Evaluating structures derived from X-ray powder diffraction data using entropy

So far, in the field of X-ray powder diffraction, the maximum entropy method (MEM) has been used to (i) solve the phase problem, (ii) estimate the intensities of overlapping reflections, (iii) predict the intensities of missing reflections, and (iv) improve electron density maps generated during Rietveld refinement. We found a new application for MEM in a recent study, in which the powder charge flipping algorithm [1] in Superflip was applied to all-light-atom structures [2]. It proved to be difficult to identify the few fully interpretable maps within in the 200 generated in a typical Superflip job using the standard evaluation criteria. In 1992, Sato reported that entropy could be used as a solution evaluation criterion if the basis set is large, the phases are close to the correct ones, and the structure contains a small molecule [3]. Reasoning that these requirements would be fulfilled by the better Superflip solutions, all solutions were input to the MEM program MICE to calculate the corresponding ME maps and their entropies. Tests performed on several datasets showed no direct correlation between entropy and the solution quality. However, it was noted that a certain number of solutions show entropy values significantly lower than the others. This group usually contained one fully interpretable map. Refinement of the approach led to a relatively straightforward method for recognizing the better solutions. Furthermore, phase recycling based on this approach proved to be useful. As a result, guidelines for solving structures of different levels of complexity using the pCF algorithm could be devised.

Why was the structure of the niobium silicate AM-11 so difficult to solve?

The synthesis of the polycrystalline niobium silicate catalyst AM-11 was first reported in 1998 [1], but its structure proved to be elusive. In 2007 we received two samples from the Aveiro group. At the time, we were looking for a material suitable for the application of the texture method of structure solution, and AM-11 seemed to be ideal for this purpose. One of the samples had needle and the other platelet morphology, and textured samples could be prepared in both cases. The conventional powder diffraction pattern could be indexed on a hexagonal, an orthorhombic or a monoclinic unit cell, so this was the first issue to be resolved. The texture measurements quickly revealed that the crystal system was orthorhombic, but the structure resisted solution. We then tried applying the precession electron diffraction technique in combination with high-resolution powder diffraction data, but beyond confirming the orthorhombic symmetry, these data did not help us to solve the structure. Another attempt was made with a new sample and an improved texture setup, but to no avail. Rotation electron diffraction data and high-resolution transmission electron microscopy images showed that some disorder was present and helped to define the space group, but the structure remained a mystery. The powder charge-flipping routine in Superflip [2], yielded tantalizingly clear electron density maps, but they could not be interpreted sensibly. The unit cell parameters were seen to be related to those of the titanium silicate zorite [3] (one axis doubled in AM-11), so the problem was taken up once again last year. By starting with a simplified zorite framework structure with Nb in place of Ti, and performing what amounts to manual Fourier recycling, the surprisingly simple structure (1Nb, 3 Si, 9 O), which is significantly different from zorite, finally revealed itself. There is some stacking disorder, but the structure is otherwise innocuous. What made it so difficult to solve?

When two bad data sets are better than one

High-resolution synchrotron X-ray powder diffraction (SXPD) data alone are sometimes not enough to solve the structure of a complex polycrystalline material. Such was the case for the high-silica zeolites SSZ-61 and SSZ-87, where combining data from different sources, in particular XPD and electron microscopy, was vital to success. For SSZ-61, the SXPD data feature broad peaks and a resolution of ca. 1.2 Å. Although the pattern could be indexed, structure determination failed both with the charge flipping routine in SUPERFLIP [1] and with the zeolite-specific program FOCUS [2]. The unit cell parameters and HRTEM images indicated a relationship with ZSM-12 (MTW) and SSZ-59 (SFN), so several models derived from these two frameworks were built. Eventually, after considering Si-29 MAS NMR data and the size of the organic structure directing agent (SDA), a framework model that fits all the data emerged. To complete the structure, the SDA was included as a rigid-body, and its location and orientation optimized using simulated annealing. Subsequent Rietveld refinement confirmed the structure. In contrast to SSZ-61, the SXPD pattern for SSZ-87 was quite good, and it could be indexed with a C-centered cell. However, structure solution failed, probably because of the very high degree of reflection overlap (93%). Therefore, rotation electron diffraction (RED) data [3] were collected, but they proved to be of low resolution and poor quality. Only 2 of the 7 data sets could be indexed, and these had different unit cells. Neither fit the XPD pattern directly. The problem was traced to large errors in the RED cell parameters, and eventually one RED cell could be transformed to one similar to the SXPD cell. The RED data with this cell was only 15% complete up to a resolution of 1.22 Å. Even so, the structure could be solved using a recently developed version of FOCUS that works with ED data. The SDA was found as for SSZ-61, and the structure then confirmed by Rietveld refinement.

Serial snapshot crystallography with a non-monochromatic microbeam

X-ray free-electron laser (XFEL) sources create X-ray pulses of unprecedented brilliance and open up new possibilities for the structural characterization of crystalline materials. By exposing a small crystallite (100nm-10μm) to a single ultrafast pulse, a diffraction pattern can be obtained before the crystal is damaged. If such single-pulse diffraction patterns, collected sequentially on many randomly oriented crystallites, are combined, it is possible to determine the structure of the material accurately [1]. One of the drawbacks of this approach is that only a single position of the Ewald sphere is accessed in each pattern, so, because reflections have a finite width, the diffraction condition is not satisfied completely for any of the reflections recorded. The new XFEL source that is being developed in Switzerland (SwissFEL) will provide a broad-bandpass mode with an energy bandwidth of about 4% [2]. By using the full energy range of the SwissFEL beam, a new option for structural studies of crystalline materials becomes possible. In a recent study based on simulated data, we showed that a diffraction experiment with stationary crystallites in such an `extra pink' beam not only increases the number of reflection intensities that can be collected in a single shot, but also overcome the problem of `partial reflection' measurement [3]. To test the viability of the data processing with experimental data, attempts to simulate this 4% bandpass have been carried out on SNBL at ESRF and on the microXAS beamline at SLS. On SNBL, a single crystal was rotated over 360° and a continuous scan of the monochromator over the 4% energy range was performed every 1°. At SLS, a mirror was used to cut off the higher energies of the undulator beam and the energy threshold of a Pilatus detector to eliminate the lower ones. With this setup, a series of randomly oriented crystallites were measured. A comparison of the analysis of these datasets will be presented.