Sergei A. Decterov

Critical thermodynamic evaluation and optimization of the MgO-Al2O3, CaO-MgO-Al2O3, and MgO-Al2O3-SiO2 Systems

A complete literature review, critical evaluation, and thermodynamic modeling of the phase diagrams and thermodynamic properties of all oxide phases in the MgO-Al2O3, CaO-MgO-Al2O3, and MgO-Al2O3-SiO2 systems at 1 bar total pressure are presented. Optimized model equations for the thermodynamic properties of all phases are obtained that reproduce all available thermodynamic and phase equilibrium data within experimental error limits from 25 °C to above the liquidus temperatures at all compositions. The database of the model parameters can be used along with software for Gibbs energy minimization to calculate all thermodynamic properties and any type of phase diagram section. The modified quasichemical model was used for the liquid slag phase and sublattice models, based upon the compound energy formalism, were used for the spinel, pyroxene, and monoxide solid solutions. The use of physically reasonable models means that the models can be used to predict thermodynamic properties and phase equilibria in composition and temperature regions where data are not available.

A model to calculate the viscosity of silicate melts

Abstract A model has been developed that links the viscosities of silicate melts to their thermodynamic properties. Over the past several years, through critical evaluation of all available thermodynamic and phase equilibrium data, we have developed a quantitative thermodynamic description of multicomponent silicate melts using the Modified Quasichemical Model for short-range ordering. The local structure of the liquid, in terms of the bridging behavior of oxygen, calculated using our thermodynamic model allows us to characterize the structure of the liquid semi-quantitatively using the concepts of Q-species and connectivity of Q-species. The viscosity is modeled by optimizing viscosity parameters that are related to the structure of the liquid. The viscosity of pure liquid silica is modeled using four model parameters and every other unary liquid is modeled using two. The viscosity of all binary liquids is reproduced within experimental accuracy by optimizing one or at most two binary viscosity parameters for each system. In the present article the equations for the viscosity model are derived and analyses for the experimentally well-established systems CaO – SiO2 MgO – SiO2, NaO0.5 – SiO2, KO0.5 – SiO2 and AlO1.5 – SiO2 are presented. This is the first step in the development of a predictive model for the viscosity of multicomponent silicate melts that will be presented in part II.

A model to calculate the viscosity of silicate melts Part II: The NaO0.5-MgO-CaO-AlO1.5-SiO2 system

Abstract Our recently developed model to describe the viscosity of binary silicate melts is extended to describe and predict the viscosities of multicomponent silicate melts. The viscosity of multicomponent melts containing no AlO1.5 is modeled to vary linearly as a function of the mole fractions of the basic oxides at constant SiO2 mole fraction. Systems containing AlO1.5 show a more or less pronounced viscosity maximum close to the charge compensating composition. This maximum is caused by some of the Al3+ taking on the same structural role as Si4+, thereby participating in the formation of the silica network. The network-forming Al3+ must remain associated with either one Na+, or two Al3+ ions must remain associated with one Mg2+ or Ca2+, in order to assure charge neutrality. To take this into account we introduce the associates NaAlO2, CaAl2O4 and MgAl2O4 that correspond to charge compensated network-forming Al3+. The Gibbs energy of formation of these associates determines the amount of Al3+ that takes on the network-forming role. We assume the effect on viscosity of network-forming Al3+ to be the same as Si4+ and optimize the Gibbs energies of the associates to reproduce the experimental viscosity data. Viscosities in ternary silicate systems without AlO1.5 are quantitatively predicted with no additional ternary model parameters. Ternary systems MeOx – SiO2 – AlO1.5 are modeled with only two temperature-independent ternary parameters per system. The model not only reproduces the magnitude of the observed viscosity maximum, but also its complex shape, asymmetry and temperature dependence.

Thermodynamic optimisation of the FeO-Fe2O3-SiO2 (Fe-O-Si) system with FactSage

Abstract Phase equilibrium and thermodynamic experimental data available in the literature on the FeO – Fe2O3 – SiO2 (Fe – O – Si) system were critically reviewed and used to obtain a self-consistent set of parameters for thermodynamic models for all oxide phases using the FactSage computer package. The present optimisation covers the range of oxygen partial pressures from equilibrium with pure oxygen to metal saturation and temperatures from 25 °C to above the liquidus. The present thermodynamic optimisation was performed as part of the development of a thermodynamic database for the multi-component system Al – Ca – Fe – Mg – O – Pb – Si – Zn; the thermodynamic parameters for the Fe – O – Si system therefore were chosen to be consistent not only with the experimental data in this ternary system, but also with the data in higher-order systems. The modified quasichemical model was used for the liquid slag phase. Sublattice (based upon the compound-energy formalism) and polynomial models were used for the spinel (magnetite) and monoxide (wustite) solid solutions, respectively. The use of physically reasonable models means that the models can be used to predict thermodynamic properties and phase equilibria in composition and temperature regions where experimental data are not available. From these model parameters, the optimised ternary phase diagram of the FeO – Fe2O3 – SiO2 (Fe – O – Si) system was back calculated. The database of the model parameters can be used in conjunction with computer software for Gibbs-free-energy minimisation in order to calculate all thermodynamic properties and any type of phase-diagram section in the FeO – Fe2O3 – SiO2 (Fe – O – Si) system.

Thermodynamic Optimization of the Ca-Fe-O System

The present study deals with the thermodynamic optimization of the Ca-Fe-O system. All available phase equilibrium and thermodynamic experimental data are critically assessed to obtain a self-consistent set of model parameters for the Gibbs energies of all stoichiometric and solution phases. Model predictions of the present study are compared with previous assessments. Wüstite and lime are described as one monoxide solution with a miscibility gap, using the random mixing Bragg-Williams model. The solubility of CaO in the “Fe3O4” magnetite (spinel) phase is described using the sublattice model based on the Compound Energy Formalism. The effect of CaO on the stability of the spinel phase is evaluated. The liquid CaO-FeO-Fe2O3 slag is modeled using the Modified Quasichemical Formalism. Liquid metal phase is described as a separate solution by an associate model.

A model to calculate the viscosity of silicate melts: Part III: Modification for melts containing alkali oxides

Abstract Our recently developed model to describe the viscosity of silicate melts is extended to describe and predict the viscosities of alkali-rich silicate melts. The model requires one additional binary parameter for each M2O–SiO2 system, where M is an alkali metal, to a total of three binary parameters per binary system alkali oxide – silica. In addition to unary and binary parameters, the model requires two ternary parameters for each alumina-containing ternary system MOx–Al2O3 –SiO2, where MOx is a basic oxide, to describe the viscosity maxima in these ternary systems due to the Charge Compensation Effect. The viscosity of multicomponent melts and of ternary melts MOx–NOy–SiO2, where MOx and NOy are basic oxides, is predicted by the model solely from the unary, binary and ternary parameters. The available viscosity data for the alkali-containing subsystems of the Al2O3–CaO–MgO–Na2O–K2O–SiO2 system are reviewed. The model reproduces the experimental data for binary and ternary melts and predicts the viscosities of multicomponent melts within experimental error limits. In particular, the viscosities of glass melts and melts of importance for petrology are well predicted by the model.

Thermodynamic modeling of the B2O3–SiO2 and B2O3–Al2O3 systems

Abstract A complete literature review, critical evaluation, and thermodynamic modeling of the phase diagrams and thermodynamic properties of all oxide phases in the binary systems B2O3 – SiO2 and B2O3 – Al2O3 have been performed. The molten oxide is described by the Modified Quasichemical Model. Discrepancies in the available experimental data have been resolved and an optimized set of self-consistent thermodynamic functions of all phases has been obtained. This thermodynamic database can be used with the FactSageTM thermodynamic computing system to calculate all thermodynamic properties and phase equilibria from 25 °C to above the liquidus temperatures at 1 atm of total pressure and over the entire composition range.

A model to calculate the viscosity of silicate melts Part V: Borosilicate melts containing alkali metals

Abstract Our recently developed model for the viscosity of borosilicate melts is extended to describe and predict the viscosities of melts containing alkali oxides. In addition to the two model parameters that are required for each B2O3–MOx melt, where MOx is a basic oxide, three more parameters are needed when MOx is an alkali oxide to account for the formation of clusters near the tetraborate composition. The additional parameters represent the size and Gibbs energy of formation of these clusters and their contribution to the activation energy of the viscous flow. A general algorithm for the calculation of the viscosity is presented which summarizes the application of the viscosity model to melts that can contain two network formers, SiO2 and B2O3, any basic oxide and amphoteric oxides exhibiting the Charge Compensation Effect such as Al2O3. The predictive ability of the model is tested on all ternary subsystems of the B2O3–Na2O–K2O–CaO–MgO–PbO–ZnO–Al2O3–SiO2 system containing both an alkali oxide and B2O3 for which experimental data are available and on several multicomponent glass-forming melts around commercial glass compositions.

A model to calculate the viscosity of silicate melts: Part IV: Alkali-free borosilicate melts

Abstract Our recently developed model for the viscosity of silicate melts is extended to describe and predict the viscosities of oxide melts containing boron. The model requires three adjustable parameters to reproduce the viscosity of B2O3–SiO2 melts and two parameters for each B2O3–MO x melt, where MOx is a basic oxide other than an alkali oxide. All available experimental data have been collected for binary melts formed by B2O3 with SiO2, Al2O3, CaO, MgO, ZnO, PbO to calibrate the model. The viscosities of the B2O3-containing ternary and higher-order subsystems of the B2O3–CaO–MgO–PbO–ZnO–SiO2 system and of the B2O3–CaO–MgO–PbO–ZnO–Al2O3 system are then predicted by the model without any additional adjustable parameters. Experimental data were found for only five such subsystems: B2O3–PbO–SiO2, B2O3–CaO–SiO2, B2O3–PbO–ZnO, B2O3–PbO–Al2O3 and B2O3–CaO–Al2O3. Predictions of the model are compared to these experimental data.

Modeling the Viscosity of Silicate Melts Containing Lead Oxide

Our recently developed model for the viscosity of silicate melts is applied to describe and predict the viscosities of oxide melts containing lead oxide. The model requires three pairs of adjustable parameters that are fitted to the experimental viscosities in the following systems: pure PbO, PbO-SiO2, and PbO-Al2O3-SiO2. The viscosity of other ternary and multicomponent silicate melts containing PbO is then predicted by the model without any additional adjustable model parameters. Experimental viscosity data are reviewed for melts formed by PbO with SiO2, Al2O3, CaO, MgO, Na2O, and K2O. The deviation of the available experimental data from the viscosities predicted by the model is within experimental error limits.