Statistical Approach to Crystal Nucleation in Glass-Forming Liquids

被引:13
作者
Deubener, Joachim [1 ]
Schmelzer, Juern W. P. [2 ]
机构
[1] Tech Univ Clausthal, Inst Nonmetall Mat, Zehntner Str 2a, D-38678 Clausthal Zellerfeld, Germany
[2] Univ Rostock, Inst Phys, Albert Einstein Str 23-25, D-18059 Rostock, Germany
关键词
nucleation; crystal growth; general theory of phase transitions; glasses; glass transition;
D O I
10.3390/e23020246
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In this work, methods of description of crystal nucleation by using the statistical approach are analyzed. Findings from classical nucleation theory (CNT) for the average time of formation of the first supercritical nucleus are linked with experimental data on nucleation in glass-forming liquids stemming from repetitive cooling protocols both under isothermal and isochronal conditions. It is shown that statistical methods of lifetime analysis, frequently used in medicine, public health, and social and behavioral sciences, are applicable to crystal nucleation problems in glass-forming liquids and are very useful tools for their exploration. Identifying lifetime with the time to nucleate as a random variable in homogeneous and non-homogeneous Poisson processes, solutions for the nucleation rate under steady-state conditions are presented using the hazard rate and related parameters. This approach supplies us with a more detailed description of nucleation going beyond CNT. In particular, we show that cumulative hazard estimation enables one to derive the plotting positions for visually examining distributional model assumptions. As the crystallization of glass-forming melts can involve more than one type of nucleation processes, linear dependencies of the cumulative hazard function are used to facilitate assignment of lifetimes to each nucleation mechanism.
引用
收藏
页码:1 / 28
页数:28
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