Analysis of the extended defects in 3C-SiC.pdf - Nelson Mandela ...

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8 Fig. 2.6. The extrinsic defects, substitutional and interstitial present in a lattice (from Hull et al. (1984)) Vacancies and interstitials can be produced by plastic deformation and also due to high-energy particle irradiation. Also intrinsic defects are produced by virtue of temperature, a thermodynamically stable concentration of these defects are always present above 0 K. The equilibrium fraction of point defects is given by the relation, n eq E f nt exp( ) (2.1) kT where nt is the total number of atomic sites, k Boltzmann’s constant and Ef the energy of formation of one defect. For a vacancy, the energy is that required to remove one atom from the lattice and place it on the surface of the crystal, and for the interstitial it is the energy required to remove one atom from the surface and insert it into an interstitial site. Typically the vacancy formation energy is two to four times less than that of the interstitial and consequently the concentration of interstitials is far lower than that of vacancies at a certain temperature T. 2.3.3 Defect Migration and Annealing Behaviour In general point defects are continuously attempting to migrate, the success of which critically depends on the defect migration energy Em and is largely determined by the specimen temperature. Strain induced motion is also possible but it is the aim of this section to discuss the former. The atomic jump frequency at temperature T of a point defect is given by,
v m Em vm0 exp( ) (2.2) kT 9 where Em is the migration energy of the point defect, either vacancy or interstitial and υm0 is the atomic vibration frequency. This atomic jump frequency is a measure of how often it is expected for atoms to leave their normal positions but it does not say anything about the direction the atom will take for any particular jump. The atom accordingly takes a very haphazard path as it wanders through the crystal and this path is termed a random walk and could be correlated or uncorrelated depending on the type of defect in question since the probabilities of motion for each are different. A substitutional impurity jumping through a vacancy mechanism for example is said to have a correlated random walk because there is not an equal probability of its nearest neighbours being vacant. Thus if a region in a crystal contains a concentration of point defects all of these defects will perform random walks but will also eventually disperse and spread throughout the crystal causing a net transport of matter. This happens since there is a difference in concentration of defects in the crystal causing a concentration gradient. This net transport of matter is described by Fick’s first law, dc J D (2.3) dx dc where J is the flux, the concentration gradient and D the diffusion coefficient, dx which depends on the mechanism of diffusion, type of crystal structure and jump frequency. This equation can also be given in a more useful form known as Fick’s second law, 2 dC d C D (2.4) 2 dt dx
Page 1 and 2: Analysis of the Extended Defects in
Page 3 and 4: My sincere thanks to the following
Page 5 and 6: OPSOMMING Hierdie dissertasie hande
Page 7 and 8: 4.2.5. Two-Beam Scattering Matrix 4
Page 9 and 10: Dedicated to my wife and parents
Page 11 and 12: SUMMARY The dissertation focuses on
Page 13 and 14: CONTENTS Chapter 1: INTRODUCTION 1
Page 15 and 16: 1 CHAPTER ONE INTRODUCTION Silicon
Page 17 and 18: 2.1. Introduction 3 CHAPTER TWO OVE
Page 19 and 20: 2.2.2 The Zinc-Blende Structure 5 T
Page 21: 2.3 Point Defects, Defect Migration
Page 25 and 26: 11 explained and the concept of par
Page 27 and 28: 13 Straight dislocations furthermor
Page 29 and 30: 2.5 Partial Dislocations and Slip 1
Page 31 and 32: 17 Fig. 2.13. The geometrical setup
Page 33 and 34: 19 extrinsic stacking faults are th
Page 35 and 36: 2.8 Twinning 21 Twinning is a proce
Page 37 and 38: 23 Fig. 2.20. The process of vacanc
Page 39 and 40: S n Td (3.2) 25 and is also referr
Page 41 and 42: 27 where a = a0(Z1 2/3 + Z2 2/3 ) -
Page 43 and 44: 29 Using this expression, curves of
Page 45 and 46: 31 As stated previously hard-sphere
Page 47 and 48: 33 where A is the atomic weight. Th
Page 49 and 50: 35 a vacancy dislocation loop if th
Page 51 and 52: 37 Fig. 4.1. (a) A wave incident on
Page 53 and 54: 39 Consider Fig. 4.2 which illustra
Page 55 and 56: 41 V0 is the mean inner potential o
Page 57 and 58: 43 beam left-hand side g' = 0 g' =
Page 59 and 60: 45 In addition another set of indep
Page 61 and 62: 47 When this is incorporated into t
Page 63 and 64: S ( s , z ) e T i Se ( / 0 )
Page 65 and 66: z0 z2 . xn cos and (4.47) D 1 proj
Page 67 and 68: 5.1 Introduction 53 CHAPTER FIVE LI
Page 69 and 70: 55 different orientations. The inte
Page 71 and 72: 57 Furthermore Pirouz et al. (1987)
Page 73 and 74:
59 intersection of the fault, the f
Page 75 and 76:
61 each nuclei because of the low s
Page 77 and 78:
63 (2000) found that subsequent ann
Page 79 and 80:
6.3.1 Ion Range and Defect Producti
Page 81 and 82:
67 Fig. 6.3. Total number of displa
Page 83 and 84:
7.1 Introduction 69 CHAPTER SEVEN R
Page 85 and 86:
Fig. 7.2. Simulated diffraction pat
Page 87 and 88:
73 Fig. 7.3. A HRTEM image of the S
Page 89 and 90:
75 Fig. 7.5. The stacking fault sel
Page 91 and 92:
(Si/ni) 2 0.000018 0.000016 0.00001
Page 93 and 94:
79 may be concluded that the initia
Page 95 and 96:
81 Fig. 7.11. Bright field TEM micr
Page 97 and 98:
83 Fig. 7.12 which was obtained by
Page 99 and 100:
85 Fig. 7.13. Bright-field TEM micr
Page 101 and 102:
87 (a) (b) Fig. 7.15. The (a) exper
Page 103 and 104:
89 In the following paragraphs the
Page 105 and 106:
Fig. 7.18. CBED pattern taken of th
Page 107 and 108:
93 Table 7.5. The measured paramete
Page 109 and 110:
7.4.2 Results 95 Fig. 7.22. Bright-
Page 111 and 112:
97 Twin platelets on {111} planes
Page 113 and 114:
99 REFERENCES Blumenau, A.T., Jones
Page 115 and 116:
101 Hull, D., Bacon, D.J. : (1984)
Page 117:
103 Smith, D.J., Jepps, N.W. and Pa
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