Department of Materials Science and Engineering, Kyoto University, Sakyo, Kyoto 606-8501, Japan.
J Phys Condens Matter. 2010 Mar 31;22(12):125402. doi: 10.1088/0953-8984/22/12/125402. Epub 2010 Mar 8.
We propose a cluster expansion (CE) technique that can express any function of atomic arrangement on any given lattice with the same number of lattice points in a single formalism. In the proposed CE, two types of spin variable, σ and τ, on the base lattice and virtual lattice, respectively, are introduced. The former spin variable specifies the occupation of the constituent elements for each lattice point. The latter specifies the positions of each lattice point. Basis functions constructed from the two types of spin variable satisfy completeness and orthonormality for any atomic arrangement on given lattices. As examples, the proposed CE is applied to one- and three-dimensional lattices in a binary system, which clarifies the concept of base and virtual lattices, how the functions of atomic arrangements are expressed in terms of the two types of spin variable, and the efficiency and convergence of the proposed CE with a finite number of clusters and input structures.
我们提出了一种团簇展开（CE）技术，它可以用相同数量的格点在单个形式中表达给定晶格上任何原子排列的任何函数。在所提出的 CE 中，分别在基格和虚拟格上引入了两种类型的自旋变量σ和τ。前者自旋变量指定每个格点的组成元素的占据情况。后者指定每个格点的位置。由这两种自旋变量构造的基函数对于给定格点上的任何原子排列都是完备和正交的。作为例子，将所提出的 CE 应用于二元体系中的一维和三维晶格，阐明了基格和虚拟格的概念、原子排列的函数如何用两种类型的自旋变量表示，以及有限数量的团簇和输入结构的 CE 的效率和收敛性。
