################################################################################ # SYMMETRY CIF DICTIONARY # ########################################################## # # This dictionary is designed to provide the data names # required to describe crystallographic symmetry. # # It is written in DDL2. # # The categories and items defined in this version are: # # space_group (General information on the space group) # Bravais_type # centring_type # crystal_system # id (Parent to various .sg_id's) # Laue_class # IT_coordinate_system_code # IT_number # name_Hall # name_H-M_ref # name_H-M_alt # name_H-M_alt_description # name_H-M_full # name_Schoenflies # Patterson_name_H-M # point_group_H-M # reference_setting # transform_Pp_abc # transform_Qq_xyz # space_group_symop (Symmetry operators) # id (Parent to various .symop_id's) # generator_xyz # operation_description # operation_xyz # sg_id # space_group_Wyckoff (Details of the Wyckoff positions) # coords_xyz # id (Parent to various .Wyckoff_id's to be defined) # letter # multiplicity # sg_id # site_symmetry # ########################################################## data_cif_sym.dic _dictionary.title cif_sym.dic _dictionary.version 1.0.1 _dictionary.datablock_id cif_sym.dic ################################################ # # CATEGORY: SPACE_GROUP # ################################################ save_SPACE_GROUP _category.id space_group _category.description ; Contains all the data items that refer to the space group as a whole, such as its name, Laue group etc. It may be looped, for example in a list of space groups and their properties. Space-group types are identified by their number as listed in International Tables for Crystallography Volume A, or by their Schoenflies symbol. Specific settings of the space groups can be identified by their Hall symbol, by specifying their symmetry operations or generators, or by giving the transformation that relates the specific setting to the reference setting based on International Tables Volume A and stored in this dictionary. The commonly used Hermann-Mauguin symbol determines the space-group type uniquely but several different Hermann-Mauguin symbols may refer to the same space-group type. A Hermann-Mauguin symbol contains information on the choice of the basis, but not on the choice of origin. Ref: International Tables for Crystallography (2002). Volume A, Space-group symmetry, edited by Th. Hahn, 5th ed. Dordrecht: Kluwer Academic Publishers. ; _category.mandatory_code yes loop_ _category_examples.detail _category_examples.case # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ; Example 1 - description of the C2/c space group, No. 15 in International Tables for Crystallography Volume A. ; ; _space_group.id 1 _space_group.name_H-M_ref 'C 2/c' _space_group.name_Schoenflies C2h.6 _space_group.IT_number 15 _space_group.name_Hall '-C 2yc' _space_group.Bravais_type mS _space_group.Laue_class 2/m _space_group.crystal_system monoclinic _space_group.centring_type C _space_group.Patterson_name_H-M 'C 2/m' ; # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - _category_key.name '_space_group.id' save_ save__space_group.Bravais_type _item.name '_space_group.Bravais_type' _item.category_id space_group _item.mandatory_code no _item_examples.case aP _item_examples.detail 'triclinic (anorthic) primitive lattice' _item_description.description ; The symbol denoting the lattice type (Bravais type) to which the translational subgroup (vector lattice) of the space group belongs. It consists of a lower-case letter indicating the crystal system followed by an upper-case letter indicating the lattice centring. The setting-independent symbol mS replaces the setting-dependent symbols mB and mC, and the setting-independent symbol oS replaces the setting-dependent symbols oA, oB and oC. Ref: International Tables for Crystallography (2002). Volume A, Space-group symmetry, edited by Th. Hahn, 5th ed., p. 15. Dordrecht: Kluwer Academic Publishers. ; _item_type.code char loop_ _item_enumeration.value aP mP mS oP oS oI oF tP tI hP hR cP cI cF save_ save__space_group.centring_type _item.name '_space_group.centring_type' _item.category_id space_group _item.mandatory_code no _item_description.description ; Symbol for the lattice centring. This symbol may be dependent on the coordinate system chosen. ; _item_type.code char loop_ _item_enumeration.value _item_enumeration.detail P 'primitive no centring' A 'A-face centred (0,1/2,1/2)' B 'B-face centred (1/2,0,1/2)' C 'C-face centred (1/2,1/2,0)' F 'all faces centred (0,1/2,1/2), (1/2,0,1/2), (1/2,1/2,0)' I 'body centred (1/2,1/2,1/2)' R 'rhombohedral obverse centred (2/3,1/3,1/3), (1/3,2/3,2/3)' Rrev 'rhombohedral reverse centred (1/3,2/3,1/3), (2/3,1/3,2/3)' H 'hexagonal centred (2/3,1/3,0), (1/3,2/3,0)' save_ save__space_group.crystal_system _item.name '_space_group.crystal_system' _item.category_id space_group _item.mandatory_code no _item_description.description ; The name of the system of geometric crystal classes of space groups (crystal system) to which the space group belongs. Note that crystals with the hR lattice type belong to the trigonal system. ; _item_type.code char loop_ _item_enumeration.value triclinic monoclinic orthorhombic tetragonal trigonal hexagonal cubic _item_aliases.alias_name '_symmetry_cell_setting' _item_aliases.dictionary cif_core.dic _item_aliases.version 1.0 save_ save__space_group.id loop_ _item.name _item.category_id _item.mandatory_code '_space_group.id' space_group yes '_space_group_symop.sg_id' space_group_symop no '_space_group_Wyckoff.sg_id' space_group_Wyckoff no _item_description.description ; This is an identifier needed if _space_group.* items are looped. ; _item_type.code char loop_ _item_linked.child_name _item_linked.parent_name '_space_group_symop.sg_id' '_space_group.id' '_space_group_Wyckoff.sg_id' '_space_group.id' save_ save__space_group.IT_coordinate_system_code _item.name '_space_group.IT_coordinate_system_code' _item.category_id space_group _item.mandatory_code no _item_description.description ; A qualifier taken from the enumeration list identifying which setting in International Tables for Crystallography Volume A (2002) (IT) is used. See IT Table 4.3.2.1, Section 2.2.16, Table 2.2.16.1, Section 2.2.16.1 and Fig. 2.2.6.4. This item is not computer-interpretable and cannot be used to define the coordinate system. Use _space_group.transform_* instead. Ref: International Tables for Crystallography (2002). Volume A, Space-group symmetry, edited by Th. Hahn, 5th ed. Dordrecht: Kluwer Academic Publishers. ; _item_type.code char loop_ _item_enumeration.value _item_enumeration.detail 'b1' 'monoclinic unique axis b, cell choice 1, abc' 'b2' 'monoclinic unique axis b, cell choice 2, abc' 'b3' 'monoclinic unique axis b, cell choice 3, abc' '-b1' 'monoclinic unique axis b, cell choice 1, c-ba' '-b2' 'monoclinic unique axis b, cell choice 2, c-ba' '-b3' 'monoclinic unique axis b, cell choice 3, c-ba' 'c1' 'monoclinic unique axis c, cell choice 1, abc' 'c2' 'monoclinic unique axis c, cell choice 2, abc' 'c3' 'monoclinic unique axis c, cell choice 3, abc' '-c1' 'monoclinic unique axis c, cell choice 1, ba-c' '-c2' 'monoclinic unique axis c, cell choice 2, ba-c' '-c3' 'monoclinic unique axis c, cell choice 3, ba-c' 'a1' 'monoclinic unique axis a, cell choice 1, abc' 'a2' 'monoclinic unique axis a, cell choice 2, abc' 'a3' 'monoclinic unique axis a, cell choice 3, abc' '-a1' 'monoclinic unique axis a, cell choice 1, -acb' '-a2' 'monoclinic unique axis a, cell choice 2, -acb' '-a3' 'monoclinic unique axis a, cell choice 3, -acb' 'abc' 'orthorhombic' 'ba-c' 'orthorhombic' 'cab' 'orthorhombic' '-cba' 'orthorhombic' 'bca' 'orthorhombic' 'a-cb' 'orthorhombic' '1abc' 'orthorhombic origin choice 1' '1ba-c' 'orthorhombic origin choice 1' '1cab' 'orthorhombic origin choice 1' '1-cba' 'orthorhombic origin choice 1' '1bca' 'orthorhombic origin choice 1' '1a-cb' 'orthorhombic origin choice 1' '2abc' 'orthorhombic origin choice 2' '2ba-c' 'orthorhombic origin choice 2' '2cab' 'orthorhombic origin choice 2' '2-cba' 'orthorhombic origin choice 2' '2bca' 'orthorhombic origin choice 2' '2a-cb' 'orthorhombic origin choice 2' '1' 'tetragonal or cubic origin choice 1' '2' 'tetragonal or cubic origin choice 2' 'h' 'trigonal using hexagonal axes' 'r' 'trigonal using rhombohedral axes' save_ save__space_group.IT_number _item.name '_space_group.IT_number' _item.category_id space_group _item.mandatory_code no _item_description.description ; The number as assigned in International Tables for Crystallography Volume A, specifying the proper affine class (i.e. the orientation-preserving affine class) of space groups (crystallographic space-group type) to which the space group belongs. This number defines the space-group type but not the coordinate system in which it is expressed. Ref: International Tables for Crystallography (2002). Volume A, Space-group symmetry, edited by Th. Hahn, 5th ed. Dordrecht: Kluwer Academic Publishers. ; _item_type.code numb _item_range.minimum 1 _item_range.maximum 230 _item_aliases.alias_name '_symmetry_Int_Tables_number' _item_aliases.dictionary cif_core.dic _item_aliases.version 1.0 save_ save__space_group.Laue_class _item.name '_space_group.Laue_class' _item.category_id space_group _item.mandatory_code no loop_ _item_enumeration.value -1 2/m mmm 4/m 4/mmm -3 -3m 6/m 6/mmm m-3 m-3m _item_description.description ; The Hermann-Mauguin symbol of the geometric crystal class of the point group of the space group where a centre of inversion is added if not already present. ; _item_type.code char save_ #----------------------------------------------- save__space_group.name_Hall _item.name '_space_group.name_Hall' _item.category_id space_group _item.mandatory_code no loop_ _item_examples.case _item_examples.detail 'P 2c -2ac' 'equivalent to Pca21' '-I 4bd 2ab 3' 'equivalent to Ia3d' _item_description.description ; Space-group symbol defined by Hall. _space_group.name_Hall uniquely defines the space group and its reference to a particular coordinate system. Each component of the space-group name is separated by a space or an underscore character. The use of a space is strongly recommended. The underscore is only retained because it was used in old CIFs. It should not be used in new CIFs. Ref: Hall, S. R. (1981). Acta Cryst. A37, 517-525; erratum (1981), A37, 921. International Tables for Crystallography (2001). Volume B, Reciprocal space, edited by U. Shmueli, 2nd ed., Appendix 1.4.2. Dordrecht: Kluwer Academic Publishers. ; _item_type.code char _item_aliases.alias_name '_symmetry_space_group_name_Hall' _item_aliases.dictionary cif_core.dic _item_aliases.version 1.0 save_ save__space_group.name_H-M_ref _item.name '_space_group.name_H-M_ref' _item.category_id space_group _item.mandatory_code no loop_ _item_examples.case 'P 21/c' 'P m n a' 'P -1' 'F m -3 m' 'P 63/m m m' _item_description.description ; The short international Hermann-Mauguin space-group symbol as defined in Section 2.2.3 and given as the first item of each space-group table in Part 7 of International Tables for Crystallography Volume A (2002). Each component of the space-group name is separated by a space or an underscore character. The use of a space is strongly recommended. The underscore is only retained because it was used in old CIFs. It should not be used in new CIFs. Subscripts should appear without special symbols. Bars should be given as negative signs before the numbers to which they apply. The short international Hermann-Mauguin symbol determines the space-group type uniquely. However, the space-group type is better described using _space_group.IT_number or _space_group.name_Schoenflies. The short international Hermann-Mauguin symbol contains no information on the choice of basis or origin. To define the setting uniquely use _space_group.name_Hall, list the symmetry operations or generators, or give the transformation that relates the setting to the reference setting defined in this dictionary under _space_group.reference_setting. _space_group.name_H-M_alt may be used to give the Hermann-Mauguin symbol corresponding to the setting used. In the enumeration list, each possible value is identified by space-group number and Schoenflies symbol. Ref: International Tables for Crystallography (2002). Volume A, Space-group symmetry, edited by Th. Hahn, 5th ed. Dordrecht: Kluwer Academic Publishers. ; loop_ _item_enumeration.value _item_enumeration.detail 'P 1' ' 1 C1.1' 'P -1' ' 2 Ci.1' 'P 2' ' 3 C2.1' 'P 21' ' 4 C2.2' 'C 2' ' 5 C2.3' 'P m' ' 6 Cs.1' 'P c' ' 7 Cs.2' 'C m' ' 8 Cs.3' 'C c' ' 9 Cs.4' 'P 2/m' ' 10 C2h.1' 'P 21/m' ' 11 C2h.2' 'C 2/m' ' 12 C2h.3' 'P 2/c' ' 13 C2h.4' 'P 21/c' ' 14 C2h.5' 'C 2/c' ' 15 C2h.6' 'P 2 2 2' ' 16 D2.1' 'P 2 2 21' ' 17 D2.2' 'P 21 21 2' ' 18 D2.3' 'P 21 21 21' ' 19 D2.4' 'C 2 2 21' ' 20 D2.5' 'C 2 2 2' ' 21 D2.6' 'F 2 2 2' ' 22 D2.7' 'I 2 2 2' ' 23 D2.8' 'I 21 21 21' ' 24 D2.9' 'P m m 2' ' 25 C2v.1' 'P m c 21' ' 26 C2v.2' 'P c c 2' ' 27 C2v.3' 'P m a 2' ' 28 C2v.4' 'P c a 21' ' 29 C2v.5' 'P n c 2' ' 30 C2v.6' 'P m n 21' ' 31 C2v.7' 'P b a 2' ' 32 C2v.8' 'P n a 21' ' 33 C2v.9' 'P n n 2' ' 34 C2v.10' 'C m m 2' ' 35 C2v.11' 'C m c 21' ' 36 C2v.12' 'C c c 2' ' 37 C2v.13' 'A m m 2' ' 38 C2v.14' 'A e m 2' ' 39 C2v.15' 'A m a 2' ' 40 C2v.16' 'A e a 2' ' 41 C2v.17' 'F m m 2' ' 42 C2v.18' 'F d d 2' ' 43 C2v.19' 'I m m 2' ' 44 C2v.20' 'I b a 2' ' 45 C2v.21' 'I m a 2' ' 46 C2v.22' 'P m m m' ' 47 D2h.1' 'P n n n' ' 48 D2h.2' 'P c c m' ' 49 D2h.3' 'P b a n' ' 50 D2h.4' 'P m m a' ' 51 D2h.5' 'P n n a' ' 52 D2h.6' 'P m n a' ' 53 D2h.7' 'P c c a' ' 54 D2h.8' 'P b a m' ' 55 D2h.9' 'P c c n' ' 56 D2h.10' 'P b c m' ' 57 D2h.11' 'P n n m' ' 58 D2h.12' 'P m m n' ' 59 D2h.13' 'P b c n' ' 60 D2h.14' 'P b c a' ' 61 D2h.15' 'P n m a' ' 62 D2h.16' 'C m c m' ' 63 D2h.17' 'C m c e' ' 64 D2h.18' 'C m m m' ' 65 D2h.19' 'C c c m' ' 66 D2h.20' 'C m m e' ' 67 D2h.21' 'C c c e' ' 68 D2h.22' 'F m m m' ' 69 D2h.23' 'F d d d' ' 70 D2h.24' 'I m m m' ' 71 D2h.25' 'I b a m' ' 72 D2h.26' 'I b c a' ' 73 D2h.27' 'I m m a' ' 74 D2h.28' 'P 4' ' 75 C4.1' 'P 41' ' 76 C4.2' 'P 42' ' 77 C4.3' 'P 43' ' 78 C4.4' 'I 4' ' 79 C4.5' 'I 41' ' 80 C4.6' 'P -4' ' 81 S4.1' 'I -4' ' 82 S4.2' 'P 4/m' ' 83 C4h.1' 'P 42/m' ' 84 C4h.2' 'P 4/n' ' 85 C4h.3' 'P 42/n' ' 86 C4h.4' 'I 4/m' ' 87 C4h.5' 'I 41/a' ' 88 C4h.6' 'P 4 2 2' ' 89 D4.1' 'P 4 21 2' ' 90 D4.2' 'P 41 2 2' ' 91 D4.3' 'P 41 21 2' ' 92 D4.4' 'P 42 2 2' ' 93 D4.5' 'P 42 21 2' ' 94 D4.6' 'P 43 2 2' ' 95 D4.7' 'P 43 21 2' ' 96 D4.8' 'I 4 2 2' ' 97 D4.9' 'I 41 2 2' ' 98 D4.10' 'P 4 m m' ' 99 C4v.1' 'P 4 b m' '100 C4v.2' 'P 42 c m' '101 C4v.3' 'P 42 n m' '102 C4v.4' 'P 4 c c' '103 C4v.5' 'P 4 n c' '104 C4v.6' 'P 42 m c' '105 C4v.7' 'P 42 b c' '106 C4v.8' 'I 4 m m' '107 C4v.9' 'I 4 c m' '108 C4v.10' 'I 41 m d' '109 C4v.11' 'I 41 c d' '110 C4v.12' 'P -4 2 m' '111 D2d.1' 'P -4 2 c' '112 D2d.2' 'P -4 21 m' '113 D2d.3' 'P -4 21 c' '114 D2d.4' 'P -4 m 2' '115 D2d.5' 'P -4 c 2' '116 D2d.6' 'P -4 b 2' '117 D2d.7' 'P -4 n 2' '118 D2d.8' 'I -4 m 2' '119 D2d.9' 'I -4 c 2' '120 D2d.10' 'I -4 2 m' '121 D2d.11' 'I -4 2 d' '122 D2d.12' 'P 4/m m m' '123 D4h.1' 'P 4/m c c' '124 D4h.2' 'P 4/n b m' '125 D4h.3' 'P 4/n n c' '126 D4h.4' 'P 4/m b m' '127 D4h.5' 'P 4/m n c' '128 D4h.6' 'P 4/n m m' '129 D4h.7' 'P 4/n c c' '130 D4h.8' 'P 42/m m c' '131 D4h.9' 'P 42/m c m' '132 D4h.10' 'P 42/n b c' '133 D4h.11' 'P 42/n n m' '134 D4h.12' 'P 42/m b c' '135 D4h.13' 'P 42/m n m' '136 D4h.14' 'P 42/n m c' '137 D4h.15' 'P 42/n c m' '138 D4h.16' 'I 4/m m m' '139 D4h.17' 'I 4/m c m' '140 D4h.18' 'I 41/a m d' '141 D4h.19' 'I 41/a c d' '142 D4h.20' 'P 3' '143 C3.1' 'P 31' '144 C3.2' 'P 32' '145 C3.3' 'R 3' '146 C3.4' 'P -3' '147 C3i.1' 'R -3' '148 C3i.2' 'P 3 1 2' '149 D3.1' 'P 3 2 1' '150 D3.2' 'P 31 1 2' '151 D3.3' 'P 31 2 1' '152 D3.4' 'P 32 1 2' '153 D3.5' 'P 32 2 1' '154 D3.6' 'R 3 2' '155 D3.7' 'P 3 m 1' '156 C3v.1' 'P 3 1 m' '157 C3v.2' 'P 3 c 1' '158 C3v.3' 'P 3 1 c' '159 C3v.4' 'R 3 m' '160 C3v.5' 'R 3 c' '161 C3v.6' 'P -3 1 m' '162 D3d.1' 'P -3 1 c' '163 D3d.2' 'P -3 m 1' '164 D3d.3' 'P -3 c 1' '165 D3d.4' 'R -3 m' '166 D3d.5' 'R -3 c' '167 D3d.6' 'P 6' '168 C6.1' 'P 61' '169 C6.2' 'P 65' '170 C6.3' 'P 62' '171 C6.4' 'P 64' '172 C6.5' 'P 63' '173 C6.6' 'P -6' '174 C3h.1' 'P 6/m ' '175 C6h.1' 'P 63/m' '176 C6h.2' 'P 6 2 2' '177 D6.1' 'P 61 2 2' '178 D6.2' 'P 65 2 2' '179 D6.3' 'P 62 2 2' '180 D6.4' 'P 64 2 2' '181 D6.5' 'P 63 2 2' '182 D6.6' 'P 6 m m' '183 C6v.1' 'P 6 c c' '184 C6v.2' 'P 63 c m' '185 C6v.3' 'P 63 m c' '186 C6v.4' 'P -6 m 2' '187 D3h.1' 'P -6 c 2' '188 D3h.2' 'P -6 2 m' '189 D3h.3' 'P -6 2 c' '190 D3h.4' 'P 6/m m m' '191 D6h.1' 'P 6/m c c' '192 D6h.2' 'P 63/m c m' '193 D6h.3' 'P 63/m m c' '194 D6h.4' 'P 2 3' '195 T.1' 'F 2 3' '196 T.2' 'I 2 3' '197 T.3' 'P 21 3' '198 T.4' 'I 21 3' '199 T.5' 'P m -3' '200 Th.1' 'P n -3' '201 Th.2' 'F m -3' '202 Th.3' 'F d -3' '203 Th.4' 'I m -3' '204 Th.5' 'P a -3' '205 Th.6' 'I a -3' '206 Th.7' 'P 4 3 2' '207 O.1' 'P 42 3 2' '208 O.2' 'F 4 3 2' '209 O.3' 'F 41 3 2' '210 O.4' 'I 4 3 2' '211 O.5' 'P 43 3 2' '212 O.6' 'P 41 3 2' '213 O.7' 'I 41 3 2' '214 O.8' 'P -4 3 m' '215 Td.1' 'F -4 3 m' '216 Td.2' 'I -4 3 m' '217 Td.3' 'P -4 3 n' '218 Td.4' 'F -4 3 c' '219 Td.5' 'I -4 3 d' '220 Td.6' 'P m -3 m' '221 Oh.1' 'P n -3 n' '222 Oh.2' 'P m -3 n' '223 Oh.3' 'P n -3 m' '224 Oh.4' 'F m -3 m' '225 Oh.5' 'F m -3 c' '226 Oh.6' 'F d -3 m' '227 Oh.7' 'F d -3 c' '228 Oh.8' 'I m -3 m' '229 Oh.9' 'I a -3 d' '230 Oh.10' _item_type.code char loop_ _item_related.related_name _item_related.function_code '_space_group.name_H-M_full' alternate '_space_group.name_H-M_alt' alternate save_ save__space_group.name_H-M_alt _item.name '_space_group.name_H-M_alt' _item.category_id space_group _item.mandatory_code no _item_type.code char loop_ _item_examples.case _item_examples.detail ; loop_ _space_group.name_H-M_alt _space_group.name_H-M_alt_description 'C m c m(b n n)' 'Extended Hermann-Mauguin symbol' 'C 2/c 2/m 21/m' 'Full unconventional Hermann-Mauguin symbol' 'A m a m' 'Hermann-Mauguin symbol corresponding to setting used' ; 'Three examples for space group No. 63.' _item_description.description ; _space_group.name_H-M_alt allows for an alternative Hermann-Mauguin symbol to be given. The way in which this item is used is determined by the user and should be described in the item _space_group.name_H-M_alt_description. It may, for example, be used to give one of the extended Hermann-Mauguin symbols given in Table 4.3.2.1 of International Tables for Crystallography Volume A (2002) or a full Hermann-Mauguin symbol for an unconventional setting. Each component of the space-group name is separated by a space or an underscore character. The use of a space is strongly recommended. The underscore is only retained because it was used in older CIFs. It should not be used in new CIFs. Subscripts should appear without special symbols. Bars should be given as negative signs before the numbers to which they apply. The commonly used Hermann-Mauguin symbol determines the space-group type uniquely, but a given space-group type may be described by more than one Hermann-Mauguin symbol. The space-group type is best described using _space_group.IT_number or _space_group.name_Schoenflies. The Hermann-Mauguin symbol may contain information on the choice of basis but does not contain information on the choice of origin. To define the setting uniquely, use _space_group.name_Hall, list the symmetry operations or generators, or give the transformation that relates the setting to the reference setting defined in this dictionary under _space_group.reference_setting. Ref: International Tables for Crystallography (2002). Volume A, Space-group symmetry, edited by Th. Hahn, 5th ed. Dordrecht: Kluwer Academic Publishers. ; loop_ _item_related.related_name _item_related.function_code '_space_group.name_H-M_ref' alternate '_space_group.name_H-M_full' alternate _item_aliases.alias_name '_symmetry_space_group_name_H-M' _item_aliases.dictionary cif_core.dic _item_aliases.version 1.0 save_ save__space_group.name_H-M_alt_description _item.name '_space_group.name_H-M_alt_description' _item.category_id space_group _item.mandatory_code no _item_description.description ; A free-text description of the code appearing in _space_group.name_H-M_alt. ; _item_type.code char save_ save__space_group.name_H-M_full _item.name '_space_group.name_H-M_full' _item.category_id space_group _item.mandatory_code no loop_ _item_examples.case _item_examples.detail 'P 21/n 21/m 21/a' 'full symbol for Pnma' _item_description.description ; The full international Hermann-Mauguin space-group symbol as defined in Section 2.2.3 and given as the second item of the second line of each of the space-group tables of Part 7 of International Tables for Crystallography Volume A (2002). Each component of the space-group name is separated by a space or an underscore character. The use of a space is strongly recommended. The underscore is only retained because it was used in old CIFs. It should not be used in new CIFs. Subscripts should appear without special symbols. Bars should be given as negative signs before the numbers to which they apply. The commonly used Hermann-Mauguin symbol determines the space-group type uniquely but a given space-group type may be described by more than one Hermann-Mauguin symbol. The space-group type is best described using _space_group.IT_number or _space_group.name_Schoenflies. The full international Hermann-Mauguin symbol contains information about the choice of basis for monoclinic and orthorhombic space groups but does not give information about the choice of origin. To define the setting uniquely use _space_group.name_Hall, list the symmetry operations or generators, or give the transformation relating the setting used to the reference setting defined in this dictionary under _space_group.reference_setting. Ref: International Tables for Crystallography (2002). Volume A, Space-group symmetry, edited by Th. Hahn, 5th ed. Dordrecht: Kluwer Academic Publishers. ; _item_type.code char loop_ _item_related.related_name _item_related.function_code '_space_group.name_H-M_ref' alternate '_space_group.name_H-M_alt' alternate _item_aliases.alias_name 'symmetry.space_group_name_H-M' _item_aliases.dictionary 'cif_mm.dic' _item_aliases.version '1.0.0' save_ save__space_group.name_Schoenflies _item.name '_space_group.name_Schoenflies' _item.category_id space_group _item.mandatory_code no _item_examples.case 'C2h.5' _item_examples.detail 'Schoenflies symbol for space group No. 14' _item_description.description ; The Schoenflies symbol as listed in International Tables for Crystallography Volume A denoting the proper affine class (i.e. orientation-preserving affine class) of space groups (space-group type) to which the space group belongs. This symbol defines the space-group type independently of the coordinate system in which the space group is expressed. The symbol is given with a period, '.', separating the Schoenflies point group and the superscript. Ref: International Tables for Crystallography (2002). Volume A, Space-group symmetry, edited by Th. Hahn, 5th ed. Dordrecht: Kluwer Academic Publishers. ; _item_type.code char loop_ _item_enumeration.value C1.1 Ci.1 C2.1 C2.2 C2.3 Cs.1 Cs.2 Cs.3 Cs.4 C2h.1 C2h.2 C2h.3 C2h.4 C2h.5 C2h.6 D2.1 D2.2 D2.3 D2.4 D2.5 D2.6 D2.7 D2.8 D2.9 C2v.1 C2v.2 C2v.3 C2v.4 C2v.5 C2v.6 C2v.7 C2v.8 C2v.9 C2v.10 C2v.11 C2v.12 C2v.13 C2v.14 C2v.15 C2v.16 C2v.17 C2v.18 C2v.19 C2v.20 C2v.21 C2v.22 D2h.1 D2h.2 D2h.3 D2h.4 D2h.5 D2h.6 D2h.7 D2h.8 D2h.9 D2h.10 D2h.11 D2h.12 D2h.13 D2h.14 D2h.15 D2h.16 D2h.17 D2h.18 D2h.19 D2h.20 D2h.21 D2h.22 D2h.23 D2h.24 D2h.25 D2h.26 D2h.27 D2h.28 C4.1 C4.2 C4.3 C4.4 C4.5 C4.6 S4.1 S4.2 C4h.1 C4h.2 C4h.3 C4h.4 C4h.5 C4h.6 D4.1 D4.2 D4.3 D4.4 D4.5 D4.6 D4.7 D4.8 D4.9 D4.10 C4v.1 C4v.2 C4v.3 C4v.4 C4v.5 C4v.6 C4v.7 C4v.8 C4v.9 C4v.10 C4v.11 C4v.12 D2d.1 D2d.2 D2d.3 D2d.4 D2d.5 D2d.6 D2d.7 D2d.8 D2d.9 D2d.10 D2d.11 D2d.12 D4h.1 D4h.2 D4h.3 D4h.4 D4h.5 D4h.6 D4h.7 D4h.8 D4h.9 D4h.10 D4h.11 D4h.12 D4h.13 D4h.14 D4h.15 D4h.16 D4h.17 D4h.18 D4h.19 D4h.20 C3.1 C3.2 C3.3 C3.4 C3i.1 C3i.2 D3.1 D3.2 D3.3 D3.4 D3.5 D3.6 D3.7 C3v.1 C3v.2 C3v.3 C3v.4 C3v.5 C3v.6 D3d.1 D3d.2 D3d.3 D3d.4 D3d.5 D3d.6 C6.1 C6.2 C6.3 C6.4 C6.5 C6.6 C3h.1 C6h.1 C6h.2 D6.1 D6.2 D6.3 D6.4 D6.5 D6.6 C6v.1 C6v.2 C6v.3 C6v.4 D3h.1 D3h.2 D3h.3 D3h.4 D6h.1 D6h.2 D6h.3 D6h.4 T.1 T.2 T.3 T.4 T.5 Th.1 Th.2 Th.3 Th.4 Th.5 Th.6 Th.7 O.1 O.2 O.3 O.4 O.5 O.6 O.7 O.8 Td.1 Td.2 Td.3 Td.4 Td.5 Td.6 Oh.1 Oh.2 Oh.3 Oh.4 Oh.5 Oh.6 Oh.7 Oh.8 Oh.9 Oh.10 save_ save__space_group.Patterson_name_H-M _item.name '_space_group.Patterson_name_H-M' _item.category_id space_group _item.mandatory_code no loop_ _item_examples.case 'P -1' 'P 2/m' 'C 2/m' 'P m m m' 'C m m m' 'I m m m' 'F m m m' 'P 4/m' 'I 4/m' 'P 4/m m m' 'I 4/m m m' 'P -3' 'R -3' 'P -3 m 1' 'R -3 m' 'P -3 1 m' 'P 6/m' 'P 6/m m m' 'P m -3' 'I m -3' 'F m -3' 'P m -3 m' 'I m -3 m' 'F m -3 m' _item_description.description ; The Hermann-Mauguin symbol of the type of that centrosymmetric symmorphic space group to which the Patterson function belongs; see Table 2.2.5.1 in International Tables for Crystallography Volume A (2002). A space separates each symbol referring to different axes. Underscores may replace the spaces, but this use is discouraged. Subscripts should appear without special symbols. Bars should be given as negative signs before the number to which they apply. Ref: International Tables for Crystallography (2002). Volume A, Space-group symmetry, edited by Th. Hahn, 5th ed., Table 2.2.5.1. Dordrecht: Kluwer Academic Publishers. ; _item_type.code char save_ save__space_group.point_group_H-M _item.name '_space_group.point_group_H-M' _item.category_id space_group _item.mandatory_code no loop_ _item_examples.case -4 4/m _item_description.description ; The Hermann-Mauguin symbol denoting the geometric crystal class of space groups to which the space group belongs, and the geometric crystal class of point groups to which the point group of the space group belongs. ; _item_type.code char save_ save__space_group.reference_setting _item.name '_space_group.reference_setting' _item.category_id space_group _item.mandatory_code no _item_description.description ; The reference setting of a given space group is the setting chosen by the International Union of Crystallography as a unique setting to which other settings can be referred using the transformation matrix column pair given in _space_group.transform_Pp_abc and _space_group.transform_Qq_xyz. The settings are given in the enumeration list in the form '_space_group.IT_number:_space_group.name_Hall'. The space-group number defines the space-group type and the Hall symbol specifies the symmetry generators referred to the reference coordinate system. The 230 reference settings chosen are identical to the settings listed in International Tables for Crystallography Volume A (2002). For the space groups where more than one setting is given in International Tables, the following choices have been made. For monoclinic space groups: unique axis b and cell choice 1. For space groups with two origins: origin choice 2 (origin at inversion centre, indicated by adding :2 to the Hermann-Mauguin symbol in the enumeration list). For rhombohedral space groups: hexagonal axes (indicated by adding :h to the Hermann-Mauguin symbol in the enumeration list). Based on the symmetry table of R. W. Grosse-Kunstleve, ETH, Zurich. The enumeration list may be extracted from the dictionary and stored as a separate CIF that can be referred to as required. In the enumeration list, each reference setting is identified by Schoenflies symbol and by the Hermann-Mauguin symbol, augmented by :2 or :h suffixes as described above. Ref: International Tables for Crystallography (2002). Volume A, Space-group symmetry, edited by Th. Hahn, 5th ed. Dordrecht: Kluwer Academic Publishers. Grosse-Kunstleve, R. W. (2001). Xtal System of Crystallographic Programs, System Documentation. http://xtal.crystal.uwa.edu.au/man/xtal3.7-228.html (or follow links to Docs->Space-Group Symbols from http://xtal.sourceforge.net). ; _item_type.code char loop_ _item_enumeration.value _item_enumeration.detail '001:P 1' 'C1.1 P 1' '002:-P 1' 'Ci.1 P -1' '003:P 2y' 'C2.1 P 1 2 1' '004:P 2yb' 'C2.2 P 1 21 1' '005:C 2y' 'C2.3 C 1 2 1' '006:P -2y' 'Cs.1 P 1 m 1' '007:P -2yc' 'Cs.2 P 1 c 1' '008:C -2y' 'Cs.3 C 1 m 1' '009:C -2yc' 'Cs.4 C 1 c 1' '010:-P 2y' 'C2h.1 P 1 2/m 1' '011:-P 2yb' 'C2h.2 P 1 21/m 1' '012:-C 2y' 'C2h.3 C 1 2/m 1' '013:-P 2yc' 'C2h.4 P 1 2/c 1' '014:-P 2ybc' 'C2h.5 P 1 21/c 1' '015:-C 2yc' 'C2h.6 C 1 2/c 1' '016:P 2 2' 'D2.1 P 2 2 2' '017:P 2c 2' 'D2.2 P 2 2 21' '018:P 2 2ab' 'D2.3 P 21 21 2' '019:P 2ac 2ab' 'D2.4 P 21 21 21' '020:C 2c 2' 'D2.5 C 2 2 21' '021:C 2 2' 'D2.6 C 2 2 2' '022:F 2 2' 'D2.7 F 2 2 2' '023:I 2 2' 'D2.8 I 2 2 2' '024:I 2b 2c' 'D2.9 I 21 21 21' '025:P 2 -2' 'C2v.1 P m m 2' '026:P 2c -2' 'C2v.2 P m c 21' '027:P 2 -2c' 'C2v.3 P c c 2' '028:P 2 -2a' 'C2v.4 P m a 2' '029:P 2c -2ac' 'C2v.5 P c a 21' '030:P 2 -2bc' 'C2v.6 P n c 2' '031:P 2ac -2' 'C2v.7 P m n 21' '032:P 2 -2ab' 'C2v.8 P b a 2' '033:P 2c -2n' 'C2v.9 P n a 21' '034:P 2 -2n' 'C2v.10 P n n 2' '035:C 2 -2' 'C2v.11 C m m 2' '036:C 2c -2' 'C2v.12 C m c 21' '037:C 2 -2c' 'C2v.13 C c c 2' '038:A 2 -2' 'C2v.14 A m m 2' '039:A 2 -2b' 'C2v.15 A e m 2' '040:A 2 -2a' 'C2v.16 A m a 2' '041:A 2 -2ab' 'C2v.17 A e a 2' '042:F 2 -2' 'C2v.18 F m m 2' '043:F 2 -2d' 'C2v.19 F d d 2' '044:I 2 -2' 'C2v.20 I m m 2' '045:I 2 -2c' 'C2v.21 I b a 2' '046:I 2 -2a' 'C2v.22 I m a 2' '047:-P 2 2' 'D2h.1 P m m m' '048:-P 2ab 2bc' 'D2h.2 P n n n:2' '049:-P 2 2c' 'D2h.3 P c c m' '050:-P 2ab 2b' 'D2h.4 P b a n:2' '051:-P 2a 2a' 'D2h.5 P m m a' '052:-P 2a 2bc' 'D2h.6 P n n a' '053:-P 2ac 2' 'D2h.7 P m n a' '054:-P 2a 2ac' 'D2h.8 P c c a' '055:-P 2 2ab' 'D2h.9 P b a m' '056:-P 2ab 2ac' 'D2h.10 P c c n' '057:-P 2c 2b' 'D2h.11 P b c m' '058:-P 2 2n' 'D2h.12 P n n m' '059:-P 2ab 2a' 'D2h.13 P m m n:2' '060:-P 2n 2ab' 'D2h.14 P b c n' '061:-P 2ac 2ab' 'D2h.15 P b c a' '062:-P 2ac 2n' 'D2h.16 P n m a' '063:-C 2c 2' 'D2h.17 C m c m' '064:-C 2ac 2' 'D2h.18 C m c e' '065:-C 2 2' 'D2h.19 C m m m' '066:-C 2 2c' 'D2h.20 C c c m' '067:-C 2a 2' 'D2h.21 C m m e' '068:-C 2a 2ac' 'D2h.22 C c c e:2' '069:-F 2 2' 'D2h.23 F m m m' '070:-F 2uv 2vw' 'D2h.24 F d d d:2' '071:-I 2 2' 'D2h.25 I m m m' '072:-I 2 2c' 'D2h.26 I b a m' '073:-I 2b 2c' 'D2h.27 I b c a' '074:-I 2b 2' 'D2h.28 I m m a' '075:P 4' 'C4.1 P 4' '076:P 4w' 'C4.2 P 41' '077:P 4c' 'C4.3 P 42' '078:P 4cw' 'C4.4 P 43' '079:I 4' 'C4.5 I 4' '080:I 4bw' 'C4.6 I 41' '081:P -4' 'S4.1 P -4' '082:I -4' 'S4.2 I -4' '083:-P 4' 'C4h.1 P 4/m' '084:-P 4c' 'C4h.2 P 42/m' '085:-P 4a' 'C4h.3 P 4/n:2' '086:-P 4bc' 'C4h.4 P 42/n:2' '087:-I 4' 'C4h.5 I 4/m' '088:-I 4ad' 'C4h.6 I 41/a:2' '089:P 4 2' 'D4.1 P 4 2 2' '090:P 4ab 2ab' 'D4.2 P 4 21 2' '091:P 4w 2c' 'D4.3 P 41 2 2' '092:P 4abw 2nw' 'D4.4 P 41 21 2' '093:P 4c 2' 'D4.5 P 42 2 2' '094:P 4n 2n' 'D4.6 P 42 21 2' '095:P 4cw 2c' 'D4.7 P 43 2 2' '096:P 4nw 2abw' 'D4.8 P 43 21 2' '097:I 4 2' 'D4.9 I 4 2 2' '098:I 4bw 2bw' 'D4.10 I 41 2 2' '099:P 4 -2' 'C4v.1 P 4 m m' '100:P 4 -2ab' 'C4v.2 P 4 b m' '101:P 4c -2c' 'C4v.3 P 42 c m' '102:P 4n -2n' 'C4v.4 P 42 n m' '103:P 4 -2c' 'C4v.5 P 4 c c' '104:P 4 -2n' 'C4v.6 P 4 n c' '105:P 4c -2' 'C4v.7 P 42 m c' '106:P 4c -2ab' 'C4v.8 P 42 b c' '107:I 4 -2' 'C4v.9 I 4 m m' '108:I 4 -2c' 'C4v.10 I 4 c m' '109:I 4bw -2' 'C4v.11 I 41 m d' '110:I 4bw -2c' 'C4v.12 I 41 c d' '111:P -4 2' 'D2d.1 P -4 2 m' '112:P -4 2c' 'D2d.2 P -4 2 c' '113:P -4 2ab' 'D2d.3 P -4 21 m' '114:P -4 2n' 'D2d.4 P -4 21 c' '115:P -4 -2' 'D2d.5 P -4 m 2' '116:P -4 -2c' 'D2d.6 P -4 c 2' '117:P -4 -2ab' 'D2d.7 P -4 b 2' '118:P -4 -2n' 'D2d.8 P -4 n 2' '119:I -4 -2' 'D2d.9 I -4 m 2' '120:I -4 -2c' 'D2d.10 I -4 c 2' '121:I -4 2' 'D2d.11 I -4 2 m' '122:I -4 2bw' 'D2d.12 I -4 2 d' '123:-P 4 2' 'D4h.1 P 4/m m m' '124:-P 4 2c' 'D4h.2 P 4/m c c' '125:-P 4a 2b' 'D4h.3 P 4/n b m:2' '126:-P 4a 2bc' 'D4h.4 P 4/n n c:2' '127:-P 4 2ab' 'D4h.5 P 4/m b m' '128:-P 4 2n' 'D4h.6 P 4/m n c' '129:-P 4a 2a' 'D4h.7 P 4/n m m:2' '130:-P 4a 2ac' 'D4h.8 P 4/n c c:2' '131:-P 4c 2' 'D4h.9 P 42/m m c' '132:-P 4c 2c' 'D4h.10 P 42/m c m' '133:-P 4ac 2b' 'D4h.11 P 42/n b c:2' '134:-P 4ac 2bc' 'D4h.12 P 42/n n m:2' '135:-P 4c 2ab' 'D4h.13 P 42/m b c' '136:-P 4n 2n' 'D4h.14 P 42/m n m' '137:-P 4ac 2a' 'D4h.15 P 42/n m c:2' '138:-P 4ac 2ac' 'D4h.16 P 42/n c m:2' '139:-I 4 2' 'D4h.17 I 4/m m m' '140:-I 4 2c' 'D4h.18 I 4/m c m' '141:-I 4bd 2' 'D4h.19 I 41/a m d:2' '142:-I 4bd 2c' 'D4h.20 I 41/a c d:2' '143:P 3' 'C3.1 P 3' '144:P 31' 'C3.2 P 31' '145:P 32' 'C3.3 P 32' '146:R 3' 'C3.4 R 3:h' '147:-P 3' 'C3i.1 P -3' '148:-R 3' 'C3i.2 R -3:h' '149:P 3 2' 'D3.1 P 3 1 2' '150:P 3 2"' 'D3.2 P 3 2 1' '151:P 31 2 (0 0 4)' 'D3.3 P 31 1 2' '152:P 31 2"' 'D3.4 P 31 2 1' '153:P 32 2 (0 0 2)' 'D3.5 P 32 1 2' '154:P 32 2"' 'D3.6 P 32 2 1' '155:R 3 2"' 'D3.7 R 3 2:h' '156:P 3 -2"' 'C3v.1 P 3 m 1' '157:P 3 -2' 'C3v.2 P 3 1 m' '158:P 3 -2"c' 'C3v.3 P 3 c 1' '159:P 3 -2c' 'C3v.4 P 3 1 c' '160:R 3 -2"' 'C3v.5 R 3 m:h' '161:R 3 -2"c' 'C3v.6 R 3 c:h' '162:-P 3 2' 'D3d.1 P -3 1 m' '163:-P 3 2c' 'D3d.2 P -3 1 c' '164:-P 3 2"' 'D3d.3 P -3 m 1' '165:-P 3 2"c' 'D3d.4 P -3 c 1' '166:-R 3 2"' 'D3d.5 R -3 m:h' '167:-R 3 2"c' 'D3d.6 R -3 c:h' '168:P 6' 'C6.1 P 6' '169:P 61' 'C6.2 P 61' '170:P 65' 'C6.3 P 65' '171:P 62' 'C6.4 P 62' '172:P 64' 'C6.5 P 64' '173:P 6c' 'C6.6 P 63' '174:P -6' 'C3h.1 P -6' '175:-P 6' 'C6h.1 P 6/m' '176:-P 6c' 'C6h.2 P 63/m' '177:P 6 2' 'D6.1 P 6 2 2' '178:P 61 2 (0 0 5)' 'D6.2 P 61 2 2' '179:P 65 2 (0 0 1)' 'D6.3 P 65 2 2' '180:P 62 2 (0 0 4)' 'D6.4 P 62 2 2' '181:P 64 2 (0 0 2)' 'D6.5 P 64 2 2' '182:P 6c 2c' 'D6.6 P 63 2 2' '183:P 6 -2' 'C6v.1 P 6 m m' '184:P 6 -2c' 'C6v.2 P 6 c c' '185:P 6c -2' 'C6v.3 P 63 c m' '186:P 6c -2c' 'C6v.4 P 63 m c' '187:P -6 2' 'D3h.1 P -6 m 2' '188:P -6c 2' 'D3h.2 P -6 c 2' '189:P -6 -2' 'D3h.3 P -6 2 m' '190:P -6c -2c' 'D3h.4 P -6 2 c' '191:-P 6 2' 'D6h.1 P 6/m m m' '192:-P 6 2c' 'D6h.2 P 6/m c c' '193:-P 6c 2' 'D6h.3 P 63/m c m' '194:-P 6c 2c' 'D6h.4 P 63/m m c' '195:P 2 2 3' 'T.1 P 2 3' '196:F 2 2 3' 'T.2 F 2 3' '197:I 2 2 3' 'T.3 I 2 3' '198:P 2ac 2ab 3' 'T.4 P 21 3' '199:I 2b 2c 3' 'T.5 I 21 3' '200:-P 2 2 3' 'Th.1 P m -3' '201:-P 2ab 2bc 3' 'Th.2 P n -3:2' '202:-F 2 2 3' 'Th.3 F m -3' '203:-F 2uv 2vw 3' 'Th.4 F d -3:2' '204:-I 2 2 3' 'Th.5 I m -3' '205:-P 2ac 2ab 3' 'Th.6 P a -3' '206:-I 2b 2c 3' 'Th.7 I a -3' '207:P 4 2 3' 'O.1 P 4 3 2' '208:P 4n 2 3' 'O.2 P 42 3 2' '209:F 4 2 3' 'O.3 F 4 3 2' '210:F 4d 2 3' 'O.4 F 41 3 2' '211:I 4 2 3' 'O.5 I 4 3 2' '212:P 4acd 2ab 3' 'O.6 P 43 3 2' '213:P 4bd 2ab 3' 'O.7 P 41 3 2' '214:I 4bd 2c 3' 'O.8 I 41 3 2' '215:P -4 2 3' 'Td.1 P -4 3 m' '216:F -4 2 3' 'Td.2 F -4 3 m' '217:I -4 2 3' 'Td.3 I -4 3 m' '218:P -4n 2 3' 'Td.4 P -4 3 n' '219:F -4a 2 3' 'Td.5 F -4 3 c' '220:I -4bd 2c 3' 'Td.6 I -4 3 d' '221:-P 4 2 3' 'Oh.1 P m -3 m' '222:-P 4a 2bc 3' 'Oh.2 P n -3 n:2' '223:-P 4n 2 3' 'Oh.3 P m -3 n' '224:-P 4bc 2bc 3' 'Oh.4 P n -3 m:2' '225:-F 4 2 3' 'Oh.5 F m -3 m' '226:-F 4a 2 3' 'Oh.6 F m -3 c' '227:-F 4vw 2vw 3' 'Oh.7 F d -3 m:2' '228:-F 4ud 2vw 3' 'Oh.8 F d -3 c:2' '229:-I 4 2 3' 'Oh.9 I m -3 m' '230:-I 4bd 2c 3' 'Oh.10 I a -3 d' save_ save__space_group.transform_Pp_abc _item.name '_space_group.transform_Pp_abc' _item.category_id space_group _item.mandatory_code no loop_ _item_examples.detail _item_examples.case 'R3:r to R3:h' '-b+c, a+c, -a+b+c' 'Pnnn:1 to Pnnn:2' 'a-1/4, b-1/4, c-1/4' 'Bbab:1 to Ccca:2' 'b-1/2, c-1/2, a-1/2' _item_description.description ; This item specifies the transformation (P,p) of the basis vectors from the setting used in the CIF (a,b,c) to the reference setting given in _space_group.reference_setting (a',b',c'). The value is given in Jones-Faithful notation corresponding to the rotational matrix P combined with the origin shift vector p in the expression: (a',b',c') = (a,b,c)P + p. P is a post-multiplication matrix of a row (a,b,c) of column vectors. It is related to the inverse transformation (Q,q) by: P = Q^-1^ p = Pq = -(Q^-1^)q. These transformations are applied as follows: atomic coordinates (x',y',z') = Q(x,y,z) + q Miller indices (h',k',l') = (h,k,l)P symmetry operations W' = (Q,q)W(P,p) basis vectors (a',b',c') = (a,b,c)P + p This item is given as a character string involving the characters a, b and c with commas separating the expressions for the a', b' and c' vectors. The numeric values may be given as integers, fractions or real numbers. Multiplication is implicit, division must be explicit. White space within the string is optional. ; _item.type_code char save_ save__space_group.transform_Qq_xyz _item.name '_space_group.transform_Qq_xyz' _item.category_id space_group _item.mandatory_code no loop_ _item_examples.detail _item_examples.case 'R3:r to R3:h' '-x/3+2y/3-z/3, -2x/3+y/3+z/3, x/3+y/3+z/3' 'Pnnn:1 to Pnnn:2' 'x+1/4,y+1/4,z+1/4' 'Bbab:1 to Ccca:2' 'z+1/2,x+1/2,y+1/2' _item_description.description ; This item specifies the transformation (Q,q) of the atomic coordinates from the setting used in the CIF [(x,y,z) referred to the basis vectors (a,b,c)] to the reference setting given in _space_group.reference_setting [(x',y',z') referred to the basis vectors (a',b',c')]. The value given in Jones-Faithful notation corresponds to the rotational matrix Q combined with the origin shift vector q in the expression: (x',y',z') = Q(x,y,z) + q. Q is a pre-multiplication matrix of the column vector (x,y,z). It is related to the inverse transformation (P,p) by: P = Q^-1^ p = Pq = -(Q^-1^)q, where the P and Q transformations are applied as follows: atomic coordinates (x',y',z') = Q(x,y,z) + q Miller indices (h',k',l') = (h,k,l)P symmetry operations W' = (Q,q)W(P,p) basis vectors (a',b',c') = (a,b,c)P + p This item is given as a character string involving the characters x, y and z with commas separating the expressions for the x', y' and z' components. The numeric values may be given as integers, fractions or real numbers. Multiplication is implicit, division must be explicit. White space within the string is optional. ; _item.type_code char save_ ##################################################### # # CATEGORY: SPACE_GROUP_SYMOP # ##################################################### save_SPACE_GROUP_SYMOP _category.id space_group_symop _category.description ; Contains information about the symmetry operations of the space group. ; _category.mandatory_code no loop_ _category_examples.detail _category_examples.case # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ; Example 1 - the symmetry operations for the space group P21/c. ; ; loop_ _space_group_symop.id _space_group_symop.operation_xyz _space_group_symop.operation_description 1 x,y,z 'identity mapping' 2 -x,-y,-z 'inversion' 3 -x,1/2+y,1/2-z '2-fold screw rotation with axis in (0,y,1/4)' 4 x,1/2-y,1/2+z 'c glide reflection through the plane (x,1/4,y)' ; # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - _category_key.name '_space_group_symop.id' save_ save__space_group_symop.generator_xyz _item.name '_space_group_symop.generator_xyz' _item.category_id space_group_symop _item.mandatory_code no _item_examples.case 'x,1/2-y,1/2+z' _item_examples.detail ; c glide reflection through the plane (x,1/4,z) chosen as one of the generators of the space group ; _item_description.description ; A parsable string giving one of the symmetry generators of the space group in algebraic form. If W is a matrix representation of the rotational part of the generator defined by the positions and signs of x, y and z, and w is a column of translations defined by the fractions, an equivalent position X' is generated from a given position X by X' = WX + w. (Note: X is used to represent the bold italic x in International Tables for Crystallography Volume A, Section 5.) When a list of symmetry generators is given, it is assumed that the complete list of symmetry operations of the space group (including the identity operation) can be generated through repeated multiplication of the generators, that is, (W3, w3) is an operation of the space group if (W2,w2) and (W1,w1) [where (W1,w1) is applied first] are either operations or generators and: W3 = W2 x W1 w3 = W2 x w1 + w2. Ref: International Tables for Crystallography (2002). Volume A, Space-group symmetry, edited by Th. Hahn, 5th ed. Dordrecht: Kluwer Academic Publishers. ; _item_type.code char _item_default.value 'x,y,z' _item_related.related_name '_space_group_symop.operation_xyz' _item_related.function_code alternate save_ save__space_group_symop.id _item_description.description ; An arbitrary identifier that uniquely labels each symmetry operation in the list. ; _item_type.code char _item.name '_space_group_symop.id' _item.category_id space_group_symop _item.mandatory_code yes loop_ _item_aliases.alias_name _item_aliases.dictionary _item_aliases.version '_symmetry_equiv_pos_site_id' cif_core.dic 1.0 '_symmetry_equiv.id' cif_mm.dic 1.0 save_ save__space_group_symop.operation_description _item.name '_space_group_symop.operation_description' _item.category_id space_group_symop _item.mandatory_code no _item_description.description ; An optional text description of a particular symmetry operation of the space group. ; _item_type.code char loop_ _item_dependent.dependent_name '_space_group_symop.generator_xyz' '_space_group_symop.operation_xyz' save_ save__space_group_symop.operation_xyz _item.name '_space_group_symop.operation_xyz' _item.category_id space_group_symop _item.mandatory_code no loop_ _item_examples.case _item_examples.detail 'x,1/2-y,1/2+z' 'c glide reflection through the plane (x,1/4,z)' _item_description.description ; A parsable string giving one of the symmetry operations of the space group in algebraic form. If W is a matrix representation of the rotational part of the symmetry operation defined by the positions and signs of x, y and z, and w is a column of translations defined by the fractions, an equivalent position X' is generated from a given position X by the equation: X' = WX + w. (Note: X is used to represent the bold italic x in International Tables for Crystallography Volume A, Section 5.) When a list of symmetry operations is given, it is assumed that the list contains all the operations of the space group (including the identity operation) as given by the representatives of the general position in International Tables for Crystallography Volume A. Ref: International Tables for Crystallography (2002). Volume A, Space-group symmetry, edited by Th. Hahn, 5th. ed. Dordrecht: Kluwer Academic Publishers. ; _item_type.code char _item_aliases.alias_name '_symmetry_equiv_pos_as_xyz' _item_aliases.dictionary cif_core.dic _item_aliases.version 1.0 _item_default.value 'x,y,z' _item_related.related_name '_space_group_symop.generator_xyz' _item_related.function_code alternate save_ save__space_group_symop.sg_id _item.name '_space_group_symop.sg_id' _item.category_id space_group_symop _item.mandatory_code no _item_description.description ; A child of _space_group.id allowing the symmetry operation to be identified with a particular space group. ; _item_type.code numb _item_linked.child_name '_space_group_symop.sg_id' _item_linked.parent_name '_space_group.id' save_ ##################################################### # # CATEGORY: SPACE_GROUP_WYCKOFF # ##################################################### save_SPACE_GROUP_WYCKOFF _category.id space_group_Wyckoff _category.description ; Contains information about Wyckoff positions of a space group. Only one site can be given for each special position but the remainder can be generated by applying the symmetry operations stored in _space_group_symop.operation_xyz. ; _category.mandatory_code no loop_ _category_examples.detail _category_examples.case # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ; Example 1 - this example is taken from the space group F d -3 c (No. 228, origin choice 2). For brevity only a selection of special positions are listed. The coordinates of only one site per special position can be given in this item, but the coordinates of the other sites can be generated using the symmetry operations given in the SPACE_GROUP_SYMOP category. ; ; loop_ _space_group_Wyckoff.id _space_group_Wyckoff.multiplicity _space_group_Wyckoff.letter _space_group_Wyckoff.site_symmetry _space_group_Wyckoff.coord_xyz 1 192 h 1 x,y,z 2 96 g ..2 1/4,y,-y 3 96 f 2.. x,1/8,1/8 4 32 b .32 1/4,1/4,1/4 ; # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - _category_key.name '_space_group_Wyckoff.id' save_ save__space_group_Wyckoff.coords_xyz _item.name '_space_group_Wyckoff.coords_xyz' _item.category_id space_group_Wyckoff _item.mandatory_code no _item_examples.case 'x,1/2,0' _item_examples.detail 'coordinates of Wyckoff site with 2.. symmetry' _item_description.description ; Coordinates of one site of a Wyckoff position expressed in terms of its fractional coordinates (x,y,z) in the unit cell. To generate the coordinates of all sites of this Wyckoff position, it is necessary to multiply these coordinates by the symmetry operations stored in _space_group_symop.operation_xyz. ; _item_type.code char _item_default.value 'x,y,z' save_ save__space_group_Wyckoff.id _item.name '_space_group_Wyckoff.id' _item.category_id space_group_Wyckoff _item.mandatory_code yes _item_description.description ; An arbitrary identifier that is unique to a particular Wyckoff position. ; _item_type.code char save_ save__space_group_Wyckoff.letter _item.name '_space_group_Wyckoff.letter' _item.category_id space_group_Wyckoff _item.mandatory_code no _item_description.description ; The Wyckoff letter associated with this position, as given in International Tables for Crystallography Volume A. The enumeration value '\a' corresponds to the Greek letter 'alpha' used in International Tables. Ref: International Tables for Crystallography (2002). Volume A, Space-group symmetry, edited by Th. Hahn, 5th ed. Dordrecht: Kluwer Academic Publishers. ; _item_type.code char loop_ _item_enumeration.value a b c d e f g h i j k l m n o p q r s t u v w x y z \a save_ save__space_group_Wyckoff.multiplicity _item.name '_space_group_Wyckoff.multiplicity' _item.category_id space_group_Wyckoff _item.mandatory_code no _item_description.description ; The multiplicity of this Wyckoff position as given in International Tables Volume A. It is the number of equivalent sites per conventional unit cell. Ref: International Tables for Crystallography (2002). Volume A, Space-group symmetry, edited by Th. Hahn, 5th ed. Dordrecht: Kluwer Academic Publishers. ; _item_type.code numb loop_ _item_range.maximum _item_range.minimum . 1 1 1 save_ save__space_group_Wyckoff.sg_id _item.name '_space_group_Wyckoff.sg_id' _item.category_id space_group_Wyckoff _item.mandatory_code no _item_description.description ; A child of _space_group.id allowing the Wyckoff position to be identified with a particular space group. ; _item_type.code char _item_linked.child_name '_space_group_Wyckoff.sg_id' _item_linked.parent_name '_space_group.id' save_ save__space_group_Wyckoff.site_symmetry _item.name '_space_group_Wyckoff.site_symmetry' _item.category_id space_group_Wyckoff _item.mandatory_code no loop_ _item_examples.case _item_examples.detail 2.22 'position 2b in space group No. 94, P 42 21 2' 42.2 'position 6b in space group No. 222, P n -3 n' 2.. ; Site symmetry for the Wyckoff position 96f in space group No. 228, F d -3 c. The site-symmetry group is isomorphic to the point group 2 with the twofold axis along one of the {100} directions. ; _item_description.description ; The subgroup of the space group that leaves the point fixed. It is isomorphic to a subgroup of the point group of the space group. The site-symmetry symbol indicates the symmetry in the symmetry direction determined by the Hermann-Mauguin symbol of the space group (see International Tables for Crystallography Volume A, Section 2.2.12). Ref: International Tables for Crystallography (2002). Volume A, Space-group symmetry, edited by Th. Hahn, 5th ed. Dordrecht: Kluwer Academic Publishers. ; _item_type.code char save_ ### ######################## ## DICTIONARY_HISTORY ## ######################## loop_ _dictionary_history.version _dictionary_history.update _dictionary_history.revision 0.01 1998-11-27 ; (I.D.Brown) Creation of first draft of the dictionary. Contains the categories SPACE_GROUP, SPACE_GROUP_POS, SPACE_GROUP_REFLNS and SPACE_GROUP_COORD ; 0.02 1999-02-15 ; (IDB) Changes made in response to suggestions from the project group. New categories introduced SPACE_GROUP_SYMOP SPACE_GROUP_ASYM. The following category name changes were made: SPACE_GROUP_POS to SPACE_GROUP_WYCKOFF SPACE_GROUP_REFLNS to SPACE_GROUP_WYCKOFF_CONDITIONS SPACE_GROUP_COORD to SPACE_GROUP_WYCKOFF_COORD The items are arranged in alphabetical order Many other changes made in response to comments received including new data names for space-group names ; 0.03 1999-09-01 ; IDB Definitions of _space_group.IT_number, *.name_schoenflies *.Bravais_type, *point_group_H-M, *.crystal_system and *.Laue_class changed to those supplied by Litvin and Kopsky. *.setting_code changed to *.it_coordinate_system_code. *.name_H-M-K dropped. *.Patterson_symmetry_H-M changed to *.Patterson_name_H-M and enumeration list corrected. *.reference_setting added In category space_group_symop 'operator' changed to 'operation'. _space_group_symop.operation_matrix changed to conform to IT. _space_group_symop.generator_* added. _space_group.reference_setting added. _space_group_Wyckoff.* and related categories rewritten to avoid conflicting parent-child relations. Removal of *_coord.* and addition of *_cond_link.* ; 0.04 1999-11-01 ; IDB List of reference settings imported from Ralf Grosse-Kunstleve supplied 1999-10-29 by RWGK based on http://xtal.crystal.uwa.edu.au/ (Select 'Docs', Select 'space Group Symbols') Symmetry table of Ralf W. Grosse-Kunstleve, ETH, Zuerich. version June 1995 updated September 29 1995 updated July 9 1997 last updated July 24 1998 Matrices expanded into separate items for each element. References added for *_Wyckoff.site_symmetry and *.IT_coordinate_system_code. *_asym category deleted. Numerous typographical errors corrected ; 0.05 2000-01-12 ; IDB Further clarifications to definitions as suggested by Aroyo, Wondratschek, Madariaga, Litvin and Grosse-Kunstleve. Removal of all matrix forms of matrices (leaving xyz form) in the hope that a new DDL will make matrix representation simpler. Removal of *_Wyckoff_cond and *_Wyckoff_cond_link categories until a new DDL simplifies their structure. Added _space_group.transform_* items ; 0.06 2000-05-04 ; IDB Further clarification of definitions as suggested by Aroyo, Wondratschek, Madariaga and Grosse-Kunstleve, particularly clarification of the Hermann-Mauguin symbols and Bravais types and changes to conform to the usage of ITA. ; 0.07 2000-07-18 ; IDB Further clarifications and corrections from Wondratschek and Grosse-Kunstleve. Dictionary checked in vcif. Brian McMahon: Structural review for COMCIFS. Some reformatting and cleaning up of minor typos. Checked against vcif and cyclops. ; 0.08 2000-07-20 ; J. Westbrook Miscellaneous corrections and reformatting from software scan. ; 0.09 2001-05-31 ; IDB The links between the space_group category and the space_group_symop and space_group_Wyckoff categories are corrected as well as the links between space_group_symop and the various geom_ categories. Brian McMahon: Changed type of _space_group_symop.sg_id to numb at request of IDB. ; 0.10 2001-11-07 ; IDB A number of corrections made following the approval of this dictionary in principle by COMCIFS. The underscore in all space-group names has been removed and the text modified to indicate that underscores are only permitted to allow earlier space group tables to be read. _space_group.name_H-M changed to _space_group.name_H-M_ref An enumeration list added to _space_group.name_H-M_ref The 1995 H-M names for space groups 39, 41, 64, 67 and 68 introduced Aliases to _symmetry_space_group_name_H-M removed from _*.name_H-M_ref ^ replaced by . in Schoenflies names (e.g. C2h^4 replaced by C2h.4) Changes made in the text of _*.reference_setting _*.transformation_rotation_xyz and _*_origin_shift replaced by _*.transformation_Pp_abc and _*. transformation_Qq_xyz ; 1.0 2001-12-08 ; Brian McMahon: COMCIFS public release version ; 1.0.1 2005-06-17 ; 2004-09-25 Brian McMahon: Editorial modifications for incorporation into International Tables for Crystallography Volume G. Fixed wrong example in _space_group.name_Schoenflies. Updated web reference to Xtal in _space_group.reference_setting. 2005-02-07 NJA: minor corrections to hyphenation, spelling and punctuation. References to International tables Volume A updated to refer to fifth (2002) edition. SPACE_GROUP: example 1, _space_group.name_H-M changed to _space_group.name_H-M_ref. _space_group.transform_Qq_xyz, _item_examples.case Pnnn2 to changed to Pnnn:2. 2005-06-17 NJA: small corrections to follow proof corrections for IT G Chapter 4.7. ;