Centrosymmetric or Noncentrosymmetric? Case Study, Generalization and Structural Redetermination of Sr₅Nb₅O₁₇

The possibility that the structure of the novel semiconducting perovskite-related material strontium niobium oxide, Sr₅Nb₅O₁₇, refined by Schmalle et al. [Acta Cryst. (1995), C51, 1243–1246] in space group Pnn2, might instead belong to space group Pnnm has been investigated following an analysis of the atomic coordinates that indicated the latter space group to be more likely. All I_obs were carefully remeasured, first those within a hemisphere containing c^*, then all that lay within the full sphere of reflection. Refinement was undertaken, with each of two different sets of weights, in each space group. Each data set was used under three limiting intensity conditions: I_obs > 4σ(I_obs), I_obs > 2σ(I_obs) and finally with all reflections, but setting magnitudes with I_obs ≤ 0 equal to 0. Fourteen separate tests based only upon the X-ray diffraction data may be used to distinguish between Pnn2 and Pnnm. Nine tests favored the latter choice, four were indeterminate and one was not used. Seven further tests may be made on the basis of physical measurement; of these, three strongly indicated Pnnm, one was indeterminate and three could not be used. The evidence clearly suggests the space group is Pnnm. The use of all reflections, including those with negative magnitude set equal to zero, is essential to avoid ambiguity in the X-ray diffraction tests and achieve the highest reliability. Refinement with weights based on variances of Type A and Type B [Schwarzenbach et al. (1995). Acta Cryst. A51, 565–569] resulted in improved reliability compared with that obtained from a popular empirical weighting scheme. The revised structure differs in several respects from that published previously.

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