Department of Physics and Astronomy, Brigham Young University, Provo, Utah

e-mail: stokesh@byu.edu

RELATION determines if two crystals have a group-subgroup relation.

**Input:**

(1) Title line. This line is copied to the output, but is otherwise ignored by the program.

(2) Space group of the first crystal. Enter the space group number (1-230).

(4) Lattice parameters of the first crystal structure: a,b,c,alpha,beta,gamma. The lengths a,b,c may be given in any units. The angles alpha,beta,gamma must be given in degrees. For rhombohedral space groups, the lattice parameters must be given for the hexagonal axes.

(5) The number of Wyckoff positions in the first crystal.

(6) Information about each Wyckoff position in the first crystal: The atomic symbol (eg., Ba, Si, H), the Wyckoff position (eg., a, b, c), their structural parameters x,y,z for the Wyckoff position, as listed in the International Tables of Crystallography. Each Wyckoff position must be entered on a separate line. The same atomic symbol must be used for the same kind of atoms (eg., do not use Cu1 and Cu2 for Cu atoms at two different Wyckoff positions unless you do not want the program to consider them interchangeable).

If you do not know the Wyckoff position, enter * for the position and then give the x,y,z coordinates of one of the atoms at that position. If you use this option, then the space group setting makes a difference. (Wyckoff positions and their structural parameters are independent of setting.) This program uses the following settings: for monoclinic, unique axis b and cell choice 1; for rhombohedral: hexagonal axes; for origin choices, origin choice 2 (inversion at the origin).

(7) Lattice parameters for the second crystal structure: see item (4) above.

(8) The number of Wyckoff positions in the second crystal.

(9) Information about each Wyckoff position in the second crystal: see item (6) above.

(10) Accuracy desired. Two numbers are entered here, eps1 and eps2. eps1 is the fractional accuracy of the lattice vectors. For example, eps1=0.01 means that if the two crystal are to be considered to have the same structure, all lattice vectors must agree in length to within 1%. The volume of the unit cell must agree to within 1.7*eps1 or, for this example, 1.7%.

eps2 is the accuracy of the structural parameters x,y,z for Wyckoff positions. For example, eps2=0.01 means that if x=0.345 in one crystal, then the value of x must lie between 0.335 and 0.355 in the other crystal.

**Output:**

(1) The relationship between the structures of the two crystals. They may have a group-subgroup relation. They also may have the same structure. Any enantiomorphic relation is also indicated.

(2) If the two crystals have related structures, the structure of the subgroup derived from the parent is given: lattice parameters, Wyckoff positions, lattice basis vectors of the subgroup in terms of the lattice basis vectors of the parent, and the origin shift between the parent and subgroup. This information is given in the space-group settings described in input (6) above.