On spinodal boundaries of the AgCu system

Abstract

Introduction The Ag-Cu system satisfies the Hume-Rothery criteria for the formation of a solid solution phase over the entire range of compositions. However, the phase diagram of this system exhibits a eutectic reaction between the two terminal solid solution phases, ~ and I~. Duwez et. al. [1], in their gun quenching experiments, have shown the complete solubility of Ag and Cu in the solid state. Following Duwez's work, several investigations have reported the formation and characterization of metastable solid solution phases in this system. Nagakura et al. [2], in their experiments, have shown that the metastable a' and 13' phases form from the y' phase on aging at room temperature. Systematic studies of Stoering and Conrad [3], and Boswell and Chadwick [4] confirmed the transformation of metastable y' to a' and 13' phases on aging. Stoering and Conrad [3] sometimes observed only the a' phase in the thicker region of the foil, without evidence for the existance of the y' phase. The route of formation of a metastable ~ phase in such a case is not very clear. It could form either directly from the liquid or as a decomposition product of the y' phase. However, in their mushy-quenching experiments, Prasad et al. [5] reported the formation of an a' phase from the highly undercooled liquid in metastable equilibrium with the primary 13 phase. In contrast, our recent investigation on a mushy-quenched Cu-Ag alloy showed the metastable a' phase as a decomposition product of a solid solution y' phase, having an Ag-28at.% Cu composition. This ~,' phase was shown to form by the diffusionless solidification of liquid, undercooled below a T o temperature. On further cooling, the y' phase transforms through the spinodal route [6]. In order to understand the mechanism of formation and decomposition of metastable phases in this system, the location of the spinodal boundary in the phase diagram is essential. The present work aims to present the chemical and coherent spinodals for this system. Thermodynamic Formulation Various authors have calculated the spinodal boundaries, using different thermodynamic approaches [4,7-12]. Boswell and Chadwick [4] calculated the spinodal boundary, using the expression of Cook and Hilliard [8]. Ishihara and Shingu [9], Murray [10] and Hayes et al. [11] performed a thermodynamic analysis of the phase diagram. However, there are some limitations in their procedures. As a result, conclusions drawn from these are valid only for the conditions arising for low underoooling of the melt. Jonsson and Agren [12] provided a new model, which is applicable, even at high undercooling of the melt. These investigators calculated the metastable solidus and liquidus curves in the Ag-Cu system. For calculating the metastable boundaries of the Ag-Cu system, Jonsson and Agren [12] followed the procedure of Jansson [13], while utilizing the thermodynamic data given by Murray [10], and Choudhary and Ghosh [14].