ISSN 00167029, Geochemistry International, 2010, Vol. 48, No. 11, pp. 1128–1130. © Pleiades Publishing, Ltd., 2010. Original Russian Text © V.N. Bykov, O.N. Koroleva, 2010, published in Geokhimiya, 2010, Vol. 48, No. 11, pp. 1202–1205.
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Thermodynamic Simulation of the Behavior of NetworkModifying Cations in Multicomponent Silicate Melts V. N. Bykov and O. N. Koroleva Institute of Mineralogy, Ural Division, Russian Academy of Sciences, Miass, Chelyabinsk oblast, 456317 Russia email:
[email protected] Received February 2, 2009
DOI: 10.1134/S0016702910110066
The structure and physicochemical properties of silicate and magmatic melts are currently described mostly within the scope of a model representing the structure of melts as an ensemble of silicon–oxygen structural units Qn (where n is the number of bridging oxygen atoms). The concentrations of these structural units depend on the composition and temperature and can be experimentally determined from Raman spec tra or calculated by means of thermodynamic simula tions [1–3]. At the same time, an important role in shaping the structure of melts is played by networkmodifying cat ions: their concentrations control the number of non bridging oxygen bonds and, correspondingly, the degree of melt polymerization, whereas the type of the cation controls the Qn distribution in melts and glasses [1]. It is known [4] that the determining role in the ori gin of silicate structures, including the crystallization of melts, is played by cations, to which silicon–oxygen anionic tetrahedrons “accommodate.” In general, a model for the structure of silicate melts should also account for the behavior of cations in melts (cation– anion model), which is particularly important with the transition from simple to more complicated multi component melts and naturally occurring magmas in which cations of various types coexist. In order to examine relations and trends in the behavior of networkmodifying cations, Raman spec troscopy was applied in [5] to study the structure of model threecomponent glasses of the composition (40 – х)%К2О ⋅ х%Li2O ⋅ 60%SiO2with two network modifying cations (К+ and Li+) that have significantly different ionic potentials. It was demonstrated that glasses of this composition contain structural units of two types (Q3 and Q2), and the analysis of the behavior of the characteristic vibration frequencies of Si–O…M bonds in these structural units during the systematic substitution of potassium cations for lithium cations made it possible to determine a nonstatistical distribu tion of networkmodifying cations. It was also demon strated that the K+ cation is prone to occupy cation
sites near SiO4 tetrahedrons with a single nonbridging O atom, whereas Li+ tends to occupy sites near SiO4 tetrahedrons with two nonbridging O atoms. This result is in good agreement with the polarity principle of chemical bonds and concepts currently adopted for the acid–basic interaction in silicate melts [6, 7]. Data on the nonstatistical distribution of networkmodify ing cations obtained for glasses pertain to “frozen” equilibria in melts near the vitrification temperature, and thus, cannot be immediately extrapolated to melts. It is known [1, 8–10] that the glass–melt tran sition is associated with structural transformations that affect, first of all, the state of networkmodifying cat ions in silicate systems. The aim of our research was to examine the distri bution of networkmodifying cations in melts of the model К2О–Li2O–SiO2 threecomponent system at high temperatures. Our studies were carried out by means of thermodynamic simulations, because no anal ysis of the vibration frequencies of the Q3 and Q2 struc tural units in the hightemperature Raman spectra of melts analogous to that in [5] is possible owing to a strong temperature dependence of the characteristic frequen cies due to anharmonicity of the vibrations [11]. The thermodynamics of silicate melts was described based on the model for ideal associated solu tions [2, 12, 13]. According to this model, the interac tion of acidic oxides (SiO2, B2O3, and GeO2) and oxides of alkali and alkaliearth metals in melts gives rise to saltlike products (silicates, borates, and ger manates), which are structural chemical groups of cer tain composition and stoichiometry identical to those of the corresponding crystalline compounds in the phase diagram of the system. Structural units of this type in crystalline silicates are combined with one another into an ordered anionic motif, and the values of the Gibbs free energy of formation of silicates can be regarded as thermodynamic characteristics of structural units Qn [3]. It was demonstrated in [14] that the energetics of interaction processes in silicate sys tems is largely controlled by shortrange forces, and
1128
(а)
0.8
Mole fraction of Q2 structural units
Mole fraction of Q3 structural units
THERMODYNAMIC SIMULATION OF THE BEHAVIOR
0.6
0.4
0.2
0
10
20 Li2O, %
30
1129
(b)
0.4
0.3
0.2
0.1
40
0
10
20 Li2O, %
30
40
Distribution of (a) Q3 and (b) Q2 structural units coordinated by K (solid symbols) and Li (open symbols) cations in melts of the system (40 – х)%К2О ⋅ х%Li2O ⋅ 60%SiO2 at Т = 600 K (䊏, 䊐), 1200 K (䊉, 䊊), and 1800 K(䉱, 䉭). Dashed lines show the statistical distribution (k = 1), and dotted lines correspond to the ordered distribution (k = 0).
hence, this quasicrystalline approximation can be uti lized in the thermodynamic description of silicate melts. We have confirmed this conclusion by compar ing the results of the thermodynamic simulations with data of hightemperature Raman spectroscopy of sili cate melts [3]. Melts of the system (40 – х)%К2О ⋅ х%Li2O ⋅ 60%SiO2 contain structural units of two types (Q3 and Q2), and the distribution of networkmodifying cations can be described by the exchange reaction Q3(K) + Q2(Li) = Q2(K) + Q3(Li),
(1)
where Qn(K) and Qn(Li) are structural units coordi nated by К+ and Li+ cations. In the approximation of ideal associated solutions, the equilibrium constant of this reaction has the form 2
3
[ Q ] K ⋅ [ Q ] Li . k = 3 2 [ Q ] K ⋅ [ Q ] Li
(2)
Reaction (1) between the structural units corre sponds to the following reaction between silicates: K2Si2O5 + Li2SiO3 = K2SiO3 + Li2Si2O5. (3) The equilibrium constants of this exchange reac tion were calculated using values of the free energy of formation of corresponding silicates in liquid states at high temperatures, which were compiled from the FACT thermodynamic database. The concentrations of the Q3 and Q2 structural units coordinated by К+ and Li+ cations in melts of the system (40 – х)%К2О ⋅ х%Li2O ⋅ 60%SiO2 at various temperatures and corre sponding to these equilibria constants are shown in the figure. This figure also displays hypothetical lines GEOCHEMISTRY INTERNATIONAL
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characterizing the statistically equiprobable random distribution of К+ and Li+ cations between Qn struc tural units (equilibrium constant k = 1) and lines cor responding to the fully ordered distribution with an equilibrium constant k = 0. The dependences for Q3 and Q2 at temperatures from 600 to 1800 K are system atically arranged between these lines. As can be seen in this figure, supercooled melt (glass) at a temperature of 600 K displays an ordered distribution of networkmodifying cations. The cat ions of the stronger base (K+) preferably occupy cat ionic sites near structural units Q3, whereas the cations of the weaker base (Li+) occur near Q2 structural units, a fact most clearly seen for the composition 20K2O– 20Li2O–60SiO2. This is completely consistent with Raman spectroscopic data on glasses in the system K2O–Li2O–SiO2 [5], and this testifies that our ther modynamic approach is accurate enough. As the tem perature is increased, the behavior of networkmodi fying cations changes: K+ cations appear among the cations surrounding Q3 structural units and Li+ appears near Q3. The concentrations of the Q2(К) and Q3(Li) structural units increase, while the contents of the Q3(К) and Q2(Li) structure units correspondingly decrease with increasing temperature. These transfor mations lead to a more random distribution of net workmodifying cations between Qn structural units, which correspond to a decrease in the ordering of the examined cation–anion system with increasing tem perature. The figure also shows that the distribution of networkmodifying cations at 1800 K becomes closer to a random distribution than to an ordered one. 2010
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It was demonstrated in [8, 9] that equilibrium between Qn structural units in silicate melts at high temperatures is controlled by a dynamic process of the transformation of bridging oxygen atoms into non bridging ones and vice versa. In the course of this pro cess, Si–O bonds are broken and restored at a high rate, and silicate anions occur in melts not as single molecular groups but as topologically associated shortlived structural units. Their lifetimes are con trolled by the rate of the exchange of oxygen atoms between structural units and are a few microseconds for Na disilicate glasses at 1000°С and a few nanosec onds for these glasses at 1600°С. Obviously, this pro cess is largely of random character, and the related dis ordering increases with increasing temperature. It is reasonable to suggest that networkmodifying cations that are bound to anion groups not by covalent but by weaker ionic bonds also occur in dynamic equi librium, which characterizes the continuous break down and synthesis of these cationic–anionic com plexes. It should also be mentioned that dynamic equilibrium between cations and anions is described within the scope of the polyelectrolyte model [7] by introducing “free” and “bound” networkmodifying cations. The generation of bound networkmodifying cations is explained in this model by the fact that these cations assume the ability to retain (to a certain extent) oppositely charged cations because of the high charges of the former. The distribution of networkmodifying cations of various types among anionic groups of various degree of polymerization in these shortlived cation–anion complexes at high temperatures is controlled by statis tical laws and is largely random. As the temperature decreases, the contribution of the entropy term to the energetics of these complexes decreases, and the equi libria in the melts shift toward the synthesis of energet ically preferable cation–anion groups with an ordered distribution of networkmodifying cations. Our studies have demonstrated that thermody namic simulations on the basis of a model for ideal associated solutions are applicable to the description of the fine specifics in the structure of multicompo nent silicate melts and naturally occurring magmas. We have also demonstrated that the distribution of net workmodifying cations of various types among anion groups of various degrees of polymerization is largely random, but a temperature decrease results in the ordering of this distribution in compliance with the concept of acid–base interactions in melts and the principle of chemical bond polarity. This process largely controls the crystallization means and specifics of natural magmatic melts.
ACKNOWLEDGMENTS This study was supported by the Russian Founda tion for Basic Research, project nos. 060564333 and 070596046, and Federal Program NK545R “Sci entific and Researcher–Pedagogic Rersonnel for Innovations in Russia.” REFERENCES 1. V. N. Anfilogov, V. N. Bykov, and A. A. Osipov, “Silicate Melts,” (Nauka, Moscow, 2005) [in Russian]. 2. B. A. Shakhmatkin and N. M. Vedishcheva, “Thermody namic Modelling: A Reliable Instrument for Predicting Glass Properties,” Proc. Int. Congr. Glass 1, 52–60 (2001). 3. V. N. Bykov, O. N. Koroleva, and A. A. Osipov, “Structure of Melts of the K2O–SiO2 System Based on Data of Raman Spectroscopy and Thermodynamic Modeling,” Rasplavy, No. 3, 51–59 (2008). 4. N. V. Belov, Essays on Structural Mineralogy (Nedra, Mos cow, 1976) [in Russian]. 5. I. B. Bobylev, V. N. Bykov, and V. N. Anfilogov, “Cation Partitioning between Silicate Polyanions of Different Structure: Evidence from Raman Spectroscopy,” Geokhimiya, No. 5, 732–736 (1987). 6. L. N. Kogarko, “The Principle of Polarity of Chemical Bond and Its Significance in Magmatic Geochemistry,” Geokhimiya, No. 9, 1286–1297 (1980). 7. V. N. Anfilogov and I. B. Bobylev, “Silicate Melts— Melted Polyelectrolytes,” Geokhimiya, No. 9, 1298–1307 (1980). 8. J. F. Stebbins, “Dynamics and Structure of Silicate and Oxide Melts: Nuclear Magnetic Resonance Studies,” Rev. Mineral. 32, 191–246 (1995). 9. P. F. McMillan and G. H. Wolf, “Vibrational Spectroscopy of Silicate Melts,” Rev. Mineral. 32, 247–316 (1995). 10. A. R. Ubbelohde, “Melting and Crystal Structure,” (Oxford University Press, Oxford, 1965; Mir, Moscow, 1969) [in Russian]. 11. P. Richet, B. O. Mysen, and D. Andrault, “Melting and Premelting of Silicates: Raman Spectroscopy and XRay Diffraction of Li2SiO3 and Na2SiO3,” Phys. Chem. Min erals 23, 157–172 (1996). 12. B. A. Shakhmatkin and N. M. Vedishcheva, “A Thermody namic Approach to the Modeling of Physical Properties of Oxide Glasses,” Fiz. Khim. Stekla 24 (3), 333–344 (1998) [Glass Phys. Chem. 24, 229–236 (1998)]. 13. N. M. Vedishcheva, B. A. Shakhmatkin, and A. C. Wright, “Thermodynamic Modelling of the Structure of Glasses and Melts: SingleComponent, Binary and Ternary Sys tems,” J. NonCryst. Solids 293–295, 312–321 (2001). 14. P. S. Hess, “Thermodynamic Mixing Properties and the Structure of Silicate Melts,” Rev. Mineral. 32, 145–189 (1995).
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