Harold T. Stokes and Dorian M. Hatch
Department of Physics and Astronomy, Brigham Young University, Provo, Utah

SMODES calculates the displacement modes in a crystal which brings the dynamical matrix to block-diagonal form, with the smallest possible blocks. It also chooses the modes so that its unit cell is as small as possible and its point-group symmetry is as high as possible.


line 1. Title line. This line can contain any string of characters, including no characters, and will be copied onto the first line of output.

line 2. Space group number, 1 through 230.

line 3. Lattice parameters, a,b,c,alpha,beta,gamma. Angles should be given in units of degrees.

line 4. Number of different Wyckoff positions occupied by atoms.

line 5a, 5b, 5c... The atomic symbol and its position for each Wyckoff possition. Each Wcykoff position should be on a separate line. The atomic symbol can be any character string the user wants to use to identify the atom at that position. The position is denoted by a lower-case letter (the symbol for the Wyckoff position given in the International Tables for Crystallography), followed by 3 numbers, the values of the Wyckoff structural parameters x,y,z, as defined for the Wyckoff positions in the International Tables for Crystallography. Enter a zero for any Wyckoff structural parameter not used for that Wyckoff position. You may enter no numbers at all if the Wyckoff position is at a point of symmetry and has no degrees of freedom in its coordinates.

Examples: Space group #204

Note that for Wyckoff position g, a value must be given for x, even though x is not one of the Wyckoff structural parameters for position g. The program interprets the first number to be x, the second number to be y, and the third number to be z, regardless of which of these are actually used in evaluating the coordinates of the atomic position.

The program uses the settings in the International Tables for Crystallography. Sometimes more than one setting is given in the Tables. This program uses:
(a) for monoclinic groups, unique axis b and cell choice 1,
(b) for groups where there are two choices of origin, the second choice (where the point of inversion is at the origin),
(c) for rhombohedral groups, the hexagonal axes.
Sometimes the convention for the values of x,y,z used in SMODES do not follow the one in the Tables. Always check the output to determine where the program actually put each atom.

line 6. Number of different k vectors to be treated.

line 7a,7b,7c... The k vectors to be treated, each on a separate line. The symbols for the k vectors follow the convention of Miller and Love. Greek letters gamma, delta, sigma, lambda are denoted by GM, DT, SG, LD, respectively. The general point is denoted by GP. Some k vectors must be further specified by one or more parameters, denoted by alpha,beta,gamma (not the same as the 3 angles given on line 3). Each parameter must be entered as a ratio of two integers (for example, 1/2 instead of 0.5).

Examples: Space group 115

For the gamma point (k=0), a direction may be given for the longitudinal mode, as in the last example above. The direction is given as one of the k lines of symmetry. The program separates the longitudinal mode from the transverse modes in the output.


(1) title line, copied from the first line in the input.

(2) space group number and symbol

(3) lattice parameters: a,b,c,alpha,beta,gamma

(4) Wyckoff positions

(5) k vector symbol and coordinates. The coordinates are given in terms of the basis vectors of the reciprocal lattice of the conventional lattice given in International Tables for Crystallography. Note that k vectors in Miller and Love are given in terms of basis vectors of primitive lattices and may not appear the same as the output of SMODES.

(6) Irreducible representation (irrep) symbol, following the convention of Miller and Love. For k=0, the conventional symbol for the point group irrep is also given.

(7) Degeneracy of each mode. This is the dimension of the irrep.

(8) Total number of modes for this irrep, including all of the degenerate modes.

(9) For k=0, some of the modes may be translational, i.e., they describe a translation of the entire crystal. If there are any among the modes for a particular irrep, the number of such translation modes are given here.

(10) If the modes are IR-active, this is indicated. This only occurs for k=0.

(11) If the modes are raman-active, this is indicated. This only occurs for k=0.

(12) Vectors defining the superlattice, i.e., the lattice of the distorted crystal. This lattice is primitive, but the basis vectors are given in cartesian coordinates, in terms of an orthonormal set of basis vectors (i,j,k), consistent with the values given for the lattice parameters, a,b,c,alpha,beta,gamma.

(13) Position of each atom in the unit cell, given in the same cartesian coordinates as the basis vectors of the lattice in (12).

(14) Symmetry modes. Each symmetry mode defines a coordinate transformation which brings the dynamical matrix to block diagonal form.

(15) If any of these symmetry modes are translational modes, the number of such modes is given.

(16) Each symmetry mode is given. The mode is defined by a displacement of like atoms in the unit cell. The displacements are given in the same cartesian coordinates as the basis vectors of the lattice in (12) and the atomic positions in (13).

(14) The next irrep for the k vector is given, and (6) through (16) are repeated.

(15) When all of the irreps for the k vector have been given, the next k vector is given, and (5) through (14) are repeated.