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

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.