The kinetics of nucleation of solid solutions from aqueous solutions: a new model for calculating non-equilibrium distribution coefficients

Abstract

The nucleation kinetics of binary solid solutions, with general formula B xC 1−xA, crystallising from aqueous solution can be described using a generalised expression for the nucleation rate: the function, J(x), in which supersaturation, interfacial free energy and other parameters of the classical nucleation rate equation are considered as functions of the solid composition. As an example, we studied the behaviour of such J(x) functions for the case of the (Ba,Sr)SO 4 and (Ba,Sr)CO 3 solid solutions. J(x) functions are very sensitive to slight changes in the composition of the aqueous solution, which result in strong modifications of the nucleation kinetics. The implications of the relationship between supersaturation and nucleation rate functions for the general nucleation behaviour in solid solution-aqueous solution (SS-AS) systems are discussed. Finally, we present a method for constructing non-equilibrium Roozeboom diagrams based on the nucleation kinetics in SS-AS systems. Our Roozeboom diagrams calculated for different departures from equilibrium conditions are consistent with previous experimental work and they can be used to predict actual distribution coefficients.