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 International Tables
for Crystallography Vol A number or 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 for Crystallography Vol. 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. It contains
information on the choice of the basis, but not on the
choice of origin.
<mmcif_sym:space_groupCategory>
<mmcif_sym:space_group id="1">
<mmcif_sym:IT_number>15</mmcif_sym:IT_number>
<mmcif_sym:Laue_class>2/m</mmcif_sym:Laue_class>
<mmcif_sym:Patterson_name_H-M>C 2/m</mmcif_sym:Patterson_name_H-M>
<mmcif_sym:centring_type>C</mmcif_sym:centring_type>
<mmcif_sym:crystal_system>monoclinic</mmcif_sym:crystal_system>
<mmcif_sym:name_Hall>-C 2yc</mmcif_sym:name_Hall>
<mmcif_sym:name_Schoenflies>C2h.6</mmcif_sym:name_Schoenflies>
</mmcif_sym:space_group>
</mmcif_sym:space_groupCategory>
A qualifier taken from the enumeration list identifying which
setting in International Tables for Crystallography (3rd Edn)
Vol. A (IT) is used. See IT Table 4.3.1 Section 2.16,
Table 2.16.1 Section 2.16.(i) and Fig. 2.6.4. This item is
not computer interpretable and cannot be used to define the
coordinate system. Use attribute transform_* in category space_group instead.
The number as assigned in International Tables for
Crystallography Vol 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.
The Hermann-Mauguin symbol of the geometric crystal class of the
point group of the space group where a center of inversion is
added if not already present.
The Hermann-Mauguin symbol of the type of that centrosymmetric
symmorphic space group to which the Patterson function belongs,
see Table 2.5.1 in International Tables for Crystallography
Vol A (1995).
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.
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
The symbol denoting the lattice type(Bravais type) to which the
translational subgroup (vector lattice) of the space group
belongs. It consisting 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 (see International Tables for
Crystallography A 1995 edition p.13).
triclinic (anorthic) primitive lattice
aP
Symbol for the lattice centring. This symbol may be dependent
on the coordinate system chosen.
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.
*.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
attribute name_H-M_alt_description in category space_group. It may, for example, be
used to give one of the extended Hermann-Mauguin symbols given
in Table 4.3.1 of International Tables for Crystallography
Vol A (1995) 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. The use of space is strongly
recommended. The underscore is only retained because it
was used in earlier archived files. 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 the *.IT_number or *.name_Schoenflies.
The Hermann-Mauguin symbol may contain information on the
choice of basis though not on the choice of origin. To
define the setting uniquely use *.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 *.reference_setting.
three examples for the space group number 63.
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'
A free text description of the code appearing in
attribute name_H-M_alt in category space_group
The Full International Hermann-Mauguin space group symbol as
defined in Section 2.3 and given as the second item of the
second line of one of the Space Group Tables of Section 7 of
International Tables for Crystallography Vol. A (1995).
Each component of the space group name is separated by a
space or an underscore. The use of space is strongly
recommended. The underscore is only retained because it
was used in earlier archived files. 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 the *.IT_number
or *.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 *.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 *.reference_setting.
full symbol for Pnma
P 21/n 21/m 21/a
The Short International Hermann-Mauguin space group symbol as
defined in Section 2.3 and given as the first item of each
Space Group Table in Section 7 of International Tables
for Crystallography Vol.A (1995).
Each component of the space group name is separated by a
space or an underscore. The use of space is strongly
recommended. The underscore is only retained because it
was used in earlier archived files. 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 the *.IT_number or
*.name_Schoenflies. The Short International Hermann-Mauguin
symbol contains no information on the choice of basis or
origin. To define the setting uniquely use *.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 *.reference_setting.
attribute name_H-M_alt in category space_group may be used to give the Hermann-
Mauguin symbol corresponding to the setting used.
P 21/c
P m n a
P -1
F m -3 m
P 63/m m m
Space group symbol defined by Hall (Acta Cryst. (1981) A37,
517-525) (See also International Tables for Crystallography
Vol.B (1993) 1.4 Appendix B).
Each component of the space group name is separated by a
space or an underscore. The use of space is strongly
recommended. The underscore is only retained because it
was used in earlier archived files. It should not be
used in new CIFs.
attribute name_Hall in category space_group uniquely defines the space group and
its reference to a particular coordinate system.
Equivalent to Pca21
P 2c -2ac
Equivalent to Ia3d
-I 4bd 2ab 3
The Schoenflies symbol as listed in International Tables for
Crystallography Vol. 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.
Schoenflies symbol for space group 14
C2h^5
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.
-4
4/m
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
*.transform_Pp_abc and *.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 Vol. A
(1995). 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 center 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 http://xtal.crystal.uwa.edu.au/, (select 'Docs',
select 'space-Group Symbols') Symmetry table of Ralf 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.
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 attribute reference_setting in category space_group (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.
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
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
attribute reference_setting in category space_group [(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 premultiplication 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.
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 Pnnn2
x+1/4,y+1/4,z+1/4
Bbab:1 to Ccca:2
z+1/2,x+1/2,y+1/2
This is an identifier needed if _space_group_* items are looped.
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 attribute operation_xyz in category space_group_symop.
This example is taken from the space group F_d_-3_c (number 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 coordinates of the other sites can be
generated using the symmetry operations given in the SPACE_GROUP_SYMOP
category.
<mmcif_sym:space_group_WyckoffCategory>
<mmcif_sym:space_group_Wyckoff id="1">
<mmcif_sym:letter>h</mmcif_sym:letter>
<mmcif_sym:multiplicity>192</mmcif_sym:multiplicity>
<mmcif_sym:site_symmetry>1</mmcif_sym:site_symmetry>
</mmcif_sym:space_group_Wyckoff>
<mmcif_sym:space_group_Wyckoff id="2">
<mmcif_sym:letter>g</mmcif_sym:letter>
<mmcif_sym:multiplicity>96</mmcif_sym:multiplicity>
<mmcif_sym:site_symmetry>..2</mmcif_sym:site_symmetry>
</mmcif_sym:space_group_Wyckoff>
<mmcif_sym:space_group_Wyckoff id="3">
<mmcif_sym:letter>f</mmcif_sym:letter>
<mmcif_sym:multiplicity>96</mmcif_sym:multiplicity>
<mmcif_sym:site_symmetry>2..</mmcif_sym:site_symmetry>
</mmcif_sym:space_group_Wyckoff>
<mmcif_sym:space_group_Wyckoff id="4">
<mmcif_sym:letter>b</mmcif_sym:letter>
<mmcif_sym:multiplicity>32</mmcif_sym:multiplicity>
<mmcif_sym:site_symmetry>.32</mmcif_sym:site_symmetry>
</mmcif_sym:space_group_Wyckoff>
</mmcif_sym:space_group_WyckoffCategory>
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.
Coordinates of a Wyckoff site with 2.. symmetry
x,1/2,0
The Wyckoff letter as given in International Tables for
Crystallography Vol. A associated with this position. The
enumeration value '\a' corresponds to the Greek letter 'alpha'
used in International Tables.
The multiplicity of this Wyckoff position as given in
International Tables Vol A. It is the number of equivalent
sites per conventional unit cell.
A child of attribute id in category space_group allowing the Wyckoff position
to be identified with a particular space group.
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 Vol A Section 2.12).
Position 2b in space group number 94, P 42 21 2
2.22
Position 6b in space group number 222, P n -3 n
42.2
Site symmetry for the Wyckoff position 96f in space group 228,
F d -3 c. The site symmetry group is isomorphic to the point
group 2 with the 2-fold axis along one of the {100} directions.
2..
An arbitrary identifier that is unique to a particular Wyckoff
position.
Contains information about the symmetry operations of the
space group.
The symmetry operations for the space group P21/c
<mmcif_sym:space_group_symopCategory>
<mmcif_sym:space_group_symop id="1">
<mmcif_sym:operation_description>identity mapping</mmcif_sym:operation_description>
<mmcif_sym:operation_xyz>x,y,z</mmcif_sym:operation_xyz>
</mmcif_sym:space_group_symop>
<mmcif_sym:space_group_symop id="2">
<mmcif_sym:operation_description>inversion</mmcif_sym:operation_description>
<mmcif_sym:operation_xyz>-x,-y,-z</mmcif_sym:operation_xyz>
</mmcif_sym:space_group_symop>
<mmcif_sym:space_group_symop id="3">
<mmcif_sym:operation_description>2-fold screw rotation with axis in (0,y,1/4)</mmcif_sym:operation_description>
<mmcif_sym:operation_xyz>-x,1/2+y,1/2-z</mmcif_sym:operation_xyz>
</mmcif_sym:space_group_symop>
<mmcif_sym:space_group_symop id="4">
<mmcif_sym:operation_description>c glide reflection through the plane (x,1/4,y)</mmcif_sym:operation_description>
<mmcif_sym:operation_xyz>x,1/2-y,1/2+z</mmcif_sym:operation_xyz>
</mmcif_sym:space_group_symop>
</mmcif_sym:space_group_symopCategory>
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 the equation:
X' = WX + w
(Note: X is used to represent bold_italics_x in International
Tables for Crystallography Vol. 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 operator) 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 operators
or generators and:
W3 = W2 x W1
w3 = W2 x w1 + w2
c glide reflection through the plane (x,1/4,z) chosen as
one of the generators of the space group
x,1/2-y,1/2+z
An optional text description of a particular symmetry operation
of the space group.
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 bold_italics_x in International
Tables for Crystallography Vol. 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 Vol. A.
c glide reflection through the plane (x,1/4,z)
x,1/2-y,1/2+z
A child of attribute id in category space_group allowing the symmetry operator
to be identified with a particular space group.
An arbitrary identifier that uniquely labels each symmetry
operation in the list.