Effect of Na Ions on Melt Structure and Viscosity of CaO–SiO₂–Na₂O by Molecular Dynamics Simulations

Abstract

Molecular dynamics (MD) simulations have been used to study the effect of Na ions on the structure properties of CaO–SiO₂–Na₂O melts. The short-range structure and medium-range structure of CaO–SiO₂–Na₂O in this study are consistent with existing data. The replacement of Ca²⁺ with Na⁺ in CaO–SiO₂–Na₂O melts has almost no effect on the degree of polymerization and distribution of bond angles of Si–O tetrahedron. From micro perspective, Na ions enhance the mobility of CaO–SiO₂–Na₂O melts by multiple ways. Firstly, the modification effect of Na⁺ on the melt network structure is weaker than that of Ca²⁺, the Si–O tetrahedron around Na⁺ is sparser than Ca²⁺, which is more conducive to ions movement. Secondly, the diffusion capacity of Na⁺ is much greater than other ions in CaO–SiO₂–Na₂O system, which the overall diffusion capacity of the system can be improved by adding more Na⁺. Thirdly, since Na⁺ has only one charge, there is no electrostatic restraint on the depolymerized tetrahedron which happened in multivalent charges such as Ca²⁺, so that the mobility of CaO–SiO₂–Na₂O is stronger than that of CaO–SiO₂. The micro changes provide an explanation for the improvement of macro liquidity.

1. Introduction

Lime-silicate is widely used in glass, cement, metallurgy and other fields.^1,2,3,4) For lime-silicate melts which are the basic component of metallurgical slags and have been widely and importantly used in the past decades, it can realize different properties by adjusting the ratio of CaO/SiO₂. It is generally believed that in the high temperature melting state, the network structure of slag becomes simple by increasing the initial amount of free oxygen through enhancing the ratio of CaO/SiO₂, and the viscosity of the slag lowered.^5,6) In addition, some flux materials must be added in order to meet the comprehensive physical and chemical properties of molten slag. Alkali oxides such as Na₂O, as commonly used flux materials, can effectively improve the mobility of slag.⁷⁾

The effect of Na₂O on the properties of lime-silicate melts can simply be reviewed. Kim et al.⁸⁾ have studied the effect of Na₂O on the viscosity for CaO-SiO₂-based slags. The study found that Na₂O can be utilized to lower the slag viscosity and also the critical temperature and consequently increase operational stability of blast furnace. The experimental data of CaO-SiO₂-based slag by Qi et al.⁹⁾ indicated that, within the 2.0%–10.0% range an average increase of 1.0% of Na₂O causes a decrease in viscosity of about 0.03 Pa·s. Han et al.¹⁰⁾ studied the effect of Na₂O on the viscosity and mineralogical structure of flux film of a CaO-SiO₂-based slag system. The results showed that the viscosity of mold flux decreases with the increase of Na₂O content, it is suggested that the proportion of Na₂O in mold flux should be appropriately increased in producing crack sensitive steels. The above studies^8,9,10) have shown that Na₂O play a major role in decreasing viscosity, nevertheless, due to the lack of experimental methods, there are few studies on the microscopic scale of soda-lime silicate melts, and the mechanism by which Na₂O can lower the viscosity has not been well revealed yet.

An effective method for studying the changes of microstructure is computer simulation method such as molecular dynamics (MD), which has been applied to the field of soda-lime silicate glass to explain the microstructure changes that are not easily explained by experimental methods. Cormack et al.^11,12,13) have performed a detailed study regarding the local structure of the Na⁺ and Ca²⁺ in soda-lime-silicate glass by MD simulation. The first principles molecular simulations model of structure analysis of soda-lime-silica glass was originally proposed by Machacek et al.¹⁴⁾ The structure and topology of soda-lime silicate glasses which are either silica-rich or modifier-rich have been thoroughly investigated by Laurent et al.¹⁵⁾ However, few studies on MD simulations of soda-lime silicate melts were reported. Cormier et al.¹⁶⁾ have investigated the structure of soda-lime silicate in the glassy and liquid state using neutron diffraction, X-ray diffraction and reverse Monte Carlo modeling. The correlation functions between the glass and the liquid show significant modifications at the medium range, which are mainly associated with structural relaxation of the silicate network. Therefore, it is extremely necessary to systematically study the influence of different components on the microstructure and macroscopic properties of CaO–SiO₂–Na₂O melts.

In the present study, the role of Na ions in the effect on melt structure of CaO–SiO₂–Na₂O is fully analyzed from the short-range structure to the medium-range structure by molecular dynamics simulations. The microscopic mechanism is studied that the Na⁺ ions improve the mobility of lime-silicate melts through a series of changes in the melt structure, which will provide a theoretical basis for the design of metallurgical slags.

2. Computational Methodology

In the MD simulations, the approximation of the Buckingham form¹⁷⁾ was used as the pair potential   

$$U_{ij}(r)=\frac{q_i{q}_j}{r_{ij}}+A_{ij}exp\left(-\frac{r_{ij}}{{\rho }_{ij}}\right)-\frac{C_{ij}}{r_{ij}^6}$$(1)

where, U_ij(r) is the interatomic pair potential, q_i and q_j are the selected charges, r_ij is the distance between particles i and j, A_ij and ρ_ij are repulsive potential parameters, C_ij is van der Waals force parameter. The values of the potential parameters set used in this calculation are obtained from 18) and 19), as shown in Table 1.

Table 1. Potential parameter set used in the MD simulations.

Pair	Aij/(eV)	ρij/(Å)	Cij/(eV·Å6)
Ca–O18)	717827.0	0.165	8.67
Si–O18)	62794.37	0.165	0
O–O18)	1497049.0	0.17	17.34
Na–O19)	282278.80	0.165	8.67

In the setting process of the research system, it is adopted to replace CaO with the same molar amount of Na₂O in CaO–SiO₂–Na₂O ternary system. Based on the ternary phase diagram of the research system,²⁰⁾ the molten components at 1773 K was determined. The density of each sample is obtained from the experimental equation.²¹⁾ Because of the content of Na is small, in order to have enough samples for statistical analysis, the total number of atoms in the primitive cell of the MD simulation is set to about 8000. The initial number of networked oxygen particles and free oxygen particles remain unchanged, only the effect by different metal cations is considered in this research system. The composition, atomic number, density, and box length of the research system are shown in Table 2.

Table 2. Composition, atomic number, density and box length of different samples at 1773 K.

Sample	Mole fraction/(%)			Atomic number					Density/(g/cm3)	Box length/(Å)
	CaO	SiO2	Na2O	Ca	Si	O	Na	Total
1	50	50	–	1600	1600	4800	–	8000	2.620	49.0
2	47	50	3	1504	1600	4800	192	8096	2.608	49.1
3	45	50	5	1440	1600	4800	320	8160	2.602	49.2
4	42	50	8	1344	1600	4800	512	8256	2.593	49.3
5	40	50	10	1280	1600	4800	640	8320	2.585	49.4

For the setting of the simulation conditions, the periodic boundary conditions were employed for the basic cells in NVT ensemble. The integration of the equation of motion was solved with a time step of 0.1 fs by the leap-frog algorithm. The long-range Coulomb forces were evaluated using the Ewald sum method, and the cut-off radius of the short-range repulsive force was set to 10 Å. For temperature control, the Nose-Hoover method²²⁾ was used.

In the simulation process, an appropriate number of atoms of each type were placed in the primary MD cell with a random initial state. At the beginning of the simulation, the initial temperature was performed at 4273 K for 20000 steps to mix the system completely and eliminate the effect of the initial distribution. Then, the temperature was decreased to 1773 K through 100000 steps. After equilibrium calculation, the systems relaxed for another 80000 steps. Finally, structure information of melts could be calculated and analyzed. All the calculations were carried out using LAMMPS program.

3. Melt Structure Properties

3.1. Radial Distribution Function (RDF) and Coordination Number (CN) Distribution

Figure 1 shows the RDFs and CNs of different particle pairs in CaO–SiO₂–Na₂O melt. The position of the first wave peak in the RDFs curve represents the average bond length of the corresponding two particles. The ordinate corresponding to the flat platform in the CNs curve represents the average coordination value of the particles pair. The narrower and higher the peak of the RDF curve is, the more stable the bond length of the particles pair. The wider and slower the platform of the CN curve is, the more stable the coordination structure between two particles will be. According to the RDFs in CaO–SiO₂–Na₂O melt, it can be concluded that the average bond length of Si–O, Ca–O, Na–O, O–O is 1.62, 2.33, 2.28 and 2.62 Å, respectively, with hardly change for different content, as shown in Table 3. The bond length of Si–O, Ca–O and Na–O is very consistent with results reported by 23–25). The CN of Na–O, Ca–O in this study is 4.21±0.1, 4.9±0.1, respectively, which is agreed with the experimental data (4.2±0.8, 5.0±1.0) in similar composition by Karlsson et al.²⁵⁾ The CN of Si–O is 4.0 that it is same with the data obtained by experiment²⁶⁾ and simulation.²⁷⁾

Fig. 1.

RDFs and CNs for different particle pairs in 47CaO-50SiO₂-3Na₂O melt. (Online version in color.)

Table 3. Bond length and coordination numbers of different atomic pair in this study.

Atomic pair	3Na2O·47CaO·50SiO2		5Na2O·45CaO·50SiO2		8Na2O·42CaO·50SiO2		10Na2O·40CaO·50SiO2
	Bond length (Å)	CN	Bond length (Å)	CN	Bond length (Å)	CN	Bond length (Å)	CN
Si–O	1.62	4.00	1.62	4.00	1.62	4.00	1.62	4.00
Ca–O	2.33	4.98	2.33	4.95	2.33	4.89	2.33	4.87
Na–O	2.28	4.21	2.28	4.21	2.28	4.21	2.28	4.22
O–O	2.62	4.27	2.62	4.26	2.62	4.22	2.62	4.20
Ca–(O–)Si	3.57	4.45	3.62	4.38	3.62	4.34	3.62	4.31
Na–(O–)Si	3.27	4.02	3.31	4.01	3.34	3.96	3.37	3.94

Figures 2 and 3 show the effect of Na₂O on distribution between the network modifier and the network former in CaO–SiO₂–Na₂O melt. The average distances of Ca–Si and Na–Si both increase with increasing content of Na₂O, and the average coordination number decreases accordingly. This indicates that the distribution of network modifiers and network former becomes alienated. It should be noted that both Ca²⁺ and Na⁺ are cations, they will be bonded by the only anion O²⁻, the actual forms of Ca–Si and Na–Si are Ca–O–Si and Na–O–Si.

Fig. 2.

RDFs of network modifier (Ca, Na) and network former (Si) in different content of Na₂O. (Online version in color.)

Fig. 3.

CNs of network modifier (Ca, Na) and network former (Si) in different content of Na₂O. (Online version in color.)

It can be seen from Fig. 4, the coordination number between network former and network modifier is slightly affected by the content of Na₂O, the coordination number of Na–Si is around 4.0 which Ca–Si is around 4.4. The coordination number of Na–Si is always smaller than that of Ca–Si at various content of Na₂O in CaO–SiO₂–Na₂O melt. Ca²⁺ is dominant in the cation species surrounding the [SiO₄]⁴⁻ tetrahedron to compensate for the charge, which led us to infer that the capacity of Na⁺ to modify the network structure is weaker than that of Ca²⁺. Cormack and Du¹⁰⁾ obtained comparable conclusions in MD simulations of soda lime silicate glasses.

Fig. 4.

Effect of Na₂O content on the coordination number of network former around network modifier. (Online version in color.)

3.2. Distribution of Oxygen Types and Qⁿ Species

In the analysis of the medium-range order of CaO–SiO₂–Na₂O melt, we studied the distribution of oxygen types and Qⁿ species with various content of Na₂O. The initial amount of networked oxygen in each sample remains constant by the identical mole content of SiO₂. The unique variable factor in this study is the Ca/Na ratio. As shown in Fig. 5, the oxygen types exist in three forms: trace free oxygen, non-bridging oxygen and bridging oxygen, the distribution of all oxygen types is hardly affected by the Ca/Na ratio. The ratio of bridging oxygen to non-bridging oxygen is approximately 1:2 which is consistent with classical theoretical calculations. Classic references on oxygen distribution²⁸⁾ believed that the three forms of oxygen types have a dynamic equilibrium relationship as formula (2). If it is considered that the initial oxygen type introduced by alkaline oxides is only free oxygen, which introduced by acidic oxides is only bridging oxygen, then the initial ratio of free oxygen to bridging oxygen is 1:2 in this study. According to the theoretical calculation from formula (2), when the system reaches dynamic equilibrium, the conversion of free oxygen to non-bridging oxygen is exhausted. At equilibrium, the ratio of bridging oxygen to non-bridging oxygen is 1:2.   

$$O_f+O_b\rightleftharpoons 2O_{nb}$$(2)

Fig. 5.

Distribution of oxygen types in (50-x)CaO-50SiO₂-xNa₂O (x = 0, 3, 5, 8, 10) melts. (Online version in color.)

The results of distributions of Qⁿ (n = 0 to 4) by MD simulation in CaO–SiO₂–Na₂O melt with various Ca/Na ratios are presented in Table 4 and Fig. 6. It shows that the distributions of Qⁿ change very slightly, and this fluctuation may be related to the size of the research system. If Q⁰, Q¹, Q² with low degree of polymerization are combined for statistics, and Q³, Q⁴ with high degree of polymerization are combined also, the above distributions essentially do not change by varying the Ca/Na ratios. Thus, the replacement of Ca²⁺ with Na⁺ in CaO–SiO₂–Na₂O melt has almost no effect on the Qⁿ distribution. Sasaki et al.²⁹⁾ have studied the distributions of Qⁿ in the molten CaO–Na₂O–SiO₂–CaF₂ system with various Ca/Na ratios. It shows that the substitution of Na for Ca in the CaO–Na₂O–SiO₂–CaF₂ melts has negligible effect on the Qⁿ distribution, which has the same trend as described in this paper.

Table 4. Distribution of Qⁿ in CaO–SiO₂–Na₂O melts with various CaO/Na₂O ratios.

Sample	Unit structure
	Q0	Q1	Q2	Q3	Q4
CaO·SiO2	6.33	20.67	37.98	27.31	7.71
3Na2O·47CaO·50SiO2	6.75 (0.42)	22.06 (1.39)	36 (−1.98)	27.61 (0.30)	7.58 (−0.13)
5Na2O·45CaO·50SiO2	6.98 (0.65)	22.23 (1.56)	34.73 (−3.25)	28.42 (1.11)	7.65 (−0.06)
8Na2O·42CaO·50SiO2	5.65 (−0.69)	20.33 (−0.34)	39.19 (1.21)	27.88 (0.57)	6.96 (−0.75)
10Na2O·40CaO·50SiO2	5.63 (−0.71)	22.90 (2.23)	37.31 (−0.67)	27.42 (0.11)	6.75 (−0.96)

Shown in brackets is the difference with the CaO·SiO₂ sample.

Fig. 6.

Distribution of Qⁿ species in (50-x)CaO-50SiO₂-xNa₂O (x = 0, 3, 5, 8, 10) melts. (Online version in color.)

3.3. Distribution of Bond Angles

The change of O–Si–O bond angle represents the stability of the Si–O tetrahedral structure. The O–Si–O angular distributions in Fig. 7 presents a symmetrical shape with a peak value of 109.31°, which is very close to the ideal tetrahedral angle of 109.5°. The O–Si–O angular distribution is close to that of amorphous silicon dioxide.²⁷⁾ The Ca/Na ratio has almost no effect on the distribution of O–Si–O angles in the present study, which means that the replacement of Ca²⁺ ions with Na⁺ ions will not destroy the tetrahedral structure of Si–O.

Fig. 7.

Bond angle distribution of O–Si–O in (50-x)CaO-50SiO₂-xNa₂O (x = 0, 3, 5, 8, 10) melts. (Online version in color.)

The diversity of Si–O–Si bond angle indicates the change of the spatial layout of two adjacent Si–O tetrahedrons. The larger the Si–O–Si bond angle value, the farther the distance between the two tetrahedrons. As shown in Fig. 8, the distribution of Si–O–Si is mainly distributed in the range from 120° to 180°, and there is no obvious peak. The average values of Si–O–Si bond angles have a good consistency with previous MD simulation by Feuston and Garofalini³⁰⁾ which is 154°. The average values of Si–O–Si bond angles increase with the increasing content of Na₂O, which are 155.51°, 155.71°, 156.05°, 156.18°, 156.28°, respectively. The results can be explained by assuming that the distance between adjacent Si–O tetrahedrons increases with the replacement of Ca²⁺ ions with Na⁺ ions.

Fig. 8.

Bond angle distribution of Si–O–Si in (50-x)CaO-50SiO₂-xNa₂O (x = 0, 3, 5, 8, 10) melts. (Online version in color.)

4. Correlation between Melt Structure Properties and Viscosity

4.1. Self-diffusion Capacity of Different Ions

Through trajectory data analysis of the particles by MD simulation, the function of mean square displacement (MSD) with time would be obtained by Eq. (3).   

$$MSD=⟨\mathrm{\Delta }r{(t)}^2⟩=\frac{1}{N}⟨\sum _{i=1}^N{\left|r_i(t)-r_i(0)\right|}^2⟩$$(3)

where, r_i(t) presents the location of the atom i at time t, and the angular brackets denote an ensemble average of many time origins. As shown in Fig. 9, the greater the slope of the MSD curve, the greater the movement capacity of the ions.

Fig. 9.

The MSD of different ions in 47CaO-50SiO₂-3Na₂O system at 1773 K. (Online version in color.)

The self-diffusion coefficients of different ions can be estimated by Stokes-Einstein equation, as shown in Eq. (4). The relationship D_Na>>D_Ca>D_O>D_Si can be realized from Eq. (4), which would represent the structural properties of the melt. The calculated self- diffusion coefficients for each cations and oxygen ions have the same self-diffusion ability relationship and order of magnitude as the experimental data in silicate melts reported by Zhang et al.³¹⁾ and Liang et al.³²⁾   

$$D=\underset{t\to \infty }{lim}\frac{1}{6}\frac{d\left[\mathrm{\Delta }\overline{r}{(t)}^2\right]}{dt}$$(4)

As can be seen from Fig. 10, the self-diffusion ability of other ions has been little affected with the addition of a small amount of Na⁺ ions. However, when the content of Na₂O is greater than 8%, the self-diffusion ability of other ions shows a different degree of improvement trend. Si⁴⁺ ions and O²⁻ ions form complicated tetrahedral structure as network formers, there are more resistances to their movement so that the improvement of their self-diffusion ability is limited. As network modifiers, the self-diffusion ability of Ca²⁺ ions has a more obvious upward trend. A. N. Cormack et al.³³⁾ believed that the cation located in the gaps of the network structures can jump to adjacent vacant site and then another ion jumps with it to fill its place. Because Na⁺ ions have stronger mobility, the vacant sites left by them after jumping provide more opportunities for Ca²⁺ ions to jump. Moreover, the dilution of the network structure can also provide more space for the movement of Ca²⁺ ions.

Fig. 10.

Calculated self-diffusion coefficients of Ca, Si and O ions in (50-x)CaO-50SiO₂-xNa₂O (x = 0, 3, 5, 8, 10) melts. (Online version in color.)

For metallurgical slags, we pay more attention to the effect of Na₂O addition on the overall diffusion capacity of the system, which is directly related to the viscosity of the slags. As shown in Fig. 11, the diffusion capacity of Na⁺ is much greater than other ions in this system, so that replacement of Ca²⁺ with Na⁺ enhances the overall diffusion capabilities.

Fig. 11.

Effect of Na₂O content on the overall MSD of CaO–SiO₂–Na₂O system. (Online version in color.)

4.2. Mechanism of Lower Viscosity of Slags by Na₂O Addition

In metallurgy, it is very important to choose suitable flux when designing the slag system. Some fluxes are widely used, such as Na₂O can significantly lower the viscosity of molten slag.¹⁴⁾ Generally, the macroscopic physical properties of molten slag are directly related to the microstructure, we believed that the fluidity of the melt is the macroscopic manifestation of the comprehensive mobility of all microscopic particles, which can be measured by the overall MSD of the system. In silicate system, we have summarized four ways to improve MSD: (a) Reduce the degree of polymerization of the network structure. (b) Dilute the original network structure. (c) Replace the more charged cations with less charged cations as network modifiers. (d) Add more particles with stronger mobility to the original system.

Figure 12 illustrates the difference between CaO and Na₂O to depolymerize the network structure. It can be observed that Ca²⁺ and Na⁺ have different charge compensations for the charged Si–O tetrahedron after depolymerization with their charges. The divalent calcium ions can bind together the silicate anions by electrostatic forces, which limit the mobility of particles. Since Na⁺ has only one charge, there is no electrostatic restraint caused by multivalent charge so that the mobility of CaO–SiO₂–Na₂O is stronger than that of CaO–SiO₂. It is consistent with the factor (c) mentioned in the previous paragraph.

Fig. 12.

Schematic of depolymerization of network structure by different alkaline oxides.

In 3.1 analysis, we proposed that the distribution of network modifier and network former becomes alienated by replacing Ca²⁺ ions with Na⁺ ions, the Si–O tetrahedron around Na⁺ is sparser than Ca²⁺. And in 3.3 analysis, it is obtained that the distance between adjacent Si–O tetrahedrons will increase with the increasing content of Na ions, which is more conducive to ions movement, as mentioned in factor (b). In 4.1 analysis, it can be concluded that the diffusion capacity of Na⁺ is much greater than other ions in CaO–SiO₂–Na₂O system, the overall diffusion capabilities will be enhanced by replacing Ca²⁺ ions with Na⁺ ions, which is agreed with the factor (d). Through microscopic internal factors (b)–(d), it is explained that the viscosity of CaO–SiO₂–Na₂O is lowered by replacing Ca²⁺ ions with Na⁺ ions. If Na⁺ ions are added to CaO–SiO₂ system instead of replacing Ca²⁺ ions, the degree of polymerization of the system will decrease due to the increasing content of alkaline oxide, the factors that improve the mobility of the system will include factor (a).

5. Conclusion

In this study we calculated structural properties of CaO–SiO₂–Na₂O system using MD simulations. The effect of Na₂O addition on the short-range and medium-range structure of CaO–SiO₂–Na₂O was analyzed, and the mechanism by which Na₂O can lower the viscosity was explained from the perspective of microstructure changes. The obtained results are summarized as follows:

(1) The number of Si–O tetrahedron around Na⁺ is less than that of Ca²⁺, which indicates that the modification effect of Na⁺ on the melt network structure is weaker than that of Ca²⁺.

(2) The replacement of Ca²⁺ ions with Na⁺ ions in CaO–SiO₂–Na₂O melts has almost no effect on the degree of polymerization and distribution of bond angles of tetrahedron.

(3) The diffusion capacity of ions in CaO–SiO₂–Na₂O system were estimated and they show the relationship D_Na>>D_Ca>D_O>D_Si, which would represent the structural properties of the melt.

(4) Since Na⁺ has only one charge, there is no electrostatic restraint on the depolymerized tetrahedron which happened in multivalent charges such as Ca²⁺, so that the mobility of CaO–SiO₂–Na₂O melt is stronger than that of CaO–SiO₂.

(5) From micro perspective, Na⁺ ions enhance the mobility of CaO–SiO₂–Na₂O system by multiple ways, which provide an explanation for the improvement of macro liquidity.

Acknowledgements

The authors would like to deeply acknowledge the financial support by the National Natural Science Foundation of China (No. 51874082 and U1908224).

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