Kinetic approach to the determination of the phase diagram of a solid solution

• Published in: Calphad 2006-06, Vol.30 (2), p.209-215
• Main Authors: Matovic, Marija, van Miltenburg, J.C., Oonk, H.A.J., Los, Jan H.
• Format: Article
• Language: English
• Subjects: Chemistry; Exact sciences and technology; General and physical chemistry; Phase equilibria
• ISSN: 0364-5916; 1873-2984
• DOI: 10.1016/j.calphad.2005.11.005

A binary mixture of 1,4-dichlorobenzene and 1,4-dibromobenzene, as a representative of a system that forms a solid solution, was measured in an adiabatic calorimeter. Several mixtures of different compositions were heated to 380 K, kept in the liquid phase at this temperature overnight, and then cooled slowly down to 250 K. The enthalpy path of the mixture measured during cooling carries the information that enables us to describe the crystallization process. In the first stage, crystallization develops rapidly and clearly deviates from equilibrium, while in the second stage it proceeds significantly slower, whereby we assume that the surface of the solid is in equilibrium with the existing liquid phase at the given temperature during cooling. Such an approach opposes the one that assumes equilibrium between the liquid and solid bulks, known as the equilibrium model. We show that by employing the kinetic model, the experimental enthalpy path of the mixture during cooling in the adiabatic calorimeter can be very successfully reproduced, while the equilibrium model fails in this aspect. Furthermore, we propose a procedure where the kinetic model is used to obtain the excess thermodynamic properties of the solid phase. These quantities enable the calculation of the liquid–solid phase diagram using the excess parameters obtained from the approach that does not assume the overall equilibrium between the phases during the crystallization process.