International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B. ch. 2.5, pp. 298-305   | 1 | 2 |

Table 2.5.3.5 

P. Goodmanb

Table 2.5.3.5| top | pdf |
Conditions for observation of GS bands for the 137 space groups exhibiting these extinctions

Point groups 2, m, [{\bf 2/{\bi m}}] (2nd setting unique axis [\|b])

Space groupIncident-beam direction
[u0w]
4 [P2_{1}] 0k0 S
[2_{1}]
7 Pc h0l G
c
9 Cc h0l G
c
11 [P2_{1}/m] 0k0 S
[2_{1}]
13 [P2/c] h0l G
c
14 [P2_{1}/c] 0k0 S
[2_{1}]
h0l G
c
15 [C2/c] h0l G
c

Point groups 222, mm2

Space groupIncident-beam direction
[100][010][001][uv0][0vw][u0w]
17 [P222_{1}] 00l S 00l S     00l S        
[2_{1}] [2_{1}]     [2_{1}]        
18 [P2_{1}2_{1}2] 0k0 S h00 S h00, 0k0 S     h00 S 0k0 S
[2_{1}] [2_{1}] [2_{1}]     [2_{1}] [2_{1}]
19 [P2_{1}2_{1}2_{1}] 0k0, 00l S h00, 00l S h00, 0k0 S 00l S h00 S 0k0 S
[2_{1}] [2_{1}] [2_{1}] [2_{1}] [2_{1}] [2_{1}]
20 [C222_{1}] 00l S 00l S     00l S        
[2_{1}] [2_{1}]     [2_{1}]        
26 [Pmc2_{1}] 00l GS 00l c′−     00l S     h0l G
[c + 2_{1}] [2_{1}]     [2_{1}]     c
27 [Pcc2] 00l c′− 00l c′−         0kl G h0l G
c c         c c
28 [Pma2]         h00 G         h0l G
        a         a
29 [Pca2_{1}] 00l c′− 00l GS h00 G 00l S 0kl G h0l G
[2_{1}] [c + 2_{1}] a [2_{1}] c a
30 [Pnc2] 00l n′− 00l c′− 0k0 G     0kl G h0l G
c n n     n c
31 [Pmn2_{1}] 00l GS 00l n′− h00 G 00l S     h0l G
[n + 2_{1}] [2_{1}] n [2_{1}]     n
32 [Pba2]         h00, 0k0 G     0kl G h0l G
        a b     b a
33 [Pna2_{1}] 00l n′− 00l GS h00, 0k0 G 00l S 0kl G h0l G
[2_{1}] [n + 2_{1}] a b [2_{1}] n a
34 [Pnn2] 00l n′− 00l n′− h00, 0k0 G     0kl G h0l G
n n n     n n
36 [Cmc2_{1}] 00l GS 00l c′−     00l S     h0l G
[c + 2_{1}] [2_{1}]     [2_{1}]     c
37 [Ccc2] 00l c′− 00l c′−         0kl G h0l G
c c         c c
39 [Abm2]                 0kl G    
                b    
40 [Ama2]         h00 G         h0l G
        a         a
41 [Aba2]         h00 G     0kl G h0l G
        a     b a
43 [Fdd2] 00l d′− 00l d′− h00, 0k0 G     0kl G h0l G
  d d     d d
45 [Iba2]   b′−   a′−         0kl G h0l G
            b a
46 [Ima2]       a′−             h0l G
                  a

Point group mmm

Space groupIncident-beam direction
[100][010][001][uv0][0vw][u0w]
48 P 2/n 2/n 2/n 00l, 0k0 n′− 00l, h00 n′− 0k0, h00 n′− hk0 G 0kl G h0l G
n n n n n n
49 P 2/c 2/c 2/m 00l c′− 00l c′−         0kl G h0l G
c c         c c
50 P 2/b 2/a 2/n 0k0 b′− h00 a′− 0k0, h00 n′− hk0 G 0kl G h0l G
n n b a n b a
51 [P\;2_{1}/m\;2/m\;2/a]     h00 GS h00 a′− hk0 G h00 S    
    [a + 2_{1}] [2_{1}] a [2_{1}]    
52 [P\;2/n\;2_{1}/n\;2/a] 00l, 0k0 a′− 00l, h00 n′− 0k0 GS hk0 G 0kl G h0l G
[n + 2_{1}] n
[2_{1}] n a h00 n′− a n 0k0 S
n [2_{1}]
53 [P\;2/m\;2/n\;2_{1}/a] 00l GS h00, 00l a′− h00 a′− hk0 G     h0l G
a
[n + 2_{1}] [2_{1}] n 00l S n
[2_{1}]
54 [P\;2_{1}/c\;2/c\;2/a] 00l c′− h00 GS h00 a′− hk0 G 0kl G h0l G
[a + 2_{1}] c
c 00l c′− [2_{1}] a h00 S c
c [2_{1}]
55 [P\;2_{1}/b\;2_{1}/a\;2/m] 0k0 b′− h00 a′− 0k0, h00 GS     0kl G h0l G
b a
[2_{1}] [2_{1}] [b + 2_{1}, a + 2_{1}] h00 S 0k0 S
[2_{1}] [2_{1}]
56 [P\;2_{1}/c\;2_{1}/c\;2/n] 0k0 GS h00 GS 0k0, h00 n′− hk0 G 0kl G h0l G
[n + 2_{1}] [n + 2_{1}] c c
00l c′− 00l c′− [2_{1}] n h00 S 0k0 S
c c [2_{1}] [2_{1}]
57 [P\;2/b\;2_{1}/c\;2_{1}/m] 00l GS 00l c′− 0k0 GS 00l S 0kl G h0l G
[c + 2_{1}] c
0k0 b′− [2_{1}] [b + 2_{1}] [2_{1}] b 0k0 S
[2_{1}] [2_{1}]
58 [P\;2_{1}/n\;2_{1}/n\;2/m] 00l, 0k0 n′− 00l, h00 n′− 0k0, h00 GS     0kl G h0l G
n n
n [2_{1}] n [2_{1}] [n + 2_{1}] h00 S 0k0 S
[2_{1}] [2_{1}]
59 [P\;2_{1}/m\;2_{1}/m\;2/n] 0k0 GS h00 GS 0k0, h00 n′− hk0 G h00 S 0k0 S
[n + 2_{1}] [n + 2_{1}] [2_{1}] n [2_{1}] [2_{1}]
60 [P\;2_{1}/b\;2/c\;2_{1}/n] 00l GS h00 GS 0k0, h00 n′− hk0 G 0kl G h0l G
[c + 2_{1}] [n + 2_{1}] n b
0k0 b′− 00l c′− b [2_{1}] 00l S h00 S c
n [2_{1}] [2_{1}] [2_{1}]
61 [P\;2_{1}/b\;2_{1}/c\;2_{1}/a] 00l GS h00 GS 0k0 GS hk0 G 0kl G h0l G
[c + 2_{1}] [a + 2_{1}] [b + 2_{1}] a b c
0k0 b′− 00l c′− h00 a′− 00l S h00 S 0k0 S
[2_{1}] [2_{1}] [2_{1}] [2_{1}] [2_{1}] [2_{1}]
62 [P\;2_{1}/n\;2_{1}/m\;2_{1}/a] 0k0, 00l n′− 00l GS 0k0 GS hk0 G 0kl G 0k0 S
[n + 2_{1}] [n + 2_{1}] a n
[2_{1}] h00 h00 a′− 00l S h00 S [2_{1}]
[a + 2_{1}] [2_{1}] [2_{1}] [2_{1}]
63 [C\;2/m\;2/c\;2_{1}/m] 00l GS 00l c′−     00l S     h0l G
[c + 2_{1}] [2_{1}] [2_{1}] c
64 [C\;2/m\;2/c\;2_{1}/a] 00l GS 00l c′−     hk0 G     h0l G
a
[c + 2_{1}] [2_{1}] 00l S c
[2_{1}]
66 [C\;2/c\;2/c\;2/m] 00l c′− 00l c′−         0kl G h0l G
c c c c
67 [C\;2/m\;2/m\;2/a]             hk0 G        
a
68 [C\;2/c\;2/c\;2/a] 00l c′− 00l c′−     hk0 G 0kl G h0l G
c c a c c
70 [F\;2/d\;2/d\;2/d] 00l, 0k0 d′− h00, 00l d′− 0k0, h00 d′− hk0 G 0kl G h0l G
d d d d d d
72 [I\;2/b\;2/a\;2/m]   b′−   a′−         0kl G h0l G
b a
73 [I\;2/b\;2/c\;2/a]   b′−   c′−   a′− hk0 G 0kl G h0l G
a b c
74 [I\;2/m\;2/m\;2/a]             hk0 G        
a

Point groups 4, [\bar{\bf{4}}], [\bf{4/{\bi m}}]

Space groupIncident-beam direction
[uv0]
76 [P4_{1}] 00l S
[4_{1}]
78 [P4_{3}] 00l S
[4_{3}]
85 [P4/n] hk0 G
n
86 [P4_{2}/n] hk0 G
n
88 [I4_{1}/a] hk0 G
a

Point group 422

Space groupIncident-beam direction
[uv0][0vw]
90 [P42_{1}2]     h00 S
[2_{1}]
91 [P4_{1}22] 00l S    
[4_{1}]
92 [P4_{1}2_{1}2] 00l S h00 S
[4_{1}] [2_{1}]
94 [P4_{2}2_{1}2]     h00 S
[2_{1}]
95 [P4_{3}22] 00l S    
[4_{3}]
96 [P4_{3}2_{1}2] 00l S h00 S
[4_{3}] [2_{1}]

Point group 4mm

Space groupIncident-beam direction
[100][001][110][u0w] and [0vw] [[u\bar{u}w]]
100 [P4bm]     h00, 0k0 G     h0l, 0kl G    
a b a b
101 [P4_{2}cm] 00l c′−         h0l, 0kl G    
c c
102 [P4_{2}nm] 00l n′− h00, 0k0 G     h0l, 0kl G    
n n n
103 [P4cc] 00l c′−     00l c′− h0l, 0kl G hhl G
c c c c
104 [P4nc] 00l n′− h00, 0k0 G 00l c′− h0l, 0kl G hhl G
n n c n c
105 [P4_{2}mc]         00l c′−     hhl G
c c
106 [P4_{2}bc]     h00, 0k0 G 00l c′− h0l, 0kl G hhl G
a b c a b c
108 [I4cm]             h0l, 0kl G    
c
109 [I3_{1}md]     hh0 G 00l d′−     hhl G
[{\bar h}h0]    
d d d
110 [I4_{1}cd]     hh0 G 00l d′− h0l, 0kl G hhl G
[{\bar h}h0]      
d d c d

Point groups [\bar{\bf {4}}]2m, 4/mmm

Space groupIncident-beam direction
[100][001][110][u0w] and [0vw][uuw][uv0]
112 [P{\bar 4}2c]         00l c′−     hhl G    
c c
113 [P{\bar 4}2_{1}m] 0k0 S h00, 0k0 S     0k0, h00 S        
[2_{1}] [2_{1}] [2_{1}]
114 [P{\bar 4}2_{1}c] 0k0 S h00, 0k0 S 00l c′− 0k0, h00 S hhl G    
[2_{1}] [2_{1}] c [2_{1}] c
116 [P{\bar 4}c2] 00l c′−         h0l, 0kl G        
c c
117 [P{\bar 4}b2]     h00, 0k0 G     h0l, 0kl G        
a b a b
118 [P{\bar 4}n2] 00l n′− h00, 0k0 G     h0l, 0kl G        
n n n
120 [I{\bar 4}c2]             h0l, 0kl G        
c
122 [I{\bar 4}2d]     hh0 G 00l d′−     hhl G    
[{\bar h}h0]    
d d d
124 [P\;4/m\;2/c\;2/c] 00l c′−     00l c′− h0l, 0kl G hhl G    
c c c c
125 [P\;4/n\;2/b\;2/m] 0k0 b′− h00, 0k0 n′−     h0l, 0kl G     hk0 G
n a b a b n
126 [P\;4/n\;2/n\;2/c] 0k0 n′− h00, 0k0 n′− 00l c′− h0l, 0kl G hhl G hk0 G
n
00l n c n c n
n
127 [P\;4/m\;2_{1}/b\;2/m] 0k0 b′− h00 GS     h0l, 0kl G        
[a + 2_{1}] a b
[2_{1}] 0k0 0k0, h00 S
[b + 2_{1}] [2_{1}]
128 [P\;4/m\;2_{1}/n\;2/c] 00l, 0k0 n′− h00, 0k0 GS 00l c′− h0l, 0kl G hhl G    
n
[n\quad 2_{1}] [n + 2_{1}] c 0k0, h00 S c
[2_{1}]
129 [P\;4/n\;2_{1}/m\;2/m] 0k0 GS h00, 0k0 n′−     0k0, h00 S     hk0 G
[n + 2_{1}] [2_{1}] [2_{1}] n
130 [P\;4/n\;2_{1}/c\;2/c] 0k0 GS h00, 0k0 n′− 00l c′− h0l, 0kl G hhl G hk0 G
[n + 2_{1}] c
00l c′− [2_{1}] c 0k0, h00 S c n
c [2_{1}]
131 [P\;4_{2}/m\;2/m\;2/c]         00l c     hhl G    
c c
132 [P\;4_{2}/m\;2/c\;2/m] 00l c′−         h0l, 0kl G        
c c
133 [P\;4_{2}/n\;2/b\;2/c] 0k0 b′− h00, 0k0 n′− 00l c′− h0l, 0kl G hhl G hk0 G
n a b c a b c n
134 [P\;4_{2}/n\;2/n\;2/m] 0k0, 00l n′− h00, 0k0 n′−     h0l, 0kl G     hk0 G
n n n n
135 [P\;4_{2}/m\;2_{1}/b\;2/c] 0k0 b′− h00, 0k0 GS 00l c′− h0l, 0kl G hhl G    
a b
[2_{1}] [a + 2_{1}\;b + 2_{1}] c 0k0, h00 S c
[2_{1}]
136 [P\;4_{2}/m\;2_{1}/n\;2/m] 00l, 0k0 n′− h00, 0k0 GS     h0l, 0kl G        
n
n 2 [n + 2_{1}] 0k0, h00 S
[2_{1}]
137 [P\;4_{2}/n\;2_{1}/m\;2/c] 0k0 GS h00, 0k0 n′− 00l c′− 0k0, h00 S hhl G hk0 G
[n + 2_{1}] [2_{1}] c [2_{1}] c n
138 [P\;4_{2}/n\;2_{1}/c\;2/m] 0k0 GS h00, 0k0 n′−     h0l, 0kl G     hk0 G
[n + 2_{1}] c
00l c′− [2_{1}] 0k0, h00 S n
c [2_{1}]
140 [I\;4/m\;2/c\;2/m]             h0l, 0kl G        
c
141 [I\;4_{1}/a\;2/m\;2/d]     hh0 a′− 00l, [{\bar h}h0] d′−     hhl G hk0 G
[{\bar h}h0]      
d d a d a
142 [I\;4_{1}/a\;2/c\;2/d]     hh0 a′− 00l, [{\bar h}h0] d′− h0l, 0kl G hhl G hk0 G
[{\bar h}h0]        
d d a c d a

Point groups 3m, [{\bar{\bf 3}}] m, 6, 6/m, 622, 6mm, [{\bar{\bf 6}}] m2, 6/mmm

Space groupIncident-beam direction
[100][210][2u u w][v0w]
158 P3c1     000l G [hh2{\bar h}l] G    
c c
159 P31c 000l G         [h{\bar h}0l] G
c c
161 R3c     000l G [hh2{\bar h}l] G    
[l = 6n + 3]  
c c
163 [P{\bar 3}1c] 000l G         [h{\bar h}0l] G
c c
165 [P{\bar 3}c1]     000l G [hh2{\bar h}l] G    
c c
167 [R{\bar 3}c]     000l G [hh2{\bar h}l] G    
[l = 6n + 3]  
c c
169 [P6_{1}] 000l S 000l S        
[6_{1}] [6_{1}]
170 [P6_{5}] 00l S 00l S        
[6_{5}] [6_{5}]
173 [P6_{3}] 000l S 000l S        
[6_{3}] [6_{3}]
176 [P6_{3}/m] 000l S 000l S        
[6_{3}] [6_{3}]
178 [P6_{1}22] 000l S 000l S        
[6_{1}] [6_{1}]
179 [P6_{5}22] 000l S 000l S        
[6_{5}] [6_{5}]
182 [P6_{3}22] 000l S 000l S        
[6_{3}] [6_{3}]
184 [P6cc] 000l c′− 000l c′− [hh2{\bar h}l] G [h{\bar h}0l] G
c c c c
185 [P6_{3}cm] 000l c′− 000l GS [hh2{\bar h}l] G    
[6_{3}] [c + 6_{3}] c
186 [P6_{3}mc] 000l GS 000l c′−     [h{\bar h}0l] G
[c + 6_{3}] [6_{3}] c
188 [P{\bar 6}c2]     000l G [hh2{\bar h}l] G    
c c
190 [P{\bar 6}c2] 000l G         [h{\bar h}0l] G
c c
192 [P6/mcc] 000l c′− 000l c′− [hh2{\bar h}l] G [h{\bar h}0l] G
c c c c
193 [P6_{3}/mcm] 00l c′− 000l GS [hh2{\bar h}l] G    
[6_{3}] [c + 6_{3}] c
194 [P6_{3}/mmc] 000l GS 000l c′−     [h{\bar h}0l] G
[c + 6_{3}] [6_{3}] c

Point groups 23, m3, 432, m3m

Space groupIncident-beam direction
[100][110][uv0][uuw]
(cyclic)(cyclic)(cyclic)(cyclic)
198 P [2_{1}]3 00l, 0k0 S 00l S 00l S    
[2_{1}] [2_{1}] [2_{1}]
201 [Pn\bar{3}] 00l, 0k0 n′−     [{\bar k}h0] G    
[P2/n{\bar 3}] n n
203 Pd [{\bar 3}] 00l, 0k0 d′−     [{\bar k}h0] G    
[F2/d{\bar 3}] d d
205 Pa [{\bar 3}] 00l GS 00l S 00l S    
[c + 2_{1}] [2_{1}] [2_{1}]
[P2_{1}/a{\bar 3}] 0k0 b′− [{\bar h}h0] G [{\bar k}h0] G
[2_{1}] a a
206 Ia [{\bar 3}]     [{\bar h}h0] G [{\bar k}h0] G    
[I2_{1}/a{\bar 3}] a a
212 [P4_{3}32]         00l S    
[4_{3}]
213 [P4_{1}32]         00l S    
[4_{1}]
218 [P{\bar 4}3n]     00l n hhl G    
c c
219 [F{\bar 4}3c]         hhl G    
c
220 [I{\bar 4}3d] 0kk G 00l d hhl G    
[0{\bar k}k]    
d d d
222 [Pn{\bar 3}n] 00l, 0k0 n′− 00l n hk0 G hhl G
n c n c
223 [Pm{\bar 3}n]     00l n′−     hhl G
c c
224 [Pn{\bar 3}m] 00l, 0k0 n′−     hk0 G    
n n
226 [Fm{\bar 3}c]             hhl G
c
227 [Fd{\bar 3}m] 00l, 0k0 d′−     hk0 G    
d d
228 [Fd{\bar 3}c] 00l, 0k0 d′−     hk0 G hhl G
d d c
230 [Ia{\bar 3}d] 0kk b′− 00l, [{\bar h}h0] d′− hk0 G hhl G
[0{\bar k}k]      
d d a a d
Conditions in this column are cyclic on h and k.