Contribution of the associated complex in a binary liquid to model the Ca–Pb–Sn ternary system Y. Cartigny * , J.M. Fiorani, A. Maı ˆtre, M. Vilasi Laboratoire de Chimie du Solide Mine ´ ral, UMR CNRS 7555, Universite ´ Henri Poincare ´ Boulevard des Aiguillettes, BP 239, F-54506 Vandoeuvre Le `s Nancy cedex, France Available online 20 July 2007 Abstract Thermodynamic modeling of the Ca–Pb, Ca–Sn and Ca–Pb–Sn systems was carried out with the help of the CALculation PHase Diagram (CALPHAD) method. The thermodynamic parameters related to these systems were determined from experimental phase dia- gram and thermodynamic information available in the literature and by our own ternary experimental investigations (X-ray diffraction, metallographic and thermal analyses). The calcium–tin and calcium–lead systems can be described with the association model for the binary liquid with ‘Ca 2 Sn’ and ‘Ca 2 Pb’ as the associated species composition. The introduction of new interaction parameters related to the binary and ternary liquids, leads to an accurate restoration of the most important experimental data. Thus, industrial process applied on the lead calcium tin alloys used as electrode materials in lead acid batteries find some justifications. Ó 2007 Elsevier B.V. All rights reserved. PACS: 61.20.Gy; 61.25.Mv; 61.66.Dk; 81.30.Bx Keywords: Liquid alloys and liquid metals; Liquid crystals and molecular liquids; Modeling and simulation; Optical properties; Phases and equilibria 1. Introduction Ca–Pb and Ca–Pb–Sn alloys are used in lead acid batteries as electrode materials. Their mechanical and electrochemical behavior are influenced by their metal- lurgical state (aged or overaged). As a consequence, the determination of the phase boundaries in the Ca– Pb and Ca–Sn systems, two of the three borders of the Ca–Pb–Sn ternary system, will be crucial to the heat treatments of Ca–Pb–Sn ternary alloys. This will permit an explanation of the differences existing in the age- hardening mechanism of Ca–Pb and Ca–Pb–Sn [1]. Indeed, the age-hardening process for Ca–Pb–Sn alloys greatly depends on the Sn/Ca atomic ratio: for lower values of the ratio, the mechanism seems to be identical to those for the Ca–Pb binary alloy, for a higher Sn/Ca ratio the process contains only one continuous L1 2 phase precipitation step (Ca (Pb 1x Sn x ) 3 ) [1]. The purpose of the study is the thermodynamic model- ing of the Ca–Pb, Ca–Sn and Ca–Pb–Sn systems using the CALPHAD (Calculation of Phase Diagram) method and Thermocalc TM software considering also the association model [2] in binary liquids. 2. Review on binary systems 2.1. The lead–tin system The more recent assessment of the Pb–Sn system is due to Ohtani et al. [3]. Ohtani’s work takes into account the main experimental results, and consequently, the corre- sponding database has been used for the present modeling of the Ca–Pb–Sn system. 0022-3093/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.05.138 * Corresponding author. Tel.: +33 2 35 52 29 54; fax: 33 2 35 52 29 59. E-mail address: yohann.cartigny@univ-rouen.fr (Y. Cartigny). www.elsevier.com/locate/jnoncrysol Journal of Non-Crystalline Solids 353 (2007) 3727–3732