点组和空间组之间的区别

关键区别 - 点组与SpaceGroup

The terms point group and space group are used in crystallography. Crystallography is the study of the arrangement of原子in a crystalline solid. The crystallographic point group is a set of symmetry operations that leave at least one point unmoved. A symmetry operation is an act of obtaining the original image of an object even after moving it. The symmetry operations used in point groups are rotations and reflections. A space group is the 3D symmetry group of a configuration in space. A symmetry group is the group of all transformations obtained without varying the composition during the group operation. Thekey difference在点组和太空组之间是there are 32 crystallographic point groups whereas there are 230 space groups that are created by the combination of 32 point groups and 14 Bravais lattices.

内容

1.Overview and Key Difference
2.What is Point Group
3.What is Space Group
4.Side by Side Comparison – Point Group vs Space Group in Tabular Form
5.概括

What is Point Group?

晶体学点组是一组对称操作，至少使一个点不动。点组中描述的对称操作是旋转和反射。在点组对称操作中，将对象中的一个中心点保持不动（固定），而将对象的其他面移动到同类特征的位置。在那里，对象操作之前和之后，对象的宏观特征应保持相同。

For any given object, there is a certain number of symmetry operations possible (with defined geometrical relations among symmetry operations). The object is said to have the symmetry described by the point group. Therefore, different objects having different point symmetries are described by different point groups.

在点组的符号中，有两个系统正在使用。

1. Schoenflies Notation

In Schoenflies notation system, point groups are named as C_NV, C_NH, D_NH, T_d, O_h, etc. The different symbols used in this notation system are given below.

• n is the highest number of rotation axes
• v is the vertical mirror plane (mentioned only when there are no horizontal mirror planes)
• h is the horizontal mirror planes
• T是一个四面体点组
• 是一个八面体点小组

For example, C_n使用表明该点组具有N倍旋转轴。当它作为C_NH, it means there is a C_nalong with a mirror plane (reflection plane) perpendicular to the axis of rotation. In contrast, C_NV是c_nwith a mirror plane parallel to the axis of rotation. If the point group is given as S_2n, it indicates that the point group has only a 2n-fold rotation-reflection axis.

2. Hermann-Mauguin Notation

Hermann-Mauguin符号系统通常用于空间组。但是，它也用于晶体学点组。它给出最高的旋转轴。例如，仅具有2倍旋转轴的点组表示为2。_2h通过schoenflies符号为2/m，在Hermann-Mauguin符号系统中，符号“ m”表示镜面平面，而斜线符号表示镜面垂直于两倍的轴。下表显示了不同晶格系统的点组的不同符号。

There are 32 point groups. The simplest point groups are 1, 2, 3, 4, 5 and 6. All these point groups comprise only one rotation axis. For rotary-inversions, there are axes named -1, m, -3, -4 and -6. Other 22 point groups are combinations of these point groups.

什么是空间群体？

空间组是空间中配置的3D对称组。There are 230 space groups. These 230 groups are a combination of 32 crystallographic point groups (mentioned above) and 14 Bravais lattices. The勇敢的格子are given in the below table.

A space group gives a description of symmetry of a crystal. Space groups are combinations of translational symmetry of unit cell and symmetry operations such as rotation, rotary-inversion, reflection, screw axis and glide plane symmetry operations.

What is the Difference Between Point Group and Space Group?

点组与空间组
晶体学点组是一组对称操作，至少使一个点不动。	空间组是空间中配置的3D对称组。
Components
There are 32 crystallographic point groups.	There are 230 space groups (created by the combination of 32 point groups and 14 Bravais lattices).
Symmetry Operations
The symmetry operations used in point group detection are rotation and reflection.	空间组检测中使用的对称操作是旋转，旋转转换，反射，螺钉轴和滑行平面对称操作。

概括–点组vsSpaceGroup

点组和空间组是晶体学下描述的术语。晶体学点组是一组对称操作，所有这些操作至少使一个点不动。空间组是空间中配置的3D对称组。点组和空间组之间的区别在于，有32个晶体学点组，而有230个空间组（由32个点组和14个Bravais晶格组合创建）。

Reference:

1.“ 2：对称操作和对称元素。”Chemistry libretexts，libretexts，2017年5月6日。Available here
2.“Crystallographic point group.” Wikipedia, Wikimedia Foundation, 28 Feb. 2018.Available here

Image Courtesy:

1.’Ice Ih Space Group’By Dbuckingham42 – Own work,(CC BY-SA 4.0)viaCommons Wikimedia