The crystal structure and optical activity of tellurium

The element tellurium has a crystal structure made up of spiral chains of bonded atoms packed in a hexagonal array. Its symmetry leads to the existence of enantiomorphic forms containing spirals of opposite handedness, the right-handed one belonging to space group P3(1)21 and the other to P3(2)21, which have opposite optical rotatory powers. The normal methods of crystal structure determination cannot distinguish between the enantiomorphs, nor is this feasible using anomalous dispersion unless there is sufficient asphericity in the tellurium electron density due to bonding. Such asphericity also gives rise to small but measurable differences from unity in the flipping ratios for polarized neutron scattering due to the polarization dependence of the Schwinger scattering. This effect is easier to measure than is the intensity difference between Bijvoet pairs and it has been used to determine the absolute structural configuration that corresponds to a particular sense of optical rotation in a tellurium single crystal. The plane of polarization of the transmitted light rotates in the same sense as the bonded atoms in the spiral chains. This observation disagrees with a previous theoretical calculation based on the single polarizable ion model.