Research of Materials Science March 2014, Volume 3, Issue 1, PP.10-16
Calculating Models on the Surface Tension of CaO-FeO-SiO2 Molten Slags Chengchuan Wu 1, 2)#, Guoguang Cheng 1, 2), Qiqi Ma1, 2) 1) State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083, China 2) School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083, China #
Corresponding author, E-mail: wuchengchuan163@163.com
Abstract A thermodynamic model has been developed for determining the surface tension of CaO-FeO-SiO2 molten slags based on the ion and molecule coexistence theory (IMCT) of slag structure and Butler’s equation. The temperature and composition dependence of the surface tensions in molten CaO-FeO-SiO2 slag systems was reproduced by the present model using surface tensions and molar volumes of pure oxides, as well as the mass action concentrations (activities) at the surface and at the bulk phase of the slag component. The evaluated results for the surface tension show good agreements with literature data. The iso-surface tension lines of CaO-FeO-SiO2 slag melt have also been calculated and the effects of slag composition and temperature on the surface tension were also investigated. Keywords: CaO-FeO-SiO2 Molten Slags; Surface Tension; the Ion and Molecule Coexistence Theory; Butler’s Equation; Calculating Model.
1. Introduction The surface tension of molten slag is one of the most important parameters for metallurgy processes, on account of which is closely related to the phenomena such as inclusion formation and removing in metal melt, slag foaming, slag-metal emulsification and slag-metal reaction. However, it is difficult to find the appropriate surface tension data of molten slag due to the high temperature measurement and the complicated effect of component on surface tension. Various models have been developed to predict the surface tension of molten slag systems. For slag with complicated interactions, T. Tanaka et al. [1-3] applied a model considering the anionic and cationic radii of the component oxides as the model parameters to describe the surface tension, and H. G. Lee et al. [4] calculated the surface tension using critically evaluated ionic surface distances of pure oxides. In addition, these two models are based on Butler’s equation and achieved consistent results compared to the data reported in the literature. However, all these models are not on account of the actual structures of the slag melt. The coexistence theory of slag structure [5, 6] has been proposed by N.M. Chuiko and modified by J. Zhang to express the reaction ability of components in a slag by the defined mass action concentration Ni according to the mass action law, like the traditionally applied activity ai of component i. The calculated mass action concentrations of all existed structural units or ion couples in the slags, like the traditionally measured or calculated activity of components, have been used to predict sulfur distribution and phosphate capacity, and also been used to determine the mass action concentration of structural units in the Ce2O3 and La2O3 containing slags[7-11], in which ion and molecule coexistence theory (IMCT) corresponds to the coexistence theory of slag structure. G. G. Cheng et al. [12, 13] developed a thermodynamic model for evaluating the surface tension of slag melt for considering the bulk and surface structures of slag melt based on the ion and molecule coexistence theory of slag structure as well as Butler’s equation. This model is characterized by the reasonable understanding of the slag structure with which it can be simply apply to the multi-component slag melt, because the calculations are only based on the surface tension and molar volume of the pure components, the ion and molecule coexistence theory and - 10 http://www.ivypub.org/rms
Butler’s equation. This model has also been used to simply predict the surface tension of CaO-SiO2, MnO-SiO2 and CaO-MnO-SiO2 slag melt. In the present work, a further verification of the above model was attempted for predicting the surface tensions of the CaO-FeO-SiO2 slag systems. The calculated surface tension results were compared with the data reported in the literature. In addition, to understand the effects of component on the surface tension, the iso-surface tension curves of CaO-FeO-SiO2 ternary slag were also compared.
2. Thermodynamic model for estimation of the surface tension of molten slag 2.1 Butler’s Equation Among various models suggested by previous researchers for the prediction of surface tension of liquid solutions, the present model also based on the Butler’s equation. The surface tension ( ) of the molten slag system is calculated from Eq.(1):
iPure
RT aiSurf ln Ai aiBulk
(1)
Where subscript i refer to the following component: CaO, FeO, or SiO2. Superscripts “Surf” and “Bulk” indicate the Surf Bulk surface and bulk phase, respectively. R is the gas constant and T is the absolute temperature. Where ai and ai Pure are the activities of the component i at the surface phase and at the bulk phase, respectively. i is the surface tension of the pure molten component i. And Ai is the molar surface area in a monolayer of pure molten component i, which can be figure out by Eq. (2):
Ai L N 01/ 3 Vi 2 / 3
(2)
Where N0 is Avogadro’s number, Vi molar volume of the pure molten component i, L correction factor resulting from the surface structure and usually set to be 1 for the molten salts and ionic oxide mixtures by Tanaka et al.
2.2 Hypotheses The classic hypotheses about the ion and molecule coexistence theory of slag structure are described in detail elsewhere [5, 6]. However, the key points of this model are that the surface layer is also obeying the hypotheses of the ion and molecule coexistence theory of slag structure, and the relation between surface tension of molten slag and mass action concentrations of components at the surface phase and at the bulk phase conforms to Butler’s equation, which can be summarized as follows: (a) The type of structural units at the surface phase of the studied CaO-FeO-SiO2 slag systems is the same as at the bulk phase of molten slag, composed of simple ions such as Ca2+, Fe2+ and O2-, simple molecule SiO2, and complex molecules as aluminates. (b) There are dynamic equilibrium chemical reactions between simple ions, simple molecules and complex molecules, taking silicate formation reaction for example:
2 Me 2 O 2 SiO2 Me2 SiO4
(3)
(c) The chemical reactions of forming complex molecules as shown in Eq. (3) obey the mass action law, and Eq.(4) can be gotten:
K Me2SiO4 Sulf
Sulf
Sulf N Me 2 SiO4 2
(4)
Sulf Sulf N MeO N SiO 2
Sulf
Where N Me2 SiO4 , N MeO and N SiO2 are surface mass action concentrations (surface activities) of MeO, which - 11 http://www.ivypub.org/rms
2
existed as ion couples ( Me + O
2
), SiO2 and Me2SiO4, respectively; K is chemical reaction equilibrium constant
of Eq. (1), which can be calculated by K Me2SiO4 exp r Gm,Me2SiO4 RT . (d) The relation between surface tension of slag melt and mass action concentrations of components at the surface phase and at the bulk phase conforms to Butler’s equation:
iPure Surf
RT N iSurf ln Ai N iBulk
(5)
Bulk
Where N i and N i are the mass action concentrations (activities) of the component i at the surface phase and at the bulk phase, respectively. Taking CaO-FeO-SiO2 slag melt as an example, Eq. (5) can be expressed as Eq. (6)-(8): Pure CaO-FeO-SiO CaO
N Surf RT ln CaO Bulk ACaO N CaO
(6)
Pure CaO-FeO-SiO FeO
N Surf RT ln FeO Bulk AFeO N FeO
(7)
Surf N SiO RT ln Bulk2 ASiO2 N SiO 2
(8)
2
2
CaO-FeO-SiO 2
Pure SiO2
2.3 The mass action concentrations calculating model of CaO-FeO-SiO2 The mass action concentration of the structural unit is defined as a ratio of the equilibrium mole number of structural unit i to the total equilibrium mole numbers of all structural units according to IMCT, and all structural units in the form of simple ions, simple molecules, and complex molecules can be calculated by N i ni . The N Me2O3 such as ni ion- pair (Me2++O2-), should be calculated by N MeO N 2 N O2 ,MeO Me , MeO
nMe2 ,MeO nO2 ,MeO
ni
2nMeO . ni
The mole numbers of CaO, FeO and SiO2 in 100g of total slag mass were defined as b1 nCaO , b2 nFeO and a1 nSiO2 respectively. The symbols of the mass action concentrations for all structure units were listed as following: N1 N CaO , N 2 N SiO2 , N 3 N FeO The total equilibrium mole number of all structural units in the CaO-FeO-SiO2 slag
.
can be expressed as:
ni 2n1 n2 2n3 n4 n5 n6 n7 (mol).
Mass equilibrium formulas were listed below:
b1 ni 0.5N1 N 4 2 N5 3N 6
(9)
a1 ni N 2 N 4 N5 N 6 N7
(10)
b2 ni 0.5N3 2 N 7
(11)
N1 N 2 N3 N 4 N5 N6 N7 1
(12)
Therefore, the Table.1 and equation (9)-(12) are the governing equations of the developed thermodynamic model for calculating mass action concentrations Ni of structural units or ion couples in the CaO-FeO-SiO2 slag. TABLE 1 EXPRESSION OF STRUCTURAL UNITS, THEIR MOLE NUMBERS AND MASS ACTION CONCENTRATIONS OF - 12 http://www.ivypub.org/rms
CaO-FeO-SiO2 SLAGS AT METALLURGICAL TEMPERATURE BASED ON THE ION AND MOLECULE COEXISTENCE THEORY.
Structural units
No
Reaction
G (J mol )
Mass action concentration
CaO·SiO2
4
(Ca2++O2-)+SiO2=CaO·SiO2
-18416-10.498T
N 4 K1 N1 N 2
-1
2CaO·SiO2
5
2(Ca +O )+ SiO2=3CaO·SiO2
-160431+4.016T
N 5 K 2 N12 N 2
3CaO·SiO2
6
3(Ca2++O2-)+ SiO2=3CaO·SiO2
-93366-23.03T
N 6 K 3 N13 N 2
2FeO·SiO2
7
2(Fe2++O2-)+ SiO2=2FeO·SiO2
-28595.84+3.349T
N 7 K 4 N 32 N 2
2+
2-
2.4 Model Establishing From what described above, the sequence of the established thermodynamic model for predicting the surface tension is shown in Fig.1. As shown in Fig.1, where the parameters K is the absolute temperature, and ni is the mole number of four components as CaO, FeO and SiO2 in 100 g of CaO-FeO-SiO2 slag to represent chemical composition of the slags. In addition, Kj is the chemical reaction equilibrium constant of formation complex molecules, IMCT represent the ion and molecule coexistence theory of slag structure. In addition, the chemical reaction equilibrium constant Kj Bulk Surf of formation complex molecules and the detail of N i and N i calculating model of CaO-FeO-SiO2 slag Pure system based on IMCT can be got from Table 1 [14] . Parameters of i and Ai used in the calculation are listed in Table 2 and 3 [1-3].
N iBulk can be calculated by mole fractions (or mass fraction) of components and the chemical reaction equilibrium Surf constant of complex molecule based on the ion and molecule coexistence theory. Further, and N i can be Bulk Pure calculated by N i , i and Ai based on the ion and molecule coexistence theory and the Butler’s equation. The model stated above can be extends to multi-component slag systems, so long as the bulk phase and the surface phase are both obeying the hypotheses of IMCT. Sample calculations have been made for ternary CaO-FeO-SiO2 slag system.
FIG.1 THE SEQUENCE OF THE MODEL FOR THE ESTIMATION OF THE SURFACE TENSION
TABLE 2. TEMPERATURE DEPENDENCE OF THE SURFACE TENSION OF THE PURE COMPONENTS
Components CaO FeO SiO2
Temperature (K) dependence of surface tension (mN/m) 791-0.0935 T 504-0.0984 T 243.+0.031 T - 13 http://www.ivypub.org/rms
TABLE 3. TEMPERATURE DEPENDENCE OF THE MOLAR VOLUME OF THE PURE COMPONENTS
Temperature (K) dependence of molar volume (m3/mol)
Components
20.7 1 110-4 T 1773 106 15.8 1 1 10-4 T 1773 106 27.516 1 110-4 T 1773 106
CaO FeO SiO2
3. Results and Discussions At a certain temperature, the calculation could carry out with certain slag components using the governing equations under the conditions of equilibrium state and the standard state. After linearization, Newton iterative method was used in Matlab software to gain all the mass action concentrations of each structural units or ion couples.
3.1 Model evaluation In order to evaluate the performance of the present model, the mean deviation defined as:
Mean deviation Where Calc and of the samples.
1 N
N
1
Calc Expe 100% Expe
(13)
Expe are the calculated and measured surface tension, respectively, and N represents the number
The surface tension data of melts of five different compositions in the system FeO-CaO-SiO2 were measured in the early publication [15], which has been well represented by the present model. The estimated surface tension was compared with the experimental surface tension data and is shown in Fig.2; the mean deviation was found to be 8.08%. Therefore, the present model provides a good description of the surface tension variation of the FeO-CaO-SiO2 system with regard to temperature and composition.
FIG.2 COMPARISON OF THE EVALUATED AND MEASURED SURFACE TENSION FOR THE CaO-FeO-SiO2 SYSTEM.
3.2 Model application The calculated results for the CaO-FeO-SiO2 system at 1573 K, 1623 K, 1673 K and 1708 K are shown in Fig.3. These results were basically consistent with the literature values at each temperature, although surface tension is larger estimated by the present model. The iso-surface tension curves in Fig.3, calculated using the current model, - 14 http://www.ivypub.org/rms
reproduce the composition dependence of surface tension for the CaO-FeO-SiO2 system, and show that its surface tension increases with increasing CaO content and decreases with increasing SiO2 content. Analyzing the iso-surface tension curves from Fig.3 (a), (b), (c) and (d), it can be seen that surface tension decreases with increasing temperature.
FIG.3 CALCULATED ISO-SURFACE TENSION LINES (MN/M) OF MOLTEN FEO-CAO-SIO2 SYSTEM AT (A) 1573 K, (B) 1623 K, (C) 1673 K AND (D) 1708 K.
4. Conclusions (1) Based on the ion and molecule coexistence theory (IMCT) of slag structure and Butler’s equation, a calculating model has been developed for determining the surface tension of CaO- FeO-SiO2 molten slags. (2) The evaluated results for the surface tension from the present model show good agreements with literature values in CaO-FeO-SiO2 ternary system. The mean deviation of the present model was found to be 8.08%. (3) The iso-surface tension lines of CaO-FeO-SiO2 slag melt have also been calculated. Surface tension of CaO-FeO-SiO2 slag decreases with increasing temperature and increasing SiO2 content and increases with increasing CaO content.
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Authors Chengchuan Wu (1988- ), male, ph.d.candidate, research interests are mainly in the area of metallurgical process for special steel and rare-earth steel.
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