Dependence of the critical undercooling for crystallization on the cooling rate

Crystallization in solutions under steady cooling is considered in the case of instantaneous nucleation, in which all crystallites appear at once in the solution and grow in the absence of crystallites born subsequently. Expressions are obtained for the total crystallite volume as a function of the steadily increasing undercooling. These expressions are employed for determining the dependence of the relative critical undercooling u(c) for crystallization on the cooling rate q. The resulting u(c)(q) formula reveals the physical meaning of the parameters in the linear relationship, often reported experimentally, between u(c) and q in double logarithmic coordinates. The results obtained are also directly applicable to overall crystallization of melts at sufficiently small undercoolings.