Importance of True Satellite Reflections in the Analysis of Modulated, Composite Crystal Structures. I. A New Refinement of [M₂Cu₂O₃]_7+δ[CuO₂]₁₀, M = Bi_0.06Sr_0.46Ca_0.48

A new structural model for the composite crystal bismuth strontium calcium cuprate [M₂Cu₂O₃]_7+δ[CuO₂]₁₀ with M = Bi_0.06Sr_0.46Ca_0.48 and δ = 0.03 has been determined. The structure is orthorhombic with a = 11.380 (2), b = 12.960 (4) Å and incommensurate along c. Sublattice 1 of composition (CuO₂)₄ has c₁ = 2.7522 (4) Å and sublattice 2 of composition (M₂Cu₂O₃)₄ has c₂ = 3.9155 (5) Å; superspace group F222(001 + γ)001; modulation vector q_l = γc2* with γ = 0.7029 (2). The structural analysis has been based on 603 main reflections, 428 first-order and 64 second-order satellite reflections. The final residual is R = 0.0632 for all reflections, R = 0.0614 for main reflections, R = 0.0735 for first-order and R = 0.1084 for second-order satellite reflections; λ = 0.6565 Å, μ = 19.4 mm^−l The satellite reflections have been collected with X-ray synchrotron radiation. In this context, special experimental problems are discussed. It is shown that the true satellite reflections, which are the satellite reflections that are not also main reflections for one of the sublattices, are necessary in the least-squares refinement in order to avoid large correlations between displacive modulation amplitudes and thermal vibration amplitudes and thus to obtain a reasonable coordination chemistry.