第一章固体材料的结构.doc

材料科学基础 Fundamentals of Materials Science 第一章第一章 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 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 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 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 stronger 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 an 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，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 of 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. 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 atoms 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 bonds 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 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 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, 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 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 macroscopic 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 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，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 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 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 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, 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 other 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 develop 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 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 different 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 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 frequently convenient to consider metal crystals as structures formed by stacking together hard spheres. This leads to the so-called hard-ball model of a crystalline lattice, where the radius of the spheres is taken as half the distance between the centers of the most closely spaced atoms.3.2 COORDINATION NUMBER OF THE BODY-CENTERED CUBIC LATTICEThe coordination number of a crystal structure equals the number of nearest neighbors that an atom possesses in the lattice. In the body-centered cubic unit cell, the center atom has eight neighbors touching it. We have already seen that all atoms in this lattice are equivalent. Therefore, every atom of the body-centered cubic structure not lying at the exterior surface possesses eight nearest neighbors, and the coordination number of the lattice is eight.3.3 THE FACE-CENTERED CUBIC LATTICEA complete face-centered cubic cell shows the same unit cell with a corner atom removed to reveal a close-packed plane (octahedral plane) in which the atoms are spaced as tightly as possible. It should also be pointed out that the face-centered cubic structure has four close-packed or octahedral planes. The face-centered cubic lattice, however, is unique in that it contains as many as four planes of closest packing, each containing three close-packed directions. This fact is important, since it gives face-centered cubic metals physical properties different from those of other metals, one of which is the ability to undergo severe plastic deformation.3.4 THE UNIT CELL OF THE CLOSED-PACKED HEXAGONAL LATTICEFig. 1.1 The close-packed hexagonal unit cell Fig 1.2 Stacking sequences in close-packed crystal structureThe configuration of atoms most frequently used to represent the close-packed hexagonal structure is shown in Fig.1.1. This group of atoms contains more than the minimum number of atoms needed to form an elementary building block for the lattice; therefore it is not a true unit cell. However, because the arrangement of Fig.1.1 brings out important crystallographic features, including the sixfold symmetry of the lattice, it is commonly used as the unit cell of the close-packed hexagonal structure. 3.5 COMPARISON OF THE FACE-CENTERED CUBIC ANDCLOSE-PACKED HEXAGONAL STRUCTURESA. The face-centered cubic stacking order is: A for the first plane, B for the second plane, and C for the third plane, which may be written as ABC. The fourth plane in the face-centered cubic lattice, however, does fall on the A position, the fifth on B, and the sixth on C, so that the stacking order for face-centered cubic crystals is ABCABCABC etc. B. In the close-packed hexagonal structure, the atoms in every other plane fall directly over one another, corresponding to the stacking order ABABABC. There is no basic difference in the packing obtained by the stacking of spheres in the face-centered cubic or the close-packed hexagonal arrangement, since both give an ideal close-packed structure. There is, however, a marked difference between the physical properties of hexagonal close-packed metals (such as cadmium, zinc, and magnesium) and the face-centered cubic metals, (such as aluminum, copper, and nickel), which is related directly to the difference in their crystalline structure. The most striking difference is in the number of close-packed planes. In the face-centered cubic lattice there are four planes of closest packing, the octahedral planes; but in the close-packed hexagonal lattice only one plane, the basal plane, is equivalent to the octahedral plane. The single close-packed plane of the hexagonal lattice engenders, among other things, plastic deformation properties that are much more directional than those found in cubic crystals.3.6 COORDINATION NUMBER OF THE SYSTEMS OF CLOSEST PACKINGThe coordination number of an atom in a crystal has been defined as the number of nearest neighbors that it possesses. This number is 12 for both face-centered cubic and close-packed hexagonal crystals, as may be verified with the aid of Fig.1.2. 1-3 合金相结构Sec. 1.3 The Crystal Structures of Alloy Phases1 合金 alloys An alloy is a metallic solid or liquid from an intimate combination of two or more elements.（1）合金 alloy：两种或两种以上的金属，或金属与非金属经一定方法合成的具有金属特性的物质。（2）组元 components ：组成合金最基本的物质。（如一元、二元、三元合金The components are often the metallic elements that make up the system, but they can be pure chemical compounds, too.Binary alloystwo-component systems, are mixtures of two metallic elementsTernary alloysthree-component systems.（3）合金系 alloy systems：Alloy systems mean all the possible alloys that can be formed from given set of components.给定合金以不同的比例而合成的一系列不同成分合金的总称。2 相 phases2.1 相 phases：材料中结构相同、成分和性能均一的组成部分。（如单相、两相、多相合金。）A phase can be defined as any portion, including whole of system which is physically homogenous within itself and boded by a surface so that it is mechanically separable from any other portions.A phase has the following characteristics:a. The same structure or atomic arrangement throughout;b. Roughly the same composition and properties throughout; andc. A definite interface between the phase and any surrounding or adjoining phases.2.2 相的分类 固溶体：晶体结构与其某一组元相同的相。含溶剂和溶质。 中间相（金属化合物）：组成原子有固定比例，其结构与组成组元均不相同的相。3. 固溶体 SOLID SOLUTION按溶质原子位置不同，可分为置换固溶体和间隙固溶体。按固溶度不同，可分为有限固溶体和无限固溶体。按溶质原子分布不同，可分为无序固溶体和有序固溶体。A. solid solutions When homogeneous mixtures of two or more kinds of atoms occur in the solid state, they are known as solid solutions.B. solvent The term solvent refers to the more abundant atomic form; C. soluteAnd the solute to the less abundant. These solutions are also usually crystalline.Solid solutions occur in either of two distinct types. The first is known as a substitutional solid solution. In this case, a direct substitution of one type of atom for another occurs so that solute atoms enter the crystal to take positions normally occupied by solvent atoms. Figure 1.3A shows schematically an example containing two kinds of atoms ( Cu and Ni ). The other type of solid solution is shown in Fig.1.3B. Here the solute atom ( carbon ) does not displace a solvent atom, but, rather, enters one of the holes, or interstices, between the solvent ( iron ) atoms. This type of solution is known as an interstitial solid solution.Fig 1.3 The two basic forms of solid solution3.1 置换固溶体SUBSTITUTIONAL SOLID SOLUTIONS AND THE HUME-ROTHERY RULESIn Figure 1.8A, the copper and nickel atoms are drawn with the same diameters. Actually, the atoms in a crystal of pure copper have an apparent diameter (0.2551nm) about 2 percent larger than those in a crystal of pure nickel (0.2487 nm). This difference is small and only a slight distortion of the lattice occurs when a copper atom enters a nickel crystal, or vice versa, and it is not surprising that these two elements are able to crystallize simultaneously into a face-centered cubic lattice in all proportions. Nickel and copper form an excellent example of an alloy series of complete solubility.The size factor is only a necessary condition for a high degree of solubility. It is not a sufficient condition, since other requirements must be satisfied. One of the most important requirements is th