Analysis of the effect of volume on induction time and metastable zone width using a stochastic model

• Equations for induction time and metastable zone width (MSZW) are presented.
• Reported data of induction time and MSZW are explained theoretically.
• Induction time and MSZW depend on the detection criterion of nucleation event.
• Stochastic aspect of nucleation appears even when the sample volume is large.

The effect of sample volume on induction time and metastable zone width (MSZW) is discussed theoretically by using a stochastic model. The effect of sample volume on induction time and MSZW is different depending on the detection criterion of nucleation used. The induction time and MSZW both decrease with an increase in sample volume when these values are determined on the basis of total number of crystals per sample N (an extensive variable). However, when the number density of crystals N/V (an intensive variable) is used, both of them remain unchanged even when the volume is changed. Although nucleation is stochastic by nature, the induction time and the MSZW, which are both nucleation-related, are not always observed as stochastic. In case of small samples, the stochastic aspects are usually observed, because a single crystal or a small number of crystals are used as a detection criterion of nucleation. Even for large samples, the stochastic aspect could be observed in theory. However, it is not usually the case in actual experiments because a small number of crystals are rather difficult to detect when the sample is large. The stochastic induction time and MSZW are mathematically related to the deterministic induction time and MSZW, respectively.