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

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46 solutions which in turn are combined to give a general solution from which the scattering matrix is obtained. The general solution may then be written as follows, z ) S scat ( s, z ) ( 0) (4.32) ( 0 0 It should also be noted that the scattering matrix is a complex matrix of the form, S S iS (4.33) scat r i 4.2.6 Crystal Defects and Displacement Fields The presence of a defect in a crystal causes a disruption in the positions of the atoms as predicted by the Bravais lattice translation vectors. The atoms are displaced from their positions by a vector R which is a function of position r. This vector field R(r) is known as the displacement field and relates the displaced position r’ of the atom to the ideal position r by, r ' r R(r) (4.34) Also the presence of this displacement field causes a deviation in the potential of the crystal from the perfect crystal at the deformed position given by, ' V ( r) V ( r R) V 0 V 0 g g V V g g e e 2ig( rR ) 2igR e 2igr (4.35) which shows that the electrostatic potential is modified by a phase factor αg as follows, V g i (r) g V e with ( r) 2g R(r) g g (4.36)
47 When this is incorporated into the Darwin-Howie-Whelan equations it modifies the equations to be, d dz g 2i( s g i g g ' e ' g q ' g g dR g ) g i ' (4.37) g dz which only constitutes a change in the excitation error to an effective excitation error given by, dR(r) ( r) s g (4.38) dz eff sg g 4.3. Image Contrast for Selected Defects 4.3.1 Line Defects As discussed in section 2.4 a dislocation is a linear lattice defect which may be characterised by a Burgers vector b and a dislocation line direction u. It may be characterised as being of edge character with b·u = 0 or screw character with b || u or a mixture of both. In general the displacement field of a dislocation is given by, 1 sin 2 1 2 cos R b be b u ln r (4.39) 2 4( 1 ) 2( 1 ) 4( 1 ) where υ is Poissons’s ratio, be the edge component of the Burgers vector and (r,θ) polar coordinates in a plane perpendicular to the dislocation line direction. 4.3.2 Stacking Faults The aim of this section is not to describe the full process of simulating an inclined stacking fault with its associated partial dislocations but rather to describe a relatively easy way of obtaining one-dimensional intensity profiles of stacking fault fringes. The procedure uses a scattering matrix approach discussed in Section 4.2.5 with the
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Analysis of the Extended Defects in
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My sincere thanks to the following
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OPSOMMING Hierdie dissertasie hande
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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 and 24: v m Em vm0 exp( ) (2.2) kT 9 wher
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: 45 In addition another set of indep
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-
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97 Twin platelets on {111} planes
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99 REFERENCES Blumenau, A.T., Jones
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101 Hull, D., Bacon, D.J. : (1984)
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103 Smith, D.J., Jepps, N.W. and Pa
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