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Molecular dynamics simulations of silicate slags and slag–solid interfaces
Journal of Non-Crystalline Solids 282 (2001) 24±29
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Molecular dynamics simulations of silicate slags and slag±solid interfaces Ling Zhang *, Shouyi Sun, Sharif Jahanshahi G K Williams Cooperative Research Centre for Extractive Metallurgy, CSIRO Minerals, P.O. Box 312, Clayton South, Vic. 3169, Australia
Abstract Molecular dynamics (MD) simulations of silicate melts and melt±solid interfaces were carried out by using ionic force ®eld in the form of the Born±Mayer±Huggins (BMH) pair potential. The study includes structural properties of the binary CaO±SiO2 and ternary CaO±Al2 O3 ±SiO2 melts, with particular focus on the structural role played by Al2 O3 in the silicate melts. Structural properties such as the fractions of dierent types of oxygen atoms have been obtained. It was found that as Al2 O3 gradually replaces CaO in a silicate, an increasing amount of `triclusters' (three-coordinated oxygen) forms in the melts. In the slag/MgO interface simulation, interfacial energy and distribution of elements at the interface were calculated. Magnesium atoms were found to be enriched at the interface. Information obtained from the simulations provides an insight and an improved understanding of the relationship between structure and properties of the silicate melts as well as the melt±solid interfaces. Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction Since the success of molecular dynamics (MD) simulation of silica carried out by Woodcock et al. [1] by using the Born±Mayer±Huggins (BMH) pair potential, there have been many attempts at MD simulations of silicate systems in the form of crystals, glasses and liquids [2±5]. These studies together with experimental techniques, such as X-ray diraction (XRD), Raman and nuclear magnetic resonance (NMR) spectroscopy have contributed to our understanding of the structure of silicate glasses and liquids in recent years.
* Corresponding author. Tel.: +61-3 9545 8500; fax: +61-3 9562 8919. E-mail address: [email protected] (L. Zhang).
A detailed discussion of the experimental ®ndings on the structure of the silicate and aluminosilicate melts and glasses can be found in an article by Gaskell [6]. It is generally accepted [7] that due to the bonding between Si and O atoms, the silicon atoms in silicate liquids are almost always associated with four oxygen atoms and exist as SiO44 , which link up to form dierent sized anion groups. Other singly or doubly charged metal ions surround these anions to maintain local neutrality. The degree of polymerisation in a liquid increases with increasing silica content. The notion of three types of oxygen, namely, free (O2 ), non-bridging (O , bonded to one Si) and bridging oxygen (O0 , bonded to two Si) has been used to indicate the degree of polymerisation. Alumina in a liquid is generally regarded as amphoteric [8]. This property is partly based on the observations of extrema in viscosity and other
0022-3093/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 1 ) 0 0 3 2 5 - 8
L. Zhang et al. / Journal of Non-Crystalline Solids 282 (2001) 24±29
physical properties of aluminosilicate glasses and liquids as functions of the ratio of R (Al2 O3 =Mx O, where M denotes the metal cations, such as Na and Ca) [5,9]. These extrema are attributed to the structural changes brought about by alumina. Zirl and Garofalini [5] discussed three structural models based on dierent experimental data to explain the changes in physical properties. They also presented the results from their MD simulation study of the sodium aluminosilicate glass [5]. Their ®ndings are consistent with one of the proposed structural models [10,11]. This model introduced triclusters which form by connecting three tetrahedra to the fourth type of oxygen, i.e., the three-coordinated oxygen (O3 ). They also found that the fraction of triclusters in the system increased with the R ratio. An understanding of the interaction between liquid and solid oxides is useful both in designing improved practice in smelting processes as well as optimisation of sintering of oxide ceramics involving a liquid phase. Our recent work has been aimed at exploring the potential of the simulation technique in applying to metallurgical slags and related systems [12±15]. The studies carried out include the structure of the CaO±SiO2 [12] and CaO±Al2 O3 ±SiO2 melts [13] and the properties of slag/solid interfaces [14,15].
2. Computational method Ionic type of force ®eld such as the BMH pair potential has been used for silicate systems. It has been shown that the main structural features of silicate systems can be reproduced reasonably well by using the BMH potential [4]. The original form of the BMH potential between two ions i and j was expressed as Zi Zj e2 Zi Zj ri rj r Uij r 1 ; b exp q 4pe0 r ni nj 1 where r is the distance between the two ions, Zi is the valence of the ion i, e is the electron charge, e0 is the dielectric constant, ni is the number of outer
25
shell electrons of the ion i, ri is the characteristic ionic radius, and b and q are constants. The ®rst term in Eq. (1) is the Coulombic term which describes the electrostatic interactions between charged particles. The second term is for the shortrange repulsion. A simpli®ed form of the BMH potential is commonly seen in the literature as Uij r
Zi Zj e2 Aij exp 4pe0 r
r ; Bij
2
where the parameters Aij and Bij can be obtained by ®tting the crystal structure or other properties of the ionic system [2]. Two dierent simulation packages and programs [16,17] have been used for the present work. The simulation of the CaO±SiO2 melts was carried out using a modi®ed version of the MOLDY [16] program. The force ®eld parameters were due to Belashchenko et al. [3] by using Eq. (2). The MSI Cerius2 (glass_1.01force ®eld) [17] was used for the CaO±Al2 O3 ±SiO2 melts and slag/MgO interface simulations. In both programs the long-range Coulomb interactions were treated by the Ewald sums technique. The general procedures for the simulation of amorphous phases were followed [12]. The simulation of slag alone was performed in a cubic box of constant volume with periodical boundaries. The atoms in the simulation box were started from a random con®guration at 6000 K followed by a cooling process that brought the system to a temperature at which the equilibrium data were collected. The simulation of the slag phase was performed in a constant energy and constant volume ensemble (NVE). The simulations of slag/solid interface involve the following three steps: 1. Preparation of slag cells ± the procedure is the same as described above in which the atoms in the box were brought to equilibrium state. 2. Preparation of solid ± a unit cell of crystal MgO was taken from MSI Cerius2 database [17] and multiplied in three dimensions. It was then shaped into a cubic cell. 3. Interface simulations ± a standard procedure of interface building from the instruction of the MSI Cerius2 package [17] was followed. The slag and solid cells prepared in the above two
26
L. Zhang et al. / Journal of Non-Crystalline Solids 282 (2001) 24±29
steps were brought together. During the simulation, periodical boundary conditions were used for the interface box. The coordinates of atoms in the crystal phase were ®xed, while the atoms in the slag cell were allowed to relax until the interface system reached equilibrium. The simulation results in terms of interfacial energy and elemental distribution at the interface were subsequently collected.
3. Results 3.1. Structure of CaO±SiO2 melts at 2000 K MD simulations were carried out at four compositions for the CaO±SiO2 melts (mole fractions of silica were XSiO2 0:2, 0.333, 0.5 and 0.667) to determine the composition dependence of the fractions of free (NO2 ), bridging (NO0 ) and nonbridging (NO ) oxygen. Details of the simulation conditions can be found in one of our early publications [12]. The results are shown in Fig. 1 where they are compared with the experimental data
Fig. 1. Comparison of the MD simulation results (solid symbols) with the data from experimental (open symbols) and thermodynamic modelling studies (solid lines) on the composition dependence of the fractions of free (NO2 ), bridging (NO0 ) and non-bridging (NO ) oxygen in the CaO±SiO2 melts.
obtained from the Raman spectra study of Tsunawaki et al. [18]. The calculated fractions for the three types of oxygen by using the cell model (a thermodynamic model) [19,20] are also shown in the ®gure. 3.2. Structure of CaO±Al2 O3 ±SiO2 liquids at 2000 K Simulation of the CaO±Al2 O3 ±SiO2 liquids was performed with a ®xed mole fraction of silica, i.e., XSiO2 0:4. The R ratio, (Al2 O3 =CaO) took the values of 0.2, 0.5, 1.0 and 2.0 so that the structural changes with increasing alumina could be investigated. The system size in this work is 900±1080 atoms depending on composition. The results were the average of 100 values collected during 20 ps runs with a time step of 1 fs. The calculated fractions of four types of oxygen as functions of the Al2 O3 content are presented in Fig. 2. 3.3. Slag/MgO interface at 2400 K The current work was an attempt in examining the interfacial contact between solid MgO and silicate melts. The liquid was a ternary CaO± MgO±SiO2 system (800 atoms). The composition of the liquid was XCaO 0:6, XMgO 0:2, and
Fig. 2. Variation in the fraction of four types of oxygen as a function of the mole fraction of Al2 O3 in the CaO±Al2 O3 ±SiO2 melts. The lines are drawn to guide the eye.
L. Zhang et al. / Journal of Non-Crystalline Solids 282 (2001) 24±29
XSiO2 0:2. Two orientations of the MgO crystal were chosen such that the (1 0 0) or the (1 1 1) crystal plane was in contact with the liquid. The crystal box contained 500 atoms. The time step used was 1 fs and the results were the average of 100 values collected during 20 ps runs. The distribution of the elements, i.e., Ca, Mg, Si and O by diwas analysed for the liquid layer (20 A) viding it into 20 thin slices. The results shown in Fig. 3 are the ratio of the real number of atoms N (DL) over the average number of atoms N(average) in each slice. In other words, if the atoms are evenly distributed in each slice, the ratio should be unity throughout the liquid layer. 4. Discussions 4.1. Structure of CaO±SiO2 melts at 2000 K The composition dependence of the fractions of free (NO2 ), bridging (NO0 ) and non-bridging (NO ) oxygen presented in Fig. 1 showed that the results from the MD simulation, the values cal-
27
culated by the cell model and the experimental data are in close agreement. The fraction of bridging oxygen, NO0 , increases as the mole fraction of silica (XSiO2 ) increases beyond 1/3. Note in particular that a maximum for the fraction of nonbridging oxygen atoms is obtained at a silica mole fraction of about 1/3. According to Lin and Pelton [21], the maximum NO in binary silicate MO±SiO2 melts at the orthosilicate composition is dependent on the relative basicity of MO, and the more basic MO, the closer NO is to unity. Calcium oxide is one of the strongest basic oxides found in metallurgical melts. The maximum NO in the calcium silicate melts is about 0.9. The distributions of silicate anions of dierent sizes (NSi ) were calculated from the simulation results for the four compositions of XSiO2 0:2, 0.333, 0.5 and 0.667. The NSi s were from one to six to represent silicate anions ranging from monomers (SiO44 ) to complex chains and rings of silicates with dierent number of Si per species. No direct experimental data on the calcium silicate system are available. The results from the MD simulations were compared with the results of
Fig. 3. Distribution of each type of elements in the liquid (CaO±MgO±SiO2 ) layer (20 DL slices) of the slag/MgO interface: (a) melt in contact with 100 plane; (b) melt in contact with 111 plane. In (b) the crystal plane of Mg-(1 1 1) is on the left-hand side of the box and O-(1 1 1) on the right.
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L. Zhang et al. / Journal of Non-Crystalline Solids 282 (2001) 24±29
calculations based on the cell model [21] and a statistical treatment [22]. A broad agreement between the two sets of results was obtained. According to these results, when the mole fraction of silica is 0.2, the system consists of mainly SiO44 monomers with a small amount of dimers Si2 O67 . At the silica-rich end, mole fraction of SiO2 > 0:66, large anions predominate. Between these two compositions, an increasing degree of polymerisation is apparent. These results demonstrate that MD simulation can be used to study medium- and long-range structures in silicate melts. It may complement the limited experimental capabilities in this respect.
4.3. Slag/MgO interface at 2400 K
4.2. Structure of the CaO±Al2 O3 ±SiO2 melts at 2000 K
cL=S Etotal
The aim of this study was to investigate the eect of Al2 O3 (or R ratio) on the structural properties in CaO±Al2 O3 ±SiO2 liquids at a ®xed SiO2 content. The calculated fractions of dierent types of oxygen in Fig. 2 showed that the degree of polymerisation (fraction of bridging oxygen) of these melts increases with increasing mole fraction of Al2 O3 or R. The bridging oxygen can be one of the three bonding con®gurations, i.e., Al±O±Al, Al±O±Si and Si±O±Si. Existence of triclusters or a fourth type of oxygen, i.e., a three-coordinated oxygen, O3 , was also found, at a few percent of the total oxygen. We note that the number of triclusters increases with the increasing mole fraction of Al2 O3 or R. The majority of the triclusters were three tetrahedra of AlO54 . The remaining triclusters were two AlO54 and one SiO44 . Triclusters of three SiO44 or two SiO44 and one AlO54 were not found. Furthermore, the O3 ±Al bond was found to be about 2.5% longer than other O±Al bonds of 1.74 A. Because of this the stability of the connections of the tetrahedra is expected to be less than the normal connection of two tetrahedra. We infer that the increase in the number of triclusters in the liquids with increasing R could create weak points between the linkage of the anions which cause the extremes in viscosities of the liquids found by experiments.
An analysis of the distribution of elements at the slag/MgO interface (Fig. 3) showed that Mg and Si atoms tend to increase near the liquid/ MgO(1 0 0) interface and Mg and Ca near the liquid/MgO(1 1 1) interface (oxygen surface). Such a re-arrangement of elements is driven by the energy requirement of the system. For both the (1 0 0) and (1 1 1) crystal orientations, a decrease in energy was found which is mainly due to the formation of chemical bonds established between the ions in the liquid and the MgO surface. The interfacial energy, cL=S , has been calculated by EMgO
Emelt =2A;
3
where Etotal is total energy of the interface cell, EMgO is the energy of an interior MgO crystal cell, Emelt is the energy for the interior of a silicate liquid and A is the cross-sectional area of the interface. The calculated values are )0.58 and )8.0 (N/m) for (1 0 0) and (1 1 1) crystal plane, respectively. The absolute magnitudes from the MD simulation may not agree with the measured magnitudes as the model systems used here may be oversimpli®ed, limited by the methods used. The factors such as the small size of the system and the unrelaxed surface atoms of the MgO block will have in¯uence on the accuracy of the results. However, the structural information obtained for a model interface at the atomic level which cannot be obtained otherwise is assumed to be useful. 4.4. Limitations and potential of molecular simulations The MD simulations of model systems using the BMH potential described above have demonstrated the potential of the technique. Information on the liquid structure and its relation to the other properties can be obtained. Such information at the atomic level is dicult or sometime impossible to obtain by any other means. However, the development is still at its early stage in applying the technique to practical problems. One frequently encountered problem is the availability
L. Zhang et al. / Journal of Non-Crystalline Solids 282 (2001) 24±29
and reliability of the force ®eld used for the simulations. This limitations is due to 1. the force ®eld parameters for some common elements, such as Fe, in metallurgical systems are not readily available; 2. the available force ®eld parameters in the current form may not adequately describe some effects, such as polarisation of the ions and crystal ®eld eect for transition metals. Re®nement and improvement in the force ®eld representation, together with more ecient algorithm, and more powerful computers will enable a better simulation of more realistic systems for metallurgical applications. 5. Conclusions We have carried out MD simulations in the study of structural properties in the silicate melts and MgO/solid interfaces. · The structural information obtained for the CaO±SiO2 melts is in accord with the experimental data and theoretical predictions. · Triclusters were found in the CaO±Al2 O3 ±SiO2 liquids that provides useful information in understanding the structural role played by alumina. · Mg atoms have a tendency to be enriched at a slag/MgO interface. The approaches developed in this work can be re®ned and applied to examine the trends in energetics and structural aspects for dierent slag/solid interface systems. The results presented in the present paper have demonstrated the usefulness and potential of the technique in obtaining information on the structural and interfacial properties of metallurgical systems. Acknowledgements Financial support for this work was provided by BHP, MIM, Rio Tinto and Pasminco through the Australian Mineral Industries Research Association Limited (AMIRA) and the Australian Government Cooperative Research Centres Pro-
29
gram through the G.K. Williams Cooperative Research Centre for Extractive Metallurgy, a joint venture between the CSIRO±Division of Minerals and The University of Melbourne ± Department of Chemical Engineering.
References [1] L.V. Woodcock, C.A. Angell, P. Cheeseman, J. Chem. Phys. 65 (1976) 1565. [2] D.K. Belashchenko, Russ. Chem. Rev. 66 (1997) 733. [3] D.K. Belashchenko, I.E. Gopengauz, A.B. Grytsenko, O.I. Ostrovskij, ISIJ Int. 32 (1992) 990. [4] H. Ogawa, Y. Waseda, Sci. Rep. Res. Inst., Tohoku Univ., Ser. A 36 (1991) 20. [5] D.M. Zirl, S.H. Garofalini, J. Am. Ceram. Soc. 173 (1990) 2848. [6] D.R. Gaskell, in: Fifth International Conference on Molten Slags, Fluxes and Salts'97, Sydney, Iron and Steel Society, London, 1997, p. 11. [7] Y. Waseda, Can. Metall. Quart. 20 (1981) 57. [8] G. Urbain, F. Cambier, M. Deletter, M.R. Anseau, Trans. J. Br. Ceram. Soc. 80 (1981) 139. [9] P. Kozakevitch, Rev. Metall. 57 (1960) 149. [10] E.D. Lacy, Phys. Chem. Glasses 4 (1963) 234. [11] G. Engelhardt, M. Nofz, K. Forkel, F.G. Wihsmann, M. Magi, A. Samoson, E. Lippmaa, Phys. Chem. Glasses 26 (1985) 157. [12] L. Zhang, A. Dockery, S. Jahanshahi, in: Z. Yu, Z. Xiao, X. Xie (Eds.), Proceedings of the International ConferenceMSMM'96, Chinese Society for Metals, Beijing, 1996, p. 94. [13] L. Zhang, S. Sun, S. Jahanshahi, in: Third Australian Molecular Modelling Workshop, Melbourne, 1997, p. 32. [14] L. Zhang, S. Sun, S. Jahanshahi, in: Proceedings of the Fourth Australian Molecular Modelling Conference and Workshop, Sydney, 1998, p. 29. [15] L. Zhang, I. Yarovsky, in: Proceedings of the Fourth Australian Molecular Modelling Conference and Workshop, Sydney, 1998, p. 32. [16] K. Refson, MOLDY User's Manual, Oxford, 1993. [17] Molecular Simulation Inc. http://www.msi.com. [18] Y. Tsunawaki, N. Iwamoto, T. Hattori, A. Mitsuishi, J. Non-Cryst. Solids 44 (1981) 369. [19] M.L. Kapoor, M.G. Frohberg, Chemical Metallurgy of Iron and Steel, Iron and Steel Institute, London, 1971, p. 17. [20] L. Zhang, S. Sun, S. Jahanshahi, in: Z. Yu, Z. Xiao, X. Xie (Eds.), Proceedings of the International ConferenceMSMM'96, Chinese Society for Metals, Beijing, 1996, pp. 88. [21] P.L. Lin, A.D. Pelton, Metall. Trans. B 10B (1979) 667. [22] D.R. Gaskell, Can. Metall. Quart. 20 (1981) 3.
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Molecular dynamics simulations of silicate slags and slag±solid interfaces Ling Zhang *, Shouyi Sun, Sharif Jahanshahi G K Williams Cooperative Research Centre for Extractive Metallurgy, CSIRO Minerals, P.O. Box 312, Clayton South, Vic. 3169, Australia
Abstract Molecular dynamics (MD) simulations of silicate melts and melt±solid interfaces were carried out by using ionic force ®eld in the form of the Born±Mayer±Huggins (BMH) pair potential. The study includes structural properties of the binary CaO±SiO2 and ternary CaO±Al2 O3 ±SiO2 melts, with particular focus on the structural role played by Al2 O3 in the silicate melts. Structural properties such as the fractions of dierent types of oxygen atoms have been obtained. It was found that as Al2 O3 gradually replaces CaO in a silicate, an increasing amount of `triclusters' (three-coordinated oxygen) forms in the melts. In the slag/MgO interface simulation, interfacial energy and distribution of elements at the interface were calculated. Magnesium atoms were found to be enriched at the interface. Information obtained from the simulations provides an insight and an improved understanding of the relationship between structure and properties of the silicate melts as well as the melt±solid interfaces. Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction Since the success of molecular dynamics (MD) simulation of silica carried out by Woodcock et al. [1] by using the Born±Mayer±Huggins (BMH) pair potential, there have been many attempts at MD simulations of silicate systems in the form of crystals, glasses and liquids [2±5]. These studies together with experimental techniques, such as X-ray diraction (XRD), Raman and nuclear magnetic resonance (NMR) spectroscopy have contributed to our understanding of the structure of silicate glasses and liquids in recent years.
* Corresponding author. Tel.: +61-3 9545 8500; fax: +61-3 9562 8919. E-mail address: [email protected] (L. Zhang).
A detailed discussion of the experimental ®ndings on the structure of the silicate and aluminosilicate melts and glasses can be found in an article by Gaskell [6]. It is generally accepted [7] that due to the bonding between Si and O atoms, the silicon atoms in silicate liquids are almost always associated with four oxygen atoms and exist as SiO44 , which link up to form dierent sized anion groups. Other singly or doubly charged metal ions surround these anions to maintain local neutrality. The degree of polymerisation in a liquid increases with increasing silica content. The notion of three types of oxygen, namely, free (O2 ), non-bridging (O , bonded to one Si) and bridging oxygen (O0 , bonded to two Si) has been used to indicate the degree of polymerisation. Alumina in a liquid is generally regarded as amphoteric [8]. This property is partly based on the observations of extrema in viscosity and other
0022-3093/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 1 ) 0 0 3 2 5 - 8
L. Zhang et al. / Journal of Non-Crystalline Solids 282 (2001) 24±29
physical properties of aluminosilicate glasses and liquids as functions of the ratio of R (Al2 O3 =Mx O, where M denotes the metal cations, such as Na and Ca) [5,9]. These extrema are attributed to the structural changes brought about by alumina. Zirl and Garofalini [5] discussed three structural models based on dierent experimental data to explain the changes in physical properties. They also presented the results from their MD simulation study of the sodium aluminosilicate glass [5]. Their ®ndings are consistent with one of the proposed structural models [10,11]. This model introduced triclusters which form by connecting three tetrahedra to the fourth type of oxygen, i.e., the three-coordinated oxygen (O3 ). They also found that the fraction of triclusters in the system increased with the R ratio. An understanding of the interaction between liquid and solid oxides is useful both in designing improved practice in smelting processes as well as optimisation of sintering of oxide ceramics involving a liquid phase. Our recent work has been aimed at exploring the potential of the simulation technique in applying to metallurgical slags and related systems [12±15]. The studies carried out include the structure of the CaO±SiO2 [12] and CaO±Al2 O3 ±SiO2 melts [13] and the properties of slag/solid interfaces [14,15].
2. Computational method Ionic type of force ®eld such as the BMH pair potential has been used for silicate systems. It has been shown that the main structural features of silicate systems can be reproduced reasonably well by using the BMH potential [4]. The original form of the BMH potential between two ions i and j was expressed as Zi Zj e2 Zi Zj ri rj r Uij r 1 ; b exp q 4pe0 r ni nj 1 where r is the distance between the two ions, Zi is the valence of the ion i, e is the electron charge, e0 is the dielectric constant, ni is the number of outer
25
shell electrons of the ion i, ri is the characteristic ionic radius, and b and q are constants. The ®rst term in Eq. (1) is the Coulombic term which describes the electrostatic interactions between charged particles. The second term is for the shortrange repulsion. A simpli®ed form of the BMH potential is commonly seen in the literature as Uij r
Zi Zj e2 Aij exp 4pe0 r
r ; Bij
2
where the parameters Aij and Bij can be obtained by ®tting the crystal structure or other properties of the ionic system [2]. Two dierent simulation packages and programs [16,17] have been used for the present work. The simulation of the CaO±SiO2 melts was carried out using a modi®ed version of the MOLDY [16] program. The force ®eld parameters were due to Belashchenko et al. [3] by using Eq. (2). The MSI Cerius2 (glass_1.01force ®eld) [17] was used for the CaO±Al2 O3 ±SiO2 melts and slag/MgO interface simulations. In both programs the long-range Coulomb interactions were treated by the Ewald sums technique. The general procedures for the simulation of amorphous phases were followed [12]. The simulation of slag alone was performed in a cubic box of constant volume with periodical boundaries. The atoms in the simulation box were started from a random con®guration at 6000 K followed by a cooling process that brought the system to a temperature at which the equilibrium data were collected. The simulation of the slag phase was performed in a constant energy and constant volume ensemble (NVE). The simulations of slag/solid interface involve the following three steps: 1. Preparation of slag cells ± the procedure is the same as described above in which the atoms in the box were brought to equilibrium state. 2. Preparation of solid ± a unit cell of crystal MgO was taken from MSI Cerius2 database [17] and multiplied in three dimensions. It was then shaped into a cubic cell. 3. Interface simulations ± a standard procedure of interface building from the instruction of the MSI Cerius2 package [17] was followed. The slag and solid cells prepared in the above two
26
L. Zhang et al. / Journal of Non-Crystalline Solids 282 (2001) 24±29
steps were brought together. During the simulation, periodical boundary conditions were used for the interface box. The coordinates of atoms in the crystal phase were ®xed, while the atoms in the slag cell were allowed to relax until the interface system reached equilibrium. The simulation results in terms of interfacial energy and elemental distribution at the interface were subsequently collected.
3. Results 3.1. Structure of CaO±SiO2 melts at 2000 K MD simulations were carried out at four compositions for the CaO±SiO2 melts (mole fractions of silica were XSiO2 0:2, 0.333, 0.5 and 0.667) to determine the composition dependence of the fractions of free (NO2 ), bridging (NO0 ) and nonbridging (NO ) oxygen. Details of the simulation conditions can be found in one of our early publications [12]. The results are shown in Fig. 1 where they are compared with the experimental data
Fig. 1. Comparison of the MD simulation results (solid symbols) with the data from experimental (open symbols) and thermodynamic modelling studies (solid lines) on the composition dependence of the fractions of free (NO2 ), bridging (NO0 ) and non-bridging (NO ) oxygen in the CaO±SiO2 melts.
obtained from the Raman spectra study of Tsunawaki et al. [18]. The calculated fractions for the three types of oxygen by using the cell model (a thermodynamic model) [19,20] are also shown in the ®gure. 3.2. Structure of CaO±Al2 O3 ±SiO2 liquids at 2000 K Simulation of the CaO±Al2 O3 ±SiO2 liquids was performed with a ®xed mole fraction of silica, i.e., XSiO2 0:4. The R ratio, (Al2 O3 =CaO) took the values of 0.2, 0.5, 1.0 and 2.0 so that the structural changes with increasing alumina could be investigated. The system size in this work is 900±1080 atoms depending on composition. The results were the average of 100 values collected during 20 ps runs with a time step of 1 fs. The calculated fractions of four types of oxygen as functions of the Al2 O3 content are presented in Fig. 2. 3.3. Slag/MgO interface at 2400 K The current work was an attempt in examining the interfacial contact between solid MgO and silicate melts. The liquid was a ternary CaO± MgO±SiO2 system (800 atoms). The composition of the liquid was XCaO 0:6, XMgO 0:2, and
Fig. 2. Variation in the fraction of four types of oxygen as a function of the mole fraction of Al2 O3 in the CaO±Al2 O3 ±SiO2 melts. The lines are drawn to guide the eye.
L. Zhang et al. / Journal of Non-Crystalline Solids 282 (2001) 24±29
XSiO2 0:2. Two orientations of the MgO crystal were chosen such that the (1 0 0) or the (1 1 1) crystal plane was in contact with the liquid. The crystal box contained 500 atoms. The time step used was 1 fs and the results were the average of 100 values collected during 20 ps runs. The distribution of the elements, i.e., Ca, Mg, Si and O by diwas analysed for the liquid layer (20 A) viding it into 20 thin slices. The results shown in Fig. 3 are the ratio of the real number of atoms N (DL) over the average number of atoms N(average) in each slice. In other words, if the atoms are evenly distributed in each slice, the ratio should be unity throughout the liquid layer. 4. Discussions 4.1. Structure of CaO±SiO2 melts at 2000 K The composition dependence of the fractions of free (NO2 ), bridging (NO0 ) and non-bridging (NO ) oxygen presented in Fig. 1 showed that the results from the MD simulation, the values cal-
27
culated by the cell model and the experimental data are in close agreement. The fraction of bridging oxygen, NO0 , increases as the mole fraction of silica (XSiO2 ) increases beyond 1/3. Note in particular that a maximum for the fraction of nonbridging oxygen atoms is obtained at a silica mole fraction of about 1/3. According to Lin and Pelton [21], the maximum NO in binary silicate MO±SiO2 melts at the orthosilicate composition is dependent on the relative basicity of MO, and the more basic MO, the closer NO is to unity. Calcium oxide is one of the strongest basic oxides found in metallurgical melts. The maximum NO in the calcium silicate melts is about 0.9. The distributions of silicate anions of dierent sizes (NSi ) were calculated from the simulation results for the four compositions of XSiO2 0:2, 0.333, 0.5 and 0.667. The NSi s were from one to six to represent silicate anions ranging from monomers (SiO44 ) to complex chains and rings of silicates with dierent number of Si per species. No direct experimental data on the calcium silicate system are available. The results from the MD simulations were compared with the results of
Fig. 3. Distribution of each type of elements in the liquid (CaO±MgO±SiO2 ) layer (20 DL slices) of the slag/MgO interface: (a) melt in contact with 100 plane; (b) melt in contact with 111 plane. In (b) the crystal plane of Mg-(1 1 1) is on the left-hand side of the box and O-(1 1 1) on the right.
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L. Zhang et al. / Journal of Non-Crystalline Solids 282 (2001) 24±29
calculations based on the cell model [21] and a statistical treatment [22]. A broad agreement between the two sets of results was obtained. According to these results, when the mole fraction of silica is 0.2, the system consists of mainly SiO44 monomers with a small amount of dimers Si2 O67 . At the silica-rich end, mole fraction of SiO2 > 0:66, large anions predominate. Between these two compositions, an increasing degree of polymerisation is apparent. These results demonstrate that MD simulation can be used to study medium- and long-range structures in silicate melts. It may complement the limited experimental capabilities in this respect.
4.3. Slag/MgO interface at 2400 K
4.2. Structure of the CaO±Al2 O3 ±SiO2 melts at 2000 K
cL=S Etotal
The aim of this study was to investigate the eect of Al2 O3 (or R ratio) on the structural properties in CaO±Al2 O3 ±SiO2 liquids at a ®xed SiO2 content. The calculated fractions of dierent types of oxygen in Fig. 2 showed that the degree of polymerisation (fraction of bridging oxygen) of these melts increases with increasing mole fraction of Al2 O3 or R. The bridging oxygen can be one of the three bonding con®gurations, i.e., Al±O±Al, Al±O±Si and Si±O±Si. Existence of triclusters or a fourth type of oxygen, i.e., a three-coordinated oxygen, O3 , was also found, at a few percent of the total oxygen. We note that the number of triclusters increases with the increasing mole fraction of Al2 O3 or R. The majority of the triclusters were three tetrahedra of AlO54 . The remaining triclusters were two AlO54 and one SiO44 . Triclusters of three SiO44 or two SiO44 and one AlO54 were not found. Furthermore, the O3 ±Al bond was found to be about 2.5% longer than other O±Al bonds of 1.74 A. Because of this the stability of the connections of the tetrahedra is expected to be less than the normal connection of two tetrahedra. We infer that the increase in the number of triclusters in the liquids with increasing R could create weak points between the linkage of the anions which cause the extremes in viscosities of the liquids found by experiments.
An analysis of the distribution of elements at the slag/MgO interface (Fig. 3) showed that Mg and Si atoms tend to increase near the liquid/ MgO(1 0 0) interface and Mg and Ca near the liquid/MgO(1 1 1) interface (oxygen surface). Such a re-arrangement of elements is driven by the energy requirement of the system. For both the (1 0 0) and (1 1 1) crystal orientations, a decrease in energy was found which is mainly due to the formation of chemical bonds established between the ions in the liquid and the MgO surface. The interfacial energy, cL=S , has been calculated by EMgO
Emelt =2A;
3
where Etotal is total energy of the interface cell, EMgO is the energy of an interior MgO crystal cell, Emelt is the energy for the interior of a silicate liquid and A is the cross-sectional area of the interface. The calculated values are )0.58 and )8.0 (N/m) for (1 0 0) and (1 1 1) crystal plane, respectively. The absolute magnitudes from the MD simulation may not agree with the measured magnitudes as the model systems used here may be oversimpli®ed, limited by the methods used. The factors such as the small size of the system and the unrelaxed surface atoms of the MgO block will have in¯uence on the accuracy of the results. However, the structural information obtained for a model interface at the atomic level which cannot be obtained otherwise is assumed to be useful. 4.4. Limitations and potential of molecular simulations The MD simulations of model systems using the BMH potential described above have demonstrated the potential of the technique. Information on the liquid structure and its relation to the other properties can be obtained. Such information at the atomic level is dicult or sometime impossible to obtain by any other means. However, the development is still at its early stage in applying the technique to practical problems. One frequently encountered problem is the availability
L. Zhang et al. / Journal of Non-Crystalline Solids 282 (2001) 24±29
and reliability of the force ®eld used for the simulations. This limitations is due to 1. the force ®eld parameters for some common elements, such as Fe, in metallurgical systems are not readily available; 2. the available force ®eld parameters in the current form may not adequately describe some effects, such as polarisation of the ions and crystal ®eld eect for transition metals. Re®nement and improvement in the force ®eld representation, together with more ecient algorithm, and more powerful computers will enable a better simulation of more realistic systems for metallurgical applications. 5. Conclusions We have carried out MD simulations in the study of structural properties in the silicate melts and MgO/solid interfaces. · The structural information obtained for the CaO±SiO2 melts is in accord with the experimental data and theoretical predictions. · Triclusters were found in the CaO±Al2 O3 ±SiO2 liquids that provides useful information in understanding the structural role played by alumina. · Mg atoms have a tendency to be enriched at a slag/MgO interface. The approaches developed in this work can be re®ned and applied to examine the trends in energetics and structural aspects for dierent slag/solid interface systems. The results presented in the present paper have demonstrated the usefulness and potential of the technique in obtaining information on the structural and interfacial properties of metallurgical systems. Acknowledgements Financial support for this work was provided by BHP, MIM, Rio Tinto and Pasminco through the Australian Mineral Industries Research Association Limited (AMIRA) and the Australian Government Cooperative Research Centres Pro-
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gram through the G.K. Williams Cooperative Research Centre for Extractive Metallurgy, a joint venture between the CSIRO±Division of Minerals and The University of Melbourne ± Department of Chemical Engineering.
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