X-ray analysis of the incommensurate modulation in the 2:2:1:2 Bi-Sr-Ca-Cu-O superconductor including the oxygen atoms

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Abstract
Single-crystal x-ray diffraction data on the 2:2:1:2 Bi-Sr-Ca-Cu-O superconducting phase have been used in a four-dimensional refinement of the modulations of both the metal and oxygen atoms. An expression for an analytical temperature-factor modulation function has been derived and applied to the bismuth atoms. The large value of the temperature factor of Bi in some of the unit cells indicates a contribution from static disorder. The modulation of the oxygen atoms in the bismuth layer is best described by a function that allows the displacement to vary linearly with unit-cell position and incorporates the possibility of excess oxygen near the end of a modulation period. The results on oxygen occupancy and the behavior of the Bi temperature factor are compatible with models that attribute the origin of the modulation to the existence of extra oxygen atoms in the Bi-O layers. Refinement in the noncentrosymmetric super space group M:A2aa:1¯11 leads to significantly better results than the centrosymmetric treatment.