International Tables for Crystallography: Subperiodic Groups by V. Kopsky, D.B. Litvin

By V. Kopsky, D.B. Litvin

Foreign Tables for Crystallography, quantity E, Subperiodic teams covers the seven frieze teams, the seventy five rod teams and the eighty layer teams. the data tabulated for those teams is the same in structure and content material as that given for the 230 area teams in quantity A. furthermore, scanning tables are given for every of the 230 area teams. those scanning tables supply the biggest subgroup of the gap workforce that leaves the given aircraft invariant. using the scanning tables is proven in making a choice on the symmetry of area partitions.

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10 11 12 45 46 47 48 58 57 61 62 67 68 59 60 63 64 65 66 69 70 71 72 49 50 54 53 51 52 55 56 76 73 78 79 77 74 75 80 D2h p  D2h p  D2h c  D2h c  C4 p S4 p C4h p  C4h p  D4 p 11 D4 p 21 C4v p  C4v p  D2d p 1 D2d p 2 D2d c 1 D2d c 1 D4h p  D4h p   D4h p   D4h p  C3 c S6 p D3 c 1 D3 h 1 C3v c  C3v h  D3d c 1 D3d h 1 C6 c C3h c  C6h c  D6 c 11 C6v c  D3h c  D3h h  D6h c  Vh7 Vh8 Vh4 Vh12 C41 S14 1 C4h 2 C4h D14 D24 1 C4v 2 C4v Vd1 Vd2 Vd3 Vd4 D14h D24h D34h D44h C31 C3i1 D13 D23 2 C3v 1 C3v D23d D13d C61 1 C3h 1 C6h D16 1 C6v D13h D23h D16h 18 19 p1 p20 p2 p10 p0b 1 p210 p0b 2 pm0 pg0 cm0 pm pg cm pmm0 pmg0 pgg0 pm0 g cmm0 pm0 m0 pm0 g0 pg0 g0 cm0 m0 pmm2 pmg2 47 1 48 64 2 65 3 4 5 6 49 50 51 14 17 18 16 21 15 20 19 22 52 53 13 14 15 16 17 aP2gm nP2mm mC2mm aC2mm 1P4 1P4 ða : bÞ Á b : 2 Á a ða : bÞ Á ab : 2 Á m Àaþb Á 2 =a : bÁ Á m : 2 Á m Àaþb  :2Ám 2 =a : b Á a ða : aÞ : 4 ða : aÞ : 4 ap21 =b21 =m2 np21 =m21 =m2 mc2=m2=m2 ac2=m2=m2 1p4 1p4 p0a0 2gm 0 p0b mg p0c mm mP4 nP4 1P422 1P421 2 1P4mm 1P4gm 1P4 2m 1P4 21 m 1P4 m2 1P4 g2 mP4mm nP4gm mP4gm nP4mm 1P3 1P3 ða : aÞ : 4 : m ða : aÞ : 4 : ab ða : aÞ : 4 : 2 ða : aÞ : 4 : 21 ða : aÞ : 4 Á m ða : aÞ : 4  b ða : aÞ : 4 : 2 ða : aÞ : 4  21 ða : aÞ : 4 Á m ða : aÞ : 4  b ða : aÞ Á m : 4 Á m ða : aÞ : ab : 4  b ða : aÞ Á m : 4  b ða : aÞ Á ab : 4 Á m ða=aÞ : 3 ða=aÞ : 3 mp4 np4 1p422 1p421 2 1p4mm 1p4bm 1p4 2m 1p4 21 m 1p4 m2 1p4 b2 mp42=m2=m np42=b2=m mp421 =b2=m np421 =m2=m 1p3 1p3 1P312 1P321 1P3m1 1P31m 1P3 1m 1P3 m1 1P6 mP3 mP6 1P622 1P6mm mP3m2 mP32m mP6mm ða=aÞ : 2 : 3 ða=aÞ Á 2 : 3 ða=aÞ : m Á 3 ða=aÞ Á m Á 3 ða=aÞ Á m Á 6 ða=aÞ : m Á 6 1p312 1p321 1p3m1 1p31m 1p3 12=m 1p3 2=m1 1p6 mp3 mp6 1p622 1p6mm mp3m2 mp32m mp6mm ða=aÞ : 6 ða=aÞ : 3 : m ða=aÞ Á m : 6 ða=aÞ Á 2 : 6 ða=aÞ : m Á 6 ða=aÞ : m Á 3 : m ða=aÞ Á m : 3 Á m ða=aÞ Á m : 6 Á m c 2mm cà 2mm p0a0 b0 2mm p4 p40 pà 4 c0 4 p4m0 m0 p4g0 m0 p4mm p4gm p40 m0 m p40 g0 m p40 mm0 p40 gm0 pà 4mm c0 4m0 m pà 4gm c0 4mm p3 p60 p3m0 1 p31m0 p3m1 p31m p60 m0 m p60 mm0 p6 pà 3 pà 6 p6m0 m0 p6mm pà 3m1 pà 31m pà 6mm c0 mm p4 p40 p0 4 p4m0 m0 p4g0 m0 p4mm p4gm p40 m0 m p40 g0 m p40 mm0 p40 gm0 p0 4gm p0 4mm p3 p60 p3m0 1 p31m0 p3m1 p31m p60 m0 m p60 mm0 p6 p6m0 m0 p6mm (c) Columns 18–25.

Die 80 zweidimensionalen Raumgruppen. Z. Kristallogr. 70, 328–345, 460. Aroyo, M. I. & Wondratschek, H. (1987). Private communication. 27 1. SUBPERIODIC GROUP TABLES: FRIEZE-GROUP, ROD-GROUP AND LAYER-GROUP TYPES Press. [Revised editions: 1965, 1969 and 1977. ] Janovec, V. (1981). Symmetry and structure of domain walls. Ferroelectrics, 35, 105–110. Koch, E. & Fischer, W. (1978). Complexes for crystallographic point groups, rod groups and layer groups. Z. Kristallogr. 147, 21–38. Ko¨hler, K. J. (1977).

Vol. E, Frieze group 1, p. 30. 1 Oblique p1 No. 1 p Patterson symmetry 2 Origin arbitrary Asymmetric unit 0≤x≤1 Symmetry operations (1) 1 Generators selected (1); t(1) Positions Coordinates Multiplicity, Wyckoff letter, Site symmetry 1 a 1 Reflection conditions General: (1) x, y no conditions Symmetry of special projections Along [10] 1 Origin at x, 0 p Along [01] 1 a = ap Origin at 0, y Maximal non-isotypic subgroups I none IIa none IIb none Maximal isotypic subgroups of lowest index IIc [2] p 1 (a = 2a) (1) Minimal non-isotypic supergroups I [2] p 2 1 1 (2); [2] p 1 m 1 (3); [2] p 1 1 m (4); [2] p 1 1 g (5) II none Copyright © 2006 International Union of Crystallography 30 p211 International Tables for Crystallography (2006).

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