1、Chapter 3Imperfections in Solids,WHY STUDY Imperfections in Solids?,The properties of some materials are profoundly influenced by the presence of imperfections. Consequently, it is important to have a knowledge about the types of imperfections that exist and the roles they play in affecting the beha

2、vior of materials.,For example：,brass (70% copper/30% zinc) is much harder and stronger than pure copper.,Learning ObjectivesAfter studying this chapter, you should be able to do the following:,1. Describe both vacancy and self-interstitial crystalline defects. 2. Calculate the equilibrium number of

3、 vacancies in a material at some specified temperature, given the relevant constants. 3. Name the two types of solid solutions and provide a brief written definition and/or schematic sketch of each. 4. Given the masses and atomic weights of two or more elements in a metal alloy, calculate the weight

4、 percent and atom percent for each element.,5. For each of edge, screw, and mixed dislocations: (a) describe and make a drawing of the dislocation, (b) note the location of the dislocation line, and (c) indicate the direction along which the dislocation line extends. 6. Describe the atomic structure

5、 within the vicinity of (a) a grain boundary and (b) a twin boundary.,3.1 INTRODUCTION,Thus far it has been tacitly assumed that perfect order exists throughout crystalline materials on an atomic scale. However, such an idealized solid does not exist; all contain large numbers of various defects or

6、imperfections. As a matter of fact, many of the properties of materials are profoundly sensitive to deviations from crystalline perfection; the influence is not always adverse, and often specific characteristics are deliberately fashioned by the introduction of controlled amounts or numbers of parti

7、cular defects.,A crystalline defect refers to a lattice irregularity having one or more of its dimensions on the order of an atomic diameter. Classification of crystalline imperfections is frequently made according to the geometry or dimensionality of the defect.,Several different imperfections are

8、discussed in this chapter, including point defects (those associated with one or two atomic positions); linear (or one-dimensional) defects; and interfacial defects, or boundaries, which are two-dimensional. Impurities in solids are also discussed, because impurity atoms may exist as point defects.

9、Finally, techniques for the microscopic examination of defects and the structure of materials are briefly described.,3.2 Point Defects,（1）VACANCIES AND SELF-INTERSTITIALS,The simplest of the point defects is a vacancy, or vacant lattice site, one normally occupied but from which an atom is missing.,

10、Scanning probe micrograph that shows a vacancy on a (111)-type surface plane for silicon.,Two-dimensional representations of a vacancy and a self-interstitial.,in essence, the presence of vacancies increases the entropy (i.e., the randomness) of the crystal.,The equilibrium number of vacancies Nv fo

11、r a given quantity of material (usually per meter cubed) depends on and increases with temperature according to,N is the total number of atomic sites (most commonly per cubic meter), Qv is the energy required for the formation of a vacancy (J/mol or eV/atom), T is the absolute temperature in kelvins

12、, and k is the gas or Boltzmanns constant. The value of k is 1.38 10-23 J/atomK, or 8.62 10-5 eV/atomK, depending on the units of Qv.,Thus, the number of vacancies increases exponentially with temperaturethat is, as T increases, so also does the term exp(-Qv/kT).,For most metals, the fraction of vac

13、ancies Nv/N just below the melting temperature is on the order of 10-4that is, one lattice site out of 10,000 will be empty.,A self-interstitial is an atom from the crystal that is crowded into an interstitial sitea small void space that under ordinary circumstances is not occupied.,Two-dimensional

14、representations of a vacancy and a self-interstitial.,In metals, a self-interstitial introduces relatively large distortions in the surrounding lattice because the atom is substantially larger than the interstitial position in which it is situated.,Consequently, the formation of this defect is not h

15、ighly probable, and it exists in very small concentrations that are significantly lower than for vacancies.,A Frenkel defect is a type of defect in crystalline solids wherein an atom is displaced from its lattice position to an interstitial site, creating a vacancy at the original site and an inters

16、titial defect at the new location within the same element without any changes in chemical properties,Frenkel pair,Frenkel vacancy,vacancy + interstitial,moving an atom to the surface produces a vacancy,Schottky defect,If in an ionic crystal of type A+Ban equal number of cations and anions are missin

17、g from their lattice sites (so that electrical neutrality as well asstoichiometryis maintained), then this defect is called a Schottky defect.,EXAMPLE PROBLEM 1,Calculate the equilibrium number of vacancies per cubic meter for copper at 1000. The energy for vacancy formation is 0.9 eV/atom; the atom

18、ic weight and density (at 1000 ) for copper are 63.5 g/mol and 8.4 g/cm3, respectively.,Solution,it is first necessary, however, to determine the value of Nthe number of atomic sites per cubic meter for copper, from its atomic weight ACu, its density r, and Avogadros number NA, according to,(2) meta

19、llic solid solutions,A pure metal composed of only one type of atom is impossible in reality. It is difficult to refine metals to a purity of 99.99999% There is always some level of impurity or foreign atoms in a metal, leading to the formation of an alloy Alloys which impurity atoms have been added

20、 intentionally to impart specific characteristics to the material; a mixture of two or more metals or a metal and a nonmetal. Concept: solvent the matrix or host; solute minor component, e.g. Al-2.5%Cu alloy Zn-30% Cu alloy Pt900,950,Solid solutions: the simplest type of alloy A solid solution is a

21、solid that consists of two or more elements atomically dispersed om a single-phase structure .,Several terms,Solvent is the element or compound that is present in the greatest amount, also called host atoms.,Solute is used to denote an element or compound present in a minor concentration.,A solid so

22、lution forms when, as the solute atoms are added to the host material, the crystal structure is maintained and no new structures are formed.,Classification of solid solutions,(a) Substitutional solid solution solute or impurity atoms replace or substitute for the host atoms (b) Interstitial solid so

23、lution solute atoms fit into the spaces/voids between the solvent or parent atoms,Several features of the solute and solvent atoms determine the degree to which the former dissolves in the latter. These are expressed as four HumeRothery rules, as follows:,(a) Substitutional solid solution,1. Atomic

24、size factor. Appreciable quantities of a solute may be accommodated in this type of solid solution only when the difference in atomic radii between the two atom types is less than about 15%. Otherwise, the solute atoms create substantial lattice distortions and a new phase forms.,2. Crystal structur

25、e. For appreciable solid solubility, the crystal structures for metals of both atom types must be the same.,3. Electronegativity factor. The more electropositive one element and the more electronegative the other, the greater the likelihood that they will form an intermetallic compound instead of a

26、substitutional solid solution.,4. Valences. Other factors being equal, a metal has more of a tendency to dissolve another metal of higher valence than to dissolve one of a lower valence.,An example: a substitutional solid solution of copper and nickel.,These two elements are completely soluble in on

27、e another at all proportions. With regard to the aforementioned rules that govern degree of solubility, the atomic radii for copper and nickel are 0.128 and 0.125 nm, respectively; both have the FCC crystal structure; and their electronegativities are 1.9 and 1.8 (Chapter 1). Finally, the most commo

28、n valences are 1 for copper (although it sometimes can be 2) and 2 for nickel.,form when the atomic diameter of an interstitial impurity substantially smaller than that of the host atoms. atoms: hydrogen, carbon, nitrogen and oxygen.,(b) Interstitial solid solution,Carbon forms an interstitial solid

29、 solution when added to iron; the maximum concentration of carbon is about 2%. The atomic radius of the carbon atom is much less than that of iron: 0.071 nm versus 0.124 nm.,Normally, the maximum allowable concentration of interstitial impurity atoms is low (less than 10%). Even very small impurity

30、atoms are ordinarily larger than the interstitial sites, and as a consequence, they introduce some lattice strains on the adjacent host atoms.,Summary: point defects,3.3 Linear Defects-DISLOCATIONS,A dislocation is a linear or one-dimensional defect around which some of the atoms are misaligned.,an

31、extra portion of a plane of atoms, or half-plane, the edge of which terminates within the crystal. This is termed an edge dislocation;,it is a linear defect that centers on the line that is defined along the end of the extra half-plane of atoms. This is sometimes termed the dislocation line, which f

32、or the edge dislocation, is perpendicular to the plane of the page.,Within the region around the dislocation line there is some localized lattice distortion.,The atoms above the dislocation line in Figure are squeezed together, and those below are pulled apart; this is reflected in the slight curvat

33、ure for the vertical planes of atoms as they bend around this extra half-plane.,The magnitude of this distortion decreases with distance away from the dislocation line; at positions far removed, the crystal lattice is virtually perfect.,negative edge dislocation,positive edge dislocation,the edge di

34、slocation is represented by the symbol , indicates the position of the dislocation line,An edge dislocation may also be formed by an extra half-plane of atoms that is included in the bottom portion of the crystal; its designation is a,刃型位錯,刃型位錯運動示意圖,Another type of dislocation, called a screw disloc

35、ation may be thought of as being formed by a shear stress that is applied to produce the distortion,滑移方向,the upper front region of the crystal is shifted one atomic distance to the right relative to the bottom portion. The atomic distortion associated with a screw dislocation is also linear and alon

36、g a dislocation line, line AB,螺型位錯線,A,B,C,D,滑移面上下原子的錯排情況,未滑移 錯排 重合,螺型位錯的運動,Most dislocations found in crystalline materials are probably neither pure edge nor pure screw but exhibit components of both types; these are termed mixed dislocations. All three dislocation types are represented schematical

37、ly in Figure 4.6; the lattice distortion that is produced away from the two faces is mixed, having varying degrees of screw and edge character.,圖 混合位錯的原子組態(tài),Burgers vector,The magnitude and direction of the lattice distortion associated with a dislocation are expressed in terms of a Burgers vector, d

38、enoted by b.,the nature of a dislocation (i.e., edge, screw, or mixed) is defined by the relative orientations of dislocation line and Burgers vector.,For an edge, they are perpendicular，whereas for a screw, they are parallel，they are neither perpendicular nor parallel for a mixed dislocation.,even

39、though a dislocation changes direction and nature within a crystal, the Burgers vector is the same at all points along its line.,3.4 INTERFACIAL DEFECTS,Interfacial defects are boundaries that have two dimensions and normally separate regions of the materials that have different crystal structures a

40、nd/or crystallographic orientations.,These imperfections include external surfaces, grain boundaries, phase boundaries, twin boundaries, and stacking faults.,(a) External Surfaces,One of the most obvious boundaries is the external surface, along which the crystal structure terminates. Surface atoms

41、are not bonded to the maximum number of nearest neighbors and are therefore in a higher energy state than the atoms at interior positions. The bonds of these surface atoms that are not satisfied give rise to a surface energy, expressed in units of energy per unit area (J/m2 or erg/cm2).,The higher e

42、nergy of the atoms on the surface makes the surface susceptible to erosion and react with elements in the environment. To reduce this energy, materials tend to minimize, if at all possible, the total surface area. For example, liquids assume a shape having a minimum areathe droplets become spherical

43、. Of course, this is not possible with solids, which are mechanically rigid.,(b) Grain Boundaries,boundary separating two small grains or crystals having different crystallographic orientations in polycrystalline materials.,Within the boundary region, which is probably just several atom distances wi

44、de, there is some atomic mismatch in a transition from the crystalline orientation of one grain to that of an adjacent one.,The atomic packing in grain boundaries is lower than within the grains because of the atomic mismatch. Grain boundaries also have some atoms in strained position that raise the

45、 energy of the grain-boundary region. the high energy of the grain boundaries and their more open structure make them a more favorable region for the nucleation and growth of precipitates. allow for more rapid diffusion of atoms in the grain boundary boundaries restrict plastic flow by making it mor

46、e difficult for the movement of dislocations in the grain boundary region.,When this orientation mismatch is slight, on the order of a few degrees, then the term small- (or low-) angle grain boundary is used.,These boundaries can be described in terms of dislocation arrays. One simple small-angle grain boundary is formed when edge dislocations are aligned in the manner of Figure,tilt boundary,angle of misorientation, ,The atoms are bonded less