Influence of CaF 2 on viscosity of aluminosilicate melts

Introduction

CaF₂ is utilised widely in the pyrometallurgy process for its strong ability of decreasing melting point, enhancing fluidity, controlling the crystallisation temperature of molten slag, etc. Therefore, research on the CaF₂ slag is very important. The fluidity of molten slag evaluated by viscosity is considered to be a crucial physical property for controlling the metallurgical process operation. Therefore, accurate viscosity values are essential for the optimisation and improvement of smelting processes. However, obtaining data only by experimental measurements is time consuming and difficult because of the high volatilisation ability of CaF₂ as well as the difficulties associated with high temperature operations. Consequently, there is an urgent need for a model to correlate the viscosity of CaF₂ containing slag with temperature and chemical composition. Recently, the Riboud et al. model,1 optical basicity models,2, 3 the Iida et al. model4 and the Miyabayashi et al. model5 have been proposed to solve this problem. However, among these models:

Meanwhile, all these viscosity models cannot give a good estimation result for the slag system without SiO₂.

In our previous papers,7 ^– 10 a structurally based viscosity model was derived, which considered the network structure of aluminosilicate melts based on definitions of different types of oxygen ions. The model has been applied to aluminosilicate melts involving Al₂O₃, SiO₂, MgO, CaO, SrO, BaO, FeO, MnO, Li₂O, Na₂O and K₂O components. In this study, the application range of the model is extended to aluminosilicate melts containing CaF₂.

Influence of Caf₂ on structure of aluminosilicate melts

In order to incorporate CaF₂ into the viscosity model, its influence on the melt structure must be clear. The structure of aluminosilicate melts containing CaF₂ has been studied using various types of spectroscopic measurements, such as infrared absorption spectroscopy,11 ^– 15 Raman spectroscopy,16 ^– 18 X-ray photoelectron spectroscopy15,19 ^– 21 and nuclear magnetic resonance spectroscopy,22 ^– 24 as well as molecular dynamic simulation.18, 25, 26 The conclusions derived from these literatures about the existence of CaF₂ can be classified into three types:

Recently, the third viewpoint has gained more and more evidences from spectroscopic data16, 19, 22, 23 and molecular dynamics simulation.18, 25, 26 However, even if only considering the Ca–F bond, there are still two structural models related to CaF₂: the Baak–Bills model27, 28 and the Sasaki model.29 The schematic diagrams of these two models are given in Fig. 1.

OPEN IN VIEWER

Figure 1.

Schematic diagrams for Baak–Bills and Sasaki models

The Baak–Bill model may be effective only in the case of the mole fraction of CaO higher than that of CaF₂ that also leads to the limitation of the model by Miyabayashi et al.,5 in which the Baak–Bill model is utilised to describe the influence of CaF₂ on the melt structure. It is found by Hayakawa et al. 19 that Ca²⁺ and F⁻ ions introduced as CaF₂ are located favourably among the Si–O skeletons, forming Ca–F clusters, and cannot change the relative distribution of structural units Q ⁱ, which have 4, 3, 2, 1 and 0 non-bridging oxygen per silicon, i.e. , , , and respectively. In other words, CaF₂ only acts as a diluter. According to the results of molecular dynamics simulation,25 the coordination number for F⁻ ion around Ca²⁺ ion is ∼2, which also confirms the existence of CaF₂ clusters. Based on the above analyses, CaF₂ is only considered as a diluter in this model, and its addition cannot change the types of oxygen ions as well as their relative fractions. The possible existence of the modified effect of CaF₂ on the melt structure is neglected for the convenience of model treatment.

Model

The temperature dependence of viscosity is described by the Arrhenius law (1) where η is the viscosity (P), A is the pre-exponent factor (P), E is the activation energy (J mol⁻¹), R is the gas constant (8·314 J mol⁻¹ K⁻¹) and T is the absolute temperature (K). Compensation effect exists between the logarithm of pre-exponent factor A and the activation energy E (2) where the E of 572 516 and the ln A of 17·47 are the Arrhenius parameters of pure SiO₂. Parameter k in equation (2) is constant for a specific SiO₂ containing binary system. For the multicomponent system ΣM_xO_y–CaF₂–SiO₂, the value of parameter k is assumed to be the linear addition of the parameter for binary systems M_xO_y–SiO₂ and CaF₂–SiO₂ with the renormalised mole fractions of oxides M_xO_y and CaF₂ as the weighting factors. Therefore, parameter k is calculated as follows (3) The activation energy E in equation (2) is expressed by the reciprocal function of the linear addition of mole fraction of different types of oxygen ions with different weighting factors. Since CaF₂ is only considered as a diluter and has no influence on the distribution of different types of oxygen ions, the numbers of oxygen ions can also be calculated according to the formulae given in our previous works.7 ^– 10 Therefore, the activation energy of viscosity can be expressed as follows (4) where , and are the mole numbers of bridging oxygen O_Si, other types of oxygen ions and CaF₂ respectively; parameter α describes the deforming ability of bond around the corresponding units.

In the denominator of equation (4), the first, second, third, fourth, fifth, sixth and seventh terms represent the contributions of bridging oxygen bonded with Si⁴⁺ ion, oxygen bonded with Al³⁺ ion not being charge compensated, bridging oxygen bonded with compensated Al³⁺ ion, non-bridging oxygen bonded with Si⁴⁺ion, non-bridging oxygen bonded with Al³⁺ ion, free oxygen bonded with cation of basic oxide and CaF₂ respectively.

The parameters of the present model can be obtained as follows:

The parameters for SiO₂, Al₂O₃, MgO, CaO, SrO, BaO, FeO, MnO, L₂O, Na₂O and K₂O components have been optimised previously.7 ^– 10 In this study, only parameters and are optimised to be −2·352×10⁻⁵ and 23·7. All the assessed parameters are listed in Tables 1 and 2.

OPEN IN VIEWER

Table 1.

Values of model parameters for different components

i	k i/×105		α i	α Al,i
Mg	−2·106	6·908	15·54	5·606	3·975
Ca	−2·088	7·422	17·34	4·996	7·115
Sr	−2·450	9·502	18·50	4·980	9·374
Ba	−2·490	10·30	23·74	4·270	5·602
Fe	−2·195	10·76	33·62	8·702	6·828
Mn	−2·147	8·452	27·83	5·857	4·204
Li	−2·412	11·06		5·918	12·01
Na	−2·767	13·35	40·56	4·308	10·46
K	−3·200	16·59		4·156	17·43
Al	−2·594		5·671
CaF2	−2·352		23·7

OPEN IN VIEWER

Table 2.

Value of model parameter

8·334	8·694	9·787	7·593	8·015

Results and discussion

CaO–FeO–CaF₂–SiO₂ system

The viscosity data of the CaO–CaF₂–SiO₂ system are taken from Yasukouchi et al. 30 and Shahbazian et al. 31 A small quantity of FeO present in the Shahbazian data is probably because of the use of iron spindle and iron crucible during viscosity measures. The viscosities of the CaO–FeO–CaF₂–SiO₂ system32, 33 with high content of FeO are also taken for the evaluation of the model. The comparisons between model estimated viscosities and those measured by experiments are shown in Fig. 2, with the mean deviation of 24·4% defined as where η _i,cal and η _i,mea are the calculated and measured viscosities respectively, and N represents the number of samples. The reasons for the relatively large deviation may be from the continuously changing chemical composition of molten slag during the viscosity measuring process resulting from the volatilisation of CaF₂ and the hard control of Fe³⁺ ions in the melt with high content of FeO.

OPEN IN VIEWER

Figure 2.

Comparisons between estimated and measured viscosity values for CaO–FeO–CaF₂–SiO₂ system

CaO–Al₂O₃–CaF₂–SiO₂ system

CaO, Al₂O₃, CaF₂ and SiO₂ are the main components of electroslag remelting slag, which possesses a quite high content of CaF₂. The viscosity data of CaO–Al₂O₃–CaF₂–SiO₂ type electroslag remelting slag have been compiled by Mills.34 The calculated viscosities of this system using the present model with the parameters regressed in the CaO–FeO–Al₂O₃–SiO₂ system and comparing with the measured values are shown in Fig. 3. The mean deviation for this system is 17·6%.

OPEN IN VIEWER

Figure 3.

Comparisons between estimated and measured viscosity values for CaO–Al₂O₃–CaF₂–SiO₂ system

CaO–Na₂O–CaF₂–SiO₂ system

The viscosities of four compositions in the CaO–Na₂O–CaF₂–SiO₂ system were measured by Kim and Sohn.21 Although two basic oxides exist in this system, it has been pointed out that F⁻ ions seem to be preferentially bonded to higher field strength modifier cations;22 thereby, Ca–F may still be considered as the main coordination type of F⁻ ions. The assumptions that CaF₂ acts as a diluter may not bring a large error in this system. Comparisons between the calculated and measured values are shown in Fig. 4, with the mean deviation of 24·3%.

OPEN IN VIEWER

Figure 4.

Comparisons between estimated and measured viscosity values for CaO–Na₂O–CaF₂–SiO₂ system

CaO–FeO–CaF₂–Al₂O₃–SiO₂ system

The viscosity data of the CaO–FeO–CaF₂–Al₂O₃–SiO₂ system are taken from the experimental measurement of Shahbazian et al. 35 Comparisons between the estimated and measured values are shown in Fig. 5, with the mean deviation of 19·1%. In Fig. 5, both contents of FeO and SiO₂ are equal to 0 for the points in the highlighted ellipse (or equivalent to the CaO–CaF₂–Al₂O₃ ternary system). Thus, the present model can also obtain good results for the system without SiO₂.

OPEN IN VIEWER

Figure 5.

Comparisons between estimated and measured viscosity values for CaO–FeO–CaF₂–Al₂O₃–SiO₂ system

Discussion

In order to get a clear view of the influence of CaF₂ on viscosity, the isoviscosity curves of the CaO–CaF₂–SiO₂ system at 1873 K obtained by the present model are given in Fig. 6. Two ways of CaF₂ additions will be used to discuss its influence on viscosity: adding CaF₂ to melts directly. When adding CaF₂ to aluminosilicate melts, it can be seen from Fig. 6 that viscosity gradually decreases along the line from a particular point to the CaF₂ vertex. Although Sasaki et al. 29 and Hayakawa et al. 19 assumed that the relative distribution of Q ⁱ (i = 0–4) units does not change, the addition of CaF₂ decreases the absolute amounts of Q ⁱ units and provides lots of new cutoff points for the viscous flow. Thereby, a decreasing tendency may be anticipated when adding CaF₂.

OPEN IN VIEWER

Figure 6.

Isoviscosity curves of CaO–CaF₂–SiO₂ system at 1873 K

When substituting CaF₂ for CaO, it can be seen from Fig. 6 that the viscosity decreases in an acidic composition area where the SiO₂ content is high, but almost keeps constant in the basic composition area with high CaO content. The same conclusion was also obtained by Miyabayashi et al. 5 by using a neural network approach and Nakamoto et al.,36 who produced an isoviscosity map based on values from the literature. In the acidic composition area, Luth16 found that the substitution of CaF₂ for CaO in a molten CaO–CaF₂–SiO₂ system enhanced the degree of polymerisation. Although this factor may increase viscosity, the introduction of new cutoff points due to the addition of CaF₂ may be more important in the acidic range where the viscosity is very high, thereby a viscosity decrease occurs when replacing CaO by CaF₂, whereas in the basic range, the aluminosilicate melt is mainly composed of polyanions with short chains, and the existence of lots of non-bridging oxygen and free oxygen leads to the small value and gent changing tendency of viscosity. Therefore, in this case, the viscosity will not be affected seriously. In general, viscosity is strongly dependent on the basicity in the acidic region, but not in the basic region.

Conclusions

A model to estimate the viscosity of aluminosilicate melts containing CaF₂ is developed by considering different types of oxygen ions and CaF₂ clusters as cutoff points during the viscous flow. In the model, two parameters are endowed to describe the influence of CaF₂. The composition and temperature dependences of the viscosity for molten CaO–FeO–CaF₂–SiO₂, CaO–Al₂O₃–CaF₂–SiO₂, CaO–Na₂O–CaF₂–SiO₂ and CaO–FeO–CaF₂–Al₂O₃–SiO₂ systems can be represented well by the present model.