Statistical treatment of nucleation and growth in a thin layer between two interfaces

✍ Scribed by Takashi Tagami; Shun-Ichiro Tanaka

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 252 KB
• Volume: 46
• Category: Article
• ISSN: 1359-6454
• DOI: 10.1016/s1359-6454(97)00263-2

✦ Synopsis

AbstractÐThe statistical distribution of phantom crystallites in the Kolmogorov±Johnson±Mehl±Avrami (KJMA) model is corrected to account for the shrinking of phantom crystallites to eective size owing to the halting of crystal growth between two interfaces. In a previous paper, a stochastic treatment of shrinkage led to a kinetic equation, dX(t)/ dV ex =[1 À X(t)] 2 À g , where X(t) is the transformed fraction, V ex is the KJMA extended volume fraction, and g is a overlap probability between a phantom crystallite and a crystallite. The present paper focuses on the statistical meaning of the kinetic equation to ®nd that crystallites of size k and phantom crystallites of dierent size kg m (m = 1, 2, 3,...) are generated according to the Poisson distribution as determined by g. The other statistical features of the phantom crystallites and crystallites are fully explained in terms of g.