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Manuscript Title: Improved version of group-theoretical analysis of lattice dynamics.
Authors: J.L. Warren, T.G. Worlton
Catalogue identifier: ACMI_v2_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 8(1974)71
Programming language: Fortran.
Computer: CDC 6600.
Operating system: SCOPE 3.1 (LASL VERSION).
RAM: 137K words
Word size: 60
Keywords: Solid state physics, Lattice dynamics, Group theory, Phonons, Symmetry, Dispersion curves, Dynamical matrix, Irreducible multiplier Representations, Molecular vibrations, External modes, Time reversal invariance, Projection operators.
Classification: 7.8.

Nature of problem:
The original version of the program symmetry-reduced the dynamical matrix characterizing lattice vibrations of solids, constructed symmetry coordinates which were labeled by the irreducible multiplier representationsof the group of the wavevector, and block-diagonalized the dynamical matrix. This improved version of the program allows one to calculate the symmetry properties of the external modes of vibration of molecular crystals, to generate the irreducible multiplier representation (IMR's), and to include the effects of time reversal invariance (TRI) on the symmetrycoordinates.

Solution method:
The invariance of the dynamical matrix unitary transformations by matrices in a reducible multiplier representation of the time reversal invariant point group of the wave-vector leads to a fromula for the symmetry-reduction of the dynamical matrix. The projection operator method is used to construct the symmetry coordinates. The projection operator method is used to construct the symmetry coordinates. The projection operator is dependent on the reducible multiplier representation used and the IMR's of the group of the wavevector. These IMR's are generated in the program by the method of orbitals from the representations of cyclic subgroups of the group of the wavevector which in turn are constructed from the roots of unity. The symmetry coordinate vectors from a matrix, which transforms the symmetry-reduced dynamical matrix into block-diagonalized form.

The program is dimensioned for up to 30 degrees of freedom per unit cell but this may be increased to 60. Redundant coordinates for linear molecules are not eliminated. For certain low-symmetry crystals in the trigonal and hexagonal systems, the symmetry-reduction of the dynamical matrix is incomplete because of complicated relations between elements of the matrix.

Unusual features:
By changing three cards in subroutine POASC, the symmmetry coordinates can be punched out for use in calculating neutron scattering structure factors for one phonon scattering.

Running time:
Calcium-tungstate, which has 18 degrees of freedom (2 atoms and 2 molecular units/cell), with 10 independent wavevectors takes 45 s on a CDC-6600.