Conditions for Singularity of Twist Grain Boundaries between Arbitrary 2-D Lattices

• 作者: Alfredo Gómez David Romeu Gerardo Aragón-González Jose L. Aragón Marco A. Rodríguez-Andrade
• 来源期刊: 晶体结构理论与应用(英文)
• 学科: 数学
• 关键词: Grain Boundaries CRYSTALLOGRAPHY of Interfaces COINCIDENCE Site Lattice
• 年，卷（期）: 2012,（3）
• 页码范围: 52-56
• 页数: 5页
• 分类号: O1

摘要

We have shown that the expression =2tan-1/ derived by Ranganathan to calculate the angles at which there exists a CSL for rotational interfaces in the cubic system can also be applied to general (oblique) two-dimensional lattices provided that the quantities 2 and /cos() are rational numbers, with =|b|/|a| and is the angle between the basis vectors a and b. In contrast with Ranganathan’s results, N;given by N=tan2() needs no longer be an integer. Specifically, vectors a and b must have the form a=(1,0);b=(r,tan) where r is an arbitrary rational number. We have also shown that the interfacial classification of cubic twist interfaces based on the recurrence properties of the O-lattice remains valid for arbitrary two-dimensional interfaces provided the above requirements on the lattice are met.