A general structure model for Bi-Se phases using a superspace formalism

Solid-state synthesis in the Bi-Se system produced both commensurate and incommensurate phases of compositions ranging from Bi2Se3 to Bi4Se3, all crystallising in rhombohedral or trigonal layer structures. The a parameters are very similar for all phases but the c parameters vary irregularly between 10 and 100 Angstrom. A general model for all these phases was developed, using single crystal X-ray diffraction and a four-dimensional superspace formalism. The 4D superspace group is P: R (3) over bar :m (1) over bar1, with approximate cell parameters of a approximate to 4.2 Angstrom and c approximate to 5.7 Angstrom valid for all phases. The q vector value in this model, ranging from 1.70[001]* to 1.80[001]1* is the only parameter that varies with the composition. Two different modelling options were developed for the structures. One of them was a single-atom refinement model consisting of harmonic modulation waves and the other was a two-atom model based on a displacive sawtooth modulation of the Se atom. Both models converged to low R-values (R-all < 0.07) and small residual electron density values for all phases. The q vector may be physically interpreted as arising from the average distance between homoatomic layers in the structures. (C) 2003 Editions scientifiques et medicales Elsevier SAS. All rights reserved.