Harold T. Stokes and Branton J. Campbell, Department of Physics and Astronomy, Brigham Young University, Provo, Utah, 84602, USA, firstname.lastname@example.org
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).
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.).
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 (mx,my,mz) components of the magnetic moment vector, or if you elected to enter rotational moments, the drop-down entry for each Wyckoff site also includes the (rx,ry,rz) components of the rotational moment vector. Magnetic and rotational moments are defined in crystal-axis coordinates, such that the magnitude of the vector indicates the total magnetic moment (in μB/Å units) or total rotation angle (in radian units), and the direction of the vector defines the moment direction (e.g. rotation axis). This is very different from the presentation of Euler angles (or other similar parameters); the components of a moment vector in crystal-axis coordinates are not intended to be applied in any particular order. It may be convenient to specify the direction of the moment vector using integer components and then specify the magnitude separately in the "renormalized magnitude" box, in which case, the entire vector will be rescaled so as to have the specified magnitude. It is common to define a matrix B=(a|b|c) whose columns are the three lattice vectors in Cartesian coordinates, so that B transforms an atomic coordinate from lattice coordinates to Cartesian coordinates. If we futher define a diagonal matrix L whose diagonal elements are the lengths of the a, b, and c unit cell axes, then the matrix B.Inverse[L] will transform a moment vector from crystal-axis coordinates to Cartesian coordinates. The matrix B.Inverse[L] is like B except that each column has been divided by the corresponding cell parameter. See the ISODISTORT help pages for more information about moment vectors.
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/μB) 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 ABO3 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.