Modeling distribution of polymerized anions on the liquidus of the Na₂O-SiO₂ system

Shildt A.V.*, Ariskin A.A.**, Polyakov V.B.***

* Department of Geology, Moscow State University, Moscow, Russia;

** Vernadsky Institute of Geochemistry and Analytical Chemistry, Moscow, Russia;

*** Institute of Experimental Mineralogy, Chernogolovka, Russia

In previous studies, we have presented a STRUCTON computer program designed for statistical simulations of molecular-size distribution of Si-anions in polymerized silicate melts (Polyakov, Ariskin, 2008). The INPUT file of this model includes proportions of five Qⁿ- structons– “SiO₄-groups” (0 ≤ n ≤ 4, Q⁰ corresponds to the SiO₄^4- ion) which are distinguished by the number of bridging oxygen. A system of OUTPUT files includes statistical characteristics for the modeled ensembles of the chain, branched, and ring complexes corresponding to a general formula (Si_iO_3i+1-j)^2(i+1-j)-, where i is the size of an anion, j is the number of the ring bonds. First calculations were conducted for the compositions ranging from ortho- to metasilicates based on a random distribution of Qⁿ-structons suggesting an equal reactivity of various atoms of non-bridging oxygen. According to our calculations, the number of polymerized anion species varies from 3 (SiO₄^4-, Si₂O₇^6-, Si₃O₁₀^8-) in Na₄SiO₄ composition to 153 in metasilicate, whereas the average size of polymer species varies from 1 to 7.2 (Ariskin, Polyakov, 2008). Further development of the model accounts for the non-equal reactivity of Qⁿ-species which are known to disproportionate in silicate melts and glasses due to three structure-based reactions:

Q^n-1 + Qⁿ⁺¹ = 2Qⁿ ,š

k_n=[Qⁿ]²/{[Q^n-1][Qⁿ⁺¹]} (1 ≤ n ≤ 3). (1)

These reactions cause fractions of Q¹, Q² and Q³-structons to increase with respect to fractions of “end-member” Q⁰- andš Q⁴-structons, The distribution of Qⁿ-structons observed from Raman and NMR spectroscopy is never coincides with the random distribution for a given melt composition (Mysen, Richet, 2005) Such deviation of the real Q⁴-structon distribution fromš the random one affects the distribution of polymer species and should be taken into account in correct models. For this purpose, a special subroutine of the STRUCTON program was developed. It calculates the distributionš of Qⁿ-structons for a given composition using values of constants of the disproportionation reactions (1). The spectroscopic data on these constants were rationalized using the following Arrhenius temperature dependence:

, (2)
where s_n is the entropic factors; H is the enthalpy; n = 1,2,3; and R and T have a common meaning. s₁ = s₃ = 8/3 and s₂ = 9/4 are the same for silicate systems in our model, whereas the enthalpy depends on a cation type. The realistic distribution of Qⁿ-structons calculated using the disproportination constants (2) is used as an INPUT information for the STRUCTON model. This allows one to estimate distribution of (Si_iO_3i+1-j)^2(i+1-j)- species more correctly than in the the scope of the random model. Since the random distribution of Qⁿ-structons corresponds to infinite temperature in (2), one can conclude that accounting for the disproportionation reactions provides evaluations of the effect of temperature on the distribution of anion polymer species in the melt.

As an example, we have carried out a set of testing calculations for the Na₂O-SiO₂ system in the range of 33.3-50.0 mol% of SiO₂. Results of these calculations along the liquidus of the binary system have demonstrated a systematic decrease in the proportion of Q⁰-species with respect to that following from stochastic modeling. Na₆Si₂O₇ (40 mol% SiO₂) and Na₂SiO₃ (50 mol% SiO₂) melts are enriched in Q¹- and Q²-structons, respectively (see Shildt et al., 2009). This results in the predominance of Si₂O₇^6- dimers in the Na₆Si₂O₇ melt and “flat” rings Si_nO_3n^2n-(Si₃O₉^6-, Si₄O₁₂^8-, Si₅O₁₅^10-, etc.) in the Na₂SiO₃ melt. Such predominance of stoichiometric polymeric compounds in the melts follows directly from our modeling.

References:

Ariskin A.A., Polyakov V.B. Simulation of molecular mass distributions and evaluation of O^2- concentrations in polymerized silicate melts // Geochemistry International. 2008. Vol. 46. P. 429-447.

Mysen B., Richet P. Silicate glasses and melts: properties and structure. Amsterdam: Elsevier, 2005. 560 p.

Polyakov V.B., Ariskin A.A. Simulation of the composition and proportions of anions in polymerized silicate melts // Glass Physics and Chemistry. 2008. Vol. 34. P. 50-62.

Shildt A.V., Polyakov V.B., Ariskin A.A. Calculation of distributions of Q-species on the liquidus of the Na₂O-SiO₂ system: Updating the STRUCTON model // Abs. of Annual seminar on experimental mineralogy, petrology, and geochemistry (Moscow, Vernadsky Institute, 2009).š

This study was supported by the RFBR grant 08-05-00194-a.