Comparison of the structure refinements for Ca6(Nb,Ti)6O20 using superspace approach and standard crystallography

Abstract

The crystal structure of Ca₆(Nb,Ti)₆O₂₀, an n = 6 member of the perovskite-related series A_nB_nO_3n+2 which has been recently determined using standard crystallographic approach from single-crystal X-ray diffraction data, is reanalyzed using superspace approach. In the standard three-dimensional (3-D) crystallography, one must specify the space group and cell parameters for each composition in the series. The superspace approach employs a unique and composition-independent structural model for all composition within the series. In the present work, structure refinements in (3+1)-dimensional space were performed using as starting model the superspace structural parameters recently determined for Ca₅Nb₄TiO₁₇, an n = 5 member of the homologous series. Only the modulation vector and the width of the crenel functions used to describe the occupational modulations of the atoms were varied and adapted to the composition of the compound. Superspace refinements have reproduced the structural features obtained from 3-D refinements while employing much fewer parameters. The higher quality of the superspace refinements is illustrated by the computed valences for Nb and Ti ions which are closer to their formal valences than those derived from the 3-D refinements. The centrosymmetric superspace symmetry employed in the superspace refinements provides a natural explanation for the pseudo-symmetries as they have been observed in the acentric supercell structure of this compound.