Modelling the atomic displacements in Bi 2Sr 2Ca n−1 Cu nO x superconductors

Abstract

The incommensurate displacive modulation waves in Bi 2Sr 2Ca n-1 Cu n O x are investigated using high resolution transmission electron microscopy. The image contrast is compared with simulated images calculated with different models of the modulation waves. The static atomic displacements are calculated in one step on all equivalent sites of a periodically continued average structure. In contrast to other methods symmetry operations are not required for the evaluation of the correct phase parameters to create the whole modulated structure. This facilitates the creation of the simulated structure, and incommensurate modulation wave vectors can be used, too. The superstructures of the 2212, 2223 and especially the 2201 phase can be simulated by this method. For the 2201 phase both types of the incommensurate modulation known from the literature are simulated. A connection between the type of the 2201 modulation and the modulation wave vector is found. The Pb modulation in (Bi,Pb) 2Sr 2Ca n-1 Cu n O x is also described by a similar formalism using data from the literature. Different models of the oxygen arrangement in the Bi layers of the 2212 phase are compared using HREM images and contrast simulations. The correlation between atomic shifts of the Bi atoms in [100] direction and the occupations of different oxygen sites in the BiO layers is shown.