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

More documents

Recommendations

Info

48 associated displacement field of the stacking fault to obtain a line intensity profile of the fringes. As discussed in Section 2.6 stacking faults are produced by a disruption of the regular stacking sequence of a material. It can also be seen as two regions of the crystal having been shifted relative to one another by a distance given by a displacement vector R which may be a non-lattice translation as shown by Fig. 4.4. The displacement vector has a component parallel to the fault plane R|| and normal to it R . Thus the presence of this fault will introduce a phase shift α = 2πg·R which modifies the solution to the DHW equations for the bottom section (section II) of the crystal. If α is an integer multiple of π no defect contrast will be seen which shows that R is a lattice translation vector and effectively no modification of the solutions to the DHW equations result. If R is a non-lattice translation, α is not an integer multiple of π and image contrast of the form of alternating light and dark fringes will be formed. Fig. 4.4. (a) Schematic illustration of a planar defect separating crystal sections I and II; (b) inclined planar defect combined with the column approximation (from De Graef (2003)) To simulate such an intensity profile the following procedure is used. Consider a crystal with thickness z0 containing a stacking fault as shown in Fig. 4.4 (b). Region 1 has been shifted with respect to region II by a vector R. The top section of the crystal (region 1) is defect free and is described by a scattering matrix Sscat(s1.z1) where z1 is the distance from the top surface to the fault. The bottom section is shifted with respect to the top and is described by a different scattering matrix M(s2.z2) since it lies in a different orientation with respect to the top. The two scattering matrices are as follows,
S ( s , z ) e T i Se ( / 0 ) z1 scat 1 1 M ( s , z ) e 2 2 ' 0 ( / ) z ' 2 T i Se g g Se T Se T i ( ) i g ( ) M can further be decomposed into, i g 1 0 T S e 1 0 2 2 M M P( g ) S 2P( g ) i g i g ( ) i g 0 e S e T 0 e 2 2 g 49 (4.40) (4.41) 2 (4.42) with P being the defect phase shift matrix, 1 0 P( ) (4.43) i 0 e Using this, the transmitted and scattered amplitudes at the exit plane of the crystal are obtained by the product of the scattering matrices for each section using the initial condition (1,0) T , 0 g 1 ( g ) S 2P( ) S1 0 P g From this the intensities are obtained by squaring the wave functions. (4.44) Note that the values of z1 and z2 depend on the incoming beam direction B, foil normal N and the plane normal P of the plane in which the fault lies, note also that the extinction distance used depends on the diffraction vector g. Thus to solve the problem the following geometrical setup is used and shown in Fig. 4.5.
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 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: 47 When this is incorporated into t
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
show all

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

Create successful ePaper yourself

Delete template?

Save as template?