A nuclear glass is a multicomponent and multiphase material. The methodology for thermodynamic modelling of such materials, namely the CALPHAD approach [1]⁠[2]⁠, is well established and widely used. It has been applied for many years with great success, for example on steels or other metal alloys such as Al or Ni based ones. However, nuclear glasses have unique characteristics that present many challenges from the point of view of thermodynamic modelling
The first, most striking and probably most complex feature of nuclear glasses is the massively multi-component nature of the chemical system involved. Taking the French R7T7 glass as a typical example [3][4]⁠, about 30 radioelements are present in the reference solution of fission products, to which must be added the constituents of the glass matrix itself. The chemical system resulting from the melting operation hence contains more than 40 chemical components. It is likely to be more multicomponent than any other material of industrial interest.
Secondly, the liquid phase must be accurately described over a wide temperature range, the lower limit of which is the glass transition temperature, i.e. down to a large supercooling. Therefore, the evaluation of thermodynamic functions of the liquid phase must be based on physical models that have reliable extrapolation behavior.
Thirdly, demixing, which is a subtle effect occurring in a solution when the destabilization effect of a positive enthalpy of mixing outweighs the stabilization effect of the entropy of mixing, may take place in both the liquid and glassy phases. In addition, this demixing can sometimes lead to the formation of liquid phases with different types of chemical bonds, e.g. phase separation between a metallic liquid and an oxide liquid [5]⁠.
Fourthly, many crystalline phases precipitate because of the limited solubilities of some components in the melt or in the glass [6]⁠[5]⁠ and this phenomena is enhanced by prior liquid-liquid demixing [7]⁠. Moreover, experimental thermodynamic data are sometimes missing for these often complex crystalline phases.
Fifthly, structural relaxation is arrested when the glass transition range is crossed during cooling and the configurational state of the metastable liquid oxide is then frozen-in. The glass matrix is a solution phase that is in a non-equilibrium state requiring a specific modeling approach compared to conventional equilibrium phases such as the gas, liquid and crystalline phases.
In this context, the various methodologies which have been adopted in literature for modeling unary and multicomponent glasses and glass forming liquids will be reviewed, with particular emphasis put on the 2nd and 5th items in the above list.
Thermodynamics is the first fundamental brick to build a modeling tool capable of predicting the nature, compositions and quantities of phases in nuclear glasses. A more complete modeling should include additional building blocks to take into account kinetic phenomena such as diffusion, nucleation and growth.
References
[1] N. Saunders, A.P. Miodownik, CALPHAD (Calculation of Phase Diagrams): A Comprehensive Guide, Elsevier Science Ltd, 1998.
[2] H.L. Lukas, S.G. Fries, B. Sundman, Computational Thermodynamics: The Calphad Method, Cambridge University Press, 2007. https://doi.org/10.1017/CBO9780511804137.
[3] T. Advocat, J.-L. Dussossoy, V. Petitjean, Vitrification des déchets radioactifs, Tech. l’ingénieur. BN3664 V1 (2008) 1–25.
[4] S. Gin, P. Jollivet, M. Tribet, S. Peuget, S. Schuller, Radionuclides containment in nuclear glasses: an overview, Radiochim. Acta. 105 (2017) 927–959. https://doi.org/10.1515/ract-2016-2658.
[5] S. Gossé, C. Guéneau, S. Bordier, S. Schuller, A. Laplace, J. Rogez, A Thermodynamic Approach to Predict the Metallic and Oxide Phases Precipitations in Nuclear Waste Glass Melts, Procedia Mater. Sci. 7 (2014) 79–86. https://doi.org/10.1016/j.mspro.2014.10.011.
[6] P.B. Rose, D.I. Woodward, M.I. Ojovan, N.C. Hyatt, W.E. Lee, Crystallisation of a simulated borosilicate high-level waste glass produced on a full-scale vitrification line, J. Non. Cryst. Solids. 357 (2011) 2989–3001. https://doi.org/10.1016/j.jnoncrysol.2011.04.003.
[7] S. Schuller, P. Benigni, S. Gossé, S. Bégaud-Bordier, G. Mikaelian, R. Podor, J. Rogez, Liquid-liquid phase separation in borosilicate glass enriched in MoO3 – experimental investigations and thermodynamic calculations, J. Non. Cryst. Solids. 600 (2023) 121997. https://doi.org/10.1016/j.jnoncrysol.2022.121997.