The significance of anharmonic motion in polymer crystal structure analysis

Nonsystematic absences along certain reciprocal-lattice directions have been observed in the diffraction patterns of the macroscopic single crystals of various materials, both in our laboratory and in the literature. These extinctions are not space-group related nor are they the result of secondary scattering. Incorporation of the lowest-order anharmonic interaction terms, cubic and quartic in displacement, into the Hamiltonian of the molecular lattice, has made it possible to give a complete interpretation of these observations. A General intensity distribution was deduced with the assumption of elastic scattering. The final result provides new insight into the interaction of molecular units within a crystal and reveals new avenues for the solution of some unsolved crystal structures. A general procedure for the application of the required correction term to the intensity distribution is outlined, along with appropriate examples.