作者： Lei.Kang

The Unit Cell

This section deals with the geometry of crystaline systems. These could describe how metal atoms pack when they form metallic solids, or how ions pack when they form ionic crystals. We will look at the ionic structures in the next section, and here focus on the generic unit cell and it's application to metallic structures.

There are 7 types of unit cells, defined by edge lengths (a,b,c) respectively along the x,y,z axis and angles α, β, and γ. In this class we will only focus on the cubic unit cell, and there are three types of cubic cells that you need to be familiar with, and these are represented in figure 12.1.b.

• α = angle in the yz plane
• β = angle in the xz plane
• γ = angle in the xy plane

The 7 types of unit cells. In this class we will only look at cubic systems, and will identify 3 types of cubic unit cells

面角恒等定律（law of constancy of interfacial angles）又称面角守恒定律、斯台诺定律 (law of Steno)。 系由丹麦学者斯台诺 (Nicolaus Steno)于1669年所提出的。 其内容为：同种物质晶体之间,其对应晶面间的夹角恒相等。 这一定律的意义在于它从千变万化的歪晶中揭示出了晶体在外形上所固有的规律性,从而奠定了 几何结晶学 的基础。 它的提出,也是结晶学正式成为一门学科的标志。 但是,现代对晶体研究的结果表明,实际晶体的内部结构总是或多或少地偏离理想状况的,且可能受环境温度和压力的变化而发生各向异性的膨胀或收缩,因此,晶体的面角恒等只是在一定的精确度上而言的。

The law of the constancy of interfacial angles (or 'first law of crystallography') states that the angles between the crystal faces of a given species are constant, whatever the lateral extension of these faces and the origin of the crystal, and are characteristic of that species. It paved the way for Haüy's law of rational indices.

空间格子（lattice）是：表达晶体结构周期重复规律的几何图形。即空间格子就是描述晶体结构格子构造的简单几何图形。

The crystal lattice is the symmetrical three-dimensional structural arrangements of atoms, ions or molecules (constituent particle) inside a crystalline solid as points. It can be defined as the geometrical arrangement of the atoms, ions or molecules of the crystalline solid as points in space.

Crystal, any solid material in which the component atoms are arranged in a definite pattern and whose surface regularity reflects its internal symmetry.

晶体（Crystal）是指内部质点(原子、离子或分子)在三维空间周期性地重复排列构成的固体物质。这种质点在三维空间周期性地重复排列也称格子构造，所以，晶体就是具有格子构造的固体。