大学化学 >> 2018, Vol. 33 >> Issue (9): 95-104.doi: 10.3866/PKU.DXHX201802035

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浅谈质心分数坐标在确定等径圆球密堆积空隙中的应用

张文静*(),汤华彪,朱艳艳,魏东辉,刘春梅,唐明生*()   

  • 收稿日期:2018-02-27 发布日期:2018-09-28
  • 通讯作者: 张文静,唐明生 E-mail:zhangwj@zzu.edu.cn;mstang@zzu.edu.cn
  • 基金资助:
    国家自然科学基金(21503191);中国博士后科学基金(2015M572115)

Applications of Centroid Fractional Coordinates in Locating Interstices in Close Packings of Equal Spheres

Wenjing ZHANG*(),Huabiao TANG,Yanyan ZHU,Donghui WEI,Chunmei LIU,Mingsheng TANG*()   

  • Received:2018-02-27 Published:2018-09-28
  • Contact: Wenjing ZHANG,Mingsheng TANG E-mail:zhangwj@zzu.edu.cn;mstang@zzu.edu.cn
  • Supported by:
    国家自然科学基金(21503191);中国博士后科学基金(2015M572115)

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摘要：

理解等径圆球密堆积的性质和特点是学习金属晶体结构和性质的基础，密堆积中的空隙问题对学习和理解离子晶体的结构和性质非常重要。但晶体结构的多样性和复杂性，导致这部分内容成为结构化学课程中讲解和学习的一个难点问题。本文将以A1，A2，A3这三种最常见的密堆积结构为例，详细介绍一种利用质心分数坐标计算推导密堆积结构中四面体和八面体空隙中心的方法，以及如何通过坐标计算求解中心到顶点的距离和中心到堆积球面的最短距离。与立体几何方法相比较，质心分数坐标法不仅更加简洁易学，而且更有助于理解空隙在晶胞中的位置和分布问题。

关键词: 空隙, 分数坐标, 质心, 密堆积

Abstract:

Deep understanding of the nature and characteristics of close packings of equal spheres is fundamental for further study towards structure and property of metallic crystals. And the knowledge to number and distribution of various interstices in close packings of equal spheres is very important to help illustrate the structure and property of ionic crystals. However, the diversity and complexity of the crystal structures make it difficult in teaching and learning structural chemistry. In this paper, based on discussions on the three most common close packing models (A1, A2, A3), a method to locate centers of interstices according to calculating the centroid fractional coordinates (CFC) of particles constructing these interstices was introduced. In addition, the way using CFCs to calculated distance between vertex and interstice center and the shortest distance from interstice center to surface of the packing sphere was also illustrated in detail. Compared with the traditional solid geometry method, the CFC method is demonstrated to be much simpler, easier to learn, and most importantly, helpful for understanding number and distribution of various interstices in close packings.

Key words: Interstice, Fractional coordinate, Centre of mass, Close packing