Charge distribution and atomic thermal vibration in lead chalcogenide crystals

Charge distribution in crystals of lead chalcogenides, PbX (X = S, Se and Te), has been studied by X-ray diffraction. The structure of PbX is of the rock salt type: cubic, Fm3m, a = 5.934 (1), 6.128 (1) and 6.462 (1)A for PbS, PbSe and PbTe, respectively. Final agreement factors for PbS, PbSe and PbTe were R = 0.015, 0.011 and 0.015 for 144, 147 and 130 independent reflections, respectively. The direct integration of charge density, the observed atomic scattering factors, and the population analysis of the valence electrons unanimously indicated that the Pb atom is negatively charged. This observation suggests predominant covalency for the chemical bond in lead chalcogenide crystals. No overlap density was observed in the deformation density map. The bonding electrons in these crystals may be delocalized like free electrons in metals. The thermal parameters of the Pb atoms were found to be larger than those of the chalcogen atoms and the ratio Bpb/B x increases in the order: PbS < PbSe < PbTe. Anharmonic thermal vibration of the Pb atom was detected in the difference electron density maps. A positive peak of 2 (0.3) e A -3 was observed in the (111) direction at 0.4 A from the Pb nucleus for all three compounds. Its height was reduced to 1 (0-3) e A -3 by introducing anharmonic potential parameters for the Pb atom.