Physical Principles of Electron Microscopy: An Introduction to TEM ...

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110 Chapter 4 Close examination of the rings reveals that they consist of a large number of spots, each arising from Bragg reflection from an individual crystallite. Equation (4.21) predicts only the radial angle (� = 2�B) that determines the distance of a spot from the center of the diffraction pattern. The azimuthal angle � of a spot is determined by the azimuthal orientation of a crystallite about the incident-beam direction (the optic axis). Because the grains in a polycrystalline specimen are randomly oriented, diffraction spots occur at all azimuthal angles and give the appearance of continuous rings if many grains lie within the path of the electron beam (grain size
TEM Specimens and Images 111 Figure 4-13. Unit cell for a face-centered cubic crystal: a cube of side a with atoms located at each corner and at the center of each face. Another common crystal structure is the bodycentered cubic (bcc) structure, whose unit cell is a cube with eight corner atoms and a single atom located at the geometrical center of the cube. For a material whose lattice parameter is known (for example, from x-ray diffraction), the expected d-spacings can be calculated, using the additional condition that (for the fcc structure) h, k, and l must be all odd or all even. Therefore, the first few rings in the diffraction pattern of a polycrystalline fcc metal correspond to (h kl) = (1 1 1), (2 0 0), (2 2 0), (3 1 1), (2 2 2), … (4.24) Knowing a, the d-spacing for each ring can be calculated using Eq. (4.23) and its electron-scattering angle � obtained from Eq. (4.21). From Eq. (4.22), a value of L can be deduced for each ring and these individual values averaged to give a more accurate value of the camera length. Recording the diffraction pattern of a material with known structure and lattice parameter therefore provides a way of calibrating the camera length, for a given intermediate-lens setting. Knowing L, the use of Eq. (4.22) and then Eq. (4.21) can provide a list of the d-spacings represented in the electron-diffraction pattern recorded from an unknown material. In favorable cases, these interplanar spacings can then be matched to the d-values calculated for different crystal structures, taking h, k, and l from rules similar to Eq. (4.24) but different for each structure, and with a as an adjustable parameter. In this way, both the lattice parameter and the crystal structure of the unknown material can be determined, which may enable the material to be identified from previously-tabulated information.
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Physical Principles of Electron Mic
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Ray F. Egerton Department of Physic
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Contents Preface xi 1. An Introduct
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Contents ix 7. Recent Developments
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xii Preface textbooks, such as Will
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2 1.1 Limitations of the Human Eye
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4 Chapter 1 parallel beam of light
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6 Chapter 1 Figure 1-3. One of the
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8 Chapter 1 Figure 1-5. Light-micro
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10 Chapter 1 Figure 1-7. Scanning t
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12 Chapter 1 Figure 1-8. Early phot
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14 Chapter 1 Figure 1-10. JEOL tran
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16 Chapter 1 hydrated. But high-ene
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18 Chapter 1 Figure 1-14. Scanning
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20 Chapter 1 Figure 1-16. Photograp
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22 Chapter 1 visible-light photons
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24 Chapter 1 Typically, the STM hea
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Chapter 2 ELECTRON OPTICS Chapter 1
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Electron Optics 29 a c b object len
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Electron Optics 31 � a n 2 ~1.5
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Electron Optics 33 We can define im
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Electron Optics 35 electron source
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Electron Optics 37 symmetry and use
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Electron Optics 39 As we said earli
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Electron Optics 41 2.4 Focusing Pro
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Electron Optics 43 � = [e/(8mE0)
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Electron Optics 45 image plane. Whe
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Electron Optics 47 procedure that i
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Electron Optics 49 The basic physic
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Electron Optics 51 From Eq. (2.7),
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Electron Optics 53 y +V 1 +V 2 -V 2
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Electron Optics 55 point from the o
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58 Chapter 3 3.1 The Electron Gun T
Page 68 and 69: 60 Chapter 3 The rate of electron e
Page 70 and 71: 62 Chapter 3 electron emission curr
Page 72 and 73: 64 Chapter 3 As seen from the right
Page 74 and 75: 66 Chapter 3 � r r s r � (a) (b
Page 76 and 77: 68 Chapter 3 Table 3-2. Speed v and
Page 78 and 79: 70 Chapter 3 where G is a large amp
Page 80 and 81: 72 Chapter 3 The second condenser (
Page 82 and 83: 74 Chapter 3 Figure 3-9 summarizes
Page 84 and 85: 76 Chapter 3 resolution (especially
Page 86 and 87: 78 Chapter 3 The major advantage of
Page 88 and 89: 80 Chapter 3 contrast (for a given
Page 90 and 91: 82 Chapter 3 A more correct procedu
Page 92 and 93: 84 Chapter 3 diffraction pattern (s
Page 94 and 95: 86 Chapter 3 Nowadays, photographic
Page 96 and 97: 88 Chapter 3 A related concept is d
Page 98 and 99: 90 Chapter 3 molecules, imparting a
Page 100 and 101: 92 Chapter 3 Frequently, liquid nit
Page 102 and 103: 94 Chapter 4 -e -e -e -e +Ze Figure
Page 104 and 105: 96 Chapter 4 � (a) elastic z x m
Page 106 and 107: 98 Chapter 4 � b a (a) (b) Figure
Page 108 and 109: 100 Chapter 4 fraction of electrons
Page 110 and 111: 102 Chapter 4 whose composition or
Page 112 and 113: 104 Chapter 4 replica crystallites
Page 114 and 115: 106 Chapter 4 4.5 Diffraction Contr
Page 116 and 117: 108 Chapter 4 remain undiffracted (
Page 120 and 121: 112 Chapter 4 Unfortunately, the va
Page 122 and 123: 114 Chapter 4 Crystals can also con
Page 124 and 125: 116 Chapter 4 A simple example of p
Page 126 and 127: 118 Chapter 4 High-magnification ph
Page 128 and 129: 120 Chapter 4 At this stage it is c
Page 130 and 131: 122 Chapter 4 All of the above meth
Page 132 and 133: 124 Chapter 4 The procedures outlin
Page 134 and 135: 126 Chapter 5 specimen scan coils o
Page 136 and 137: 128 Chapter 5 functions with m and
Page 138 and 139: 130 Chapter 5 inelastic collisions
Page 140 and 141: 132 Chapter 5 Figure 5-5. Dependenc
Page 142 and 143: 134 Chapter 5 Figure 5-7. (a) Secon
Page 144 and 145: 136 Chapter 5 Because each secondar
Page 146 and 147: 138 Chapter 5 Backscattered electro
Page 148 and 149: 140 Chapter 5 Whereas Ip remains co
Page 150 and 151: 142 Chapter 5 Figure 5-14. Red, gre
Page 152 and 153: 144 Chapter 5 the SE2 and SE3 compo
Page 154 and 155: 146 Chapter 5 just-observable loss
Page 156 and 157: 148 Chapter 5 Section 4-10. Films o
Page 158 and 159: 150 Chapter 5 A backscattered-elect
Page 160 and 161: 152 Chapter 5 One example of this p
Page 162 and 163: Chapter 6 ANALYTICAL ELECTRON MICRO
Page 164 and 165: Analytical Electron Microscopy 157
Page 166 and 167: Analytical Electron Microscopy 159
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Analytical Electron Microscopy 161
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178 Chapter 7 Figure 7-1. Modified
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180 Chapter 7 7.2 Aberration Correc
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182 Chapter 7 Besides decreasing th
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184 Chapter 7 7.4 Electron Holograp
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186 Chapter 7 There are now many al
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188 Chapter 7 holography could ther
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Appendix MATHEMATICAL DERIVATIONS A
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Mathematical Derivations 193 A.2 Im
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REFERENCES Binnig, G., Rohrer, H.,
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INDEX Aberrations, 3, 28 axial, 44
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Index 199 EELS, 172 Electromagnetic
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Index 201 Principal plane, 32, 80 P
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