材料导论 (6)

Module 2 Crystal Systems

There are seven fundamentally different kinds of unit cells. They differ in the lengths of the edges and the angles between them. We call them seven crystal systems. The names of the seven crystal systems are listed here. They are Cubic, Tetragonal, Orthorhombic, Trigonal, Hexagonal, Monoclinic, and Triclinic.

The lattice parameters of these seven crystal systems are shown in this picture. We will learn three of them: Cubic, Tetragonal and Hexagonal, in a few minutes.

译文：

晶胞一共有七种不同的基本类型。这些晶胞因边的长度和两边之间的夹角不同而不同。我们称其为七种晶系。七种晶系的名字如下所示：立方、四方、斜方、三方、六方、单斜和三斜。

七种晶系的晶格常数如图所示，我们会在下面学习其中的三个：立方、四方和六方

By combining the 7 crystal systems and the 4 lattice types, we get fourteen Bravais lattices. As shown here, the four lattice types are: Primitive (sometimes called simple, represented by letter P), means lattice points on the cell corners only; Body-centered (B or I): refers to one additional point at the center of the cell; Face-centered (F): refers to one additional point at the center of each of the faces of the cell; Side-centered (C): refers to one additional point at the center of each face of one pair of parallel faces of the cell.

译文：

7种晶系和4种点阵类型相组合，我们可以得到14种布拉维点阵。四种点阵类型是：简单（P）即阵点只位于晶胞顶点；体心（字母B或I）即除八个顶点外，体心上还有一个阵点；面心（F）即除八个顶点外，每个面心上还有一个阵点；底心（C）即除八个顶点外，两个相对的面心上有阵点。有缘学习更多驾卫星ｙｇｄ３０７６

The fourteen Bravais lattices are illustrated here. There are three Cubic Bravais lattices, two Tetragonal Bravais lattices, four Orthorhombic Bravais lattices, one Hexagonal Bravais lattice, one Trigonal Bravais lattice, two Monoclinic Bravais lattices, and one Triclinic Bravais lattice. Next, we will study six of them.

译文：

14种布拉维点阵如图所示：立方晶系有三种布拉维点阵，四方晶系有两种布拉维点阵，

斜方晶系有四种，六方晶系有一种，三方晶系有一种，单斜晶系有两种，三斜晶系有一种。接下来我们将学习其中的六个。

In the cubic unit cells, all sides have the same length and all angles are 90°. If the cubic unit cell consists of eight component atoms, molecules, or ions located at the corners of the cube, then it is called simple cubic (SC). If the unit cell also contains an identical component in the center of the cube, then it is body-centered cubic (BCC). If there are components in the center of each face in addition to those at the corners of the cube, then the unit cell is face-centered cubic (FCC). In FCC structure, the atoms can pack closer together than they are in the BCC structure. The closer the atoms come to each other, the less energy they have and the more stable is their structure.

Metallic iron and chromium have BCC structure. And aluminum, copper, silver and gold all have FCC structure.

译文：

在立方晶胞中，所有边长相等，所有轴间夹角都是90°，如果立方晶胞中原子、分子或离子都位于8个顶点位置，则称其为简单立方（SC）。如果晶胞中除顶点原子外，还有一个位于立方中心，则称其为体心立方（BCC）。如果立方晶胞中除了顶点原子外，每个面心上还有一个原子则称其为面心立方（FCC）。在面心立方结构中，原子排列比体心立方更加紧凑。原子排列越紧凑，体系能量越低，晶体结构越稳定。

铁和铬是体心立方结构，铝、铜、银和金都是面心立方结构。

Tetragonal unit cells result from stretching a cubic unit cell along one of its edge.In a tetragonal unit cell, all angles are 90°, but length c is different from a and b (a=b≠c). There are two tetragonal Bravais lattices: the simple tetragonal and the body-centered tetragonal. Examples of Tetragonal unit cells are Tin, Zircon and Wulfenite.

译文：

四方晶胞是由立方晶胞沿着一个边拉伸得到的。在四方晶胞中，所有的轴间夹角都是90°，但是边c的长度与边a和边b不同(a=b≠c)。四方晶系有两种布拉维点阵：简单四方和体心四方。四方晶胞的物质有锡、氧化锆和钼铅矿石。

A hexagonal unit cell has two equal axes a = b; height c, is different from a and b (a=b ≠ c); two equal angles (α and βboth are 90o), and γ is 120o. The Hexagonal Close-Packed (HCP) is another common close packed structure. In HCP structure, the top and bottom faces of the

unit cell have six atoms, these six atoms form regular hexagons and surround a single atom in the center. Between the top and bottom planes is another plane containing three additional atoms.

Examples of HCP metals are Zinc, Magnesium, Titanium and Zirconium.

译文：

六方晶胞有两个相等的边，a = b，高c不等于a和b(a=b ≠ c)，有两个相等的轴间夹角（α和β都是90°），γ角是120°。密排六方（HCP）是另一种常见的密排结构。在密排六方中，晶胞顶面和底面各有6个原子，这6个原子组成六边形。顶面和底面六边形的中心各有一个原子。在顶面和底面之间还有三个共面原子。

密排六方的金属有锌、镁、钛和锆。

Typical lattices of most metals are BCC, FCC, or HCP. Three typical crystal structures for most of the common ceramics are simple cubic, FCC or HCP.

译文：

典型的金属晶体结构有体心立方、面心立方或者密排六方。典型的陶瓷晶体结构有简单立方、面心立方和密排六方。

In conclusion, there are seven crystal systems (Cubic, Tetragonal, Orthorhombic, Trigonal, Hexagonal, Monoclinic, and Triclinic). Four lattice types (Primitive, Body-centered, Face-centered, Side-centered) combine with seven crystal systems to form 14 Bravais lattices. Typical crystal unit cells are Body-Centered Cubic, Face-Centered Cubic, Body-Centered Tetragonal, and Hexagonal Close-Packed.

译文：

总结一下，晶体一共有7种晶系（立方、四方、斜方、三方、六方、单斜和三斜）四种点阵类型（简单、体心、面心和底心），7种晶系和4种点阵类型组合形成14种布拉维点阵。典型的晶体结构是体心立方，面心立方，体心四方和密排六方。