第章 金属的晶体结构（The first chapter is about the crystal structure of metal）

1、第1章 金属的晶体结构（The first chapter is about the crystal structure of metal）IntroductionMetallograpy is the relationship between composition, organization, structure and mechanical properties of metals and alloys of science. The mechanical properties mainly refers to material strength, hardness and plasti

2、city. Usually the loading parts require materials with good mechanical properties, we call this kind of material for structural materials. Another kind of material and corresponding structural materials are functional materials, it is generally not required to bear the load, the main use of its phys

3、ical properties, such as optical, electrical and magnetic properties, etc. Functional materials use it sensitive to light, the production of various types of electric and magnetic sensor.Metallograpy only discuss the mechanical properties of metal materials, does not involve physical properties.Soli

4、d metal is usually the smallest structural unit of metal crystal, study the atom. Atomic through different arrangement can form crystal structure different, have different performance. The category is not the study of metal atomic structure.The first chapter of the crystal structure of metal1-1 meta

5、l and metal bondThe metal is defined according to different disciplines have a variety of classification methods. I tend to bond the classified nature, which is a kind of material with metal metal bond. The advantage of this classification is to explain related phenomena and mechanical properties of

6、 metals. For example, why metals have good plasticity?What is the metal bond, ionic bond and covalent bond we already know, the biggest characteristic of metal bond is no saturation, no direction. We will see later, it is these characteristics that metal has better plasticity.Research shows that the

7、 solid metal is usually the crystal, and the structure tends to close packed structure. This is why? Below we illustrated with double atom model.When the two atoms are far apart, they are not. When they come close to that between one atom nucleus and another atom will produce gravitational repulsion

8、 between nuclei; and two atomic and electronic. Research shows that gravity is Cheng Li, the repulsion force is a short-range force, namely distance, gravity is bigger than the repulsion, is attracted to each other. With the decrease of repulsive atom distance, the rate of increase gradually increas

9、e the speed greater than gravity. Obviously this result there must be a balance distance d0, at this time, is equal to the gravitational repulsion, deviate from this distance, there will be a restoring force, such as P3 in figure 2. DC corresponding to the maximum recovery of gravity, namely the max

10、imum binding capacity, which corresponds to the theoretical tensile strength of metal.Here, we from the angle of energy to consider the stability of the system. Under the force of gravity atoms closer to the work done to reduce the potential energy of atoms, so can attract is negative. On the contra

11、ry, rejection can be positive. Can attract and repulsion energy and binding energy is algebra. The P3 can be seen in Figure 2, when the atoms to the equilibrium distance d0, the combination can reach the minimum value, the minimum potential energy of the system, the most stable state. Figure EAB bin

12、ding energy between atoms, or bond energy.The model is extended to a large number of diatomic metal atoms combine into a solid, in order to make the solid metal has the lowest energy, the atoms in three-dimensional space must also balance a certain distance. This is the reason for the solid metal cr

13、ystal.You want to take in one of the atoms in solid metals, work must be done on it,To overcome the action of the surrounding atom on it. Obviously, the more the number of atoms in the neighboring neighborhood of the atom to be removed, the greater the work required to do. It can be seen that the mo

14、re the nearest neighbor atoms, the lower the binding energy, i.e., the lower the potential energy, the more stable the state. So the atoms in the metal tend to pile up tightly.1-2 crystal structure of metalA solid metal is usually a crystal and the atoms in the crystal are arranged periodically in a

15、ccordance with certain rules. Different metals have different crystal structures and exhibit different mechanical properties. In this section, we consider crystals as ideal crystals. The ideal crystals are assumed to be free of defects in the crystal, and the atoms are stationary at equilibrium with

16、out thermal vibration. In addition, ideal crystals also include volume infinity (or large enough).I. characteristics of crystals1, the geometric shape of the ruleIf the size of the crystal is large enough, regular shapes can be seen. Such as natural diamond (diamond), all kinds of precious stones an

17、d so on.2, have a definite melting point3, anisotropyTwo. Crystal structure and space latticeCrystal structure is the concrete way in which the atoms in the crystal are arranged periodically in the three-dimensional space. The same atoms may have different arrangements in different conditions; the s

18、ame arrangement may be made up of different atoms. So, in theory, there are many kinds of crystal structures.One of the important purposes of studying the crystal structure is to understand the periodicity and symmetry of this structure. However, in the actual crystal structure, it is sometimes diff

19、icult to see the periodicity of atoms in three-dimensional space. To this end, we will be in the crystal atom or group of atoms as abstract geometric point, called lattice. These points can represent individual atoms, can represent the atomic group, but all points must have the same meaning and spac

20、e environment, such points in three-dimensional space array called space lattice, referred to as the matrix.In order to observe, with three sets of parallel lines connect these points, called the lattice. In fact, the quality is still a space lattice, usually not distinguished. However, using three

21、different sets of parallel lines connecting these points, there will be a different lattice, therefore, people, three groups of parallel lines should have the most right angle. Thus, the same lattice has a unique lattice.Since the space lattice in three dimensions of space is periodic, it is not nec

22、essary to all points are all drawn, usually only points for vertex, the minimum volume of the parallelepiped, called cell. However, sometimes the cell cannot reflect the symmetry of the lattice, then we would rather give up the minimum volume principle, selected volume is slightly larger, but the ed

23、ge between the right most can reflect the parallelepiped symmetry as the basic unit of dot matrix, called cell.Usually the right, back and lower corners of the cell are the origin of the coordinate system, and the three edges connected with the origin are axes X, Y and Z, also called the crystal axi

24、s. The size and shape of the cell are represented by three edge lengths a, B, C, and edge angles, alpha, beta, and gamma. These six parameters are called lattice parameters, in which a, B and C are also called lattice constants or lattice constants.As we mentioned earlier, there are many kinds of cr

25、ystal structures. Then, how many kinds of spatial lattices are there? Bravais points in accordance with the same environment requirements,It is proved by mathematical method that there are only 14 kinds of lattices in space, and these 14 lattices are called lattice lattices. P6 Table 1 gives the 14

26、Bravais lattice cell.Three, crystal systemIn crystallography, according to the relation of a, B, C and alpha, beta and gamma, the space lattice is divided into seven kinds, called the seven crystal system. Table 1 P6 14 belonging to different Bravais lattice crystal.Four, crystallographic index and

27、plane indexIn crystals, an orientation consisting of atomic wires is called a crystallographic direction; a plane consisting of atoms is called a crystal surface. In different crystallographic directions, the periods of atomic arrangement are different, but the different crystal planes and the cryst

28、al surface spacing are different. These differences lead to anisotropy of crystal properties. In the analysis of crystals, we often point out some crystallographic orientations or crystallographic planes. For this reason, crystal orientation and crystallographic planes must be named, called crystall

29、ographic index and plane index. The commonly used nomenclature is the Miller index.(I) crystallographic index1, the calibration of crystal orientation index2 、 crystallographic family(two) crystal plane index1, the calibration of the crystal surface index2, crystal face family3, crystal band: to the

30、 cubic system, the crystal band and the axis satisfy:(three) the crystal face (crystal orientation) index of the six square system1, crystal face index:2, crystal orientation index:Five, three typical metal crystal structures (A1, A2, A3)(I) face centered cubic structure A1In the periodic table, the

31、re are about 20 metals with FCC structure. The cell cell of the fcc structure is shown in figure P8 6. Below we analyze the characteristics of FCC structures from several aspects.1. Atomic diameter (think of atom as rigid sphere)The diameter of a pure metal atom is defined as the distance between th

32、e nearest atoms and the center of the atom. In face centered cubic structures, the nearest neighbor atoms lie on the diagonal of the faces. Assuming that the lattice constant is a, then2, the number of atoms in the cell3, coordination numberThe coordination number is defined as the number of atoms n

33、earest to an atom and equal distances. The larger the coordination number, the greater the degree of tightness in the arrangement of atoms in the structure. The coordination number of fcc structure is 12.4, densityDensity is defined as the spatial occupancy of the atom. Face centered cubic structure

34、(two) body centered cubic structure A2In the periodic table, there are about 30 metals with a bcc structure, accounting for about half of the metal elements. The unit cell of a bcc structure is shown in figure P7 5.1, atomic diameter:2, the number of atoms in the cell:3, coordination number: 84, den

35、sity:Thus, the density of A1 structure is larger than that of A2 structure. For example, when the gamma structure of the fcc structure changes to alpha -Fe in the body centered cubic structure, volume expansion occurs in -Fe. If the diameter of the atom does not change, theoretical calculations show

36、 that 9% of the volume expansion should be produced. But the test shows that only 0.8% of the volume is actually inflated. There is only one possibility that the atomic diameter becomes smaller (energy is related to the volume density of free electrons).(three) closely arranged six party structure A

37、3In the periodic table, there are about 25 metals with closely spaced six - party structures. Close packed six party cell cell see P9, figure 8.1, atomic diameter:2, the number of atoms in the cell:3, coordination number: 124, density:It can be seen that the structure of A1 and A3 is different and h

38、as the same density. Available atomic stacking instructions.Six. The stacking and gap of atoms in crystals(1) the stacking of atoms in a crystal(two) the gaps in the crystal (the tetrahedral gap and the eight body gap)1, A1 structure: P13 diagram 16a, for the positive eight surface gap, the eight bo

39、dy gap is shown in the location, the number is the same as the number of atoms.The tetrahedral clearance is seen to be smaller than the positive eight body gap. For example, the austenite is a interstitial solid solution of C in gamma -Fe, and the gamma -Fe is a face centered cubic structure, and th

40、e gap between the eight faces is larger, so the C atom is in the gap position of the positive eight body surface. The position of the tetrahedral gap is shown in figure 8.2, A2 structure: P12, figure 15a, for the flat eight surface gap, flat eight body gap location see figure, the quantity is.The ir

41、regular tetrahedral gap is larger than the flat eight body gap. Ferrite is the interstitial solid solution of C in alpha -Fe, and alpha -Fe is bcc. It is shown that the C atom is located in the gap between its eight flat bodies. The locations of irregular tetrahedral spaces are shown in figures of.3

42、 and A3 structure: with the A1 structure of the eight body gap and tetrahedral gap in the same shape, when the diameter of the atom at the same time, the size is also exactly the same, but the gap is different location (P13, Figure 17).Seven. Anisotropy of crystalGenerally speaking, crystals are ani

43、sotropic, which means single crystals. A single crystal is a crystal that grows out of a core. In a single crystal, all atoms are arranged in the same direction in the same direction. Since the arrangement of atoms in different directions is different in different directions, that is, the binding fo

44、rce between atoms is different, so they exhibit different physical or mechanical properties. But generally, a metallic crystal is a polycrystal grown from a large number of cores (nuclei) with different orientations. Its interior is made up of many small crystals of different orientations. Although

45、each small crystal corresponds to a single crystal and has anisotropy, the orientations of these small crystals are random and are isotropic together. As shown in figure P19 28, these small crystals are called grains, and the interface between grains is called grain boundaries. When these crystals t

46、end to converge for some reason, anisotropy occurs.Eight, polymorphsMost metals have only one crystal structure in the solid state, but there are a few metals that have several crystalline structures in the solid state, which are said to have polymorphs. For example, Fe is A2 structure at 912 degree

47、s C and A1 structure at 912-1394. When the temperature changes, the crystal structure will change, said allotropic transformation, also called solid phase transformation.1-3 the crystal structure of real metalIdeal crystals do not exist. There are a lot of defects in real crystals. There are mainly

48、three kinds of defects: point defects, line defects and surface defects. Here we do not discuss the vibration defects caused by thermal motion.One point defectAtomic scale defects, called point defects, include vacancies, interstitial atoms, and substitutional atoms, see figure P20, 30.(I) vacancies

49、 and interstitial atoms (refer to pure metals)The atoms undergo thermal vibrations in equilibrium.The higher the temperature amplitude. At a certain temperature, each atomic vibration energy is not the same, this energy uneven phenomenon called energy fluctuation. In a moment, some atomic energy may

50、 be higher, when the energy is high enough to overcome the restriction of the surrounding atoms will migrate from equilibrium position. So have a vacancy.There are three places from the equilibrium position of atoms: one is migrated to the grain boundaries or the crystal surface, so the generated sp

51、ace called Xiao Tuoji is moved to the vacancy; two lattice gap, also produced a interstitials generated in a vacancy at the same time, this space called Frank space; the three is to move to the other the empty place, equivalent to the vacancy occurred reverse migration.Vacancy and interstitial will

52、make the surrounding atoms deviate from the equilibrium position, called lattice distortion. The lattice distortion energy increases, the increase of energy called distortion energy.Unlike other defects, defects can exist in the system thermodynamic equilibrium, which is why? According to the thermo

53、dynamic formula, free energy, visible, distortion point defects can increase the energy of the system, but also increases the degree of chaos system, the chaos entropy increases, the energy of the system is reduced, the thermodynamic calculation indicated that:The equilibrium concentration of vacanc

54、ies for:In the formula, n is the number of empty seats; N is the number of atomic positions; for a vacancy of the energy needed to form, is decided by the vibration; coefficient of entropy, it is estimated that about 110 in between.The equilibrium concentration of interstitial atoms and the like, ju

55、st for interstitial atom formation. Obviously, the higher the temperature is, the greater the equilibrium concentration of point defects.The research shows that the formation of interstitial atoms can be large, about 3-4 times the vacancy formation energy. Therefore, at the same temperature, the equ

56、ilibrium concentration of interstitial atoms is much lower than the equilibrium concentration of vacancies, the vacancy is usually negligible (but in high-energy irradiation, resulting in a large number of Frank gap defects, atomic number increased, can not be ignored).Although the vacancy and inter

57、stitial at a certain temperature to determine the equilibrium concentration, but the equilibrium concentration belongs to dynamic balance, namely new vacancies and interstitials generated continuously, at the same time, the original vacancy and interstitial are disappearing, general equilibrium.(two

58、) movement of point defectsVacancies and interstitials are not fixed, but changing. Figure 32 shows the P20 vacancy movement. When the vacancy and interstitial movement to the middle position when the energy is higher, the migration must gain enough energy to overcome this obstacle, can increase the energy transfer said.The migration of point defects caused by self diffusion phenomenon in metal crystal, is the basis of diffusion type solid phase transformation, chemical heat treatment and other phys