Violation of Adiabatic Scaling in the Distribution of Particles Nucleated in a Rapid Quench

A singular perturbation type analysis is applied to nucleation and growth equations with rapidly changing temperature. It is shown that conventional adiabatic scaling breaks down in a nonanalytical manner for any finite quench rate. An "effective" nucleation rate is introduced, which allows one to reconstruct the nonadiabatic distribution at large sizes. A new, nonadiabatic scaling law for the third moment of the distribution (i.e., volume fraction of the new phase) as a function of the quench rate is proposed and tested for several glass-forming systems.