Group Theoretical Treatment of Crystal Vibrations; Application to Orthorhombic Polyethylene

Irreducible representations of k groups of the space group Pnam were derived with Slater’s method. Degeneracies of crystal vibrations due to space symmetry and time reversal symmetry were treated on the basis of Maradudin’s theory. With irreducible representations of k groups, symmetry coordinates of the carbon atoms of orthorhombic polyethylene were constructed from translational-symmetry coordinates with nonintegral index vectors. A general matrix method was worked out for treating crystal vibrations of any phase-difference vector. Useful methods were derived for treating molecular crystals and chain polymer crystals and for approximate treatment of low frequency lattice vibrations.