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Using a power-law relation between three-dimensional nucleation rate J and dimensionless supersaturation ratio S, and the theory of regular solutions to describe the temperature dependence of solubility, a novel Nyvlt-like equation of metastable zone width of solution relating maximum supercooling Delta T(max) with cooling rate R is proposed in the form: ln(Delta T(max)/T(0)) = Phi + beta lnR, with intercept Phi = {(1-m)/m}ln(Delta H(s)/R(G)T(lim)) + (1/m)ln(f/KT(0)) and slope beta = 1/m. Here T(0) is the initial saturation temperature of solution in a cooling experiment, Delta H(s) is the heat of dissolution, R(G) is the gas constant, T(lim) is the temperature of appearance of first nuclei, m is the nucleation order, and K is a new nucleation constant connected with the factor f defined as the number of particles per unit volume. It was found that the value of the term Phi for a system at saturation temperature T(0) is essentially determined by the constant m and the factor f. The value of the factor f for a solute-solvent system at initial saturation temperature T(0) is determined by solute concentration c(0). Analysis of the experiment data for four different solute-water systems according to the above equation revealed that: (1) the values of Phi and m for a system at a given temperature depend on the method of detection of metstable zone width, and (2) the value of slope beta= 1/m for a system is practically a temperature-independent constant characteristic of the system, but the value of Phi increases with an increase in saturation temperature T(0), following an Arrhenius-type equation with an activation energy E(sat). The results showed, among others, that solubility of a solute is an important factor that determines the value of the nucleation order m and the activation energy E(sat) for diffusion. In general, the lower the solubility of a solute in a given solvent, the higher is the value of m and lower is the value of E(sat).
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