Harold T. Stokes and Branton J. Campbell, Department of Physics and Astronomy, Brigham Young University, Provo, Utah, 84602, USA, branton_campbell@byu.edu

ISOCIF is a utility for creating and modifying CIF files.

In this document, "*International Tables*" refers to
*International Tables for
Crystallography*, Vol. A, Edited by Theo Hahn (Kluwer Academic,
Dordrecht).

Quick links

Space group preferences

ISOCIF home page

ISOCIF: space group

ISOCIF: atomic coordinates

ISOCIF: input CIF file

ISOCIF: preprocessed CIF file

ISOCIF: modify and save CIF file

The
*International Tables* gives more than one setting for some space
groups. An appropriate setting can be specified when creating or
modifying a CIF.

Monoclinic space groups have settings for six different orientations of the
axes: *a(b)c*, *c(-b)a*, *ab(c)*, *ba(-c)*,
*(a)bc*, or *(-a)cb*. Unique axes are in parentheses. See
Table 4.3.1 in *International Tables* for more details.

Most monoclinic space groups also have settings for different cell choices: 1, 2, or 3.

Orthorhombic space groups have six different choices for the
orientation of axes: *abc*, *ba-c*, *cab*,
*-cba*, *bca*, or *a-cb*. See Table 4.3.1 in
*International Tables* for more details.

Trigonal space groups (for example, #146, R3) have settings using hexagonal axes and rhombohedral axes.

Some orthorhombic, tetragonal, and cubic space groups (for example, #227 Fd-3m) have two choices for the position of the origin: 1 or 2. For origin choice 2, the origin is always chosen at a point of inversion.

When you start ISOCIF, you are given two choices: (1) Create new CIF file and (2) Modify existing CIF file. Clicking on the link, "Create new CIF file," takes you to the page, "ISOCIF: space group." Clicking on the link, "Modify existing CIF file," takes you to the page, "ISOCIF: input CIF file."

**Space group**. Enter the space-group
symmetry or magnetic space-group symmetry of your structure. You may
either choose the space group from the drop-down box on the left or
enter the space group number in the box on the right. Each line in the
drop-down box contains (1) the space-group number
from *International Tables*, (2) the short Hermann-Mauguin
symbol, and (3) the Schoenflies symbol. The Hermann-Mauguin symbols in
the drop-down box are generic and do not influence the space-group
preferences. If any character is entered into the box on the right,
the drop-down box selection will be ignored.

**Lattice parameters**. Enter the values of the
lattice parameters *a*, *b*, *c*, alpha, beta, gamma, where
*a*, *b*, *c* are lengths of the sides of the conventional unit
cell defined for each space group in the *International Tables*,
and alpha
is the angle between *b* and *c*, beta is the angle between *a*
and *c*, and gamma is the angle between *a* and *b*. Give
*a*, *b*, *c* in Angstroms, and give alpha, beta, and
gamma in degrees. You do not need to give values for any lattice
parameters which are determined by the symmetry of the space
group. For example, for a cubic space group, you only need to enter a
value for *a* since *b=c=a* and alpha=beta=gamma=90.
You may indicate the accuracy of any value by enclosing it in parentheses.
For example, 3.456(2) indicates an uncertainty of 0.002 in the value.

**Number of unique atomic positions**. All of the
atomic positions in a crystal can be generated by applying symmetry
operations to a finite set of unique atomic positions within the
asymmetric unit. These are the Wyckoff positions in your
*International Tables*. Enter the number of unique atomic
positions in your structure.

**Atomic rotational moments**. Check this
box if you want to enter rotational-moment vectors (in crystal-axis coordinates)
for the pivot atoms (possibly dummy atoms) of any rigid-units in the structure.
Crystal-axis units are also commonly used for presenting magnetic moments in crystals.
The components of such a rotation vector **r** have radian units and
indicate contributions to the rotation along each of the unit cell axes.
One does *not* apply the three component rotations in a particular order.
Instead, the magnitude *r* of **r** is the angle of rotation and the normalized
vector **r**/*r* defines the rotation axis.

**Space group preferences**.
If the space-group symmetry you selected has more than one setting in
*International Tables*, then you should select the desired
setting. This selection affects the
interpretation of the lattice parameters you entered above as well as
the atomic positions you will enter on the next page. The same
settings are available to both non-magnetic and magnetic space groups.

Clicking on "OK" takes you to a page, "ISOCIF: atomic coordinates."

At the top of the page is given the selected space-group symmetry,
the lattice parameters, and the space-group preferences that apply to
this space group. If there is only one setting of this space group
in *International Tables*, no space-group preferences will be
shown here.

Enter information about each unique atomic position:

**Atom name**. This is a label of your
own choice, but every unique atom must have a different
label. Traditionally, one uses the chemical symbol for the element
(Na, O, Si, etc.). If the same type of atom occupies more than one
unique position, then number them (for example Na1, Na2, etc.).

**Atom type**. This is the
chemical symbol for the element (Na, O, Si, etc.). If you leave this
field blank, we will extract the atom type from the atom name (first
one or two alphabetic characters).

**Wyckoff site**. This drop-down box
contains all of the unique atomic positions listed in
the *International Tables* for the selected space-group symmetry.
Each site in the drop-down box contains (1) the multiplicity of the
site (i.e. the number of symmetry-equivalent atoms generated in the
conventional unit cell), (2) the Wyckoff-site symbol, and (3) the
atomic-position coordinates. For a given site, some of the
(*x*,*y*,*z*) parameters will be restricted. For
example, only *x* is free in (*x*,0,0). The text-entry boxes
below each site must be used to specify the values of all free
parameters. Any data entered into the boxes of restricted parameters
will be ignored. If all of the parameters are restricted,
e.g. (0,0,0), you won't need to enter anything. Enter all values in
decimal form. You may indicate the accuracy of any value by enclosing
the estimated error in parentheses. For example, 0.345(2) indicates
an uncertainty of 0.002 in the value, and 0.25(3) indicates an
uncertainty of 0.03.

If a magnetic space group was selected, the drop-down entry for each
Wyckoff site also includes the
(*m _{x}*,

Clicking on "OK" takes you to the page, "ISOCIF: modify and save CIF file." Note that at this point, ISOCIF generates the positions of all of the atoms in the unit cell and, from these positions, determines the actual space-group symmetry of the structure you entered. If this space-group symmetry is not that same as what you entered, you will receive a warning message.

You enter this page from the ISOCIF home page by clicking on "Modify existing CIF file." To input an existing CIF file there are two options:

**Upload CIF file**: Click on "Browse..." to locate a local
copy of the CIF file. Then click on "Upload." This takes you to the
page, "ISOCIF: preprocessed CIF file."

**Copy and paste contents of CIF file**: Copy the contents
of the CIF file and then paste it into the text field. Clicking
on "OK" takes you to the page, "ISOCIF: preprocessed CIF file."

You enter this page from either option on the page, "ISOCIF: input CIF file." The CIF file is read and then rewritten with all of the nonessential data removed. At this point, you may edit the preprocessed CIF file displayed in the text field.

Clicking on "OK" causes the CIF file to be interpreted
and takes you to the page,
"ISOCIF: modify and save CIF file."
ISOCIF first tries to determine the space-group symmetry from the
operators. This fails if the operators are given in some setting
not found in *International Tables*. In this case, ISOCIF
issues a warning and then
determines the space-group symmetry from the lattice parameters
and the positions of atoms in the unit cell.
Note that the program will recognize rational numbers rounded to the
nearest 0.001. For example, 0.667 will be recognized to be exactly 2/3.

You enter this page from either the "ISOCIF: atomic coordinates" page or the "ISOCIF: preprocessed CIF file" page. You also re-enter this page by clicking on "Change lattice parameters," "Change setting," or "Find actual symmetry."

At the top of the page is given the selected space-group symmetry, the lattice parameters, the space-group preferences that apply to this space group, and the nearest-neighbor distances between different sets of unique atomic positions. These nearest-neighbor distances are only displayed when you enter this page from either the "ISOCIF: atomic coordinates" page or the "ISOCIF: preprocessed CIF file" page and are provided so that you can check that you haven't entered any unreasonable values for the atomic positions.

**View structure**. If you click on "View
structure," you will see a three-dimensional rendition of the unit
cell of the structure. If no image appears, you may need to install a
new version of Java on your computer. Each type of atom is represented
by a different color. There are several input parameters. Reasonable
default values for these parameters are already entered and may be
used without any adjustment. After viewing the graphical rendition,
you may return to this page and adjust the values of these parameters
if you wish. (1) Atomic radius (Å) determines how large the atoms
appear to be in the graphical rendition. For visual clarity, this
value should be somewhat smaller than the actual atomic radii. (2)
Maximum bond length (Å) determines which bonds are displayed. A line
will be drawn between any two atoms with a center-to-center distance
less than this value. (3) Length of magnetic moment vectors
(Å/μ_{B}) determines how large the magnetic moment
vectors appear to be relative to interatomic distances. (4) Applet
width (pixels) allows you to adjust the size of the applet window so
that it fits on your computer screen.

**Improve lattice parameters**. For monoclinic and triclinic
space groups, there are an infinite number of
choices for the lattice parameters.
*International Tables* gives the criteria for the "best"
choice. If your choice is not the "best" choice, an "Improve lattice
parameters" button will be displayed, along with the values of the
lattice parameters for the "best" choice. Clicking on the button changes
your lattice parameters to this "best" choice and returns you to this
page.

**Change setting**. If there
is more than one setting in *International Tables* for this
space group, a "Change setting" button will be displayed, along
with choices of space-group preferences available for this space group.
Selecting new choices and clicking on the button changes the
setting of the space group and returns you to this page.

**Change lattice and origin**. For many space groups, it is possible to
change the lattice vectors and/or the origin without changing the form
of the operators (i.e. without changing the setting). The
transformation matrix must have a determinant of 1 and must contain
only integer values. The origin shift must contain only integers and
rational fractions (no decimal values). We list a few possible
applications: (1) Permute the axes of a triclinic cell. (2) Transform
a triclinic cell into an equivalent cell with a different shape. (3)
Perform an arbitrary *z*-axis origin shift in space group Pmm2. (4)
Shift the origin of a cubic ABO_{3} perovskite (Pm-3m) by (1/2, 1/2,
1/2), which moves A from the "a" site to the "b" site, B from the "b"
site to the "a" site, and O from the "c" site to the "d" site.

**Find actual symmetry**. The actual space-group symmetry of the
structure you entered may be different from what you said it was.
(For example, a tetragonal unit cell with
a=c may actually have cubic symmetry.) If so,
then a "Find actual symmetry" button will be displayed. Clicking
on this button causes the actual symmetry to be found and then
returns you to this page.

**Reduce symmetry to P1**. This changes the space-group symmetry
of the structure to the triclinic space group #1 P1. You can specify
the lattice vectors and origin of the P1 structure. Every atom inside
the specified unit cell will be listed in the resulting CIF file.

**Save CIF file**, Clicking on this button
produces a CIF file for your structure, which you can save to a file.
The "Use alternate setting checkbox allows you to enter the transformation from
the current setting of the group to an alternate (and possibly non-standard)
setting. As visually organized on the page, these fields comprise S-1t, the
inversed transpose of the matrix S that transforms an atomic coordinate or
superspace coordinate x from the current setting to the new setting, i.e. x' = S x.
The structure of this matrix for an incommensurate group is described in detail
HERE.