Geometry of coincident-site lattice boundaries and fractal aspect in grain boundary energy landscape

晶界能量景观中重合点晶界的几何形状和分形方面

• 批准号: 08640490
• 负责人: FUCHIZAKI Kazuhiro
• 金额: $ 0.83万
• 依托单位: KYUSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08640490/
• 关键词: twist boundary; grain boundary energy; fractal; glass; amorphous; slow dynamics; molecular dynamics method

New mathematical method which can describe systematically various lattice patterns showing up at a grain boundary between the two crystallines was devised. This method is based on the conformal mapping regarding the grain boundary as a Gauss-Argand plane, and is easily extended to a case of resultant lattice patterns which are made of low symmetry crystalline structures. In fact, the method was applicable to the twist boundaries as well which are constructed from (110)-plane twist of simple cubic structure. By using the two-dimensional version of Frenkel-Kontrova Hamiltoinan upon evaluation of grain boundary energy, the energy landsape, which is spanned on the parameter space (misorientation angle in the twist boundary case) specifying the precise location of the geometry of the boundary, is shown to have the exact self-similarity consisting of energy cusps. That is the the energy surface is made up of fractal aggregates of energy cusps with various depth, the largest ones being observed experimentally.Application of this grain boundary energy as a function of misorientation angle between the two grains divided by the boundary to the two-dimensional vertex model that is capable of describing grain growth has led to a dicovery of quite intriguing property that a relaxation process to the stationary growth process is 'stretched'. This is found to be ascribed to a hierarchical nature in the relaxation processes, and is supposed to have some connection with the recent experimental findings regarding the glassy properties at grain boundaries.A series of this research will be presented in a talk in Third International Conference on Grain Growth held in Pittsburgh, USA in coming June. A primary purpose, which is to make my powerful scheme be worldwide, is therefore said to be achieved.

设计了一种新的数学方法，可以系统地描述两晶晶界上出现的各种晶格图案。该方法基于将晶界视为高斯-阿尔冈平面的共形映射，并且很容易推广到由低对称性晶体结构构成的合成晶格图的情况。实际上，该方法同样适用于由简单立方结构(110)-平面扭转构成的扭转边界。利用二维版的Frenkel-Kontrova Hamiltoinan对晶界能量进行评估，在参数空间（扭曲边界情况下的取向角）上跨越的能量格局表明边界几何的精确位置具有由能量尖点组成的精确自相似性。也就是说，能量表面是由不同深度的能量尖的分形聚集体组成的，其中最大的是实验观察到的。将晶界能量作为两个晶粒之间的取向角除以能够描述晶粒生长的二维顶点模型的边界的函数的应用，发现了一个相当有趣的特性，即静止生长过程的松弛过程被“拉伸”。这被认为是弛豫过程中的层次性质，并被认为与最近关于晶界玻璃性的实验发现有一定的联系。今年6月在美国匹兹堡举行的第三届国际谷物生长会议上，将发表一系列的研究成果。因此，一个主要的目的，即使我的强大计划在世界范围内传播，可以说已经实现了。

项目成果

K.Fuchizaki et al.: "Molecular dynamics simulation study of the behavior of molecular crystal tin tetraiodide under hydrostatic pressure" J.Phys.Soc.Jpn.66. 1575-1578 (1997)

K.Fuchizaki等：“静水压力下分子晶体四碘化锡行为的分子动力学模拟研究”J.Phys.Soc.Jpn.66。

K.Fuchizaki et al.: "Molecular dynamics simulation study of the behavior of molecular crystal tin tetra-iodide under hydrostatic pressure" J.Phys.Soc.Jpn.66. 1575-1578 (1997)

K.Fuchizaki等：“分子晶体四碘化锡在静水压力下行为的分子动力学模拟研究”J.Phys.Soc.Jpn.66。

K.Kawasaki et al.: "Monte Carlo Simulation of the Dynamical Density Functional Equation for Supercooled Liquids" Prog.Theor.Phys.Suppl.126. 305-308 (1997)

K.Kawasaki 等人：“过冷液体动态密度泛函方程的蒙特卡罗模拟”Prog.Theor.Phys.Suppl.126。

K.Kawasaki et al.: "Three Topics on Glassy Dynamics in Condensed Matter" J.Res.Inst.Sci.Tech. (Chubu University). 9. 1-10 (1997)

K.Kawasaki 等人：“凝聚态玻璃动力学的三个主题”J.Res.Inst.Sci.Tech。

N.Hamaya et al.: "Amorphization and Molecular Dissociation of Sn14 at High Pressure" Phys.Rev.Lett.79. 4597-4600 (1997)

N.Hamaya 等人：“高压下 Sn14 的非晶化和分子解离”Phys.Rev.Lett.79。