对数正态分布的起源：解析推导及其在成核和生长过程中的应用
On the Origin of Logarithmic-Normal Distributions: An Analytical Derivation, and its Application to Nucleation and Growth Processes
摘要：
对数正态分布是自然界中最常见的分布之一，描述了大量的物理，生物甚至社会学现象。因此，这种分配的起源引起了广泛的兴趣，但仍然缺乏从基本原则出发的一般推导。使用随机形核和生长来描述结晶过程，我们得到的时间发展的晶粒尺寸分布。我们的推导提供了，第一次，对数正态型分布的形式的尺寸分布的解析表达式。我们将我们的结果固相结晶硅膜的晶粒尺寸分布。
英文摘要：
The logarithmic-normal (lognormal) distribution is one of the most frequently observed distributions in nature and describes a large number of physical, biological and even sociological phenomena. The origin of this distribution is therefore of broad interest but a general derivation from basic principles is still lacking. Using random nucleation and growth to describe crystallization processes we derive the time development of grain size distributions. Our derivation provides, for the first time, an analytical expression of the size distribution in the form of a lognormal type distribution. We apply our results to the grain size distribution of solid phase crystallized Si-films.
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