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

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10 in which the rate of change of the concentration with time is described. This is useful since it enables the change in concentration to be determined at different time intervals. Furthermore the diffusion coefficient may be given as, D Q / kT D0e (2.5) where D0 is called the pre-exponential factor and is temperature independent and Q is the energy of activation for diffusion which depends on the diffusing species. In general the formation energy of interstitials is considerably higher than that of vacancies but their migration energy is far lower. This is due to the considerable lattice strain created by the interstitial and thus relieving this strain by means of migration should be highly probable. If interstitials are formed thermally or by other means they will rapidly migrate to sinks. Such sinks will include the surface, other interstitials or vacancies and extended defects. If the interstitials come into contact they will form stable clusters and if they come into contact with vacancies mutual annihilation will occur. If two interstitials form a cluster it is termed a di-interstitial and if three form a cluster it is a tri-interstitial etc. The probability of migration of these clusters within the lattice become increasingly less probable as they increase in size and will when reaching a sufficient size act as a sink for the migration of other point defects. The same process holds for vacancy migration with the only difference being that the migration energy for vacancies are much higher than that of interstitials. In general the migration energy of substitutional impurities in the lattice is also higher than that of the interstitial. 2.4. Dislocations 2.4.1 Introduction In this section the theory of dislocations is presented. Concepts of dislocation line and Burgers vector are explained and also different types of dislocations in a crystal are discussed. The motion of dislocations through the processes of glide and climb is
11 explained and the concept of partial dislocations and slip discussed since it is important in the understanding of the formation of stacking faults. 2.4.2. The Dislocation Line and Burgers Vector To understand the concept of the dislocation line and Burgers vector the following geometrical analogy may be followed and is shown in Fig. 2.7. Imagine a dislocation being produced by making a cut in a perfect crystal. Following this the two sides of the crystal are shifted with respect to one another by a translation vector of the lattice. Then the missing material is added or surplus material removed. The shifted surface of the cut may grow together in such a way that the cut is no longer discernable. Thus at the inside of the crystal, at the edge of the former cut surface, a line of strongly disturbed material remains. This line is called the “dislocation line”. (a) (b) (c) Fig 2.7. The geometrical analogy of a Volterra-cut describing a dislocation present in a crystal (from Bollmann (1970)). (a) A cut is made in a perfect crystal. (b) The two sides of the crystal are shifted with respect to one another by a translation vector of the lattice. (c) The shifted surface of the cut may grow together in such a way that the cut is no longer discernable.
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 and 22: 2.3 Point Defects, Defect Migration
Page 23: v m Em vm0 exp( ) (2.2) kT 9 wher
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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