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

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36 CHAPTER FOUR DYNAMICAL THEORY OF ELECTRON DIFFRACTION AND IMAGE SIMULATION 4.1 Introduction This chapter discusses in basic terms the technique of image simulation of two-beam TEM images of defects. The theory presented is taken from the book “An Introduction to Conventional Electron Microscopy” written by Marc de Graef (2003) and it is once again left to the reader to consult this book for any further information. The theory of electron diffraction is discussed from a dynamical point of view introducing the concepts of the Bragg equation, reciprocal space and the Ewald sphere. This is then used to derive the Darwin Howie Whelan equation which in turn is used for image simulations. Only the two-beam case is considered and the scattering matrix approach is explained. Finally a simple method to obtain line intensity profiles from stacking faults and twinned areas on inclined planes is shown. 4.2. Theory of Electron Diffraction 4.2.1 The Direct Space Bragg Equation Although the process of electron scattering within a crystal is in general a complicated process it may be explained in a simple way through the Bragg relation. Consider Fig. 4.1.
37 Fig. 4.1. (a) A wave incident on a set of hkl planes at an angle θ, (b) the incident and diffracted directions and the plane normal must lie in a planar section through a conical surface with its top in the plane (from De Graef (2003)) A wave is incident on a set of planes with indices (hkl) at an angle θ. Assuming the planes to be semi-transparent mirrors, part of the intensity of the wave will be transmitted through the first plane and part of it reflected. If Snell’s law is applied since an ideal mirror was assumed, the incident and reflected angles must be the same, and both directions of the wave must be coplanar about a normal n to the (hkl) planes. Next, if the reflected waves from the first and second planes are considered it is seen that there is a difference in path length between the two which relate to the waves being in or out of phase. This path length difference is given by the sum of the distance PO’ and O’Q which in turn is related to the interplanar spacing dhkl and the angle θ as follows: PO'O'Q d hkl 2d sin d hkl sin hkl sin (4.1) For in-phase propagation of the two reflected waves, known as constructive interference, the path length difference should be an integral number of wavelengths and thus for constructive interference the relation is, 2 sin n (4.2) d hkl
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 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: 35 a vacancy dislocation loop if th
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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