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Algorithms

A set of algorithms was devised. They all support arbitrary space groups and unit cell sizes. The main limitation is overlap of the diffraction spots. The algorithms can be divided into two groups:

1. Multi-grain crystallography: Here the aim was to solve and refine crystal structures based on polycrystalline diffraction patterns acquired with a conventional set-up, comprising a monochromatic beam, a fully illuminated sample and a large-area 2D detector.  This has required new algorithms for finding peaks, harvesting the intensities and for indexing. Once these have generated a list of grains with associated reflections, then - for each grain - crystal solution & refinement can be performed with state-of-the-art single crystal programs such as JANA, ShellX and MOSFLM.  Three approaches have been explored:

·  Approach I (little overlap): Here the overlap is neglected. For this case, a comprehensive data analysis chain was completed including modules for peaksearching and calibration of experimental geometry (ImageD11), indexing  (GrainSpotter), integration (Fabric) and filtering (FitAllB). Simulations as well as experiments demonstrate that in best case hundreds of grains may be characterised simultaneously with resulting structural parameters of a quality comparable to single crystal diffraction studies. First version of programs required the unit cell to be known a priori, e.g. from powder diffraction – this restriction is lifted in later versions.

·  Approach II (medium overlap): Here the approach is to use a set of non-overlapping low-index reference reflections to calculate peak profiles for all reflections. Once peak profiles are known it is possible to divide integrated intensities of overlapping spots into contributions or to perform constrained refinements to all grains simultaneously.  The mosaic spread is assumed to plays a key part in the defining the peak-profiles. For each grain, the mosaic spread can be determined directly if a grain orientation distribution function (ODF) is known. In collaboration with P.C. Hansen from DTU, Denmark the relevant algorithm for reconstructing ODFs for each grain has been developed and successfully tested on simulated and real data.

·  Approach III (high overlap): Here the approach is to consider the entire sample as one single crystal with a very unusual mosaic spread. This mosaic spread can be determined directly, if an ODF for the complete sample – the sum of all the grain ODFs so to speak – can be determined with the relevant very high angular resolution. To enable this, a new mathematical representation of orientations has been conceived (the first in more than 100 years). With this representation, uniquely the reconstruction of the sample ODF became possible. The mathematics underlying the novel reconstruction technique has been published. Work on using Approach III for analysis of real data is still ongoing.

2. Grain mapping: The aim is to reconstruct 3D grain maps from a set of diffraction images acquired with one or more high-resolution area detectors placed in close proximity of the sample.

Highlights include:  

-          A program for mapping undeformed specimens in 3D: the Grainsweeper. This has been applied to several real data sets (published work)

-          New mapping programs based on the use of combined diffraction and tomography information, so-called Diffraction Contrast Tomography (published).

-          Two algorithms for 3D orientation mapping of moderately deformed materials. The algorithms have been tested on simulated data and were shown to provide near perfect reconstructions (published). First experimental maps have been made, the results of which are currently in the process of being written up for publication.

Implementation of algorithms

The completed algorithms mentioned above have all been translated to modular programs, using C or Python. The programs are stand-alone, fully portable, fully documented and publicly available as executables (and source code) on the homepage. Furthermore, with exclusion of Approach III they are all implemented within FABLE. FABLE is an integrated framework for fast on-line analysis and visualization for TotalCryst data, which comes complete with a powerful Graphical User Interface. Two versions of the FABLE program suite have been released.

The work on developing and testing code for FABLE has grown to include groups outside TotalCryst, most notably from APS, Argonne Nat. Lab. in Chicago. The work on generalizing and maintaining the code will continue after the TotalCryst funding period.

Hardware

The instrumental requirements for multigrain crystallography are modest – as such this type of experiments have already been performed at 6 different synchrotron beamlines in Europe as well as on laboratory based x-ray equipment. In contrast, the program on grain mapping has required substantial R&D – in particular to fulfill the objective of enabling the use of the technique also for grains smaller than 1 µm. The resulting hardware has been commissioned at beamline ID11, ESRF.

A main achievement has been the commissioning of a battery of new focusing optics elements for high energetic (30-100 keV) x-rays. As an example, a set of silicon compound refractive lenses were shown to provide a record-breaking stable 50 keV X-ray beam with a size of ~250 nm. Using such optics dynamic studies of hundreds of illuminated grains with an average size as small as 100 nm have been demonstrated.

Another main focus has been detector development.  Highlights include:

·         A structured scintillator – a new type of scintillator for grain mapping and tomography with an improved efficiency. In collaboration with KTH, Sweden, scintillators were developed with high aspect ratios and pitches in the range 1-4 µm. The superior quality of these screens was demonstrated at tests at ESRF.

·         A 3D X-ray detector – a first in the world, with three (semi-transparent) screens mounted behind each other. This was commissioned in May 2009 with conventional screens, and is now used routinely. In 2010 the screens will be replaced by the structured scintillator screens mentioned above. This detector has and will vastly improve options for time-resolution and for mapping poly-crystals, which are deformed.

Applications to pharmaceutics, structural biology and photochemistry

To illustrate the broad range of potential disciplines that can benefit from TotalCryst, three disciplines were singled out. With a focus on multi-grain crystallography, feasibility was proven by a combination of simulations and actual experiments. In addition, first applications were pursued. (Most of this work is currently in the process of being written up for publication.)

Pharmaceutics:  The main object was to introduce a “third road in small molecule crystallography”, in order to enable the identification and structural characterization of numerous structures, which cannot be characterized today as single crystals are not available. This could accelerate the process of structure determination, a bottleneck in the process of registration of new drugs. Furthermore, it provides new options for characterization of polymorphism.

Extensive simulations showed that the approach is viable even when the number of grains become in excess of 100.  A first demonstration on the simple compound Cu(C2O2H3)2.H2O was reported in Vaughan et al. Z. Kristall. (2004) 219, 813.  Further demonstration experiments were attempted on several unknown compounds delivered by the industrial partner, Novo Nordisk. Among these were two polymorphs of 6-chloro-3-alkylamino-4H-thieno[3,2-e]-1,2,4-thiadiazine1,1 dioxide. The structure of Polymorph A (1273 ų) is known while that of Polymorph B (5834 ų) is unknown. The experimental data was associated with several problems, which is representative of “real data” such as irradiation damage, large mosaic spread and parts of the sample rotating out of the beam. Nevertheless, grains of both polymorphs could be indexed.  Unfortunately the problems finding samples with a good quality crystals has meant that the despite the success indexing the data, it proved difficult to obtain diffraction data of the quality needed for structure determination.  

Structural biology: Current commonly available software in macromolecular crystallography (MX) cannot be used to index diffraction patterns of more than one, or at most two, crystals, which have been simultaneously irradiated by the X-ray beam. There are two compelling reasons why TotalCryst will be a significant development for MX. The first is that during X-ray exposure the crystals are radiation damaged even when held at 100K, and so being able to combine sections of the first part of the data collected from an ensemble of crystals will allow us the to find the structure before too much damage has been inflicted, and with the crystals at similar stages in their intensity decay. Thus more reliable biological results can be extracted, especially if the mechanism involves particularly radiation sensitive amino acids. The second reason is that for membrane proteins and large protein-protein complexes, it can be very challenging to grow large single crystals, and the TotalCryst methodology may allow an ensemble of micro crystals to be utilized for structure solution. 

Experiments were performed on a series of proteins including lysozyme (228306 ų) and two forms of insulin (472729 and 185374 Å3).  We found that single crystal quality refinements in all cases were possible for at least 7 simultaneously illuminated crystals. Simulations suggest that the limit is substantially higher. Hence, the issue of overlapping reflections, originally feared to be a major stumbling block for this method, has not emerged as a bottleneck.  

Photochemistry: TotalCryst enables, for the first time, characterization of the multi-scale dynamics of the individual embedded grains. This makes it very attractive for a wide range of time-resolved work. This includes conventional dynamic studies with time constants of the order of seconds as well as investigations in the femto-second regime based on a laser pump/X-ray probe scheme. In particular, we note that the latter type of experiments today tend to be severely limited by long data collection procedures. This problem can be substantially reduced by characterizing (artificially made) polycrystals comprising say 10 grains each. Another intrinsic problem of the pump-probe experiments is the 3 orders of magnitude difference between the penetration depth of the optical pump and the X-ray probe. As a result, the structural response will often be very dependent on both the size and position (depth) of the grains. Measuring the average properties will therefore give rise to problems with interpretation of the results. In contrast, TotalCryst differentiates between grains, and provides information on their position, size and shape. 

The systems studied were TTFCA: tetrathiafulvalene-p-chloroaniline (784 ų) and BBCP: 2-benzyl-5-benzylidene-cyclopentanone (2946 ų).  The multigrain approach was found to lead to a remarkable improved structure determination during both time-resolved and static photo-crystallographic experiments. It was demonstrated that the reduction of the size of investigated materials up to grain sizes of 1 to 5 mm increases the overall transformation rate of the crystallites during the photoreaction. The increased transformation rate together with the improved data statistics leads to a more precise determination of the photo-created transient structures without loosing spatial resolution (as compared to a powder diffraction approach).

First diffraction experiments on periodic assemblies and structures were performed at the worlds first Free Electron Laser in the soft x-ray energy regime FLASH / DESY. They reveal that the methodology developed in TotalCryst can also be applied to the determination of nanostructures with FEL radiation. In future, this route will be followed by partners to reach the goal of creating a molecular movie of time-evolving structures on the femto-second scale.