A thermodynamic model of the Cs-Pb system

Abstract

A comprehensive thermodynamic assessment of the Cs-Pb system was performed with the CALPHAD method using the experimental thermodynamic and phase diagram data available in literature supplemented by density functional theory (DFT) calculations. The exact nature of the stable compounds in the phase diagrams reported in the literature is uncertain, except for CsPb and Cs₄Pb₉ whose crystalline structures are well known. Therefore, DFT calculations were performed to calculate the energy of formation at 0 K of different possible compounds with various crystalline structures. The enthalpies of formation of the compounds CsPb, Cs₄Pb₉, and CsPb₄, found to be the stable ones by DFT, were then used in the CALPHAD model. The result of this process has enabled the development of a more refined phase diagram comparing to experimental ones, providing more comprehensive insights into the phase equilibria in this system. Moreover, the CALPHAD model succeeded in describing the peculiar behavior of the heat capacity of the liquid phase, by using an ionic two-sublattice model (Cs+1)_P(Pb−1,Va,Pb)_Q which takes into account the short-range ordering taking place at the equimolar composition CsPb, related to the formation of clusters Cs₄Pb₄, modelled as (Cs+1) (Pb−1). The model allows for the prediction of important thermodynamic properties, which are of interest for a range of applications, including lead-cooled fast reactors and perovskite-based photovoltaics.