The crystal structure of NaY was re-determined in space group Fd (3) over barm from 87 unique electron diffraction amplitudes obtained at 1250 kV by A. Carlsson, et al. (Chem. Eur. J. 5 (1999) 244), where a = 24.7 angstrom. The determination, based on maximum entropy and likelihood (computer program MICE), leads to a clearly resolved structure, in contrast to the use of crystallographic phases derived from the Fourier transforms of experimental high-resolution images cited in the above paper. Potential maps from a trial solution contain density sites that correspond closely to the known T-site locations of this FAU framework. Although only framework T-site positions and not linkage oxygens are observed in the map, they can be linked with theoretical oxygens. Subsequent distance least squares (DLS) refinement of the linked model converges to a complete framework structure very close to the one found in earlier X-ray diffraction studies. Contrasting to the earlier study, where no counterion positions were identified, two possible Na positions were clearly visible in the direct phasing map. One of these corresponds to a site postulated in previous studies. The other is near a site proposed in a separate electron microscopic/electron diffraction study of Na,FeY. Least squares refinement verifies the former position while eliminating the latter. On the other hand, a separate direct analysis of a dataset from the Y zeolite containing both Na and Fe (Carlsson et al., loc. cit.) was not successful, owing to the smaller number of recorded amplitudes.

Intermolecular interactions between 2-amino-4-methylpyrimidine and 2-methylbenzoic acid in the crystalline solid state, used in a recent blind test of crystal structure prediction, are classified using cluster analysis and multivariate statistics. The analysis is repeated on crystal structures containing the 2-aminopyrimidine group and carboxylate group interactions. The potential of the method as an aid to crystal structure prediction is discussed.

Fifteen years ago, a very important paper, "Double conical beam-rocking system for measurement of integrated electron diffraction intensities", was published by Roger Vincent and Paul Midgley (Ultramicroscopy 53 (1993) [271][272][273][274][275][276][277][278][279][280][281][282], representing the synthesis of two dissenting viewpoints on the prospects of quantitative electron crystallography.An original thesis by Russian workers, based on oblique texture electron diffraction intensities collected from large illuminated sample areas with an electron diffraction camera, was that angular averaging over many crystal orientations would average out many dynamical diffraction effects.The antithesis, expressed by many workers in the West and based on observed electron diffraction patterns from micron to nanometer diameters, was that all such intensity data were strongly dynamical in nature so that no structural information could be retrieved from recorded intensities.In accord with J. M. Cowley's sympathetic analysis of the early Russian work (Proc.Mater.Sci. 13 (1967) 267-321), agreeing that orientational averaging might indeed minimize non-systematic dynamical interactions, Vincent and Midgley constructed an apparatus that permitted true integrated electron diffraction intensities to be recorded while preserving single crystal sampling, eliminating the overlap problems inherent in texture diffraction patterns.In later papers they revealed how useful structural information could be obtained by electron diffraction from inorganic materials.The Vincent-Midgley experiments in precession electron diffraction encouraged further work with this new method of collecting diffraction intensities, leading to a number of inorganic crystal structures determined by electron crystallography.Because of light atom content of such materials, the strength of electron crystallography was once felt to favor the analysis of organic and biological materials.Nowadays the new precession technique has shifted the emphasis of electron crystallographic analyses to inorganic areas.A commercial apparatus that is conveniently fitted to any modern electron microscope has also been marketed.In this special issue "Precession Electron Crystallography" of Zeitschrift fu ¨r Kristallographie, the precession technique, including the possible benefits indicated by early oblique texture electron diffraction experiments is discussed, using derived crystal structures to demonstrate its utility.Equally important, some of the pitfalls of the technique are also reviewed -most importantly, that not all dynamical diffraction is eliminated by this technique.Other uses of the technique besides crystal structure analysis are also introduced.The papers are especially wide ranging and demonstrate the broad applicability of the precession method to structural science:Theoretical aspects of the method are discussed by Sinkler and Marks showing that the precession method reduces the oscillatory behaviour of electron diffraction intensities as a function of thickness, and a reduced sensitivity to structure factor phases.Looking at structural aspects of the method, the structure of an intermediate form of tin oxide is investigated by White et al. using the precession method.The results support a revised version of a layered, vacancy-ordered structure for Sn 3 O 4 proposed in the existing literature.In contrast, Abrahams looks at protein crystallography in the electron beam to obtain phase information in a spiral confinement procedure that allows the use of the standard deviations of the intensity measurements Other aspects of electron crystallography are explored in two further structural papers: Sun et al. solve the structure of the complex zeolite IM-5 using selected area electron diffraction, reconstruction of high resolution transmission electron microscopy and distance least squares refinement.This is a large structure for electron diffraction with 24 unique Si positions.In contrast, Dorset re-visits pioneering Russian texture diffraction amplitudes and the diketopiperazine molecule solved and refined with new techniques and compared with the X-ray single crystal structure.

PolySNAP3 is a computer program for the classification of powder diffraction, spectroscopic and numerical data either separately or combined. A correlation matrix is generated by matching full data profiles; for numerical data the standard Euclidean distance is calculated. The matrices are combined by the INDSCAL method [Carroll & Chang (1970). Psychometria , 35 , 283–319] to give either a single interpretation of the data or combinations of any of the data types. Cluster analysis, multivariate data analysis and extensive data visualization routines are used to automatically classify the patterns into groups, validate the classification, and thus identify polymorphs, mixtures and salts.

The dSNAP computer program has been used to classify searches of the Cambridge Structural Database for two ligands: -O-CH(2)-CH(2)-O- and N(CH(2)CH(2)O-)(3) commonly found in metal-organic systems. The clustering method used is based on total geometries (i.e. all the lengths and angles involving all the atoms in the search fragment, whether bonded or not) and proved capable of distinguishing in a wholly automatic, objective way between different types of metal complex purely on the basis of the geometry of the ligand and the relative positions of the O atoms to the metals.

In high-throughput crystallography it is possible to accumulate large numbers of powder diffraction patterns on a series of related compounds, often polymorphs, salts or co-crystals. In previous papers [Gilmore, Barr & Paisley (2004). J. Appl. Cryst. 37 , 231–242; Barr, Dong & Gilmore (2004). J. Appl. Cryst. 37 , 243–252] it has been shown how such data can be analysed by generating an ( n × n ) correlation matrix, ρ , by correlating n full powder diffraction patterns, point by point. The ρ matrix is used as a source of dendrograms and metric multidimensional plots in three or more dimensions which classify the patterns into sets related by similarity. In this paper, it is shown how Raman spectroscopy data can be used by themselves or as an adjunct to powder diffraction data by combining the two techniques using the individual differences scaling method (INDSCAL) of Carroll & Chang [ Psychometria , (1970), 35 , 283–319]. The method is very robust, and can be extended to other forms of spectroscopy. It is available as an option in the commercial PolySNAP3 computer program.

Recently we have performed a systematic quantitative analysis of crystal structure distortion for ~1300 ABX3 perovskites in terms of Ato B-site polyhedra volume ratios VA/VB [1].The analysis identified a number of compositions close to the boundary of perovskite type stability which we have studied experimentally by in situ highpressure synchrotron X-ray powder diffraction.Here we will present the results of these experiments for several materials studied under pressure for the first time and will discuss our theoretical and experimental findings focusing on the following aspects of perovskite (pv) and post-perovskite CaIrO3 (ppv) structure types: (1) interplay between geometry and symmetry in distorted perovskites (is there any intermediate phase between pv and ppv?); (2) topological and geometrical constraints for ABX3 stoichiometry (what might be the structure of hypothetical structure types denser than ppv?); and (3) the effect of vacancies in ABX3 and pressure-induced amorphization as an alternative to pv-ppv transition.

ITQ-26 was synthesized via the fluoride procedure using 1,3-bis-(triethylphosphoniummethyl)-benzene as the structure-directing agent. The unit cell and space group were initially determined from electron diffraction experiments on individual tilted microcrystals, using material that had been sectioned by ultramicrotomy. The material crystallizes in space group I4/mmm, where after refining against synchrotron powder data (lambda = 0.8714 angstrom), a = 26.7769(8) and c = 13.2505(5) angstrom. Integrated electron diffractionintensities (hk0 + 0kl) were assigned phases with the program MICE to yield electrostatic potential maps with the first informative view of the microporou's framework. As a constraint for subsequent phasing trials of the powder data with FOCUS, one useful solution was found after 500 000 trials, conforming to the electron crystallographic determination. The final model, refined by Rietveld methods, comprises 7 unique T-sites forming a framework with a straight 12-MR channel along [001]. Two other 12-MR channels are tilted with respect to this one. The T-site density is 14.3 T/1000 A(3).

A density-building function is used to solve the crystal structures of zeolites from electron diffraction data using both two- and three-dimensional data sets. The observed data are normalized to give unitary structure factors |U(h)|(obs). An origin is defined using one to three reflections and a corresponding maximum-entropy map, q(ME)(x), is calculated in which the constraints are the amplitudes and phases of the origin-defining reflections. Eight strong reflections are then given permuted phases and each phase combination is used to compute P(deltaq) = integral(V)deltaq(x)(2)/q(ME)(x)dx, where deltaq(x) is the Fourier transform of |U(h)|(obs)exp(i\phi_(perm)h - |U(h)|(ME)exp(i\phi_(ME)h), phi_(perm)h is the permuted phase for reflection h and phi_(ME)h is the phase angle for reflection h predicted from the Fourier transform of q(ME)(x). The 64 phase sets with minimum values of P(deltaq) are subjected to entropy maximization and, following this procedure, those with the five highest log-likelihood gains are examined. Sometimes auxiliary potential histogram information is also used. The method worked routinely with seven zeolite structures of varying complexity and data quality, but failed with an eighth structure.

The maximum-entropy and likelihood method for solving zeolite crystal structures from electron diffraction data is modified to use potential-map-density histograms as an additional figure of merit. The experimental histogram is compared to an idealized one (based on known zeolite structures) using Pearson and Spearman correlation coefficients. These supplement the use of log-likelihood estimates as figures of merit to select the optimal solution from a collection of phase sets. The method has been applied with success to seven zeolite and one inorganic crystal structures that have varying associated data quality. The technique works easily even with two-dimensional data sets of less than 50 unique diffraction data and a resolution of less than 2 A. The method is very fast, and the computer time needed on a modest PC was never more than a few minutes.

The debate about the definition of the term co-crystal is a distraction from the quality of molecular solidstate science being published.

A method of analyzing mixtures of APIs and excipients using X-ray powder diffraction is described. It uses a simple algorithm based on linear regression in which the pure component phases are fitted to the mixture pattern using linear least squares. Unlike many methods that use only the peaks in the powder pattern, this technique uses all the measured data points in the 2θ scan with minimal data processing. In practice, using 33 different samples on three diffractometers, the method can be shown to work well for mixtures with up to three components, giving mean errors between 1.7% and 3.9% for two-phase mixtures, and 4.0% and 8.6% for three-phase mixtures. These results compare favorably to those given by traditional Rietveld refinement. It is also shown that the Bruker GADDS system, which is designed for high throughput crystallization experiments, is capable of giving results of comparable accuracy to those derived from traditional, single sample diffractometers. It is possible to identify those mixtures for which one or more pure phase X-ray powder patterns are not available with a detection limit around 10%. The techniques are implemented in the PolySNAP computer program. The method requires very little computer time or user interaction.

The prospect for improving the success of ab initio zeolite structure investigations with electron diffraction data is evaluated. First of all, the quality of intensities obtained by precession electron diffraction at small hollow cone illumination angles is evaluated for seven representative materials: ITQ-1, ITQ-7, ITQ-29, ZSM-5, ZSM-10, mordenite, and MCM-68. It is clear that, for most examples, an appreciable fraction of a secondary scattering perturbation is removed by precession at small angles. In one case, ZSM-10, it can also be argued that precession diffraction produces a dramatically improved 'kinematical' data set. There seems to no real support for application of a Lorentz correction to these data and there is no reason to expect for any of these samples that a two-beam dynamical scattering relationship between structure factor amplitude and observed intensity should be valid. Removal of secondary scattering by the precession mode appears to facilitate ab initio structure analysis. Most zeolite structures investigated could be solved by maximum entropy and likelihood phasing via error-correcting codes when precession data were used. Examples include the projected structure of mordenite that could not be determined from selected area data alone. One anomaly is the case of ZSM-5, where the best structure determination in projection is made from selected area diffraction data. In a control study, the zonal structure of SSZ-48 could be determined from selected area diffraction data by either maximum entropy and likelihood or traditional direct methods. While the maximum entropy and likelihood approach enjoys some advantages over traditional direct methods (non-dependence on predicted phase invariant sums), some effort must be made to improve the figures of merit used to identify potential structure solutions.

Cluster analysis is shown to be an effective method to analyse and classify metal coordination geometry in a very large number of four-coordinate bis -salicylaldimato (or bis- β-iminoketonate) transition-metal complexes available in the Cambridge Structural Database. The methods described require no prior knowledge of chemistry to be input; retrieved structures are automatically clustered into groups based purely on the geometric similarity of the fragments and these groupings can then be interpreted by the structural chemist.

Clustering and multivariate analysis is used to analyse all the intermolecular interactions between carboxylic acids and secondary amides from structures mined from the Cambridge Structural Database.

The efficacy of direct methods for solving the crystal structures of zeolites from electron diffraction data is evaluated for a series of related materials, i.e. MCM-22, MCM-49 and ITQ-1. First, it is established by tilting experiments that all materials share the same MWW framework. The calcined product of a delaminated MCM-22 precursor, ITQ-2, also shares this framework structure within the limited number of stacked unit cells. For all materials, the underlying space group is P6/mmm where a approximately 14.21, c approximately 24.94 A. Traditional direct methods are useful for determining the projected structure down the hexagonal axis but are not very effective for finding the three-dimensional structure. On the other hand, maximum-entropy and likelihood approaches are effective for determining either 2D projections or 3D frameworks. The major restriction to 3D determinations by direct methods is the limited goniometric tilt range of the electron microscope, hence the ;missing cone' of information. Potential maps from the most accurate phase sets are, therefore, observed as continuous density envelopes to the true structure. Some improvement is found when the Sayre equation predicts missing amplitudes and phases but it is clear that better specimen preparation methods are required to include projections containing the c( *) axis of the reciprocal lattice.

This discussion of powder protein powder diffraction looks at what is currently achieved with small molecule powder data, and low resolution single crystal protein crystallography and asks what techniques from these areas can be translated into the world of protein powders: 1. Qualitative PXRD: Pattern matching can we classify and match patterns using the full pattern profile and not just the peaks as in the SNAP-1D [1] and PolySNAP [2] computer software, and can this information be used as an aid to crystallization? 2. Quantitative PXRD: Can we identify components in powders in a quantitative mode using full powder profiles as used in the SNAP1D/PolySNAP software? 3. Unit Cells with protein PXRD: Can we index poor quality patterns? Can using the full profile help? What about brute force methods using grid computing techniques? 4. Single crystal low resolution protein diffraction can give the molecular envelope; can this be achieved with powder data? All these issues will be discussed with examples where possible.