Using a structure envelope to facilitate structure solution from powder diffraction data

Abstract

Given just a few strong low-index reflections, a periodic nodal surface (PNS), which divides the unit cell into regions of high and low electron density, can be generated. Fourteen known zeolite structures were examined to verify the validity of the procedure developed and in all cases the framework atoms were found to lie on just one side of the calculated curved surface. In other words, the surface defines a structure envelope. The same approach was applied to a few ionic and organic structures and was found to be equally valid. Since these reflections, with large d spacings, are precisely the ones that are least likely to be involved in overlap in a powder diffraction pattern, such a PNS can also be calculated using powder data. The resulting restriction in the region of the asymmetric unit in which atoms are likely to be found has immediate implications for any of the direct-space methods of structure determination from powder data. The use of this structure envelope as a mask in a straightforward grid search procedure reduced the computer time required to solve several framework structures by as much as two orders of magnitude.

Zeolite structure determination from powder diffraction data: applications of theFOCUSmethod

“…Nonetheless, given enough computer time and somè thinking', this structure could have been solved eventually using this method. For such borderline cases where computing time becomes a limitation, the generation of a structure envelope (Brenner et al, 1997) to restrict the regions of the asymmetric unit in which the structure is to be sought might accelerate structure solution.…”

Electron crystallography as a complement to X-ray powder diffraction techniques

“…For this purpose, the concept of a structure envelope was introduced [20]. The main difference between this structure envelope and the molecular envelope that is used in protein crystallography is that the former does not necessarily have a closed form.…”

Combining Structure Modeling and Electron Microscopy to Determine Complex Zeolite Framework Structures

“…For example, a structure envelope, which can be generated by a Fourier transform from a small number of strong reflections with low indices, can be used. [24] Such a structure envelope can define the pore system of a zeolite in real space, and has been shown to facilitate zeolite structure solution. [25] For the solutions of the highly complex framework structures of IM-5 and TNU-9, only the space group, the cell parameters, the number of T atoms, and one or two HRTEM images showing the pores were required.…”