Graef M. Introduction to conventional transmission electron microscopy

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668 Appendices

Table A4.1. (cont.).

Point group Stereographic

information projection Rendered 3D view

Order: 2

Crystal Class: m

Laue Class: 2/m

Diffraction Groups:

1, 2, m

# Space Groups: 3

2 –[C

]

Order: 2

Crystal Class: m

Laue Class: 2/m

Diffraction Groups:

1, 1

, m

# Space

Groups:

m –[C

]

Order: 4

Crystal Class: m

Laue Class: 2/m

Diffraction Groups:

, 21

, 2

# Space Groups: 6

2/m –[C

]

Order: 4

Crystal Class: o

Laue Class: mmm

Diffraction Groups:

1, m

, 2m

# Space Groups: 9

222 –[D

]

Order: 4

Crystal Class: o

Laue Class: mmm

Diffraction Groups:

1, m

, m, m1

, 2mm

# Space Groups: 22

mm2 –[C

]

A4 Point groups and space groups 669

Table A4.1. (cont.).

Point group Stereographic

information projection Rendered 3D view

Order: 8

Crystal Class: o

Laue Class: mmm

Diffraction Groups:

, 2

, 2mm1

# Space Groups: 28

mmm –[C

]

Order: 4

Crystal Class: t

Laue Class: 4/m

Diffraction Groups:

1, m

, 4

# Space

Groups:

4 –[C

]

Order: 4

Crystal Class: t

Laue Class: 4/m

Diffraction Groups:

1, m

, 4

# Space Groups: 2

4 –[S

]

Order: 8

Crystal Class: t

Laue Class: 4/m

Diffraction Groups:

, 2

, 41

# Space Groups: 6

4/m –[C

]

Order: 8

Crystal Class: t

Laue Class: 4/mmm

Diffraction Groups:

1, m

, 2m

, 4m

# Space Groups: 10

422 –[D

]

670 Appendices

Table A4.1. (cont.).

Point group Stereographic

information projection Rendered 3D view

Order: 8

Crystal Class: t

Laue Class: 4/mmm

Diffraction Groups:

1, m

, m, m1

, 4mm

# Space Groups: 12

4mm –[C

]

Order: 8

Crystal Class: t

Laue Class: 4/mmm

Diffraction Groups:

1, m

, m, m1

, 2m

# Space Groups: 12

42m –[D

]

Order: 16

Crystal Class: t

Laue Class: 4/mmm

Diffraction Groups:

, 2

, 2mm1

4mm1

# Space Groups: 20

4/mmm –[D

]

Order: 3

Crystal Class: R

Laue Class:

Diffraction Groups:

1, 3

# Space Groups: 4

3 –[C

]

Order: 6

Crystal Class: R

Laue Class:

Diffraction Groups:

, 6

# Space Groups: 2

3 –[C

]

A4 Point groups and space groups 671

Table A4.1. (cont.).

Point group Stereographic

information projection Rendered 3D view

Order: 6

Crystal Class: R

Laue Class:

Diffraction Groups:

1, 2, m

, 3m

# Space Groups: 7

32 –[D

]

Order: 6

Crystal Class: R

Laue Class:

Diffraction Groups:

1, 1

, m, 3m

# Space

Groups:

3m –[C

]

Order: 12

Crystal Class: R

Laue Class:

Diffraction Groups:

2, 21

, 2

# Space Groups: 6

3m –[D

]

Order: 6

Crystal Class: h

Laue Class: 6/m

Diffraction Groups:

1, m

, 6

# Space Groups: 6

6 –[C

]

Order: 6

Crystal Class: h

Laue Class: 6/m

Diffraction Groups:

1, m, 31

# Space Groups: 6

6 –[C

]

672 Appendices

Table A4.1. (cont.).

Point group Stereographic

information projection Rendered 3D view

Order: 12

Crystal Class: h

Laue Class: 6/m

Diffraction Groups:

, 2

, 61

# Space Groups: 2

6/m –[C

]

Order: 12

Crystal Class: h

Laue Class: 6/mmm

Diffraction Groups:

1, m

, 2m

, 6m

# Space Groups: 6

622 –[D

]

Order: 12

Crystal Class: h

Laue Class: 6/mmm

Diffraction Groups:

1, m

, m, m1

, 6mm

# Space Groups: 4

6mm –[C

]

Order: 12

Crystal Class: h

Laue Class: 6/mmm

Diffraction Groups:

1, m

, m, m1

, 2mm,

3m1

# Space Groups: 4

6m2 –[D

]

Order: 24

Crystal Class: h

Laue Class: 6/mmm

Diffraction Groups:

, 2

, 2mm1

6mm1

# Space Groups: 4

6/mmm –[D

]

A4 Point groups and space groups 673

Table A4.1. (cont.).

Point group Stereographic

information projection Rendered 3D view

Order: 12

Crystal Class: c

Laue Class: m

Diffraction Groups:

1, m

, 2m

, 3,

# Space Groups: 5

23 –[T ]

Order: 24

Crystal Class: c

Laue Class: m

Diffraction Groups:

, 2

, 2mm1

# Space Groups: 7

3 –[T

]

Order: 24

Crystal Class: c

Laue Class: m

Diffraction Groups:

1, m

, 2m

, 4m

# Space Groups: 8

432 –[O ]

Order: 24

Crystal Class: c

Laue Class: m

Diffraction Groups:

1, m

, m, m1

, 4

# Space Groups: 6

43m –[T

]

Order: 48

Crystal Class: c

Laue Class: m

Diffraction Groups:

, 2

, 2mm1

4mm1

, 6

# Space Groups: 10

3m –[O

]

674 Appendices

Table A4.2. The 73 symmorphic space groups, with sequential

number and corresponding point group.

S.G.# PG Symbol S.G.# PG Symbol

11P1 139 I4/mmm

1 P

1 143 3 P3

32P2 146 R3

5 C2 147

3 P

6 m Pm 148 R

8 Cm 149 32 P312

10 2/m P2/m 150 P321

12 C2/m 155 R32

16 222 P222 156 3m P3m1

21 C222 157 P31m

22 F222 160 R3m

23 I222 162

3m P

31m

25 mm2 Pmm2 164 P

3m1

35 Cmm2 165 R

38 Amm2 168 6 P6

42 Fmm2 174

6 P

44 Imm2 175 6/m P6/m

47 mmm Pmmm 177 622 P622

65 Cmmm 183 6mm P6mm

69 Fmmm 187

6m2 P

6m2

71 Immm 189 P

62m

75 4 P4 191 6/mmm P6/mmm

79 I4 195 23 P23

4 P

4 196 F23

82 I

4 197 I23

83 4/m P4/m 200 m

3 Pm

87 I4/m 202 Fm

89 422 P422 204 Pm

97 I422 207 432 P432

99 4mm P4mm 209 F432

107 I4mm 211 I432

111

42m P

42m 215

43m P

43m

115

4m2 P

4m2 216 F

43m

119

4m2 I

4m2 217 I

43m

121

42m I

42m 221 m

3m Pm

123 4/mmm P4/mmm 225 Fm

229 Im

A4 Point groups and space groups 675

Table A4.3. The non-symmorphic space groups, with

sequential number and corresponding point group.

S.G.# PG Symbol S.G.# PG Symbol

42P2

57 Pbcm

7 m Pc 58 Pnnm

9 Cc 59 Pmmn

∗

11 2/m P2

/m 60 Pbcn

13 P2/c 61 Pbca

14 P2

/c 62 Pnma

15 C2/c 63 Cmcm

17 222 P222

64 Cmca

18 P2

2 66 Cccm

19 P2

67 Cmma

20 C222

68 Ccca

∗

24 I2

70 Fddd

∗

26 mm2 Pmc2

72 Ibam

27 Pcc2 73 Ibca

28 Pma2 74 Imma

29 Pca2

76 4 P4

30 Pnc2 77 P4

31 Pmn2

78 P4

32 Pba2 80 I4

33 Pna2

84 4/m P4

34 Pnn2 85 P4/n

∗

36 Cmc2

86 P4

∗

37 Ccc2 88 I4

∗

39 Abm2 90 422 P41

40 Ama2 91 P4

41 Aba2 92 P4

43 Fdd2 93 P4

45 Iba2 94 P4

46 Ima2 95 P4

48 mmm Pnnn

∗

96 P4

49 Pccm 98 I4

50 Pban

∗

100 4mm P4bm

51 Pmma 101 P4

52 Pnna 102 P4

53 Pmna 103 P4cc

54 Pcca 104 P4nc

55 Pbam 105 P4

56 Pccn 106 P4

∗

indicates multiple origin settings.

676 Appendices

Table A4.3. (cont.).

S.G.# PG Symbol S.G.# PG Symbol

108 4mm I4cc 170 P6

109 I4

md 171 P6

110 I4

cd 172 P6

112

42m P

42c 173 P6

113 P

m 176 6/m P6

114 P

c 178 622 P6

116 C

4c2 179 P6

117 P

4b2 180 P6

118 P

4n2 181 P6

120 I

4c2 182 P6

122 I

42d 184 6mm P6cc

124 4/mmm P4/mcc 185 P6

125 P4/nbm

∗

186 P6

126 P4/nnc

∗

188

6m2 P

6c2

127 P4/mbm 190 P

62c

128 P4/mnc 192 6/mmm P6/mcc

129 P4/nmm

∗

193 P6

/mcm

130 P4/ncc

∗

194 P6

/mmc

131 P4

/mmc 198 23 P2

132 P4

/mcm 199 I2

133 P4

/nbc

∗

201 m

3 Pn

∗

134 P4

/nnm

∗

203 Fd

∗

135 P4

/mbc 205 Pa

136 P4

/mnm 206 Ia

137 P4

/nmc

∗

208 432 P4

138 P4

/ncm

∗

210 F4

140 I4/mcm 212 P4

141 I4

/amd

∗

213 P4

142 I4

/acd

∗

214 I4

144 3 P3

218

43m P

43n

145 P3

219 F

43c

151 32 P3

12 220 I

43d

152 P3

21 222 m

3m Pn

∗

153 P3

12 223 Pm

154 P3

21 224 Pn

∗

158 3m P3c1 226 Fm

159 P31c 227 Fd

∗

161 R3c 228 Fd

∗

163

3m P

31c 230 Ia

165 P

3c1

167 R

169 6 P6

List of symbols

Latin letters

, B

) Magnetic ﬁeld components

in cylindrical coordinates

(p. 145)

A Elastic anisotropy factor

(p. 488)

A(q) Diffraction aperture

function (p. 591)

a, b, c Lengths of Bravais basis

vectors (p. 3)

∗

, b

∗

, c

∗

Length of reciprocal basis

vectors (p. 14)

Direct structure matrix

(p. 56)

B Debye–Waller factor

(p. 127)

B(z) Axial magnetic ﬂux density

(p. 145)

Reciprocal structure matrix

(p. 59)

C Normalization constant

(p. 84)

C(r) Bloch wave function

(p. 321)

C, K , k, A, Seidel aberration

a, F, D, d Coefﬁcients for a round

lens (p. 168)

Chromatic aberration

coefﬁcient (p. 192)

Spherical aberration

coefﬁcient (p. 169)

a,x

, C

a,y

Two-fold astigmatism

(Cartesian) (p. 629)

ijkl

Elastic moduli tensor

(p. 482)

, C

( j )

Bloch wave coefﬁcient

(p. 321)

D Distance between two

points (p. 5)

D Normalized defocus

(p. 594)

D Photographic density

(p. 228)

D(i, j) Background image

intensity (p. 224)

D(U

) Transmission coefﬁcient

(p. 181)

D(r) Shape function for crystal

(p. 119)

(k)

Point symmetry matrix

(p. 45)

∗(k)

Reciprocal point symmetry

matrix (p. 45)

hkl

Interplanar spacing for

(hkl) planes (p. 13)

Point symmetry matrix

(p.

40)

Depth

of focus (p. 161)

Depth of ﬁeld (p. 161)

, D

Image displacement

(Cartesian) (p. 630)

E Electron exposure (p. 228)

E Electrostatic acceleration

potential (p. 92)

e Electron charge (p. 87)

(q) Spatial incoherence

envelope function

(p. 610)

(q) Temporal incoherence

envelope function (p. 610)

677