2019 Volume 59 Issue 6 Pages 1018-1026
Based on the structure of slag, the revised structure based viscosity model was improved for viscosity prediction of the fully liquid slag in the Al2O3–CaO–MgO–SiO2 quaternary system and its subsystems. Experimental procedures and available data in the literature have been critically reviewed. In this modified model, the oxygen ions bonded with non-compensated Al3+ ions were defined as excess bridge oxygens. The concentration of different types of oxygen ions are calculated and used to express the activation energy. The present model is capable of predicting the viscosities in the Al2O3–CaO–MgO–SiO2 quaternary system and its subsystems over the wide composition and temperature ranges above liquidus within experimental uncertainties; the average of relative errors for this model was found to be 17.97%. CaO has a greater ability to decrease the viscosity than that of MgO in the system without Al2O3 because of the weaker bond strength of CaO. A viscosity maximum occurs for MO–Al2O3–SiO2 (M=Ca or Mg) slag with a fixed SiO2 content. The estimated viscosities decrease with the increase of MgO content, decrease with increasing of the Al2O3/SiO2 ratio at 5 mass% of MgO, and keep almost constant or even slightly increase with the increase of the Al2O3/SiO2 ratio at 10 mass% MgO.
As an important high temperature physical property of slag, the viscosity is dramatic effect on the operation of pyro-metallurgical processes. Therefore, the suitable viscosity is the guarantee for the smooth operation and optimization of the metallurgical processes. Slag viscosities can be measured by many methods, however, high-temperature measurements are very difficult, fallible, high cost and time-consuming. Thus, a reliable, accurate model is required to estimate the viscosity for the molten slags. The CaO–MgO–Al2O3–SiO2 systems are very important not only in the metallurgical processes, but also in the glass manufacture and magmatic processes in petrology. In iron and steel industry, CaO, SiO2, Al2O3, and MgO are the basic component for blast furnace (BF) slags and steelmaking slags. In petrology, approximately 95% of magma composition can be expressed within the system metal oxides-alumina-silicate.1) Over the past decades, abundant viscosity models have been developed, and the details and limitations of these models have been well documented.2,3,4,5,6)
In the previous work of Reddy et al.,7,8,9,10,11) a structure-based viscosity model was proposed to represent the viscosity of the silicate and borate systems. The present paper describes the recent development of the model formalism and its application for fully liquid CaO–MgO–Al2O3–SiO2 slag. It should be noted that the application of the model to the CaO–MgO–Al2O3–SiO2 system is parts of development of the viscosity model for the CaO–MgO–FeO–Al2O3–SiO2–TiO2 multi-component system.
Bockris and Reddy12) deduced a model based on the hole theory to understand the transport processes in molten slag. In this model, a fluid in motion is assumed to be moving layers of fluid in the direction parallel to liquid layers. According to the hole theory, the viscous forces are thought to occur due to the momentum transfer between moving fluid layers when particles jump from one layer to another, as shown in Fig. 1. The following Eq. (1) for liquid viscosity was derived using the above principles:
Viscous forces arise from transfer of momentum between moving layers in fluid. (Online version in color.)
The hole model shows that the activation energy (E) for a particle motion includes two steps. One is the energy required to form a hole and another is the energy required to make a particle and jump into the hole. The assumptions are that the number of holes (Nh) in the melt are equal to the number of tetrahedral units present in the slag and also that all the holes are filled by the tetrahedral units. Therefore, the number of holes (Nh) are related to the concentration of bridge oxygen (NO0). The NO0 was calculated using the atomic pair model proposed by Yokokawa.13) Furth14) has showed that for a typical hole in as liquid, the radius of a hole (Rh) is roughly as same as an ion and can accommodate an ion. Table 1 summaries the description of previous Reddy models.7,8,9,10,11) The Hu and Reddy model7) was developed to predict the viscosity of binary silicate slag, and could not give a good performance for more complicated liquids such as aluminosilicate systems. The model developed by Yen et al.,8) and Zhang et al.10,11) only can be applied to the borate systems. The model proposed by Zhang and Reddy model9) is specifically for industrial lead slags, which exit some limitations in the prediction of viscosities in other slag systems. Therefore, the present paper describes the recent development of the model formalism and its application for fully liquid CaO–MgO–Al2O3–SiO2 slag.
In silica slag without Al2O3, three types of oxygen exist. The species of oxygen atoms are classified by the cations they connect. The bridging oxygen (BO or O0) connects two tetrahedrons, the non-bridging oxygen (NBO or O−) connects a tetrahedron to a modifier, whereas, the free oxygen (FO or O2−) links two network modifiers. Silicate slag consist [SiO4]4− tetrahedral network, which the Si4+ may be partially replaced by other tetrahedral coordinated cations such as Al3+ whose ionic radius (0.47Å) is slightly larger than that of Si4+ (0.34Å). The charge compensation are required of [AlO4]5− tetrahedral due to the difference in the valence comparing with [SiO4]4− which are usually achieved by alkali metals and alkaline earths, resulting the structural role of A13+ become more complex. This kind of cations also act as network modifiers to depolymerize the aluminosilicate structure by forming non-bridging oxygen. Figure 2 shows the schematic illustrations of the structure for different types of oxygen atoms in the slag. For peralkaline slag (MO/Al2O3>1, here M=Ca or Mg), Al3+ is in tetrahedral position. Merzbacher et al.15) concluded that Al3+ is entirely tetrahedral coordinated, and the conclusions are consistent with the results from Cormier16) et al. and Neuville et al.17,18) by neutron and X-ray spectroscopy. In the present model, the MAl2O4 is treated as a network former and can be depolymerised by the exceed MO contributing network modifier. Ca2+ ions have priority over Mg2+ ion for charge compensation of the Al3+ ion based on the thermochemical and spectroscopic data.19,20,21) In peraluminous composition (MO/Al2O3<1), the local charge balance of the [AlO4]5− tetrahedral is no longer attained because not enough alkali metals atoms are present for charge-balance. The tricluster form (triply coordinated oxygen atoms are shared by three [Al(Si)O4]− tetrahedral units)22,23,24) and/or that some A13+ cation have higher coordination number of oxygen25,26) were proposed to maintain local charge balance in peraluminous slag. This two mechanisms could not be independent, as the relatively long cation-oxygen bonds expected in triclusters could allow a fifth oxygen atom into one or more of the cation coordination shells.23,27) Based on this discussion above, the oxygen ions bonded with non-compensated Al3+ ions were defined as excess bridge oxygen (EBO, or O*BO). Therefore, for CaO–SiO2–Al2O3–MgO system, four types of oxygen ions are present: bridging oxygen , non-bridging oxygen , free oxygen O2−, and excess bridging oxygen . For the system C mol% CaO–S mol% SiO2–A mol% Al2O3–M mol% MgO, the details of the calculation of the different types of oxygen are given as follows.
Schematic illustrations of the structure for different types of oxygen atoms in the slag. (Online version in color.)
The total number of oxygen can be calculated as:
Case a: For Al2O3–SiO2–MO (XMO>XAl2O3, MO=CaO+MgO):
In this case, all the Al3+ ions form in tetrahedral position after the charge compensation by MO, which means there is no excess bridging oxygen ( = 0). According to the charge and mass balance, the numbers of other types oxygen can be expressed as Eqs. (4) and (5), respectively.
ΔG0 is the Gibbs energy of depolymerization reactions, and can be expressed as
Case b: For Al2O3–SiO2–MO (XMO<XAl2O3, MO=CaO+MgO):
In this case, the content of MO is not sufficient to compensate all the Al3+ ions. Therefore, there are no free oxygen and non-bridging oxygen. The fraction of other types oxygen can be calculated as:
Specific examples: Pure SiO2: ; Pure Al2O3: ; For Al2O3–SiO2: ; ;
The fraction of different types oxygen used for viscosity modeling can be calculated using Eqs. (2) through (10) over the entire composition range of the Al2O3–CaO–MgO–SiO2 quaternary system and its subsystems.
More than 2900 experimental points from over 40 literatures for the CaO–SiO2–Al2O3–MgO quaternary system and its subsystems have been critically reviewed for use in the model optimization.30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60, 61,62,63,64,65, 66,67,68,69,70,71) A summary of the sources is shown in Table 3. Firstly, the experimental procedures were carefully analyzed. The rotating method is a more reliable viscosity measurement technique compared with falling sphere method and oscillation method.29) The container/sensor materials and atmosphere would lead the changes in slag composition. Thus, experimental results which include post-chemical analysis were preferred. Secondly, temperature control and liquidus temperature are also essential-experimental results, where temperature measured by thermocouple closed to the sample were preferred and only the viscosity data of fully liquid were taken into account for viscosity modeling (liquidus were predicted by FactSage). Last but not least, the viscosities measured from different researchers at close compositions were carefully compared to cross check the reliability of the data.
Equation (1) is a general expression for viscosity calculation and its application to aluminosilicate slag needs calculation of (2πmkT)1/2, Nh, Rh, and E. The methods of calculation of these parameters are given below.
The term of (2πmkT)1/2 can be rearranged as:
The radius of the tetrahedral units (Rh) can be expressed as:
The number of holes per unit volume (Nh) was expressed in terms of NO0 and NO*. Thus
The value of E can be calculated based on the available experimental viscosities by using Eq. (1), and a polynomial expression was deduced that is given by Eq. (15). The bridging oxygens (BOs) of aluminosilicate system have been commonly classified into three types of BOs: Si–O–Si, Si–O–Al and Al–O–Al. However, there is no thermodynamic model that can be used to calculate the concentration of these three types of BOs. The concentration of different types of oxygen can be obtained by molecular dynamics simulation (MD), but the MD calculation severely limit the application of the viscosity model. These three types of BOs are dependent of each other, and exist in equilibrium. In addition, there are only two kinds of bonds: Si–O and Al–O bond. So only two parameters of and are used for aluminosilicate system in this model.
The viscosities of molten silica have been studied by many researchers due to its significance role in high temperature processes. Compared with silica, the number of viscosities data of molten alumina is lesser due to its high melting temperature. As shown in Fig. 3, the experimental viscosities data of liquid silica and alumina are reproduced very well by the present viscosity model and the viscosity increases with decreasing temperature. The experimental data of silicate by Bockris et al.40) is lower than that of other researchers, which was rejected for modeling. Bruckner et al.41) suggested that the significant deviation is due to the pollution of silica by carbon vapors from heating elements. The area pointed by the arrow is the liquid phase which calculated by FactSage.28) It can be seen that the fused silica have a much higher viscosity than do fused alumina. Hole theory in liquids based on elementary acts, each act including two steps: holes are formed and particles jump into these holes. In molten silica and alumina, holes are easily formed because the rate of hole formation is controlled by the vibrations of the atoms relative to each other. Therefore, the bond-rupture step is the rate-determining process. The strength of the Si–O–Si bond is stronger than Al–O–Al bond which holding the network together resulting the higher viscosity.
Comparison between experimental data and calculated data for silica and alumina. (Online version in color.)
The calculated mole fraction of the different type oxygen ions in binary silicate systems is shown in Fig. 4(a). For Al2O3–SiO2 system, the fraction of O0 increased and that of O* decreases with increasing SiO2 content. Urbain et al.38) and Kozakevitch et al.35) measured the viscosity of slag in the Al2O3–SiO2 system, with the Al2O3 mole fraction range of 0.06–0.70. The effect of SiO2 content on the viscosity in Al2O3–SiO2 system at 2126 K and 2226 K are shown in Fig. 4(b), from which it can be seen that the viscosity increases with increasing SiO2 content and the present model reproduce good of the viscosities compared with the experimental data. As mentioned before, although both Al2O3 and SiO2 act as network formers, the Al–O bond strength are weaker than that of Si–O bond, resulting the decrease of viscosity. The previous Reddy model7) treats Al2O3 as basic oxide in the Al2O3–SiO2 system, which also give a good performance at 2223 K but there is no reported parameters for other temperatures.
Distribution different type oxygen ions of binary silicate systems (a), and the viscosity for Al2O3–SiO2 system (b), CaO–SiO2 system (c), and MgO–SiO2 system (d) at various temperature as a function of composition. (Online version in color.)
Unlike Al2O3, CaO and MgO are basic oxides and act as network modifiers to decrease the viscosity. As seen from Fig. 4(a), the fraction of O0 increases and fraction O2− decreases, while O− has maximum value at 0.33 with increasing SiO2 content. The calculated viscosity as a function of compositions at specific temperatures for these binary systems are compared with the experimental data in Figs. 4(c), and 4(d). It is should be noted that the viscosity values have also been calculated for the compositions outside the liquid region for hypothetical. It was demonstrated from Figs. 4(c), and 4(d) that the viscosity decreases sharply when MO added in high silica region. With the increase of basic oxides, the network structure of melt does not change too much, resulting the viscosity tends to be more gently. The present model describes the experimental data in general better than the previous Reddy7) model. The activation energy (E) term of previous model expressed by NO0 without temperature, which resulted the calculated viscosity values in MgO–SiO2 system were very close at different temperatures.
Licko et al.46) reported that the substitution of CaO by MgO will decrease the viscosity of CaO–MgO–SiO2 slag, which means that the non-bridge oxygen (O−) linked with Ca2+ or Mg2+ have different effect on the viscosity and should be distinguished. In the present model, the NO−j (j=Ca2+, or Mg2+) is introduced to describe the effect of different cations on the modification of the network structure. It can be seen from Fig. 5(a), the replacement of CaO for MgO at a fixed SiO2 content at 50 mol% causes a decrease in viscosity at 1973 K and 1873 K, and the calculated viscosities agree well with the experimental data. In Fig. 5(b), the fraction of O0 and O2− almost keep constant, while NO−Ca and NO−Mg replace with each other at a same amount, indicating that CaO has a greater ability to decrease the viscosity than that of MgO in the system.
Viscosity (a), and distribution of different type oxygen ions in the CaO–MgO–50 mol% SiO2 system. (Online version in color.)
The ternary system of MO–Al2O3–SiO2 is not only a fundamental slag system in steel industry and magmatic process, but also can give a better understanding of the role of Al3+ in the slag. According this model, the viscosity of alumonosilicate slag can be predicted from peralkaline composition (MO>Al2O3) to peraluminous slag (MO<Al2O3). The viscosity for the MO–Al2O3–SiO2 systems are well described for a constant SiO2 content of 67 mol%, as shown in Figs. 6(a), and 6(b). It is found that the position of the viscosity maximum is at the fully charge-compensated composition. The calculated mole fraction of the different type oxygen ions in MO–Al2O3–SiO2 systems is shown in Figs. 6(c), and 6(d). The substitution of MO (M=Ca, or Mg) by Al2O3 decrease the fraction of O− and increase the fraction of O0 in peralkaline region, resulting the increase of viscosity. In peraluminous composition, the fraction of O0 decrease and fraction of O* increase, and the strength of the Al–O–Al bond is weaker than that of Si–O–Si bond which contribute to the decrease of viscosity.
Viscosity in the CaO–Al2O3–SiO2 system (a), MgO–Al2O3–SiO2 system (b), and distribution of different type oxygen ions in the CaO–Al2O3–SiO2 system (c), MgO–Al2O3–SiO2 system (d). (Online version in color.)
As a fundamental slag system during in ironmaking and steelmaking processes also in petrology processes, the viscosity of CaO–SiO2–Al2O3–MgO melt has been widely investigated by many workers. Figure 7(a) shows the effect of basicity (CaO/SiO2 mass ratio) and Al2O3 content on the predicted viscosity of CaO–SiO2–Al2O3–MgO melt at fixed MgO content, compared with some experimental values. It is can be seen that melt viscosities decrease with increasing basicity at fixed Al2O3 content and increase with increasing Al2O3 content at fixed basicity. It is easy to understand that from Fig. 7(b), the increase of the fraction of O− and the decrease of the fraction of O0 result in the decreasing of viscosity with increasing basicity at fixed Al2O3 content. When the content of Al2O3 increases at fixed basicity, the metallic cations act as the charge compensators lead to the decrease of O−, thus increasing the slag viscosity. The calculated viscosities are agree well with the measured values by Hyuk Kim et al.52) and G-Hyun Kim et al.64) but a litter higher than the values reported by Machin et al.30,31,32,33) at high alumina content.
Viscosity (a) and distribution of different type oxygen ions (b) in the CaO–SiO2–Al2O3–MgO melt as function of CaO/SiO2 mass ratio; Slag viscosity (c) and distribution of different type oxygen ions (d) in the CaO–SiO2–Al2O3–MgO melt as function of Al2O3/SiO2 mass ratio. (Online version in color.)
Figure 7(c) shows the effect of Al2O3/SiO2 mass ratio and MgO content on the estimated viscosity of CaO–SiO2–Al2O3–MgO melt at fixed CaO content, compared with some experimental values. It is demonstrated that the estimated viscosities decrease with the increase of MgO content, decrease with increasing of the Al2O3/SiO2 ratio at 5 mass% of MgO, and keep almost constant or even slightly increase with the increase of the Al2O3/SiO2 ratio at 10 mass% MgO. From Fig. 7(d), increasing MgO content increase the fraction of O− that contribute to the viscosity decrease. When the content of basic oxides fixed, the substitution of SiO2 by Al2O3 increase the fraction of O0. The strength of Al–O bonding is weaker than that of Si–O bonding, which seems to contribute to the decrease in viscosity. While, with further additions of Al2O3, the basic oxides will be consumed to maintain charge neutrality within the [AlO4]5− tetrahedra, which decreases the basic oxides as network modifiers and increases the viscosity. The calculated viscosities by present model are agree good with the experimental data reported by Machin et al.,30,31,32,33) Tang et al.,66) and Kim et al.64)
The calculated viscosity values are compared with the selected experimental values in the Al2O3–CaO–MgO–SiO2 quaternary system and its subsystems over a wide composition and temperature ranges, as summarized in Fig. 8(a). Mills et al.72) reported that experimental uncertainties of the recommended viscosity measurements were determined as approximately 30%, and the present model reproduces most of the experimental data within experimental uncertainties. The average of relative errors was used to evaluate the performance of the current model in estimating slag viscosities. This can be calculated as the following equation:
Comparison between experimental data and calculated data (a), and the average of relative errors (b) for CaO–SiO2–Al2O3–MgO system and its subsystems. (Online version in color.)
The revised hole theory viscosity model was improved for viscosity prediction of aluminosilicate slag. The following conclusions can be drawn:
(1) Contributions from the different types of oxygen to activation energy were calculated. The oxygen ions bonded with non-compensated Al3+ ions which called excess bridge oxygen were considered for the peraluminous slag.
(2) The present model is capable of predicting the viscosities in the Al2O3–CaO–MgO–SiO2 quaternary system and its subsystems over the wide composition and temperature ranges above liquidus within experimental uncertainties; the average of relative errors for this model was found to be 17.97%.
(3) The calculated results obtained from the model indicated that CaO has a greater ability to decrease the viscosity than that of MgO in the system SiO2–CaO–MgO. A viscosity maximum occurs for MO–Al2O3–SiO2 (M=Ca or Mg) slag with a fixed SiO2 content. The predicted viscosities decrease as the MgO content increases, decrease with the increase of the Al2O3/SiO2 ratio at 5 mass pct of MgO, and remain almost constant or even slightly increase with the increase of the Al2O3/SiO2 ratio at 10 mass pct MgO.
This study was supported by Natural Science Fund Outstanding Youth Project Funding of China (Grant No. 51522403) and China Scholarship Council. Authors are pleased to acknowledge the financial support provided by ACIPCO for this research project. We also thank Department of Metallurgical and Materials Engineering, The University of Alabama for providing the experimental and analytical facilities for this research work.