Table 2.5.3.4

Goodman, P.

doi:10.1107/97809553602060000558

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

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International Tables for Crystallography (2006). Vol. B. ch. 2.5, pp. 296-297 | 1 | 2 |

Table 2.5.3.4

P. Goodman^b ^‡

Table 2.5.3.4 | top | pdf |
Tabulation of principal-axis CBED pattern symmetries against relevant space groups given as IT A numbers

Three columns of diperiodic groups (central section) correspond to (i) symmorphic groups, (ii) non-symmorphic groups (GS bands) and (iii) non-symmorphic groups (zero-layer absences arising from horizontal glide planes). Cubic space groups are given underlined in the right-hand section with the code: underlining = [001](cyclic) setting; italics + underlining = [110](cyclic) setting. Separators `;' and `:' indicate change of Bravais lattice type and change of crystal system, respectively.

DG	I		II			SG	III
	Point groups		Diperiodic groups				Space groups
	H–M	BESR	(i)	(ii)	(iii)		Subgroups IIb (Subgroups 1)
Oblique						Triclinic
1	1	1	p1			1
2*	$[\bar{1}]$	$[2_{R}]$	$[p\bar{1}']$			2
						Monoclinic (Oblique)
3	12	2	p2			3	4, 5
4	1m	$[1_{R}]$	pm′			6	8
5	1m				pb′	7	9
6*		$[21_{R}]$				10	11, 12
7*		$[21_{R}]$				13	14, 15
Rectangular						(Rectangular)
8	21	$[m_{R}]$	p2′			3	5²: 195; 197, 199
9	21	$[m_{R}]$		$[p2'_{1}]$		4	198
10	21	$[m_{R}]$	c2′			5	196
11	m1	m	pm			6²	7, 8²
12	m1	m		pa		7²	9²
13	m1	m	cm			8	9
14*		$[2_{R}mm_{R}]$				10	13, 12²: 200, 201; 204
15*		$[2_{R}mm_{R}]$		$[p2'_{1}/m]$		11	14
16*		$[2_{R}mm_{R}]$				13²	15²: 206
17*		$[2_{R}mm_{R}]$		$[p2'_{1}/m]$		14²	205
18*		$[2_{R}mm_{R}]$				12	15: 202, 203
						Orthorhombic
19	222	$[2m_{R}m_{R}]$	p2′2′2			16	17; 21²; 22: 195; 196, 207, 206; 211, 214
20	222	$[2m_{R}m_{R}]$		$[p2'_{1}2'2]$		17²	18²; 20²: 212, 213
21	222	$[2m_{R}m_{R}]$		$[p2'_{1}2'_{1}2]$		18	19: 198
22	222	$[2m_{R}m_{R}]$	c2′2′2			21	20; 23, 24: 197, 199, 209, 210
23	mm2	2mm	pmm2			25	26, 27; 38, 39; 42
24	mm2	2mm		pbm2		28	29, 30, 31²; 40, 41
25	mm2	2mm		pba2		32	33, 34; 43
26	mm2	2mm	cmm2			35	36, 37; 44, 45, 46
27	mm2	$[m1_{R}]$	p2′mm′			25²	28¹; 35², 42²; 38², 39²: 215; 217
28	mm2	$[m1_{R}]$		$[p2'_{1}m'a]$		26¹	31¹; 36¹
29	mm2	$[m1_{R}]$		$[p2'_{1}ab']$	$[(p2'_{1}ab')]$	29²	33²
30	mm2	$[m1_{R}]$			$[p2'_{1}ma']$	26²	29¹; 36²
31	mm2	$[m1_{R}]$			$[p2'_{1}mn']$	31²	33²
32	mm2	$[m1_{R}]$			p2′mb′	28²	32², 40², 41²
33	mm2	$[m1_{R}]$			p2′aa′	27²	30²; 37²
34	mm2	$[m1_{R}]$				30¹	34²; 43²: 218; 219
35	mm2	$[m1_{R}]$	c2′mm′			38¹	40¹; 44², 46¹: 216; 220
36	mm2	$[m1_{R}]$			c2′mb′	39¹	41¹; 45², 46²
37*	mmm	$[2mm1_{R}]$	pmmm′			47	49, 51¹; 65², 67²; 69:
							200; 202, 221, 224, 226, 228, 229
38*	mmm	$[2mm1_{R}]$		$[pbmm'\; (2'_{1})]$		51²	53¹, 57, 59²; 63¹, 64¹
39*	mmm	$[2mm1_{R}]$		$[pbam'\; (2'_{1}2'_{1})]$		55	58, 62²
40*	mmm	$[2mm1_{R}]$		$[pmab'\; (2'_{1}2'_{1})]$		57¹	60², 61, 62: 205
41*	mmm	$[2mm1_{R}]$		$[pbaa'\; (2'_{1})]$		54²	52, 56², 60¹
42*	mmm	$[2mm1_{R}]$			$[pmma'\; (2'_{1})]$	51	54, 55², 57²; 63², 64²
43*	mmm	$[2mm1_{R}]$			pmmn′ $[(2'_{1}2'_{1})]$	59	56, 62¹
44*	mmm	$[2mm1_{R}]$			$[pbmn'\; (2'_{1})]$	53²	52¹, 58¹, 60
45*	mmm	$[2mm1_{R}]$			pmaa′	49²	50², 53, 54¹; 66², 68¹: 222, 223
46*	mmm	$[2mm1_{R}]$			pban′	50	52², 48; 70: 201; 203, 230
47*	mmm	$[2mm1_{R}]$	cmmm′			65	63, 66; 72, 74², 71: 204, 225, 227
48*	mmm	$[2mm1_{R}]$			cmma′	67	64, 68; 72¹, 74, 73: 206
Square						Tetragonal
49	4	4	p4			75	77, 76, 78; 79, 80
50		$[41_{R}]$				83	84; 87
51		$[41_{R}]$				85	86, 88
52	422	$[4m_{R}m_{R}]$				89	93, 91, 95; 97, 98:
							207, 208; 209, 210; 211, 214
53	422	$[4m_{R}m_{R}]$		$[p42'_{1}2']$		90	94, 92, 96: 212, 213
54	4mm	4mm				99	101, 103, 105; 107, 108
55	4mm	4mm				100	102, 104, 106; 109, 110
56*		$[4mm1_{R}]$				123	124, 131, 132; 139, 140;
							221, 223; 225, 226; 229
57*		$[4mm1_{R}]$		$[p4/m'bm\; (2'_{1})]$		127	128, 135, 136
58*		$[4mm1_{R}]$				125	126, 133, 134; 141, 142:
							222, 224; 227, 228; 230
59*		$[4mm1_{R}]$			$[p4/n'mm\; (2'_{1})]$	129	130, 137, 138
60	$[\bar{4}]$	$[4_{R}]$	$[p\bar{4}']$			81	82
61	$[\bar{4}2m]$	$[4_{R}mm_{R}]$	$[p\bar{4}'m\bar{2}']$			115	116; 119, 120
62	$[\bar{4}2m]$	$[4_{R}mm_{R}]$		$[p\bar{4}b2']$		117	118; 122: 220
63	$[\bar{4}2m]$	$[4_{R}mm_{R}]$	$[p\bar{4}'2'm]$			111	112; 121: 215; 216; 217; 218; 219
64	$[\bar{4}2m]$	$[4_{R}mm_{R}]$		$[p4'2'_{1}m]$		113	114
Hexagonal						Trigonal
65	3	3	p3			143	144, 145; 146
66	$[\bar{3}]$	$[6_{R}]$	$[p\bar{3}']$			147	148
67	32	$[3m_{R}]$	p312′			149	151, 153
68	32	$[3m_{R}]$				150	152, 154; 155
69	3m	3m	p31m			157	159
70	3m	3m	p3m1			156	158; 160, 161
71*	$[\bar{3}m]$	$[6_{R}mm_{R}]$	$[p\bar{3}'1m]$			162	163
72*	$[\bar{3}m]$	$[6_{R}mm_{R}]$	$[p\bar{3}'m1]$			164	165; 166, 167
						Hexagonal
73	6	6	p6			168	171, 172, 173, 169, 170
74	$[\bar{6}]$	$[31_{R}]$	$[p3/m'\; (p\bar{6}')]$			174
75	622	$[6m_{R}m_{R}]$				177	180, 181, 182, 178, 179
76	6mm	6mm				183	184, 185, 186
77*		$[61_{R}]$				175	176
78*		$[6mm1_{R}]$				191	192, 193, 194
79	$[\bar{6}m2]$	$[3m1_{R}]$	$[(p\bar{6}'m2')]$			189	190
80	$[\bar{6}m2]$	$[3m1_{R}]$	$[(p\bar{6}'2'm)]$			187	188