Monte Carlo simulation of induction time and metastable zone width; stochastic or deterministic?

The induction time and metastable zone width (MSZW) measured for small samples (say 1 mL or less) both scatter widely. Thus, these two are observed as stochastic quantities. Whereas, for large samples (say 1000 mL or more), the induction time and MSZW are observed as deterministic quantities. The reason for such experimental differences is investigated with Monte Carlo simulation. In the simulation, the time (under isothermal condition) and supercooling (under polythermal condition) at which a first single crystal is detected are defined as the induction time t and the MSZW Delta T for small samples, respectively. The number of crystals just at the moment of t and Delta T is unity. A first crystal emerges at random due to the intrinsic nature of nucleation, accordingly t and Delta T become stochastic. For large samples, the time and supercooling at which the number density of crystals N/V reaches a detector sensitivity (N/V)(det) are defined as t and Delta T for isothermal and polythermal conditions, respectively. The points of t and Delta T are those of which a large number of crystals have accumulated. Consequently, t and Delta T become deterministic according to the law of large numbers. Whether t and Delta T may stochastic or deterministic in actual experiments should not be attributed to change in nucleation mechanisms in molecular level. It could be just a problem caused by differences in the experimental definition of t and Delta T. (C) 2017 Elsevier B.V. All rights reserved.