Release 2006/1 of the Inorganic Crystal Structure Database contains 155 entries under space group R3. Atomic coordinate analysis of the first 81 structures, with 52 different structure types, in Part I [Abrahams (2006). Acta Cryst. B62, 26–41] identified a total of 18 new types that satisfy the structural criteria for ferroelectricity, five that are more likely to have or undergo a transition to 3m symmetry, 19 more likely to be or undergo a transition to nonpolar symmetry and ten with a lower property predictability. Coordinate analysis of the remaining 71 entries with 54 different structure types in Part II leads to 11 materials including Al4B6O15, PbTa3(PO4)(P2O7)3.5, the KCd4Ga5S12 family, the LiZnPO4 family, Ca3Nb1.95O8V0.05 and Mn4Ta2O9 as new candidates which satisfy the structural criteria, together with the three known ferroelectrics Na3MoO3F3, Pb2ScTaO6, and RbTi2(PO4)3 at 6.2 GPa. Two additional ferroelectric predictions are at a lower level of confidence. The analysis also reveals nine materials, two of which are isostructural, that more likely belong or are capable of undergoing a transition to crystal class 3m. There are 14 additional structure types which are more likely to be nonpolar or undergo a transition to nonpolarity, ten have reduced predictive properties, with a further nine for which the space group is expected to remain R3 over the full thermal stability range. The increasing use of methods for identifying overlooked inversion centers in structural determinations may be extended by using coordinate analysis for detecting additional commonly overlooked symmetry elements.
DECOMPOSITION OF UNITARY MATRICES AND QUANTUM GATES