∑_1关系式的概率联系及其230空间群表

• 作 者: 刘永盛 金钟声 郭东耀
• 机 构: 中国科学院长春应用化学研究所rrrrrrrrn,中国科学院长春应用化学研究所rrrrrrrrn,吉林大学理论化学研究所 长春
• 出 处: 中国科学(B辑 化学 生物学 农学 医学 地学)
• 发表日期: 1982年05期
• 关键词: 概率值 结构因子 空间群 晶体结构测定 简并度 立方晶系 代数的 文中 约束条件 求和号

本文以单晶体结构测定的直接法为对象,从Hauptman和Karle Σ_1关系的P+(h_1)出发,利用结构因子代数的方法,讨论了惯用Σ_1关系式之间的联系和区别及P+(h_1)概率值。文中引入h_1等效点权ω及h_2简并度权ε_2的概念,使得用Σ_1关系式表示的P+(h_2)更为严密;并且发现,在高级晶系(四方、三方、六方和立方晶系)中存在着大量相关的Σ_1关系式。按本文的结果,只需保留其为数不多的独立的Σ_1关系式。文中采用线性化原则,完成了高级晶系156个空间群Σ_1关系式的造表工作。加上Haek完成的74个后,提供一份包括230空间群的简明完备的Σ_1关系式表。另外,还对Haek表做了三处勘误。

In this paper, the direct method of single crystal structure determination is taken as the object. Based on the P + (h_1) of Hauptman and Karle Σ_1, the relationship and difference between the conventional Σ_1 and the probability of P + (h_1) are discussed by using structural factor algebra. . In this paper, we introduce the concept of h_1 equivalent weight ω and h_2 degeneracy weight ε_2, so that P + (h_2) expressed by Σ_1 relation is more rigorous. It is also found that in the higher order crystal system (tetragonal, tripartite, hexagonal and cubic ) There is a large number of related Σ_1 relations. According to the result of this paper, we only need to keep a few independent Σ_1 relations. In this paper, we use the principle of linearization to complete the tabulation of the Σ_1 relation of 156 space groups of the advanced crystal system. Together with the 74 completed by Haek, a concise Σ_1 relational table consisting of 230 space groups is provided. In addition, Haek form also made three errata.