Predicting Phase Equilibria of Spinel‐Forming Constituents in Waste Glass Systems

A modified associate species thermochemical model has been developed for the liquid/glass in nuclear waste glass systems, and provides a simple means for relatively accurately representing the thermochemistry of the liquid/glass phase. A modification of the methodology is required when two immiscible liquids are present, such that a positive interaction energy is included in the representation. The approach has been extended to include spinel-forming constituents together with the base glass system as well as development of a models for spinel phases. INTRODUCTION The production of nuclear materials for defense applications at several sites in the United States over almost six decades has resulted in the accumulation of a substantial quantity of radioactive waste. These materials are currently stored in a variety of forms including liquids, sludges, and solids. In addition, there are similar wastes that have resulted from the reprocessing of commercial spent fuel, although this has occurred to a much smaller extent. While the composition and characteristics of the various high-level wastes (HLW) differ, their behavior is similar in many respects. The focus of current U. S. Department of Energy efforts with regard to permanent disposal of these materials is that they will be incorporated in a stable, insoluble host solid (a glass or specific crystalline phase). Components such as Fe, Cr, Zr, and Al have limited solubility in HLW glasses (1-3). These components precipitate as oxide minerals such as spinel, zircon, and nepheline once their solubility in glass is exceeded. Precipitated minerals may cause melter failure (4) and can alter the physical properties such as the leach resistance of the glass (2). To avoid these problems, current HLW glasses are formulated to assure oxide minerals do not precipitate in the melter (2,5,6). The solubility of these components can dictate HLW glass volume produced at the Savannah River Site (7) and West Valley and to be produced at Hanford (5, 8). Thermochemical assessment of the phase equilibria and modeling of the liquid/glass phase can support optimization of glass formulations with regard to stability and waste loading. In order to provide a sufficient thermochemical understanding of the liquid and glass system used for sequestering HLW, an approach using the associate species technique was chosen (9, 10). It is attractive because it (a) accurately represents the thermodynamic behavior of very complex chemical systems over wide temperature and composition ranges, (b) accurately predicts the activities of components in metastable equilibrium glass phases, (c) allows logical estimation of unknown thermodynamic values with an accuracy much greater than that required for predicting useful engineering limits on thermodynamic activities in solutions, and (d) is relatively easy for non-specialists in thermochemistry to understand and use. Ideal mixing of associate species accurately represent the solution energies in which end member components exhibit attractive forces. A modification to the associate species model, hence the term “modified” associate species model, is the incorporation of positive solution model constants to represent any positive interaction energies in a solution. With these it is possible to accurately represent reported immiscibility in solution phases (e.g., the liquid-liquid immiscibility common in many silica-containing systems). The results are simple, well-behaved equations for free energies that can be confidently extrapolated and interpolated into unstudied temperature and composition ranges. Thus, in support of the nuclear waste glass development effort, a model of the Na2O-Al2O3-B2O3-SiO2 was developed using the modified associate species approach and described elsewhere (9,10). The work described here is focused on modeling spinel phases along with attendant liquid/glass and other crystalline phases in HLW systems. As noted above, previous efforts have successfully modeled the base glass system. Progress to date to include spinel-related constituents has resulted in modeling of the Fe-O, Mn-O, Al-Fe oxide, Cr-Fe oxide, and Al-FeCr oxides. The basic data for the calculations are obtained from the 1996 version of the Scientific Group Thermodata Europe (SGTE) Pure Substance Database (12) and calculations are performed using the ChemSage (13) and FactSage (14) thermochemical software packages. Continuing efforts will seek to include other important elements in spinel phases, most notably Mn. Fe-O SYSTEM With the multivalent nature of iron and the importance of redox potential in many glass systems, the Fe-O system must be correctly modeled for its accurate inclusion in any liquid/glass system. This is less of an issue for HLW glass as efforts are made to fully oxidize species in the melter. Following the formalism described by Spear, et al. (9), liquid species’ stoichiometry are chosen such that they contain 2 non-oxygen atoms per formula weight. The liquid/glass for Fe-O has been treated as a solution of Fe2, Fe2O2, Fe3O4:2/3, and Fe2O3 species. The nomenclature for Fe3O4:2/3 indicates that the species has the Fe3O4 relative stoichiometry, although all values are multiplied by 2/3 in order to obtain 2 non-oxygen atoms per formula weight. The thermodynamic values for crystalline phases and liquid species were derived and are given in Tables I-IV. These were based on the SGTE database (12), the procedures described by Spear et al. (9), and from fitting published phase equilibria,. The liquid-liquid immiscibility of the Fe-O system, however, required that the solution be described using positive (repulsive) energetic terms. A simple Redlich-Kister (15) model, for which the values were manually fit to reproduce the phase equilibria, is adequate. It has the general formalism Gex = xixjΣ ( Ln (xi-xj) n-1) (J/mol) (1) where Gex is the excess free energy of the solution, xi and xj are the mol fractions of species i and j, respectively. For the liquid phase the interacting species and interaction parameters are given in Table V. Table I. Thermodynamic values for the crystalline phases based on the SGTE database and modified as necessary to develop associate species models. (∆Hf,298 is the 298K heat of formation, S298 is the 298K entropy, T is absolute temperature, Tfus is the melting temperature, and ∆Hfus is the heat of fusion.)____________________________________________________ Crystalline Phase -∆Hf,298(J/mol) S298(J/K-mol) Tfus(K) ∆Hfus(J/mol) Mn --32.008 1517 12058.3 MnO 384928. 59.831 2058 54392. Mn3O4 1386580. 153.971 1833 20920. Mn2O3 956881. 110.458 --decomposes MnO2 520071. 53.053 --decomposes Fe --27.28