Abstract
The structure of sodium saccharinate 1.875-hydrate is presented in three- and (3+1)-dimensional space. The present model is more accurate than previously published superstructures, due to an excellent data set collected up to a high resolution of 0.89 Å-1. The present study confirms the unusual complexity of the structure comprising a very large primitive unit cell with Z' = 16. A much smaller degree of correlated disorder of parts of the unit cell is found than is present in the previously published models. As a result of pseudo-symmetry, the structure can be described in a higher-dimensional space. The X-ray diffraction data clearly indicate a (3+1)-dimensional periodic structure with stronger main reflections and weaker superstructure reflections. Furthermore, the structure is established as being commensurate. The structure description in superspace results in a four times smaller unit cell with an additional base centring of the lattice, resulting in an eightfold substructure (Z' = 2) of the 3D superstructure. Therefore, such a superspace approach is desirable to work out this high-Z' structure. The displacement and occupational modulation of the saccharinate anions have been studied, as well as their conformational variation along the fourth dimension.
Highlights
The lattice parameters, space-group symmetry and spatial arrangement of the atoms of the asymmetric unit are sufficient to describe a crystal structure considered as a static idealized state of matter
There have been a number of studies dealing with high-Z0 structures (Steed, 2003; Steed & Steed, 2015; Desiraju, 2007; Brock, 2016) and one of the conclusions is that sometimes such structures must be described as modulated, as considerable pseudo-symmetry can be identified
The analysis of X-ray diffraction data intensity statistics shows that the structure of sodium saccharinate 1.875-hydrate is well described in (3+1)D superspace as a commensurate case in a C-centred lattice with a modulation wavevector q of (0, 34, 0)
Summary
The lattice parameters, space-group symmetry and spatial arrangement of the atoms of the asymmetric unit are sufficient to describe a crystal structure considered as a static idealized state of matter. This formalism is the very essence of crystallography. In the vast majority of cases, there is only one molecule (or formula unit in the case of multi-component phases) in the asymmetric unit (Z0 = 1). It has been reported, that Z0 > 1 for around 8% of crystal structures (Steed, 2003). There have been a number of studies dealing with high-Z0 structures (Steed, 2003; Steed & Steed, 2015; Desiraju, 2007; Brock, 2016) and one of the conclusions is that sometimes such structures must be described as modulated, as considerable pseudo-symmetry can be identified
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