Structural and viscosity properties of CaO-SiO2-Al2O3-FeO slags based on molecular dynamic simulation

Journal of Non-Crystalline Solids 450 (2016) 23–31

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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol

Structural and viscosity properties of CaO-SiO2-Al2O3-FeO slags based on molecular dynamic simulation Ting Wu a, Qian Wang a, Chengfeng Yu b, Shengping He a,⁎ a b

College of Materials Science and Engineering, Chongqing University, Chongqing 400044, PR China Manufacture Management Department, Baoshan Iron & Steel Co., Ltd., 5th Floor Baosteel Management Building, No.885 FuJin Road, Baoshan District, Shanghai, PR China

a r t i c l e

i n f o

Article history: Received 4 May 2016 Received in revised form 18 July 2016 Accepted 19 July 2016 Available online xxxx Keywords: Structural property Viscosity Molecular dynamics CaO-SiO2-Al2O3-FeO slag

a b s t r a c t Since CaO-SiO2-Al2O3-FeO is one of the most important slag systems in metallurgic processes, it is important to explore its microstructural characteristics and viscosity. Molecular dynamics (MD) simulation was carried out to investigate the effect of basicity (R = CaO/SiO2 mole ratio) on both the structural and viscosity properties of CaO-SiO2-Al2O3-FeO slags. The viscosities were estimated based on the atomic self-diffusion coefficients obtained from MD simulations, and were compared with mathematical models and experimental data. The results showed that both Si-O and Al-O network depolymerized into simple structure with increasing basicity, while atomic selfdiffusion coefficients increased and viscosities decreased. The increase in basicity has a lower influence on the structure of Al2O3 rich samples. In addition to the basicity effect, the CaO-SiO2-Al2O3-FeO slag with high Al2O3 content trended to form more complex structures. Finally, a correlation between structural properties and viscosity of CaO-SiO2-Al2O3-FeO slags was established. © 2016 Elsevier B.V. All rights reserved.

1. Introduction CaO-SiO2-Al2O3-FeO quaternary system is one of the most important slag systems in metallurgy field, especially in secondary refining processes owing to their important role in desulfurization, dephosphorization, and inclusion control [1–5]. Viscosity is one of the key properties of slags, which has a notable effect on metallurgic processes such as reaction kinetics and transport phenomena in metal-slag systems at high temperatures [6]. Consequently, a considerable number of experimental investigations [7–11] have been carried out, and numerous mathematical models [7,8,12–16] have been developed to provide detailed discussions on the general behaviour of slag viscosity as a function of composition and temperature. However, viscosity data for CaO-SiO2-Al2O3-FeO slags is limited because of the difficulties encountered in experimental studies, which mainly focus on the chemical attack of the container materials and the difficulty in controlling the oxidation states of FeO in melts. Hence, owing to the experimental limitations and the widely recognised fact that slag macro properties are determined by their micro-structure, molecular dynamics (MD) simulation has been widely applied in the structure analysis of metallurgic slags in recent years [17– 20]. Lee et al. [1] studied the viscous behaviour of a CaO-SiO2-Al2O3MgO-FeO slag, and proposed that the driving force for the decrease in slag viscosity was the increase in silicate network depolymerization for CaO/SiO2 mass ratios lower than, or equal to, 1.3. The structural properties such as pair distribution functions and fractions of bonding ⁎ Corresponding author. E-mail address: [email protected] (S. He).

http://dx.doi.org/10.1016/j.jnoncrysol.2016.07.024 0022-3093/© 2016 Elsevier B.V. All rights reserved.

types of oxygen in CaO-FeO-2SiO2 melts have been studied using extended X-ray absorption fine structure (EXAFS) spectroscopy and MD simulation [21–23]. The thermodynamic properties of FeO-SiO2 and CaO-FeO-SiO2 have been calculated by MD simulation [24,25], and the results are in good agreement with previously measured and estimated values. The studies have broadly supported experimental interpretation, particularly regarding the structure, but in general did not mention the phenomenon of ionic transport. This is largely due to the long relaxation times associated with glass structures, which demand long simulation times to accumulate sufficient statistical accuracy. In this study, MD simulations were carried out to investigate the effect of basicity (CaO/SiO2 mole ratio) on the structural properties of CaO-SiO2-Al2O3-FeO slags in two different regions: one with high SiO2 content and one with high Al2O3 content. The viscosities of the CaOSiO2-Al2O3-FeO slag were estimated based on the atomic self-diffusion coefficients obtained from MD simulation, and were compared with mathematical models and experimental data. A correlation between structure properties and viscosity for the CaO-SiO2-Al2O3-FeO slag was established. The results can provide a theoretical foundation for further investigation of the CaO-SiO2-Al2O3-FeO slag system.

2. Research method 2.1. Molecular dynamics simulation The primary job of molecular dynamics simulation is to choose an appropriate potential function and its corresponding parameters

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T. Wu et al. / Journal of Non-Crystalline Solids 450 (2016) 23–31

which are suitable for the calculation of particle interactions. Usually, simulations are either purely ionic, with the charges of the constituent ions determined from chemical considerations, or purely covalent, neglecting Coulomb interactions. Regarding structure information, the two-body potential function Born-Mayer-Huggins (BMH), which belongs to purely ionic MD simulations, has been successfully used in silica and silicate systems [17,26–28]. In a previous study [23], the ionic-covalent approximation, instead of the purely ionic one, was used in the SiO2-CaO-FeO system. It was concluded that the average charge state of the silicon ions varied from 3 + to 4+, depending on composition. This had little effect on the diffusion processes in the oxides and their structure, because the effective ion sizes are nearly the same in both approximations. Therefore, the purely ionic approximation, which gives roughly the same results as ionic-covalent simulations, can be used to reduce the time needed to calculate self-diffusion coefficients in liquid oxides. In the present study, the BMH function, composed of the longrange Coulomb interaction, short-range repulsion interaction, and van der Waals force, was applied to describe O\\O, O\\Fe, O\\Al, O\\Si, O\\Ca, Al\\Al, Al\\Si, Al\\Ca, Si\\Si, Si\\Ca and Ca\\Ca pair interactions. On the other hand, since there are no accurate parameters for Fe\\Fe, Fe\\Al, Fe\\Si and Fe\\Ca pairs corresponding to the BMH function, a Lennard-Jones (L-J) two-body potential function was used. The BMH and L-J functions are as follows. U ij ðr Þ ¼


 C ij qi q j þ Aij exp −Bij r − 6 r ij r ij (

U ij ðr Þ ¼ D0

R0 r ij

12

 6 ) R0 −2 r ij

ð1Þ

ð2Þ

where Uij(r) is the interatomic-pair potential; qi and qj are the selected charges, and in order to ensure the transferability of the interaction potential with the melt composition, the valence assigned to the atoms is usually kept fixed for all compositions; rij represents the distance between atoms i and j; Aij and Cij are energy parameters for the pair ij describing the repulsive and van der Waals attractive forces, respectively; and Bij is a e-folding length characterizing the radially symmetric decay of electron repulsion energy between atom pair ij; D0 is the depth of the potential well; R0 is the distance at which the potential reaches its minimum, at R0 the potential function has the value −D0. As for the potential parameters, there are three categories including force field, empirical and non-empirical parameters. Considering a compromise between accuracy and computational cost, empirical values were applied in this study. Parameters for Fe-O were obtained from calculations performed by Belashchenko [25]; parameters for other pairs with BMH potential were taken from Hirao's work [29], while parameters for L-J potential were collected from Rappé's work [30]. Parameters for BMH and L-J potentials are listed in Table 1 and Table 2, respectively. During the simulation process, the system should be chosen when in the completely molten composition range, at the corresponding temperature. Since the content of FeO in the CaO-SiO2-Al2O3-FeO slag is relatively small, the molten melts composition was determined according to the phase diagram for CaO-SiO2-Al2O3 systems [31]. In the CaO-SiO2Al2O3 ternary system, there are two main liquid-phase areas at 1873 K. One area contains high SiO2 content, where the two main low melting point compounds are CaO·Al2O3·2SiO2 and 2CaO·Al2O3·SiO2, while the other area possesses a high Al2O3 content, and the main low melting point compound is 12CaO·7Al2O3. Two groups of samples were designed to investigate the basicity effect on the structural properties and viscosity in CaO-SiO2-Al2O3-FeO slags: SiO2 rich samples and Al2O3 rich samples. The density of each sample was obtained from the experimental formulas [32] presented in Eqs. (3) and (4). The compositions, atom numbers, and densities for each sample are presented in Table 3. The total atom number for each sample was set as at about 5000. Assuming that all 5000 atoms are placed in a cubic model box,

Table 1 Parameters for BMH potential. Atom 1

Atom 2

Aij (eV)

Bij (1/Å)

Cij (eV·Å6)

O O O O O Al Al Al Si Si Ca

O Fe Al Si Ca Al Si Ca Si Ca Ca

1,497,693.5 1900.0 86,094.6 62,821.4 718,136.0 4143.9 2994.1 36,934.4 2163.3 26,686.2 329,193.3

5.88 3.45 6.06 6.06 6.06 6.25 6.25 6.25 6.25 6.25 6.25

17.34 0 0 0 8.67 0 0 0 0 0 4.33

the molar mass and density together determine the box length, which is also listed in Table 3. 1=ρ1673K ¼ 0:45ωðSiO2 Þ% þ 0:285ωðCaOÞ% þ0:285ωðFeOÞ% þ 0:402ωðAl2 O3 Þ%

ð3Þ

ρt ¼ ρ1673K þ 0:07ð1673−T Þ

ð4Þ

where ω (MOx)% is the mass fraction of the oxide MOx. The MD simulations were performed with the Materials Explorer program [33] (FUJITSU LIMITED) in the NVT ensemble, meaning that the simulations were run maintaining a constant number of particles (N), sample volume (V), and temperature (T) of a system. The equations of motions for atoms were solved with a time step of 1 fs (10−15 s) via a leap-frog algorithm and the data were saved by each of 10 steps. As the atoms bore charges, the long-range Coulomb forces, presented in the first term of Eq. (1), were evaluated using the Ewald-sum method with a precision of 10−5. When calculating the repulsive forces, the potential cutoff was set to 10 Å, a good trade-off between accuracy and computational cost. Meanwhile, the pressure of system is controlled by the Parrinello and Rahmann method [34]. In the simulation process, the number of atoms of each sample was placed in the primary MD cell with a random initial state, and the volume of the cell was decided by the number of atoms and the density. Since the number of atoms in real world always far more than the quantities that the computer can support, the periodic boundary conditions were applied on all sides of the model box to create an infinite system with no boundaries so that the calculation results were more convincible. Through a lot of preliminary explorations, a stable simulation process was determined as follows for each sample. At the beginning of the simulation, the initial temperature was fixed at 5000 K for 24,000 steps to mix the system completely and eliminate the effects of the initial distribution. Then, the temperature was cooled to 1873 K through 96,000 steps, and the temperature reduction was accomplished via the direct velocity rescaling of each molecule. Then the system was relaxed for another 60,000 steps in equilibrium calculation. Finally, the position coordinates at the end of the equilibrium calculation were used as the initial conformation for the following simulation of 180,000 time steps at 1873 K to get the structure information and transport properties of melts.

Table 2 Parameters for L-J potential. Atom 1

Atom 2

D0 (eV/mol)

R0 (Å)

Fe Fe Fe Fe

Fe Al Si Ca

0.00056 0.00360 0.00310 0.00240

2.91 3.71 3.60 3.16

T. Wu et al. / Journal of Non-Crystalline Solids 450 (2016) 23–31

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Table 3 Compositions, atomic numbers, density and length of cubic box model for samples at 1873 K. Sample

SiO2 rich samples

Al2O3 rich samples

Basicity R = CaO/SiO2

Mole fraction CaO

SiO2

Al2O3

FeO

Ca

Atomic number Si

Al

Fe

O

Total

0.57 0.75 0.98 1.28 1.67 2.22 0.71 1.07 1.61 2.14 2.49 3.20

0.30 0.36 0.41 0.47 0.52 0.57 0.24 0.30 0.36 0.40 0.42 0.44

0.53 0.47 0.42 0.37 0.31 0.26 0.34 0.28 0.22 0.18 0.17 0.14

0.08 0.08 0.08 0.08 0.08 0.08 0.33 0.33 0.33 0.33 0.33 0.33

0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09

543 655 772 892 1016 1145 361 458 557 626 660 712

950 869 786 699 610 517 505 427 347 292 264 222

298 304 308 314 320 326 992 1006 1022 1032 1038 1046

159 162 164 167 170 173 141 143 145 146 147 148

3049 3011 2970 2928 2886 2841 3000 2964 2929 2904 2892 2873

4999 5001 5000 5000 5002 5002 4999 4998 5000 5000 5001 5001

Density (g/cm3)

Length (Å)

2.67 2.73 2.79 2.86 2.92 3.00 2.67 2.72 2.77 2.81 2.83 2.86

41.41 41.33 41.26 41.15 41.11 40.98 41.11 41.00 40.96 40.90 40.87 40.83

2.2. Viscosity calculation

3. Structure properties

Through statistical analysis of the particles trajectory by means of MD simulation, the function of the mean square displacement (MSD) with time would be generated.

3.1. Pair distribution function (RDF) and coordination number (CN) distribution

* 2+ N D E 1 X 2 jr ðt Þ−r i ð0Þj MSD ¼ Δrðt Þ ¼ N i¼1 i

ð5Þ

where, ri(t) presents the location of the atom i at time t, and the angular brackets denote an ensemble average of many time origins. The self-diffusion coefficient D is calculated by Eq. (6).

D ¼ lim t→∞

h i 2 1 d Δr ðt Þ 6

dt

ð6Þ

Equations that correlate the viscosity and diffusivity have been widely used in the study of silicate melts [35–40], with the two most common being the Eyring, and Stokes-Einstein ones. These are derived in completely different ways, but relate the diffusivity and viscosity by the same functional form, as shown in Eq. (7).

η¼

KBT Dλ

ð7Þ

where, KB is the Boltzmann constant, which is equal to 1.38 × 10−23 J·K−1, T is the temperature of the system, and λ in the Eyring relation is the jump distance for a diffusive event, which is often considered as the diameter of one of the diffusing species, λ=2R. Some investigations have found that λ=2RO, where the radius of oxygen was taken as 1.4 Å, provides a good correlation between the viscosity and the oxygen diffusivity in silicate melts [35,36,40]. The viscosity results were compared with mathematical models and experimental data to validate its accuracy. The mathematical models for viscosity calculation can be divided into two classes: one includes structural models such as the NPL model by Mills [8,9,12] and viscosity model applied in Factsage based on modified quasichemical model (MQM) [15,16], while the other one consists on semi-empirical or empirical viscosity models such as Urbain [7,14] and Riboud [13] models. Based on the calculation results, the correlation between structure information and viscosity was established and discussed, and these could help us understand the action mechanisms of melts.

The nearest-neighbour distributions, which are determined by statistical analysis of the atom locations using pair correlation functions (RDFs), could incorporate short-range order [41] in melts and enable the correlation between atomic structure and macro properties to be understood. The equation of RDF is expressed as:   V X nij ðr−Δr=2; r þ Δr=2Þ g ij ðr Þ ¼ Ni N j j 4πr 2 Δr

ð8Þ

where, V is the volume of the MD primary cell and N is the number of particles. nij(r − Δr/2, r + Δr/2) is the average number of atom j surrounding a central i atom within a defined cut-off distance r ± Δr/2. In a word, the RDF gives the probability of finding an ion within a distance Δr from a specified particle at the location of r. The CN for atom i around atom j is determined by numerical integration of the RDF within the cut-off radius, which corresponds to the first minima of RDF. The cut-off distance is uniquely determined at each state point. Since the probability that Si-O and Al-O distances are, respectively, 2.0 and 2.5 Å (corresponding to the first valley for the Si-O and Al-O RDF curves), is nearly zero, the cut-off radii 2.0 Å for Si-O and 2.5 Å for Al-O were chosen in this study. Fig. 1 shows the RDFs and CNs for different atom pairs using two samples as an example. The positions of the first peak of the RDFs represent the average distances of the corresponding two atoms. If the RDF peak shape is narrow and sharp, it means the atomic bond is stable. The ordinate value corresponding to the CN platform is considered to be the average CN of the bond. The wider and gentler the platform of CN curve, the more stable the pair bond will be. According to RDFs in CaO-SiO2-Al2O3-FeO systems, it can be obtained that the average bond lengths of Si\\O, Al\\O, Ca\\O, Fe\\O, Si\\Ca, Al\\Ca are 1.61, 1.75, ~2.29–2.33, ~2.02–2.04, ~ 3.45–3.51, and ~3.14– 3.20 Å, respectively, with almost no difference for different compositions, while the average bond lengths of O\\O increase from 2.16 to 2.64 Å in SiO2 rich samples and from 2.66 to 2.70 Å in Al2O3 rich samples. The Si\\O and Al\\O bond lengths are very consistent with results obtained by Neutron and EXAFS [42–46]. Since it was reported that the average Si-BO (bridge oxygen) bond length is ~0.04–0.05 Å longer than the average Si-NBO (non-bridge oxygen) bond length [47,48], the average Si\\O bond length is expected to decrease with the increase in basicity, which makes the Si-BOs convert into Si-NBOs. However, in the present study, since the increment in basicity is small, there is no apparent increase in the Si\\O average bond length. The Fe\\O distances are

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Fig. 1. RDFs and CNs for different atom pairs: (a) and (c) R = 0.98 (SiO2 rich sample), (b) and (d) R = 1.61 (Al2O3 rich sample).

similar to that 2.04–2.09 Å reported by Hoppe et al. [49] and 2.03–2.09 Å reported by Waseda et al. [50]. As for the average bond length for O\\O, it is somewhat longer than 2.6 Å, which is consistent with other published works [42,43]. The average O\\O bond length increases with increasing basicity, which implies a weakened bond, and is due to the depolymerization of [SiO4] and [AlO4] networks. In addition, the average bond length for O\\O in Al2O3 rich samples is longer than that in SiO2 rich samples, as a result of the increased proportion of [AlO4] tetrahedra. From Fig. 1(c) and (d), the average CNs for Si\\O, Al\\O, Ca\\O, Fe\\O, Si\\Ca, Al\\Ca and O\\O pairs are 4.07, 4.36, 6.25, 4.86, 5.70, 5.43 and 10.31, respectively for the SiO2 rich sample when R = 0.98; while those for the Al2O3 rich sample when R = 1.61 are, respectively, 4.03, 4.28, 6.19, 4.78, 2.09, 2.17 and 10.42. The average CNs for Si-Ca and Al-Ca in the SiO2 rich sample are much bigger than those in the Al2O3 rich sample, which means that the structure of the SiO2 rich sample is much simpler, with a larger proportion of non-bridge oxygen. Fig. 2 shows the distribution of CNs for Si and Al with varying basicities. With increasing basicity, the high coordinated Si (SiV and SiVI) and Al (AlV and AlVI) increased, this illustrates that the [SiO4] and [AlO4]

tetrahedrons become unstable. Comparing the distribution of CNs, the proportion of SiIV is much higher than that of AlIV, which means that the [SiO4] tetrahedron is much more stable than the [AlO4] one. This has been demonstrated before [51–53]. SiV species were also found in earlier studies [54,55], and the phenomenon of increasing amounts of SiV and AlV is often explained as resulting from SiV and AlV instability in speeding liquid dynamics [56]. 3.2. Distribution of oxygen types and Qn species It is commonly considered that the oxygens in traditional silicate network structure can be divided into bridge oxygen (BO), non-bridge oxygen (NBO) and free oxygen (FO). However, in an aluminosilicate network, the oxygen triclusters (TO) occur to balance the charge. The BO in this study can be divided into three types including SOS, SOA and AOA, which represent the oxygen connected to two Si atoms, one Si atom and one Al atom, and two Al atoms respectively; the NBO can be classified into two types including OS and OA, which illustrate the oxygen connected to one Si atom and one Al atom, respectively.

Fig. 2. Distribution of CNs of Si and Al: (a) SiO2 rich samples (b) Al2O3 rich samples. SiIV (AlIV), SiV (AlV), and SiVI (AlVI) are corresponding to the four-coordinated Si (Al), five-coordinated Si (Al), and six-coordinated Si (Al).

T. Wu et al. / Journal of Non-Crystalline Solids 450 (2016) 23–31

In Matlab programming, the oxygen whose distance to Si or Al smaller than the aforementioned cut-off radius 2.0 Å or 2.5 Å, is considered to be coordinated with Si or Al. According to the Si or Al numbers, each particular oxygen atom coordinated with, all kinds of oxygen types have been distinguished and counted. Another key aspect of the shortrange network structure is the distribution of Qn species. It can be analyzed by counting the number of BOs and TOs which connected to the network former T (Si or Al). For example, Q4 means there are 4 BOs connected to Si or 4 BOs and TOs connected to Al. In SiO2 rich samples shown in Fig. 3(a), with the increase in basicity, the SOS and SOA decreased, while the OS and OA increased. This means the increasing basicity results in depolymerization of SOS and SOA into OS and OA. Since the Al2O3 content is relatively low, the AOA and TO proportions are small and do not vary much with the increase in basicity. From Fig. 3(b), it can be seen that with the increase in basicity, the AOA and OA increased dramatically, whereas SOA, SOS and TO decreased, and OS and FO barely changed under low concentration. Hence, for Al2O3 rich samples, the increasing basicity makes the SOA, SOS and TO break down into OA and OS. However, the network formation ability of Al2O3 will be enhanced with the increase in basicity, since the concentration of AOA increased significantly. Comparing Fig. 3(a) and (b), the BOs (AOA and SOA) are dominant in Al2O3 rich samples, while NBOs (OS) account for the largest proportion in SiO2 rich samples with varying basicities. Hence, it can be concluded that melts with high Al2O3 content tend to form more complex network structures. The same conclusion was also proposed by Shimoda [57] and Lee [58] using MD and NMR, respectively. In addition, “Al avoidance principle” has been investigated by analyzing the tetrahedron types linked by Al. According to the theory, the [AlO4] tetrahedron is more favorably linked with the [SiO4] tetrahedron rather than the [AlO4] one [59]. This principle has proved to be correct in SiO2rich regions [33]. However, in low-silica glasses, Cormier [60] found that there is no significant trend favoring the existence of Si-O-Al linkages at the expense of Al-O-Al and Si-O-Si, as it would be expected if the Al avoidance rule applied. The results in the present study show completely consistent conclusions: the concentration of SOA is much higher than that of AOA in SiO2 rich samples shown in Fig. 3(a), while AOA proportion is bigger than SOA in Al2O3 rich samples shown in Fig. 3(b). According to Fig. 4(a) and (b), in SiO2 rich samples, Q3 and Q4 of Si depolymerize into Q0, Q1 and Q2 while Q4 and Q5 of Al break down into Q1, Q2 and Q3 with increasing basicity. The existence of Q5 of Al is due to the TO in aluminate melts. The increasing basicity prompts depolymerization of the [SiO4] and [AlO4] tetrahedrons, so that the network structure becomes simpler. However, in Al2O3 rich samples shown in Fig. 4(c) and (d), the effect of basicity on the structure is not that obvious, with relatively small amounts of Q4 of Si depolymerizing into Q1, Q2 and Q3, and very small amounts of Q4 and Q5 of Al breaking down into Q1, Q2 and Q3. In addition, Q3 and Q4 of both Si and Al account for the

27

largest proportion in structure of Al2O3 rich samples, once again proving that it tends to form more complex network structures in melts with high Al2O3 content. 3.3. Distributions of bond angles The O-Si-O angular distributions from Fig. 5(a) and (c) present symmetric shapes with peak values of 109°, which is very close to the ideal tetrahedral angle of 109.5°. Hence, it can be inferred that the Si-O network is dominated by [SiO4] tetrahedra. In an experimental work, Grimely et al. [61] found the O\\Si\\O bond angle to be 109.7°, with a variation of 10.6° (somewhat narrower than the variation of ~ 12–15° in this study), based on their Monte Carlo modeling of neutron diffraction data, assuming that the two bond lengths were not correlated. The O\\Si\\O bond angles were also reported to be 109.47° with a variation of 4.2° for silica according to models based on both neutron and high energy X-ray diffraction data [62], and have increased from 109.1° for silica to 109.3° for sodium disilicate glass, based on neutron diffraction studies [63]. Reasonable O\\Si\\O bond angle distribution and good agreement with experimental data suggest that silicon oxygen tetrahedrons were successfully modeled in the present study. However, the O-Al-O angular distributions presented in Fig. 5(b) and (d) show noise shape while the peak values are in the 106° to 112° range, indicating that [AlO4] tetrahedron is not that stable as a standard tetrahedron structure. This is because the O\\Al\\O bond angle is influenced first by the structure of the first coordination shell of the aluminium ions, and secondly by the charge-balancing cations present in the melt. Overall, the basicity did not influence the distribution of O-Si-O and O-Al-O angles in the present study. 4. Correlation between viscosity and structural properties 4.1. Self-diffusion coefficients of different ions Based on MSD curves obtained by MD simulation and Eq. (5), the diffusion coefficient of different ions can be calculated. The atomic self-diffusion coefficients follow the sequence DFe N DCa N DO N DAl N DSi with values in the range of ~ 73.2–111.4 × 10− 11, ~ 59.6–82.3 × 10− 11, ~ 19.9–61.5 × 10− 11, ~ 20.0–42.4 × 10−11, and ~ 13.1– 42.1 × 10−11 m2·s−1, respectively. In silicate melts, the DSi/DO ratio is reported to be close to 1, because the oxygen and silicon probably diffuse through migration of SiOx species [64]. However, in the current study, the sequence is DO N DAl N DSi. Thus, a criterion can be made where [SiO4] and [AlO4] tetrahedrons are the basic structural units in the process of diffusion, and O atoms move cooperatively with Al and Si in those units.

Fig. 3. Distribution of different oxygens: (a) SiO2 rich samples (b) Al2O3 rich samples. SOS, SOA and AOA are bridge oxygens which represent the oxygen connected to two Si atoms, one Si atom and one Al atom, and two Al atoms respectively; OS and OA are non-bridge oxygens which illustrate the oxygen connected to one Si atom and one Al atom respectively; TO and FO are tricluster oxygen and free oxygen respectively.

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Fig. 4. Distribution of Qn species: (a) and (b) SiO2 rich samples, (c) and (d) Al2O3 rich samples.

Comparison of our diffusivity results to experimental measurements is difficult since there are no direct measurements on this melt system. There are, however, some experimental diffusion results on compositions and structures similar to the current system. Liang et al. [65] measured self-diffusivities for a number of compositions in the CaO-Al2O3SiO2 system at 1 GPa and 1773 K. They found the ordering of self-

diffusivities was DCa N DAl N DO N DSi with values in the range of ~ 29.8–134.1 × 10−12, ~ 1.7–41.1 × 10− 12, ~ 3.1–38.0 × 10− 12, and ~ 1.3–39.2 × 10− 12 m2·s−1, respectively, for different composition ranges and duration. The diffusions in the current system are generally one order of magnitude larger than the results from Liang et al. [65]. In addition to different compositions, another possible reason is that the

Fig. 5. Distribution of angles O-Si-O and Al-O-Al: (a) and (b) SiO2 rich samples, (c) and (d) Al2O3 rich samples.

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simulated temperature in the current system is higher (1873 K), which leads to bigger atoms diffusions. 4.2. Effect of basicity on viscosity of CaO-SiO2-Al2O3-FeO system When discussing the mechanism for viscous flows, viscosity can be expected to depend on both the nearest-neighbour interactions and coordination numbers. Interionic forces in melts are characterized by the thermodynamic state of the system. Thus, viscosities in liquids can be considered linked to the order-disorder phenomenon, thereby depending on the structure of the liquid. The viscosity of every sample was estimated at 1873 K by Eq. (6), on the basis of self-diffusion coefficient of oxygen atom. Fig. 6 illustrates the effects of basicity on viscosity which compares with mathematical models and experimental data. With the increase in basicity, the viscosities of SiO2 rich samples and Al2O3 rich samples decrease from 0.465 to 0.150 Pa·s and from 0.391 to 0.198 Pa·s, respectively. The acidic SiO2 oxide forms a [SiO4] tetrahedron in melts by sharing the oxygen ions. These tetrahedrons are joined together in chains or rings to form a network structure. When basicity increases, the oxygen ions released from CaO will combine with the Si cation in the [SiO4] tetrahedron, breaking the network structure. Consequently, the viscosity, which reflects the viscous resistance of the melt in the flow process and strongly depends on big complex anions, will decrease in melts with simple structure units. Likewise, increased basicity can also destroy the Al-O network, reducing the viscosity as a consequence. From Fig. 6, it can also be seen that there are large deviations in comparison that results from NPL model are much lower than results obtained based on MD simulation, while values by Riboud model are much higher. In SiO2 rich samples, values calculated by Factsage and Urbaincorr models are close to the results obtained based on MD simulation. Since the experimental data presented by Lee et al. [1] and Kondratiev et al. [14] was obtained in a lower temperature range, we cannot positively verify the accuracy of the current work, although they show a consistent tendency. In Al2O3 rich samples, none of the selected models provide a consistent viscosity tendency comparable to that calculated results based on MD simulation. In addition to the indeterminacy of the simulation process of MSD, the discrepancies may also originate in the simplified structural sceneries in the models being used, only considering the effects of the silicate structure on viscosity, while the complex influence of Al2O3 addition on the degree of polymerization are not considered. 4.3. Relationship of viscosity and NBO/T Mills [9] suggested that it may be possible to use two parameters to represent the structure which could be used to calculate structurally dependent properties such as the viscosity and electrical conductivity of molten slags. These two parameters are the NBO/T ratio, where NBO is the number of non-bridge oxygen and T is the number of tetrahedral

Fig. 7. Correlation between NBO/T and viscosity (Pa·s) calculated based on MD simulation in CaO-SiO2-Al2O3-FeO slags at 1873 K. Square symbol are for SiO2 rich samples while sphere symbol are for Al2O3 rich samples.

coordinated atoms, and the optical basicity. The NBO/T provides a better measurement of the structure than the optical basicity. Based on linear fitting methods, the effect of viscosity functions on the NBO/T depolymerization degree in CaO-SiO2-Al2O3-FeO systems are obtained and shown in Fig. 7. The depolymerization degree represents the complexity of the melt system, where the greater the NBO/T, the simpler the melt structures, thus describing the viscosity of the corresponding melt. From Fig. 7, it can be seen that, as NBO/T increase, which means the polymerization degree of melts decreases, the viscosities decreases. The viscosity of Al2O3 rich samples is more sensitive to the NBO/T parameter since the function slope is larger, tending to form more complex network structures in systems with high Al2O3 content. 5. Conclusions Molecular dynamics simulations were carried out to investigate the effect of basicity (CaO/SiO2 mole ratio) on the structural viscosity properties of CaO-SiO2-Al2O3-FeO slags, conclusions are obtained as follows. (1) With the increase in basicity, the Si-O and Al-O network depolymerized into a simple structure, while the increase in basicity has a lower influence on the structural properties of Al2O3 rich samples. Al2O3 rich samples have a tendency to from more complex network and the [AlO4] tetrahedron is not as stable as the standard tetrahedral structure.

Fig. 6. Viscosities of CaO-SiO2-Al2O3-FeO slag at 1873 K: (a) SiO2 rich samples, and (b) Al2O3 rich samples. “MD” means viscosities are estimated based on self-diffusion coefficients obtained by MD simulation.

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(3) With increasing basicity, the atomic self-diffusion coefficients increase, while the viscosity decreases due to the structure depolymerization. Current results are consistent with experimental data and previous model results, and a correlation between structure properties and viscosities of CaO-SiO2-Al2O3-FeO slags has been established.

Acknowledgements The authors would like to deeply appreciate the fund from Chongqing Research Program of Foundation and Advanced Technology (Project No. cstc2013jcyjA50003) and the China Postdoctoral Science Foundation (2016M592119).

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