Viscosity Measurement of SiO₂–Na₂O Melts with Addition of NaF

Abstract

The viscosity of SiO₂–Na₂O–NaF melts was measured by using a rotating crucible viscometer developed by the authors. The basicity (= C_Na2O/C_SiO2 in mol%) of the melts was 0.67, 0.82, and 1.00. The concentrations of NaF were 5, 10, and 15 mol%. As a result, the viscosity of the melts showed a good Arrhenius type linearity in any melts. It was found that the sample loss occurred in highly basic composition region due to a prolonged measurement at high temperature. The viscosity of the melts decreased with increasing the concentration of NaF, and the composition dependence is similar to that for SiO₂–CaO–CaF₂ melts. Viscosity decreasing ability of NaF is higher than that of Na₂O within the composition region investigated in this study. Transitions of activation energy of viscous flow are different between Na₂O addition and NaF addition. This implies that the mechanism of enhancement of fluidity is different between Na₂O and NaF.

1. Introduction

A mold flux is indispensable for a continuous casting of steel in order to produce high quality steel products with a low energy consumption. The viscosity of mold flux is the most important thermophysical property for the process control. However, there are large discrepancies on the viscosity of molten silicate as the major component of mold flux among the reporters. Therefore, the authors developed a new viscometer based on rotating crucible method suitable for the viscosity measurement of silicate and determined the viscosity of SiO₂–CaO–CaF₂ melts. As a result, it was found that the logarithmic viscosity of melts monotonically decreased with increasing CaF₂ concentration.¹⁾

Generally, the mold flux contains not only CaO and CaF₂ but also Al₂O₃, Na₂O, and K₂O. When CaF₂ and Na₂O are added into a silicate together, it is estimated that the change in coordination of anion occurs with following reaction.   

$$\underset{\_}{{\text{CaF}}_2}+\underset{\_}{{\text{Na}}_{\text{2}}\text{O}}=\text{2}\underset{\_}{\text{NaF}}+\underset{\_}{\text{CaO}}$$(1)

  

$$\mathrm{\Delta }{G}_{(1)}^{\circ }=-131\mathrm{\hspace{0.17em} }\text{kJ}\cdot {\text{mol}}^{-1}\mathrm{\hspace{0.17em} }\text{at}\mathrm{\hspace{0.17em} }1\mathrm{\hspace{0.17em} }700\mathrm{K}$$(2)²⁾

But the reaction dose not completely proceed to the right hand, oxide ion and fluoride ion might be distributed to both calcium ion and sodium ion along with the composition of melt. When a silicate contains multiple cations, the distribution of fluoride ion and oxide ion becomes complicated. Therefore, it is not easy to reveal the relationship between coordination style and viscosity. The authors investigate the relationship by determining the composition dependency of viscosity of the melts from simple system to complex system. Anyway, in the molten state, origin of fluoride ion is not knowable. The fluoride ions from CaF₂ and that from other fluoride are equivalent. Therefore, the addition of NaF instead CaF₂ gives same effect under specified conditions.

In this study, the viscosity of SiO₂–Na₂O–NaF melts is precisely measured using the viscometer developed by the authors. There are several reports on the viscosity of SiO₂–Na₂O melts, but there is no report on the viscosity of SiO₂–Na₂O–NaF melts.

2. Experimental

2.1. Experimental Apparatus

The principle of measurement and the experimental apparatus have been described in the previous article.¹⁾ Important points including differences and improvements from previous study are described below.

A crucible made of graphite (Isotropic graphite: IG-15, Toyo Tanso Co., Ltd.) with the inner diameter of 18 mm and the depth of 60 mm was used. The crucible is connected to a motor (Brushless DC motor, Oriental Motor Co., Ltd.) under the furnace through an alumina spindle (ϕ 25 mm). By replacing spindle material from graphite to alumina, the eccentricity was decreased and the durability was improved. Inner cylinders made of the graphite with the diameters of 14 mm and 10 mm over the range of 20 mm height were used. The inner cylinder is suspended by a tungsten spindle (ϕ 3 mm) to be connected to a torque sensor (MD-201C, Ono Sokki Co., Ltd.). The determinable torque range of the sensor is 0.001 to 2 mN·m. The difference between the centers of the inner cylinder and the crucible were less than 0.5 mm. The tip of the inner cylinder was placed 20 mm above the bottom of the crucible. The length of shaft of the inner cylinder immersed in the sample melt is about 10 mm. The crucible and the inner cylinder are placed in an alumina tube (99.5% purity) contained in the furnace hermetically closed. Totally, whole the apparatus including motor and torque sensor is closed to control the atmosphere inside.

Prior to the measurement at elevated temperatures, a calibration curve, which shows the relationship between viscosity and torque, was made by using several silicone oils as the standard fluid (20–3000 mPa·s) at room temperature. When the crucible was rotated at the rate of 6.29 rad·s^–1 (60 rpm), the linearity of calibration curve was the best. Therefore, the crucible was rotated at 60 rpm even at elevated temperatures.

In the rotating crucible method, sample liquid in the crucible should make laminar flow around the axis of rotation. A convection flow disarranges the laminar flow and hinders the precise measurement. A special attention was then paid to keep the temperature uniformity inside the furnace as it is difficult to keep temperature uniformity and to prevent the convection flow at high temperature. Concretely, a furnace consisted of three stacked heating elements made of molybdenum disilicide (MoSi₂) was used, and the heating elements were controlled independently. Furthermore, the radiation from the center of furnace was decreased by placing many tungsten plates as the thermal shield. As a result, the excellent temperature uniformity (±0.4 K around a whole crucible) was obtained.

2.2. Measurement Procedure

The compositions of samples are shown in Table 1. SiO₂ powder (>99.5%, Kanto Chemical Co., Inc.), Na₂CO₃ powder (>99.5%, Kanto Chemical Co., Inc.), and NaF powder (>99.0%, Kanto Chemical Co., Inc.) were used as the starting chemicals. The mixture of SiO₂ and Na₂CO₃ was fused after CO₂ degassing and held at 1673 K in a platinum crucible for 30 to 60 minutes under air in order to prepare SiO₂–Na₂O master slags. The melt was poured on a cold copper plate to make a cullet. For ternary component samples, the mixture of master slag and NaF was fused and held at 1573 K in a platinum crucible for 10 minutes under air in order to prepare SiO₂–Na₂O–NaF sample. The mass of sample after the preparation was in agreement with the mass of sample estimated at the difference of ±0.5%. In this study, basicity B was defined by the ratio of C_Na2O/C_SiO2 in mol%. The B was 0.67, 0.82, or 1.00. The concentrations of NaF were 0, 5, 10, and 15 mol%.

Table 1. Experimental conditions and results for the viscosity measurement.

Exp. No.	Concentration of component i, Ci (mol%) a			Basicity, CNa2O/CSiO2	Temperature range measured, T/K	Viscosity of melts, log (η/Pa·s) = a + b/T		log (η/Pa·s) at 1473 K	Activation energy, E/kJ·mol–1
	Na2O	NaF	SiO2			a	b
A	40.0	0	60.0	0.67	1312–1473	–6.741	10817	0.602	207
B	38.4	5.0	57.6	0.67	1263–1473	–4.745	7718	0.495	148
C	36.0	10.0	54.0	0.67	1193–1471	–4.697	7225	0.208	138
D	34.0	15.0	51.0	0.67	1273–1472	–4.696	6882	–0.024	132
E	45.0	0	55.0	0.82	1314–1471	–5.595	8486	0.166	163
F	42.8	5.0	52.2	0.82	1274–1472	–4.945	7314	0.020	140
G	40.5	10.0	49.5	0.82	1232–1473	–4.421	6172	–0.231	118
H	50.0	0	50.0	1.00	1373–1473	–3.375	5362	–0.095	103

a:  Value of initial composition in sample preparation.

The sample charged in the graphite crucible was placed in the alumina tube of the furnace. After the evacuation of the alumina tube, argon dehydrated by sulfuric acid and phosphorus pentoxide was introduced in the tube. It was revealed that the loss of fluoride from melts was effectively suppressed by measuring the viscosity of melts in the hermitically sealed apparatus under dehydrated argon atmosphere in the previous study.¹⁾ The effect was expected in a similar way in this study. The samples were heated and fused at 1473 K. The inner cylinder was immersed in the melts and held for 30 minutes. The outer cylinder was then rotated at the rate of 6.28 rad·s (60 rpm), and the torque given to the inner cylinder was measured. The torque was recorded for 120 s by the interval of 0.5 s, and the 240 points were averaged. The measurement was also conducted in a cooling step, and the sample was reheated when the torque was drastically increased by the starting of solidification. The measurement was then conducted in the heating step. The procedure was repeated in order to confirm the reproducibility.

The viscosity of the melt was determined by using the calibration curve. Dimensions of the crucible and the inner cylinder were corrected by using the thermal expansion coefficient of the graphite (α = 4.8 × 10^–6 K^–1). After the experiment, the crucible and the inner cylinder were detached and recovered from the graphite spindle and the tungsten spindle, respectively. The mass change of sample was measured by weighing the sample contained in the crucible and some amount of the sample adhered on the inner cylinder.

3. Results and Discussion

3.1. Temperature Dependency

Figure 1 shows the viscosity of SiO₂–Na₂O–NaF melts with basicity of 0.67 (Exp. A, B, C, D). The measurement was carried out with the order of a cooling process (1st process), a heating process (2nd process), and a cooling process (3rd process). The results obtained in individual processes are not distinguished. The data are well consistent although the sample weight was decreased by 1.2% at the maximum after the measurement. The sample loss is discussed later. The slopes and the intercepts of the regression lines obtained by the least square method are shown in Table 1. The scattering of the plots is small in any composition, and the viscosity showed good Arrhenius type linearity. The viscosity and the slope of the line decreased with increasing NaF concentration.

Fig. 1.

Viscosity of SiO₂–Na₂O–NaF melts. B = C_Na2O/C_SiO2 = 0.67. (Exp. A, B, C, D) Concentration in the figure shows the value of initial composition in sample preparation.

Figure 2 shows the viscosity of SiO₂–Na₂O–NaF melts with basicity of 0.82 (Exp. E, F, G). The measurement data were from a cooling process (1st process) and a heating process (2nd process). The data are well consistent although the sample weight was decreased by 2.4% at the maximum after the measurement. The viscosity showed good Arrhenius type linearity in the same manner as the basicity of 0.67.

Fig. 2.

Viscosity of SiO₂–Na₂O–NaF melts. B = C_Na2O/C_SiO2 = 0.82. (Exp. E, F, G). Concentration in the figure shows the value of initial composition in sample preparation.

Figure 3 shows the viscosity of SiO₂–Na₂O melts with basicities of 0.67, 0.82, and 1.00 (Exp. A, E, H). The measurement data for SiO₂–Na₂O melt with basicity of 1.00 were only from a cooling process. When the viscosity was measured with the order of a cooling process (1st process), a heating process (2nd process), and a cooling process (3rd process), the data were not consistent and the viscosity increased by continuing measurement. The sample weight was decreased by 7.0% at the maximum after the measurement. The reason was estimated that Na₂O in the melts was reduced to Na by a graphite (crucible and/or inner cylinder) and Na evaporated. The standard Gibbs energy change of formation of Na₂O (l) is expressed below. The standard Gibbs energy change of reduction of Na₂O by carbon is expressed below.   

$${\text{Na}}_{\text{2}}\text{O}\hspace{0.17em}\text{(}l\text{)}+C\hspace{0.17em}\text{(}s\text{)}=\text{2Na}\hspace{0.17em}(\mathrm{g})+{\text{CO}}_{\text{2}}\hspace{0.17em}(\mathrm{g})$$(3)

  

$$\mathrm{\Delta }{G}_{(3)}^{\circ }=417\mathrm{\hspace{0.17em} }088-328.8\text{ (}T/\mathrm{K}) [\mathrm{J}\cdot \mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}]$$(4)²⁾

The Gibbs energy is also expressed by activity and vapor pressure of components as following equation.   

$$\mathrm{\Delta }{G}_{(3)}^{\circ }=-RTln\frac{p_{\text{Na}}^2{p}_{\text{CO}}^{}}{a_{{\text{Na}}_{\text{2}}\text{O}}^{}{a}_{\text{C}}^{}}$$(5)

Hence, vapor pressure of Na is expressed as follows.   

$$p_{\text{Na}}^{}=\frac{a_{{\text{Na}}_{\text{2}}\text{O}}^{\text{1/2}}{a}_{\text{C}}^{\text{1/2}}}{p_{\text{CO}}^{1/2}}exp\left(-\frac{\mathrm{\Delta }{G}_{(3)}^{\circ }}{2RT}\right)$$(6)

The calculation results are shown in Table 2 by using a_Na2O determined by Tsukihashi et al.³⁾ and by assuming a_C = p_CO = 1. Since p_Na reaches to 1.5×10^–2 atm in SiO₂–50 mol% Na₂O at 1473 K, Na might evaporate slowly. Namely, there is a risk of weight loss in a prolonged measurement at high temperature. It was found that weight loss can’t be ignored in a highly basic composition.

Fig. 3.

Viscosity of SiO₂–Na₂O melts. B = C_Na2O/C_SiO2 = 0.67 (Exp. A), 0.82 (Exp. E), 1.00. (Exp. H). B is calculated from initial composition in sample preparation.

Table 2. Vapor pressure of Na formed by the reduction of Na₂O with a graphite.

Concentration of Na2O in Silicate, CNa2O (mol%)	Temperature, T/K	Activity of Na2O, aNa2O (–) a	Standard Gibbs energy change of reaction (3), $\mathrm{\Delta }{G}_{(3)}^{\circ }$ /kJ·mol–1	Vapor pressure of Na, pNa (atm)
40	1373	2.51×10–8	–34.25	7.1×10–4
40	1473	6.31×10–8	–67.12	3.9×10–3
45	1373	1.00×10–7	–34.25	1.4×10–3
45	1473	2.51×10–7	–67.12	7.8×10–3
50	1373	3.98×10–7	–34.25	2.8×10–3
50	1473	1.00×10–6	–67.12	1.5×10–2

a:  Value determined by Tsukihashi et al.³⁾

3.2. Composition Dependency

Figure 4 shows the viscosity of the SiO₂–Na₂O melts at 1473 K calculated from the regression lines versus mol% Na₂O. Literature values are also shown in the figure.^4,5,6,7,8,9) Lillie et al. determined the viscosity by using a rotating crucible viscometer originally developed with a Pt inner cylinder and a Pt crucible under air.⁴⁾ Bockris et al. used an original crucible viscometer with a Mo inner cylinder and a Mo crucible under nitrogen flow in a partially sealed apparatus.⁵⁾ Eipeltauer et al. used a ball pulling-up method with a Pt ball and Pt crucible under air.⁶⁾ Kawahara et al. used an original rotating crucible viscometer with a Pt-Rh inner cylinder and a Pt-Rh crucible under air.⁷⁾ Urbain et al. used a rotating crucible viscometer with a Mo inner cylinder and a Mo crucible under Ar.⁸⁾ Neuville used a rotating inner cylinder viscometer (Rheomat 115, proRheo GmbH) with a Pt-Rh inner cylinder and a Pt-Rh crucible in air.⁹⁾ It is note that the composition of sample measured by Neuville was SiO₂ – 0.05 mol% CaO – 40.09 mol% Na₂O.⁹⁾ The plots in the figure are slightly scattered, but it seems that logarithmic viscosity monotonically decreases by increasing Na₂O concentration in mol%.

Fig. 4.

Viscosity of SiO₂–Na₂O melts at 1473 K. Data of Neuville is on SiO₂–0.05 mol% CaO– 40.09 mol% Na₂O. Concentration in this study shows the value of initial composition in sample preparation.

Figure 5 shows the viscosity of the SiO₂–Na₂O–NaF melts at 1473 K calculated from the regression lines versus mol%NaF. The viscosity of pure NaF was determined by using oscillation method with a nickel crucible by the authors.¹⁰⁾ The viscosity determined in this study monotonically decreased with increasing NaF concentration. The quadric curves (Eqs. (7) and (8)) well fit the plots of ternary melts and the plot of pure NaF.   

$$\begin{array}{c}\mathrm{l}\mathrm{o}\mathrm{g}\hspace{0.17em}(\eta /\mathrm{P}\mathrm{a}\cdot \mathrm{s})=0.645-0.0442\mathrm{\hspace{0.17em} }{C}_{\mathrm{N}\mathrm{a}\mathrm{F}}+8.12\times {10}^{-5}{C}_{\mathrm{N}\mathrm{a}\mathrm{F}}{ }^2\\ (\mathrm{B}\mathrm{a}\mathrm{s}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}:0.67)\end{array}$$(7)

  

$$\begin{array}{c}\mathrm{l}\mathrm{o}\mathrm{g}\hspace{0.17em}(\eta /\mathrm{P}\mathrm{a}\cdot \mathrm{s})=0.183-0.0404\mathrm{\hspace{0.17em} }{C}_{\mathrm{N}\mathrm{a}\mathrm{F}}+8.93\times {10}^{-5}{C}_{\mathrm{N}\mathrm{a}\mathrm{F}}{ }^2\\ (\mathrm{B}\mathrm{a}\mathrm{s}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}:0.82)\end{array}$$(8)

This composition dependence is similar to that for SiO₂–CaO–CaF₂ melts.¹⁾

Fig. 5.

Viscosity of SiO₂–Na₂O–NaF melts at 1473 K. B denotes C_Na2O/C_SiO2. Concentration in this study shows the value of initial composition in sample preparation.

3.3. Viscosity Decreasing Ability of Na₂O and NaF

Compositions of sample in Exps. A and H are Na₂O–60 mol%SiO₂ and Na₂O–50 mol%SiO₂, respectively (see Table 1). This means that 10 mol% of SiO₂ was replaced by Na₂O. The logarithm of viscosity (in Pa·s) decreased from 0.602 to –0.095. Compositions of sample in Exps. A and G are Na₂O–60 mol%SiO₂ and Na₂O–10.0 mol% NaF–49.5 mol%SiO₂, respectively (see Table 1). This means that about 10 mol% of SiO₂ was replaced by NaF. The logarithm of viscosity (in Pa·s) decreased from 0.602 to –0.231. Namely, viscosity decreasing ability of NaF is higher than that of Na₂O although supply capacity of cation (Na⁺) is half.

Figure 6 shows the activation energy of viscous flow of (a) SiO₂–Na₂O melts and (b) SiO₂–Na₂O–NaF melts. The activation energy linearly decreases by increasing Na₂O concentration in SiO₂–Na₂O melts. On the other hand, in SiO₂–Na₂O–NaF melts, the activation energy significantly decreases by increasing NaF concentration at first, but that sluggishly decreases with further addition of NaF. This implies that the mechanism of enhancement of fluidity is different between Na₂O and NaF.

Fig. 6.

Activation energy of viscous flow. (a) SiO₂–Na₂O melts, (b) SiO₂–Na₂O–NaF melts. Concentration shows the value of initial composition in sample preparation.

Sasaki et al. analyzed Na₂O–NaF–SiO₂ glasses by using Raman spectroscopy and molecular dynamic simulation and reported that F^– coordinated Na⁺ but not Si ion which is surrounded by oxide ion, at least within low NaF concentration region.¹¹⁾ Namely, F^– does not modify the silicate network and plays just as a diluter. Since Na₂O supplies non-bridging oxygen and modifies the silicate chain, the roles of Na₂O and NaF are different. The different behavior of activation energy discussed above may be reflected in different coordination style of Na₂O and NaF in silicate network.

4. Conclusions

The viscosity of SiO₂–Na₂O–NaF melts was measured by using a rotating crucible viscometer developed by the authors. As a result, the viscosity of the melts showed a good Arrhenius type linearity in any melts. It was found that the sample loss occurs in highly basic composition region due to a prolonged measurement at high temperature. The viscosity of the melt decreased with increasing the concentration of NaF, and the composition dependence is similar to that for SiO₂–CaO–CaF₂ melts. Viscosity decreasing ability of NaF is higher than that of Na₂O within the composition region investigated in this study. Transitions of activation energy of viscous flow are different between Na₂O addition and NaF addition. This implies that the mechanism of enhancement of fluidity is different between Na₂O and NaF.

Acknowledgement

The authors are grateful to Assistant Prof. Souhei Sukenaga, Associate Prof. Noritaka Saito and Prof. Kunihiko Nakashima of Kyushu University for their valuable comments throughout this project. This work was financially supported by the Grant for fundamental research from the Advanced Research and Education Center for Steel (ARECS) of Tohoku University.

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