Crystal imperfections

The ideal, perfectly regular crystal structures in which atoms are arranged in a regular way does not exist in actual situations. In actual cases, the regular arrangements of atoms disrupted . These disruptions are known as Crystal imperfections or crystal defects

1. CRYSTAL IMPERFECTIONS The ideal, perfectly regular crystal structures in which atoms are arranged in a regular way does not exist in actual situations. In actual cases, the regular arrangements of atoms disrupted . These disruptions are known as Crystal imperfections or crystal defects . Any deviation from the perfect atomic arrangement in a crystal is said to contain imperfections or defects. 1

2. CRYSTAL IMPERFECTIONS The fact that real materials are not perfect crystals is critical to materials engineering. If materials were perfect crystals then their properties would be dictated by their composition and crystal structure alone, and would be very restricted in their values and their variety. It is the possibility of making imperfectly crystalline materials that permits materials scientists to tailor material properties into the diverse combinations that modern engineering devices require . 2

3. Crystal imperfections have strong influence upon many properties of crystals, such as strength, electrical conductivity and hysteresis loss of ferromagnets . Thus some important properties of crystals are controlled by as much as by imperfections and by the nature of the host crystals. The conductivity of some semiconductors is due entirely to trace amount of chemical impurities. Color, luminescence of many crystals arise from impurities and imperfections Atomic diffusion may be accelerated enormously by impurities or imperfections Mechanical and plastic properties are usually controlled by imperfections The most important features of the microstructure of an engineering material are the crystalline defects that are manipulated to control its behavior. 3 Why do we care about defects/Imperfections?

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5. Classification 5 There are 4 major categories of crystalline defects: 1. Point defects or Zero dimensional defects occurring at a single lattice point 2. Line defects (dislocations) or One dimensional defects occurring along a row of atoms 3. Surface (Plane)defects or Two dimensional defects occurring over a two-dimensional surface in the crystal 4. Volume (bulk) (void) defects or Three Dimensional defects

6. 6 1. Point defects: a. Vacancy b. Self interstitial or Interstitialcy c.Substitutional impurity d. Frenkel defect e. Schottky defect 2. Line defects: a. Edge dislocation b. Screw dislocation 3. Surface defects: a. Grain boundaries b. Tilt boundaries c. Twin boundaries d. Stacking faults 4. Volume defects: a. Inclusions b. Voids

7. Point Defects: Point defects are where an atom is missing or is in an irregular place in the lattice structure 7

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10. 10 Frenkel and Schottky Defect • These defects are observed in ionic crystals. In an ionic crystal, even when defects are present electrical neutrality is to be maintained Frenkel Defect. When an ion is displaced from a regular site to another site, the defect is called Fenkel defect . Cations are generally the smaller ions, it is possible for them to get displaced into void spaces . To maintain the charge neutrality, a cation vacancy- cation interstitial pair occur together. • Schottky Defect. When a pair of cation and anion is missing from a lattice of an ionic crystal, the defect is known as schottky defect. This is closely related to vacancies To maintain the charge neutrality, remove 1 cation and 1 anion; this creates 2 vacancies.

11. 11 Line defects or Dislocations:

12. Types of Dislocation There are two types of dislocations which are responsible for the useful property of plasticity in metallic materials :- 1.Edge dislocation ( or Taylor- Orowan dislocation ) 2 . Screw dislocation ( or Burgers dislocation ) 12

13. Edge Dislocation 13 It may be described as an edge of an extra plane of atoms within a crystal structure. Thus regions of compression and tension are associated with an edge dislocation. The displacement distance of atoms around the dislocation is called Burger vector . This vector is right angle to edge dislocation

14. .Edge dislocation is considered positive when compressive stresses present above the dislocation line, and is represented by ┴. If the stress state is opposite i.e. compressive stresses exist below the dislocation line, it is considered as negative edge dislocation, and represented by ┬. 14

15. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 15

16. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 16

17. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 slip no slip boundary = edge dislocation Slip plane b Burgers vector 17

18. Slip plane slip no slip dislocation b t Dislocation: slip/no slip boundary b : Burgers vector magnitude and direction of the slip t : unit vector tangent to the dislocation line 18

19. Dislocation Line : A dislocation line is the boundary between slip and no slip regions of a crystal Burgers vector : The magnitude and the direction of the slip is represented by a vector b called the Burgers vector, Line vector/Slip Vector A unit vector t tangent to the dislocation line is called a tangent vector or the line vector. 19

20. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 slip no slip Slip plane b Burgers vector t Line vector Two ways to describe an EDGE DISLOCATION 1. Bottom edge of an extra half plane 2. Boundary between slip and no-slip regions of a slip plane What is the relationship between the directions of b and t ? b  t 20

21. Burgers Vector A dislocation is characterized by a vector known as Burgers vector. An atom by atom circuit is drawn around the dislocation line (Burgers circuit) and the vector needed to close the circuit is known as Burgers vector. In perfect crystal there are no, dislocation and such circuit will close without any mismatch In an edge dislocation ,the Burgers vector(b) is seen to be perpendicular to the dislocation line 21

22. 22 Burger Vector-b

23. 23 Burgers Circuit To construct the Burgers circuit, choose a direction for the dislocation line and draw a clockwise closed circuit in the perfect crystal by taking unit steps along the lattice vectors. . If the same circuit is drawn so that it encloses a dislocation, it fails to close. The vector ( from the starting position) that is required to complete the circuit is the Burgers vector , b , of the dislocation, and measures the net displacement experienced by an imaginary observer who completes a circuit around the dislocation that would be closed in a perfect crystal .

24. screw dislocation A screw dislocation can be thought of as a disturbed region formed by a shear stress applied on the crystal such that a portion of the crystal is shifted relative to the other. 24

25. 25 The upper part of the crystal right of AD has skipped relative to the lower part in the direction of slip vector In screw dislocation the Burger vector is parallel to the dislocation line (AD). The trace of the atomic planes around the screw dislocation makes a spiral or helical path (pink shade) like a screw and hence , the name. Atomic positions along a screw dislocation is represented in Fig . (b)

26. Screw Dislocation Line b t b || t 1 2 3 Screw Dislocation Slip plane slipped unslipped 26

27. 27 In screw dislocation the Burger vector is parallel to the dislocation line (AD). The trace of the atomic planes around the screw dislocation makes a spiral or helical path (pink shade) like a screw and hence , the name. Atomic positions along a screw dislocation is represented in Fig . (b)

28. 28 SCREW DISLOCATION OR BURGER’S DISLOCATION

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31. Surface Defects Surface defects are two dimensional in nature and they occur due to change in the stacking of atomic planes. They refer to regions of distortions that lie about a surface having a thickness of few atomic diameters 31

32. 32 During solidification of liquid metals, when growing crystals or grains having different orientations meet each other, the atomic packing between two adjacent grains gets distorted and region of imperfection is generated. This transition zone not aligned with either of the grains is known as grain boundary because the orientation difference between neighboring grains is generally 10 Grain Boundaries

33. Tilt Boundaries Known as low(small) angle boundaries as orientation difference between neighboring crystals is less than 10 Tilt boundaries are formed when arrays of parallel edge dislocations of same sign get arranged one above the other. They are formed in mechanically deformed materials during the process of recovery 33

34. Twin Boundaries A shear force that causes atomic displacements such that the atoms on one side of a plane (twin boundary) mirror the atoms on the other side., the boundary is known as twin boundary Twin boundaries occurs in pairs resulting in a region of different orientation in crystal Twin boundaries formed during crystal growth, mechanical deformation or during annealing

35. (c) 2003 Brooks/Cole Publishing / Thomson Learning Applied stress to a perfect crystal (a) may cause a displacement of the atoms, (b) causing the formation of a twin. Note that the crystal has deformed as a result of twinning.

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38. Stacking faults A stacking fault represents interruption of one or two layers in the stacking sequence of atom planes .In FCC structures, The Normal stacking sequence is ABCABCABCABC. Due to plastic deformation, This arrangement may be disrupted and a stacking sequence of ABCACABC. For FCC metals an error in ABCABC packing sequence Ex: ABCABABC 38

39. Role of surface defects in Crack initiation The atoms located near the grain boundaries have distorted and non equilibrium surroundings are at high energy levels Every atom at an exterior surface also having the same situtaion . The exterior surface is usually rough and contains tiny notches These notches initiate cracks and crack propagates along the grain boundaries to the bulk of the material 39

40. Volume(bulk) Defects Voids, Inclusions etc present in the crystal are called Volume or Bulk defects. Voids is a large vacancy generated when a cluster of atoms are missing Voids due to air bubble trapped is called porosity Voids due to shrinkage of material is known as cavitation Inclusions are presence of slag or impurities Precipitates are certain regions within the crystal, which are occupied some other phase other than that of host crystal. 40

41. Sources of dislocation A very large number of dislocations are necessary in a crystal to facilitate plastic deformation. Even in basic crystals there are imperfections including dislocation Originates form various sources. Primary source is natural consequence of crystal formation and growth. Source of dislocation can be vacancies, cross slip mechanism or high angle grain boundaries Another source of dislocation is dislocation is itself- It is observed that during plastic deformation the dislocation density of crystal increases by 2-6 times It indicates that there must be a mechanism of generating dislocations in cold worked steel 41

42. Frank-Read Source One scheme by which dislocations could be generated from existing dislocation is Known as “Frank-Read Source ”. 42

43. Frank-Read Source 43 (c) (f) A B A B (a) (d) (b) (e) P Q P Q A B A B

44. Frank-Read Source 44 (c) (f) A B A B (a) (d) (b) (e) P Q P Q A B A B m n

45. Frank-Read Source Consider a segment of dislocation AB as shown in the figure(a), lying on a slip plane A & B are points beyond which dislocations does not lie on the slip plane Dislocation cannot grow beyond A & B due to various reasons, If shear stress ‘ τ ’ acts on this slip plane ,the dislocation bulges out and produces a slip as shown in the figure(b). For given stress the dislocation will assume a radius of curvature and loop continues to expand under increasing stresses as in figure(c) 45

46. Frank-Read Source When the loop reaches a stage as in Fig (d) the segment m & n will meet and annihilate each another and form a large loop A new dislocation segment PQ is formed as in figure(e) Once the original loop moves into this stage ,the loop can continue to expand and the Segment PQ is in a position to repeat the Process. A Frank-Read source can operate continuosly and produce an infinite number of loops, provided loops move out and disappear at the surface of the crystal. However, if the loops are piled up, against an obstacle(grain boundary etc ), back stresses may build up at the source and it will die out 46

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48. MOVEMENT OF DISLOCATIONS The motion of a large number of dislocations within the crystal results in plastic deformation An edge dislocation moves in response to shear stress applied in the direction perpendicular to the dislocation line Slip- The process by which plastic deformation is produced by dislocation movement is termed as slip or glide 48

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50. SLIP The basic mode of dislocation movement is by way of slip or glide along a slip plane . A pure edge dislocation can slip or glide in the direction perpendicular to its length . During slip atomic bonds at one point are broken and re-established at another point. The presence of dislocation makes process easier than in a perfect crystal. In crystals where dislocations are present, atomic movement can be effected relatively easily. 50

51. Glide of an Edge Dislocation   51

52. Glide of an Edge Dislocation  crss  crss  crss is critical resolved shear stress on the slip plane in the direction of b . 52

53. Glide of an Edge Dislocation  crss  crss  crss is critical resolved shear stress on the slip plane in the direction of b. 53

54. Glide of an Edge Dislocation  crss  crss  crss is critical resolved shear stress on the slip plane in the direction of b. 54

55. Glide of an Edge Dislocation  crss  crss  crss is critical resolved shear stress on the slip plane in the direction of b. 55

56. Glide of an Edge Dislocation  crss  crss Surface step, not a dislocation A surface step of magnitudeb is created if a dislocation sweeps over the entire slip plane 56

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59. CROSS SLIP & CLIMB Dislocations also move by the process of cross slip and climb 59

60. 1 2 3 b Cross-slip of a screw dislocation Change in slip plane of a screw dislocation is called cross-slip Slip plane 1 Slip plane 2 60

61.   Atomistic mechanism of climb 61

62. Climb of an edge dislocation Climb up Climb down Half plane shrinks Half plane stretches Atoms move away from the edge to nearby vacancies Atoms move toward the edge from nearby lattice sites Vacancy concentration goes down Vacancy concentration goes up 62

63. Forest of Dislocation The dislocations moving one behind the other along an active slip plane are called forest of dislocations When dislocation forest intersects with other dislocations, jogs and kinks are formed which restricts further movement of dislocations 63

64. Dislocation Density The dislocation density is defined as the total dislocation length per unit volume of material. It can also be represented as the number of dislocation lines that move across a unit cross sectional area. Usually the unit is mm -2 64

65. Correlation of dislocation density with Strength and Nano concept All crystalline materials have certain level of dislocation density. Cold working increases the dislocation density, but leads to strain hardening Strength of material is inversely related to dislocation movement. Even though cold working increases dislocation density, Strain hardening imposes barriers on mobility which leads to an increase in strength. 65

66. Correlation of dislocation density with Strength and Nano concept In nanomaterial also yield strength is determined by the ease by which dislocation can be moved through the material Nano crystalline materials can be considered as simply special cases of poly crystalline materials in which grain size is very small. The reduction in grain size leads to a considerable degree of strengthening in nano crystalline materials. Additional strengthening due to strain hardening is tend to be relatively small. All the strengthening mechanism active in conventinal grain size material is also active in nano crystalline materials 66

67. Significance high and low angle grain boundaries on dislocation driving force for grain growth and applications during heat treatment. 67