第一章固体材料的结构.docx

1、第一章固体材料的结构第一章 固体材料的结构Chapter 1. The Structure of Materials本章要讨论的主要问题是： (1) 为什么原子能结合成固体？(2) 材料中存在哪几种键合方式？(3) 决定键合方式的主要因素有哪些？(4) 材料的哪些性能和其键合方式有密切的关系？(5) 如何描述晶体中原子的排列？(6) 金属晶体有哪些常见的晶体结构？Questions for Chapter 11. What is crystal structure? 2. What is crystal lattice?3. How many types of bonding between

2、atoms? What are the most important factors in determining the types of bonds?4. What is the relationship between bonds and properties of materials?5. How to describe the atom arrangement in crystalline?6. What are the most metals crystal structures?1-1 几何晶体学的基本知识Sec.1.1 The Fundamentals of Geometric

3、 CrystallologyThe most important aspect of any engineering material is its structure, because its properties are closely related to this feature. To be successful, a materials engineer must have a good understanding of this relationship between structure and properties. 1、原子之间的键合 The types of bonds

4、Atomic scale structure: By atomic structure we mean(1) The types of atoms present;(2) The types of bonding between the atoms;(3) The way the atoms are packed together.The two major classes of atomic bonds are primary and secondary bonds. Primary bonds are generally one or more orders of magnitude st

5、ronger than secondary bonds.The three major types of primary bonds are ionic, covalent and metallic bonds. All primary bonds involve either the transfer of electrons from one atom to another or the sharing of electrons between atoms.One of the important factors in determining the type of band that a

6、n atom will form is its electronegativity.（1）离子键与离子晶体 Ionic bondingThe most common type of bond in a compound containing both electropositive and electronegative elements is the Ionic bonds. This bond involves electron transfer from the electropositive atom to the electronegative atom.原子结合：电子转移，结合力大

7、，无方向性和饱和性；离子晶体：硬度高，脆性大，熔点高、导电性差。如氧化物陶瓷。（2）共价键与原子晶体 covalent bondingCovalent bonds form in compounds composed of electronegative elements, especially those with four or more valence electrons. Since there are no electropositive atoms present, the “extra” electrons required to fill the valence shell o

8、f the electronegative atoms must be obtained by sharing electrons.原子结合：电子共用，结合力大，有方向性和饱和性；原子晶体：强度高、硬度高（金刚石）、熔点高、脆性大、导电性差。如高分子材料。（3）金属键与金属晶体 metallic bondingSolid composed primarily of electropositive elements containing three of fewer valence electrons are generally held together by metallic bonds.

9、As mentioned above, the electropositive elements can obtain a stable electron configuration by “giving up” their valence electrons. Since no electronegative atoms present to receive the “extra” electrons, they are instead donated to the structure in general. That is, they are shared by all of the at

10、oms in the compound.原子结合：电子逸出共有，结合力较大，无方向性和饱和性；金属晶体：导电性、导热性、延展性好，熔点较高。如金属。金属键：依靠正离子与构成电子气的自由电子之间的静电引力而使诸原子结合到一起的方式。（4）分子键与分子晶体 Van der Waals bonding原子结合：电子云偏移，结合力很小，无方向性和饱和性。分子晶体：熔点低，硬度低。如高分子材料。氢键：（离子结合）X-H-Y（氢键结合），有方向性，如O-HO（5）混合键 mixed bondingIn compounds involving more than one element, ionic bon

11、ds are favored when the difference in electronegativities is large, and covalent bonds are favored when the difference in electronegativities is small. The transition from pure ionic to pure covalent bonding is gradual, and many compounds display a bond with mixed ionic/covalent characteristics. 实际材

12、料（金属和陶瓷）中结合键多为混合键 金属中主要是金属键，还有其他键如：共价键、离子键 陶瓷化合物中出现离子键和金属键的混合 一些气体分子以共价键结合，而分子凝聚时依靠范德华力 聚合物的长链分子内部以共价键结合，链与链之间则为范德华力或氢键 2、原子之间的结合力与结合能 The bond-force and bond-energy between atomsThe internal energy of a crystal is considered to be composed of two parts. First, there is the lattice energy U that is

13、defined as the potential energy due to the electrostatic attractions and repulsions that atoms erect on one another. Second, there is the thermal energy of the crystal, associated with the vibrations of atoms about their equilibrium lattice positions.The equilibrium distance between atoms is caused

14、by a balance between repulsive and attractive forces. In the metallic bond, for example, the attraction between the electrons and the ion cores is balanced by the repulsion between ion cores. Equilibrium separation occurs when the total inter-atomic energy (IAE) of the pair of atoms is at a minimum,

15、 or when no net force is acting to either attract or repel the atoms.The minimum energy is the binding energy, or the energy required to create or break the bond. Consequently, materials having a high binding energy also have a high strength and a high melting temperature. Ionically bonded materials

16、 have a particularly large binding energy because of the large difference in electro-negativities between the ions. Metals have lower binding energies because the electro-negativities of the atoms are similar.It is important to recognize that the relationships between the bond-energy curve and macro

17、scopic properties developed in this section show general trends. They are extremely helpful in understanding and predicting relative differences in properties between different materials. 3 布拉菲点阵 Bravais lattice A lattice can be defined as an indefinitely extended arrangement of points each of which

18、 is surrounded by an identical grouping of neighboring points. There are 14 valid 3-D lattices, on which the basis-atoms or groups of atoms can be placed. They are called Bravais lattices. Each of the lattice points is equivalent; that is, the lattice points are indistinguishable. 14种点阵分属7个晶系。4 晶向指数

19、与晶面指数 Miller indicesMiller indices are symbols to describe the orientation in space of important crystallographic directions and planes.The miller index notation not only simplifies the description of directions, but also permits simple vector operations like the dot and cross products.晶向：空间点阵中各阵点列的

20、方向。晶面：通过空间点阵中任意一组阵点的平面。国际上通用米勒指数标定晶向和晶面。(1) 晶向指数的标定 Indices of DirectionsMiller indices for directions are obtained using the following procedure: a 建立坐标系。确定原点（阵点）、坐标轴和度量单位（棱边）。 b 求坐标。u,v,w。 c 化整数。 u,v,w. d 加 。uvw。说明： a 指数意义：代表相互平行、方向一致的所有晶向。 b 负值：标于数字上方，表示同一晶向的相反方向。c 晶向族：晶体中原子排列情况相同但空间位向不同的一组晶向。用表示

21、，数字相同，但排列顺序不同或正负号不同的晶向属于同一晶向族。(2) 晶面指数的标定 Indices of PlanesMiller indices for planes are obtained using the following procedure: a 建立坐标系：确定原点（非阵点）、坐标轴和度量单位。 b 量截距：x,y,z。 c 取倒数：h,k,l。 d 化整数：h,k,k。 e 加圆括号：(hkl)。说明： a 指数意义：代表一组平行的晶面； b 0的意义：面与对应的轴平行； c 平行晶面：指数相同，或数字相同但正负号相反； d 晶面族：晶体中具有相同条件（原子排列和晶面间距完全

22、相同），空间位向不同的各组晶面。用hkl表示。 e 若晶面与晶向同面，则hu+kv+lw=0; f 若晶面与晶向垂直，则u=h, k=v, w=l。(3) 六方系晶向指数和晶面指数 Indices in the Hexagonal SystemThe notation used to describe directions and planes in hexagonal lattice is similar to that used in cubic systems. There are four crystallographic axes in the center of the basal

23、 plane. a 六方系指数标定的特殊性：四轴坐标系（等价晶面不具有等价指数）。 b 晶面指数的标定 标法与立方系相同(四个截距)；用四个数字(hkil)表示；i=-(h+k)。 c 晶向指数的标定 标法与立方系相同(四个坐标)；用四个数字(uvtw)表示；t=-(u+w)。 依次平移法：适合于已知指数画晶向（末点）。 坐标换算法：UVWuvtw u=(2U-V)/3, v=(2V-U)/3, t=-(U+V)/3, w=W。 (4) 晶带 a 定义：平行于某一晶向直线所有晶面的组合。 晶带轴 晶带面 b 性质：晶带用晶带轴的晶向指数表示；晶带面/晶带轴； hu+kv+lw=0 c 晶带定律

24、 凡满足上式的晶面都属于以uvw为晶带轴的晶带。推论：(a) 由两晶面(h1k1l1) (h2k2l2)求其晶带轴uvw：u=k1l2-k2l1; v=l1h2-l2h1; w=h1k2-h2k1。(b) 由两晶向u1v1w1u2v2w2求其决定的晶面(hkl)。H=v1w1-v2w2; k=w1u2-w2u1; l=u1v2-u2v1。(5) 晶面间距 interplanar SpacingThe distance between two adjacent parallel planes of atoms with the same Miller indices is called the

25、interplanar spacing. a 定义：一组平行晶面中，相邻两个平行晶面之间的距离。b 计算公式（简单立方）： d=a/(h2+k2+l2)1/2注意：只适用于简单晶胞；对于面心立方hkl不全为偶、奇数、体心立方h+k+l=奇数时，d(hkl)=d/2。1-2 纯金属的晶体结构Sec. 1.2 The Crystal Structures of Pure Metals1 空间点阵与晶体结构 crystal lattices and crystal structuresA lattice is a collection of points, called lattice points

26、, which are arranged in a periodic pattern so that the surroundings of each point in the lattice identical. In materials science and engineering, we use the concept of lattice to describe arrangements of atoms or ions. A group of one or more atoms, located in a particular way with respect to each ot

27、her and associated with each lattice point, is known as the motif or basis. We obtain a crystal structure by adding the lattice and basis （i.e., crystal structure=lattice+ basis）.A crystal is defined as an orderly array of atoms in space.（1） 空间点阵：由几何点做周期性的规则排列所形成的三维阵列。（2） 特征：a 原子的理想排列；b 有14种。其中：空间点阵

28、中的点阵点。它是纯粹的几何点，各点周围环境相同。描述晶体中原子排列规律的空间格架称之为晶格。空间点阵中最小的几何单元称之为晶胞。（3） 晶体结构：原子、离子或原子团按照空间点阵的实际排列。 特征：a 可能存在局部缺陷； b 可有无限多种。2 晶胞 UNIT CELLA. unit cell The unit cell of a crystal structure is the smallest group of atoms possessing the symmetry of the crystal which, when repeated in all directions, will de

29、velop the crystal lattice. B. body-centered cubic latticeThe body-centered cubic lattice thus has two atoms per unit cell; one contributed by the corner atoms, and one located at the center of the cell.C. face-centered cubic latticeThe unit cell of the face-centered cubic lattice has an atom in the

30、center of each face. The face-centered cubic lattice has a total of four atoms per unit cell, or twice as many as the body-centered cubic lattice. （1）定义：构成空间点阵的最基本单元。（2）选取原则：a 能够充分反映空间点阵的对称性；b 相等的棱和角的数目最多；c 具有尽可能多的直角；d 体积最小。（4） 形状和大小有三个棱边的长度a,b,c及其夹角,表示。（5） 晶胞中点的位置表示（坐标法）。3 三种常见晶体结构There are many di

31、fferent types of crystal structures, some of which are quite complicated. Fortunately, most metals crystallize in one of three relatively simple structures: the face-centered cubic, the body-centered cubic, and the close-packed hexagonal. 面心立方（A1, FCC）体心立方（A1, BCC）密排六方（A3, HCP）晶胞原子数 4 2 6点阵常数 a=2/2r

32、 a=4/3/3r a=2r配位数 12 8（86） 12致密度 0.74 0.68 0.74堆垛方式 ABCABC. ABABAB. ABABAB.结构间隙 正四面体正八面体 四面体扁八面体 四面体正八面体（个数） 8 4 12 6 12 6（rB/rA） 0.225 0.414 0.29 0.15 0.225 0.414配位数（CN）：晶体结构中任一原子周围最近且等距离的原子数。致密度（K）：晶体结构中原子体积占总体积的百分数。K=nv/V。间隙半径（rB）：间隙中所能容纳的最大圆球半径。3.1 THE BODY-CENTERED CUBIC STRUCTUREIt is frequent