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

Abstract

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.

Structure and functionality of edible fats

“…Thus the most important field in crystallization is the temperature field. There are several other conditions that can affect the crystallization at a given location: a spatial distribution of heterogeneous nucleation sites; a concentration field; 113,114 a distribution of velocities resulting in a shear rate field; 115,116 an applied ultrasound field; 117,118 the presence of magnetic 119,120 or electric fields; 121 a pressure field and the ubiquitous gravitational field. 122 We will focus our review and discussion on temperature, concentration and shear flow fields since they are the ones that are currently most relevant to fat crystallization.…”

On the Definition of a Monte Carlo Model for Binary Crystal Growth

“…A pronounced example of systems where large deviations from equilibrium can be expected are systems involving mixed solid phases, here meant as multicomponent solid solutions, due to the (usually) very low diffusion rate in the solid phase. This has been demonstrated both experimentally − and theoretically. − It certainly holds for molecular systems. In atomic systems, like metals, the diffusion rate may still be appreciable enabling relaxation to the equilibrium state within shorter time scales, especially at high temperature.…”

“…In that case the kinetics during crystallization is of decisive importance for the state of the crystallized product just after crystallization, i.e., its composition, possibly with composition gradients, and its stability. Usually equilibrium is not achieved, even if the crystallization is performed very slowly, as has recently been demonstrated for p -dichloro-/ p -dibromobenzene mixtures . The changing liquid composition during the crystallization process leads to a final solid phase built up of shells with a gradual change in composition, even if one assumes that the actual growth composition of the solid phase is in agreement with the thermodynamic equilibrium phase diagram (EPD).…”

Models for the determination of kinetic phase diagrams and kinetic phase separation domains

“…The extent of these deviations from equilibrium will depend on the history of the system, especially on the kinetics during the growth, which depend on the growth conditions and also on the scale of the system. The occurrence of such deviations is well known and has also been demonstrated experimentally [1][2][3]. Theoretically, the extent of the deviations was investigated on the basis of a kinetic crystallization model [4,5], both for well-mixing systems [4] and for systems showing phase separation [5].…”

“…In Ref. [3] the complications due to non-equilibrium states are tackled in a different way for slow crystallization processes performed in an adiabatic calorimeter by dropping the assumption of total equilibrium and replacing it by assuming equilibrium between the liquid phase and only the surface of the solid phase during growth. In this way both enthalpy and entropy excess parameters were successfully derived from experimental cooling curves.…”