35	3.25	3.55
A2	1.59	1.77	2.31	2.37	2.49	2.65	2.61	2.31	3.17	3.51
A3	1.59	1.77	2.35	2.31	2.49	2.63	2.69	2.33	2.91	3.61
A4	1.59	1.79	2.33	2.35	2.49	2.61	2.55	2.31	2.95	3.55
A5	1.59	1.77	2.31	2.33	2.47	2.61	2.69	2.31	2.97	3.63
A6	1.59	1.75	2.31	2.35	2.49	2.61	2.63	2.33	2.79	3.61
A7	1.59	1.75	2.31	2.35	2.49	2.61	2.63	2.29	2.99	3.61

. As shown in Table 5, we observed that the r1 of various ions and oxygen ions did not vary significantly as CaO/Al₂O₃ increased, and the r1 values were maintained at 1.59 Å (Si–O bond), 1.77 Å (Al–O bond), 2.31 Å (Ca–O bond), 2.35 Å (Mg–O bond), 2.48 Å (Ti–O bond), 2.62 Å (O–O bond), 2.63 Å (Fe–O bond), and 2.32 Å (Na–O bond). In addition, the r1 values of Mg–Al and Ca–Al did not vary significantly and were maintained at 3.00 Å and 3.58 Å, respectively. These values are consistent with the results obtained in the literature [28,29].

According to the peak height, the peak heights of the Mg-O and Al-O RDF curves of MgAl₂O₄ are more similar to the peak heights of the RDF curves at a CaO/Al₂O₃ of 0.3 [30], and the peak Ca-O and Ti-O RDF curves for CaTiO₃ are more similar to the peak heights of the RDF curves for CaO/Al₂O₃ of 0.9 and above [31].

As shown in Figure 4, the first peaks in the Si–O, Al–O, Ca–O, and Na–O RDF curves became more prominent with increasing CaO/Al₂O₃, indicating that the number of oxygen atoms surrounding Si, Al, Ca, and Na increased as CaO/Al₂O₃ increased. This could be attributed to the fact that CaO served as a substantial source of free oxygen. The first peak in the O–O RDF curve decreased as CaO/Al₂O₃ increased, due to stronger attraction between the Ca and O atoms compared to between the oxygen atoms. Therefore, as the number of Ca atoms increased, the oxygen atoms surrounding O gradually decreased. The second-to-third-peak ratio in the Ca–O and Na–O RDF curves was larger than in the Si–O and Al–O curves, because the impact of Ca and Na on O was larger than the impact of Si and Al on O [32]. In addition, in combination with Table 5, it can be found that the r1 value of the Al-O bond tends to decrease with the increase in CaO/Al₂O₃ in the system, which proves that the increase in CaO content affects the stability of the Al-O bond.

3.2.2. Oxygen Components

The changes in bridging and non-bridging oxygen in the red mud melts are shown in Figure 5, indicating that the Si–O–Al bonds, Al–O–Al bonds, and Si–O–Si bonds were the main components of the bridging oxygen bonds. When CaO/Al₂O₃ is 0.9, the surrounding Si-O-Al decreases by about 29% and Al-O-Al decreases by about 44%, while the Si-O-Ca and Al-O-Ca contents start to increase significantly, with no significant changes in the other bond types. This is consistent with the prediction described above that Ca atoms interact primarily with Al-O.

As can be seen in Figure 5, the number of bridging oxygen bonds decreases to less than 50% when the CaO/Al₂O₃ in the system is 0.9, and non-bridging oxygen becomes the dominant oxygen species in the melt. The oxygen species in MgAl₂O₄ are predominantly bridging oxygen bonds, whereas non-bridging oxygen bonds predominate in CaTiO₃. This difference explains well the increase in the melting point when changing from Spinel to CaTiO₃. That is, upon raising CaO/Al₂O₃ in the melt, the bridging oxygen atoms in the melt, which connect the tetrahedra to form a stable structure, are transformed into non-bridging oxygen atoms. This transformation phenomenon may be related to the free oxygen atoms provided by the Ca dispersed in the network, since free oxygen weakens the bridging oxygen bonds in the network. This is also consistent with the concept of Ca atoms as network modifiers in glass science [33]. The typical microstructures of the two mineral phases are shown in Figure 6. As the number of calcium atoms in the system increases, the Al-O bond in the melt is easily broken, making the probability of forming an [AlO₄] structure decrease and the probability of calcium atoms appearing around the Ti-O bond increase.

To characterize the degree of polymerization and complexity in the system, $Q_m^n$ was employed, where Q denotes the tetrahedral structural unit, n signifies the number of bridging oxygens in the tetrahedral structure, and m refers to the atomic species connected to the tetrahedral structure. The distribution of oxygen species in the red mud slag system is shown in Figure 7. As CaO/Al₂O₃ increased, the number of Si surrounding [SiO₄]⁴⁻ in the system did not vary significantly (Figure 7a), while the number of Al surrounding [SiO₄]⁴⁻, the number of Si surrounding [AlO₄]⁵⁻, and the number of Al surrounding [AlO₄]⁵⁻ all varied (Figure 7b,c). This could be attributed to the bridging oxygen Si–O–Si bonds in [SiO₄]⁴⁻ or [AlO₄]⁵⁻, which were more stable than the Si–O–Al bonds and less likely to be damaged. Notably, as CaO/Al₂O₃ increased, the free oxygen content gradually increased, leading to a reduction in bridging oxygen bonds and causing $S{i}_{Al}^0$, $A{l}_{Si}^0$, and $A{l}_{Al}^0$ to become the main oxygen species. This signals that the structural framework of the melt is becoming less stable.

4. Conclusions

In this study, thermodynamic calculations and molecular dynamics simulations were conducted on a red mud slag system. The liquidus temperature and primary crystal phase during the cooling process were calculated using FactSage 8.1 software, and the phase diagram and primary crystal phase structure evolution (e.g., radial distribution function and oxygen species analysis) corresponding to microstructure changes were analyzed based on MS molecular dynamics simulations.

(1)

Overall, the melting point of red mud shows a significant increase firstly and then a slow decrease with the increase in CaO/Al₂O₃ when the CaO/Al₂O₃ is in the range of 0.3 to 3.9. When CaO/Al₂O₃ in red mud increases to 0.9, the initial crystalline phase changes from MgAl₂O₄ to CaTiO₃ during melt cooling and a significant increase in melting point temperature occurs.

(2)

The increase in CaO/Al₂O₃ in red mud mainly affects the bonding of aluminum atoms with oxygen atoms, and higher CaO/Al₂O₃ leads to the change in bridging oxygen bonds (e.g., Si-O-Al or Al-O-Al) to non-bridging oxygen bonds (e.g., Si-O-Ca or Al-O-Ca), while resulting in a decrease in the degree of polymerization of the red mud melt system.

(3)

In summary, when the amount of bridging oxygen in the red mud melt is lower than 50 percent, the melt is prone to preferentially generate high-melting-point substances for precipitation during cooling, which will not be conducive to the preparation of inorganic fibers from the red mud melt. In order to keep the melting point of red mud low during the preparation of fibers, CaO/Al₂O₃ should be controlled in the range of 0.3 to 0.9.