Predication of Component Activities in the Molten Aluminosilicate Slag CaO-Al 2 O 3 -SiO 2 by Molecular Interaction Volume Model

Transcription

1 J. Mater. Sci. Technol., Vol.4 No.5, Predication of Component Activities in the Molten Aluminosilicate Slag CaO-Al O 3 -SiO by Molecular Interaction Volume Model Dongping TAO Faculty of Materials and Metallurgical Engineering, Kunming University of Science and Technology, Kunming , China [Manuscript received February 9, 007, in revised form June 1, 007] A novel thermodynamic model-the molecular interaction volume model ( which can be reduced to the Flory-Huggins equation of polymer solution was employed for the prediction of component activities in the ternary molten aluminosilicate slag CaO-Al O 3 -SiO at different temperatures. The results show that the predicted values of activity of CaO, Al O 3 and SiO are in reasonably agreement with experimental data in some ranges of their concentrations which are about x 1 <5 for CaO, x = for Al O 3 and x 3 =3 5 for SiO. This further shows that requires only two binary parameters for each sub-binary system to predict activities of all components in a multicomponent solution and is the superior alternative in a molten slag. KEY WORDS: Activity; Prediction; Molten aluminosilicate slag; Molecular interaction volume model 1. Introduction The molten aluminosilicate slag CaO-Al O 3 -SiO is a basic system for ironmaking, glass technology, igneous petrology and volcanology. Although it seems to be different only in substitution of Al O 3 for FeO in the CaO-FeO-SiO system previously published [1], the two components are virtually unlike in chemical property, for example, FeO is a basic oxide and Al O 3 is an amphoteric one, which results in the FeO bearing slags to be suitable for steelmaking and nonferrous metal smelting. It is indispensable to obtain activities of three components in the slag for understanding and describing chemical reactions of those elevated temperature processes. Recently Mclean [] pointed out that measurements and models should be considered as two interdependent requirements; and without measurements our models are incomplete and unsatisfactory; without models we fail to realize, or perhaps even comprehend, the potential significance of our measurements. During the past six decades, various thermodynamic models have been proposed for the prediction of component activities in ternary molten slags, which have been reviewed and commented in literatures [3 5]. In general, an over-simplified model leads multicomponent interaction parameters which are fitted by the multicomponent experimental data into modeling, whereas an over-complicated model brings about more restricted conditions in application, for example, Redlich-Kister polynomial and Gaye-Welfringer model [3] for silicate melts. So it is necessary to balance prediction accuracy and physical perspective due to lack of information about detailed melt structures and species interactions. The molecular interaction volume model ( [8 10] has certain physical meaning from the viewpoint of statistical thermodynamics and requires only two binary parameters for each sub-binary system for the prediction of compo- Prof., Ph.D., to whom correspondence should be addressed, dongpingt@yahoo.com.cn. nent activities in a multicomponent solution. The purpose of the work is further to show that is the superior alternative in a molten slag.. Simple Description of The was obtained from the physical perspective of molecular or atomic movements of liquid in that liquid molecules or atoms are differ from gas molecules which are being in continuous irregular motion and differ from solid ones which are vibrating constantly at lattice sites but are migrating non-randomly from one cell to another. It implied that the cell molecules are not stable and they have a chance to move into an adjacent hole as a central molecule, namely, it was assumed that liquid molecules can freely move through a cell space and the molecular interaction separation approaches the cell diameter at a certain temperature. Thus, the socalled central molecules and their closest molecules are relative and exchangeable, and cells are movable and indistinguishable. For a ternary solution there are three types of molecular cells and the molecular pair interaction taken into account. Its molar excess Gibbs energy can be expressed as [ ( G E ϕi m = RT x i ln + ε ] x i kt (1 where x i is the molar fraction of component i; ϕ i = x i V mi /V m the molar volume fraction of component i in the system; V mi and V m are the molar volumes of component and the system, respectively. The excess potential energy function of the system is ε p = ε p Z i x i ε ii ( and the mixing potential energy function ε p of the molecules can be chosen as ε p = 1 ( Z i x i x ji ε ji

2 798 J. Mater. Sci. Technol., Vol.4 No.5, 008 = 1 ( x j B ji ε ji where R i is the radius of a sphere whose volume is Z i x i 3 x (3 equivalent to that of the matter. Hence, Eq.(8 becomes jib ji where the pair-potential energy parameter is defined Q i = V Ni ( i πmkt 3Ni/ as N i h (10 B ji = exp[ (ε ji ε ii /kt ] (4 The local volume fraction of component i in the system is expressed as ξ i = x iiv mi = x ji V mj x i V mi, i = 1 to 3 (5 x j V mj B ji Thus, one can achieve a novel model of the molar excess Gibbs energy G E m of the system G E m RT = x i ln 1 V mi n x j V mj B ji Z i x j ( B ji ln B ji x j B ji In fact, Eq.(1 can be rearranged as G E m = N A ε + T R (6 ( ϕi x i ln = Hm E T Sm E (7 x i where Hm=N E A ε/ and Sm= R E 3 x i ln(ϕ i /x i are the molar excess enthalpy and molar excess entropy of the system, respectively. Thus, has naturally combined the excess entropy and excess enthalpy of a solution by means of new expressions of the configurational partition functions of liquids and their mixtures derived from statistical thermodynamics, which is approximate to actual solutions, that is and S E 0. If ε ji =ε ii or from Eqs.( to (4, then Eq.(7 can be reduced to the well-known Flory-Huggins equation [11] i.e., G E m=rt 3 x i ln(ϕ i /x i which is an essential equation for polymer solution. On the other hand, in the canonical partition function of pure liquid matter i can be obtained as Q i = 1 ( πmkt 3Ni/ Qpi N i h (8 [ π where Q pi = 0 sin θdθ ] π Ni= ( dxdydz Vi Niexp 0 N i ( Z i N i ε ii kt is the configurational partition function in which r i is the average radius of molecular cells of the matter. If molecules or atoms are free to move throughout the entire volume and their intermolecular forces approach zero, the in Eq.(8 becomes Q pi = [Q pi [ π = sin θdθ 0 ( exp π 0 Z ] iε Ni ii dxdydz kt Ri dϕ r Ni dr] = V N i i (9 0 This shows that the canonical partition function of a pure liquid matter can be exactly reduced to that of an ideal gas and thereby inserting the factor of e Ni into it artificially is avoided, where is expressed as the form k ln σ N i called the communal entropy and for the lower pressure gas but for liquid the σ is unclear, and addition of this factor is really only an ad hoc correction without theoretical justification [1], which means that liquid structure is not strict crystalline lattice. So this suggests that has certain physical meaning from the viewpoint of statistical thermodynamics and may be also called as complete free volume model. Then, under the conditions of i C, δ = 1, and i = C, where C is the number of all components in a mixture, based on the relation between partial molar and molar excess Gibbs energies G E i = RT ln γ i = G E mδ(εg E m/ε E m/εx i (11 where the subscript symbol x[j, C] represents that x j and x c are two variables for the partial differentiation and x C = 1 c 1 x j is a subordinate variable, the expression of activity coefficient of component i is thus deduced as V mi ln γ i = 1 + ln x j V mj B ji x j V mi B ij 1 ( Z i + x j B ji ln B ji x l V ml B lj Z j x j B ( x l B lj ln B lj ij ln B ij x l B lj x l B lj (1 3. Prediction of Component Activities in the CaO-Al O 3 -SiO Molten Slag At present, suppose that the coordination numbers of components CaO, Al O 3 and SiO in the CaO- Al O 3 -SiO molten slag are equivalent to those of their cations with positive valences Ca +, Al 3+ and Si 4+, i.e., Z i =6, 4, and 4, respectively [13]. And their molar volumes at melting point are 3, and 8.03 cm 3 mol 1, respectively [14]. The values of the parameters and can be determined by fitting the experimental data of activity of components in the i j molten slags CaO-Al O 3, Al O 3 -SiO and CaO-SiO using two expressions of Eq.(1 for a binary system, and Si, S j are the average fitting deviations of activities of two components i and j, respectively, as shown in Table 1 and Figs.1 to 3. The standard deviation is Si = ±[ 1 m (a i,exp a i ] 1/ (13 m and the relative error which is the values in parentheses in Table 1 is S i = ± 100 m a i,exp a i (14 m a i,exp

3 J. Mater. Sci. Technol., Vol.4 No.5, Table 1 The values of B ji, B ij and S i, S j, of the binary molten slag i j i j T, K B ji B ij ±Si ±Sj (ε ji ε ii/k, K (ε ij ε jj/k, K CaO-Al O (% 31.% Al O 3 -SiO (1% 6.% CaO-SiO (176% 137% Activity of CaO or Al O 3 Experiment CaO Al O Mole fraction of CaO Fig.1 Activity of CaO and Al O 3 in the CaO-Al O 3 system at 1773 K Activity of Al O 3 or SiO SiO Al O 3 Experimental Mole fraction of Al O 3 Fig. Activity of Al O 3 and SiO in the Al O 3 -SiO system at 1950 K 4 (a (b 3 Activity of CaO 1 Experimental Activity of SiO Experimental Mole fraction of CaO Mole fraction of CaO Fig.3 Activity of (a CaO and (b SiO in the CaO-SiO system at 1873 K where a i,exp and a i are the experimental data and the predicted values of activity of component i in the molten slags, respectively and m is the number of experimental data. From Figs.1 3 and Table 1, it can be seen that the agreement between calculated and experimental data is not good, especially for the CaO-SiO system, which could be considered that this model didn t express the relationship between micro-structural information and composition in the melts, and then failed to introduce some structural parameters. However, the energy parameters B ji and B ij characterize the non-ideality of those components in the binary molten slags because both of them are strongly associated with the infinite dilute activity coefficients γi and, i.e., γ j ln γ i ln γ j = 1 ln(v mj B ji /V mi V mi B ij /V mj (1/(Z i ln B ji + Z j B ij ln B ij (15 = 1 ln(v mi B ji /V mj V mj B ji /V mi (1/(Z j ln B ij + Z i B ji ln B ji (16 Let us assume that the pair-potential energy parameters in Eq.(4, (ε ji ε ii /k and (ε ij ε jj /k, are independent of temperature. Thus, one can get the values of B ji and B ij at other temperature from Eq.(4 if the values of B ji and B ij at given temperature are known. For example, in the binary molten slag CaO-Al O 3 in Table 1 there are (ε ji ε ii /k = T ln B ji = 1773 ln(1.85 = 1091 K, B ji = exp(1091/1873 = 1.4 at 1873 K (ε ij ε jj /k = T ln B ij = 1773 ln(1.45 = K, B ij = exp(658.8/1873 = 1.4 at 1873 K Here notice that if the activity standard state for one component i at saturation in the binary i j is saturation or pure solid, then the activities calculated by, a i, should be transferred to those at same situation or saturation standard state, a i,sat, because

4 800 J. Mater. Sci. Technol., Vol.4 No.5, 008 Table Comparison of the predicted values from with the experimental data [0] of activity of CaO in the molten slag CaO- SiO -Al O 3 at 1873 K m=4 a 1 x 1 x x 3 Experimental x /x / / / / / / / / / S1 =0.100 S 1 =±39.0% itself is suitable for a range of entire concentration, namely, for the saturation standard state a i,sat = γ i,sat =1 and γ i,sat = 1/x i,sat =1/x i,sat at x i =x i,sat ; for the pure matter standard state, a i =γ i x i =1 and γ i =1 at x i =1, so their transfer relation is a i,sat = γ i,sat a i /x i,sat (17 Similarly, for a ternary system 1--3 its one component saturation may be approached as the related binary saturations weighed by two other component concentrations, namely, x 1(1 3,sat = x x + x 3 x 1(1,sat + x 3 x + x 3 x 1(1 3,sat (18 For the ternary molten slag SiO -Al O 3 -CaO the saturation of component SiO can be estimated Table 3 Comparison of the predicted values from with the experimental data [1] of activity of CaO in the molten slag CaO- SiO -Al O 3 at 183 K m=47 a 1 x 1 x x 3 Experimental S1 =±07 S 1 =±93.5% from Eq.(18. Based on the related binary phase diagrams [19], one can choose that for the SiO -Al O 3 system x 1(1 3,sat =0.917 at K, and for the SiO -CaO system x 1(1 3,sat =0,, 4 and 6 at 173, 1773, 183 and 1873 K, respectively. Denoting the CaO-SiO -Al O 3, Al O 3 -CaO-SiO and SiO -CaO-Al O 3 molten slags as the 1--3 system, the activity coefficient of the component 1 can be calculated from Eq.(1 and Eq.(18 by using the coordination numbers and molar volumes of components CaO, SiO and Al O 3 mentioned previously and the binary parameters and from Table 1. The results are shown in Tables to 6 and Fig.4. It can be seen from the Tables and Figure that (1 the predicted values of activity of CaO are in reason-

5 J. Mater. Sci. Technol., Vol.4 No.5, (a 1873 K (b 183 K (c 1773 K (d 173 K Fig.4 Comparison of the predicted values from with the experimental data of activity of SiO in the SiO -CaO-Al O 3: (a at 1873 K, (b at 183 K, (c at 1773 K and (d at 173 K, solid lines: a 1=a 1,exp Table 4 Comparison of the predicted values from with the experimental data [0] of activity of Al O 3 in the molten slag Al O 3- CaO-SiO at 1873 K m=14 a 1 x 1 x x 3 Experimental S 1 =±93 S 1 =±16.6% ably agreement with experimental data in a range of lower concentration which is about <5 for CaO and in a range of ratio which is about more than 3/; ( those of Al O 3 are better at 1873 K except the values of activity of 0.75, and at 183 K the character of activity of Al O 3 from is being gradually shifted from negative deviation to positive one with decreasing the simple basicity x /x 3, which is consistent with the case at 1873 K; and (3 the predicted values of activity of SiO are in better agreement with experimental data in a range of entire concentrations at four temperatures, especially at 1873 K, but the standard deviation is increasing with decreasing temperature, which may be attributed to the assumption that the pair-potential energy parameters in Eq.(4, (ε ji ε ii /k and (ε ij ε jj /k, are independent of temperature. On the other hand, it can be seen from Table 4 that the standard deviations ±S1 of predicted values of components in the ternary systems, in principle, are less than or almost correspond to the average standard deviations ±S1 of fitted values of activity of components in the binary systems. It may be inferred that the pair-potential energy parameters B ji and B ij obtained by fitting can characterize the key information about binary molecular interaction which play an important role in a ternary system. If a better fit in the binary molten slags can be obtained, the Table 5 Comparison of the predicted values from with the experimental data [1] of activity of Al O 3 in the molten slag Al O 3- CaO-SiO at 183 K m=47 a 1 x 1 x x 3 Experimental S1 =0.114 S 1 =±58.0% predicted results in a ternary molten slag would be better, which should be similar to the case of multicomponent liquid alloys [8 10].

6 80 J. Mater. Sci. Technol., Vol.4 No.5, 008 Table 6 The standard deviations and the relative errors of predicted values of activities of three components in the ternary molten slag CaO-Al O 3 -SiO System 1--3 T /K m ±S 1 ±S 1 /% ±S 1 ±S 1/% CaO-SiO -Al O Al O 3-CaO-SiO SiO -CaO-Al O Conclusions The predicted values of activity of CaO, Al O 3 and SiO by the molecular interaction volume model ( in the ternary molten aluminosilicate slag CaO-Al O 3 -SiO at different temperatures are in reasonably agreement with experimental data in some ranges of their concentrations which are about <5 for CaO, x = for Al O 3 and x 3 =3 5 for SiO. The results show that can estimate activity coefficients of all components in the ternary aluminosilicate slag or oxide melt where its activity data are absent or their accuracies are questionable only when its sub-binary activities are known and reasonably reliable. Acknowledgements Financial support from the National Natural Science Foundation of China under grant No and the Applied Fundamental Research Foundation of Yunnan Province under Grant No. 006E001M are gratefully acknowledged. REFERENCES [1 ] D.P.Tao: Metall. Mater. Trans. B, 006, 37B, [ ] A.Mclean: Metall. Mater. Trans. B, 006, 37B, 319. [3 ] H.A.Fine and D.R.Gaskell ed.: Second International Symposium on Metallurgical Slags and Fluxes, The Metallurgical Society of AIME, PA, USA, 1984, [4 ] B.O.Mysen: Structure and Properties of Silicate Melts, Elsevier Science Publishers, Amsterdam, The Netherlands, 1988, [5 ] Y.Waseda and J.M.Toguri: The Structure and Properties of Oxide Melts, World Scientific Publishing Co. Pte. Ltd. Singapore, 1998, [6 ] H.Mao, M.Selleby and B.Sundman: J. Am. Ceram. Soc., 005, 88, 544. [7 ] H.Mao, M.Hillert, M.Selleby and B.Sundman: J. Am. Ceram. Soc., 006, 89, 98. [8 ] D.P.Tao: Thermochimica Acta, 000, 363, 105. [9 ] D.P.Tao: Metall. Mater. Trans. A, 004, 35A, 419. [10] D.P.Tao: J. Mater. Sci. Technol., 006,, 559. [11] J.M.Prausnitz, R.N.Lichtenthaler and E.G.D.Azevedo: Molecular Thermodynamics of Fluid-Phase Equilibria, nd ed., Prentice-Hall Inc., Englewood Cliffs, NJ, 1986, [1] A.Munster: Statistical Thermodynamics, vol.ii, Academic Press, New York, 1974, [13] M.B.Volf: Chemical Approach to Glass, Elsevier Science Publishers, Amsterdam, The Netherlands, 1984, [14] E.T.Turkdogan: Physicochemical Properties of Molten Slags and Glasses, The Metals Society, London, UK, 1983, 3-5, 95, 105. [15] R.A.Sharma and F.D.Richardson: J. Iron Steel Inst., 1961, 198, 386. [16] V.V.Bondar, S.I.Lopatin and V.L.Stolyarova: Inorg. Mater, 005, 41, 36. [17] Y.X.Zou, J.C.Zhou, Y.S.Xu and P.N.Zhao: Acta Metall. Sinica, 198, 18, 17. (in Chinese [18] J.C.Zhou, Y.X.Zou, P.N.Zhao and H.M.Li: Acta Metall. Sinica, 1988, 4(Suppl.1, SB. (in Chinese [19] X.H.Huang: Principles of Ironmaking and Steelmaking, 3rd ed., The Metallurgical Industry Publisher, Beijing, 00, (in Chinese [0] R.H.Rein and J.Chipman: Trans. Metall. Soc. AIME, 1965, 33, 415. [1] K.Kume, K.Morita, T.Miki and N.Sano: ISIJ Inter., 000, 40, 561. [] D.A.R.Kay and J.Taylor: Trans. Faraday Soc., 1960, 56, 137.