真实自回避行走中晶体生长界面结构的分形行为

The fractal behavior of interfacial structure of crystal growth on the basis of the true self-avoid walk model

晶体生长过程实际上就是生长基元从周围环境中不断地通过界面而进入晶格座位的过程。一般认为,研究生长基元以何种方式以及如何通过界面进入晶格座位是晶体生长界面结构研究中的关键。在生长基元以分子或者原子的微粒子形式在生长环境中进行无规游走的前提下,本文运用真实自回避行走(TSAW)模型,通过重整化群思想来研究晶体生长界面结构的分形行为。研究发现:晶体生长界面结构的分形行为与生长基元的游走路径形态密切相关,并且在理想状况下真实自回避行走与标准Koch曲线的分形维极为接近。

Crystal growth is a process in which the growth elements from the ambience cross the interface and enter crystal lattices. In general, the entry of the growth elements into the crystal lattice through the interface constitutes a key problem in the study of interfacial structure of crystal growth. It is held in this paper that the growth elements （molecules or atoms） walk at random in ambience. On the basis of the true self-avoid walk （TSAW） model and the principle of renormalization, the authors studied fractal behavior of interfacial structure of crystal growth. It is found that fractal behavior of interfacial structure of crystal growth has a close relationship with the shape of the walking route of the growth elements, and that there exists a close similarity in fractal dimension between TSAW and standard Koch curve under the ideal condition.