Several methods for absolute structure refinement were tested using single‐crystal X‐ray diffraction data collected using Cu Kα radiation for 23 crystals with no element heavier than oxygen: conventional refinement using an inversion twin model, estimation using intensity quotients in SHELXL2012, estimation using Bayesian methods in PLATON, estimation using restraints consisting of numerical intensity differences in CRYSTALS and estimation using differences and quotients in TOPAS‐Academic where both quantities were coded in terms of other structural parameters and implemented as restraints. The conventional refinement approach yielded accurate values of the Flack parameter, but with standard uncertainties ranging from 0.15 to 0.77. The other methods also yielded accurate values of the Flack parameter, but with much higher precision. Absolute structure was established in all cases, even for a hydrocarbon. The procedures in which restraints are coded explicitly in terms of other structural parameters enable the Flack parameter to correlate with these other parameters, so that it is determined along with those parameters during refinement.
C‐(A)‐S‐H(I) is a calcium silicate hydrate that is studied extensively as a model for the main binding phase in concrete. It is a structurally imperfect form of 14 Å tobermorite that has variable composition and length of (alumino)silicate anions. New structural–chemical formulae are presented for single‐ and double‐chain tobermorite‐based phases and equations are provided that can be used to calculate a number of useful quantities from 29Si NMR data. It is shown that there are no interlayer calcium ions when the silicate chains are of infinite length and that one is added for each tetrahedral `bridging' site that is vacant. Preparations that have Ca/Si greater than about 1.4 include an intermixed Ca‐rich phase. It is not possible to generate a structural model for a dimer that is crystal‐chemically consistent with known calcium silicate hydrates if the starting structure is an orthotobermorite, i.e. of the type that has been used in all previous studies. Crystal‐chemically plausible models are developed that are based instead on clinotobermorite. A number of models that represent different mean chain lengths are developed using crystal‐chemical and geometrical reasoning. The models account for experimental observations, including variations in Ca/Si, H2O/Si, (alumino)silicate anion structure and layer spacing.
We report on the organization and outcome of the fourth blind test of crystal structure prediction, an international collaborative project organized to evaluate the present state in computational methods of predicting the crystal structures of small organic molecules. There were 14 research groups which took part, using a variety of methods to generate and rank the most likely crystal structures for four target systems: three single‐component crystal structures and a 1:1 cocrystal. Participants were challenged to predict the crystal structures of the four systems, given only their molecular diagrams, while the recently determined but as‐yet unpublished crystal structures were withheld by an independent referee. Three predictions were allowed for each system. The results demonstrate a dramatic improvement in rates of success over previous blind tests; in total, there were 13 successful predictions and, for each of the four targets, at least two groups correctly predicted the observed crystal structure. The successes include one participating group who correctly predicted all four crystal structures as their first ranked choice, albeit at a considerable computational expense. The results reflect important improvements in modelling methods and suggest that, at least for the small and fairly rigid types of molecules included in this blind test, such calculations can be constructively applied to help understand crystallization and polymorphism of organic molecules.
The charge-flipping algorithm (CFA) is a member of the diverse family of dual-space iterative phasing algorithms. These algorithms use alternating modifications in direct and reciprocal space to find a solution to the phase problem. The current state-of-the-art CFA is reviewed and it is put in the context of related dual-space algorithms with relevance for crystallography. The CFA has found applications in many crystallographic problems. The principal applications in various fields are described with sections devoted to routine structure solution, the solution of complex structures from powder diffraction data, the solution of incommensurately modulated crystals and quasicrystals, macromolecular crystallography and single-particle imaging.
Invarioms are aspherical atomic scattering factors that enable structure refinement of more accurate and more precise geometries than refinements with the conventional independent atom model (IAM). The use of single-crystal X-ray diffraction data of a resolution better than sin/ = 0.6 angstrom 1 (or d = 0.83 angstrom) is recommended. The invariom scattering-factor database contains transferable pseudoatom parameters of the HansenCoppens multipole model and associated local atomic coordinate systems. Parameters were derived from geometry optimizations of suitable model compounds, whose IUPAC names are also contained in the database. Correct scattering-factor assignment and orientation reproduces molecular electron density to a good approximation. Molecular properties can hence be derived directly from the electron-density model. Coverage of chemical environments in the invariom database has been extended from the original amino acids, proteins and nucleic acid structures to many other environments encountered in organic chemistry. With over 2750 entries it now covers a wide sample of general organic chemistry involving the elements H, C, N and O, and to a lesser extent F, Si, S, P and Cl. With respect to the earlier version of the database, the main modification concerns scattering-factor notation. Modifications improve ease of use and success rates of automatic geometry-based scattering-factor assignment, especially in condensed hetero-aromatic ring systems, making the approach well suited to replace the IAM for structures of organic molecules.
Metal–organic frameworks (MOFs) are a class of porous crystalline materials of modular design. One of the primary applications of these materials is in the adsorption and separation of gases, with potential benefits to the energy, transport and medical sectors. In situ crystallography of MOFs under gas atmospheres has enabled the behaviour of the frameworks under gas loading to be investigated and has established the precise location of adsorbed gas molecules in a significant number of MOFs. This article reviews progress in such crystallographic studies, which has taken place over the past decade, but has its origins in earlier studies of zeolites, clathrates etc. The review considers studies by single‐crystal or powder diffraction using either X‐rays or neutrons. Features of MOFs that strongly affect gas sorption behaviour are discussed in the context of in situ crystallographic studies, specifically framework flexibility, and the presence of (organic) functional groups and unsaturated (open) metal sites within pores that can form specific interactions with gas molecules.
X‐ray diffraction (XRD) patterns were calculated and compared to literature data with the aim of investigating the crystal structure of nanocrystalline calcium silicate hydrates (C‐S‐H), the main binding phase in hydrated Portland cement pastes. Published XRD patterns from C‐S‐H of Ca/Si ratios ranging from ∼ 0.6 to ∼ 1.7 are fully compatible with nanocrystalline and turbostratic tobermorite. Even at a ratio close or slightly higher than that of jennite (Ca/Si = 1.5) this latter mineral, which is required in some models to describe the structure of C‐S‐H, is not detected in the experimental XRD patterns. The 001 basal reflection from C‐S‐H, positioned at ∼ 13.5 Å when the C‐S‐H structural Ca/Si ratio is low (< 0.9), shifts towards smaller d values and sharpens with increasing Ca/Si ratio, to reach ∼ 11.2 Å when the Ca/Si ratio is higher than 1.5. Calculations indicate that the sharpening of the 001 reflection may be related to a crystallite size along c* (i.e. a mean number of stacked layers) increasing with the C‐S‐H Ca/Si ratio. Such an increase would contribute to the observed shift of the 001 reflection, but fails to quantitatively explain it. It is proposed that the observed shift could result from interstratification of at least two tobermorite‐like layers, one having a high and the other a low Ca/Si ratio with a basal spacing of 11.3 and 14 Å, respectively.
Tin selenide‐based functional materials are extensively studied in the field of optoelectronic, photovoltaic and thermoelectric devices. Specifically, SnSe has been reported to have an ultrahigh thermoelectric figure of merit of 2.6 ± 0.3 in the high‐temperature phase. Here we report the evolution of lattice constants, fractional coordinates, site occupancy factors and atomic displacement factors with temperature by means of high‐resolution synchrotron powder X‐ray diffraction measured from 100 to 855 K. The structure is shown to be cation defective with a Sn content of 0.982 (4). The anisotropy of the thermal parameters of Sn becomes more pronounced approaching the high‐temperature phase transition (∼ 810 K). Anharmonic Gram–Charlier parameters have been refined, but data from single‐crystal diffraction appear to be needed to firmly quantify anharmonic features. Based on modelling of the atomic displacement parameters the Debye temperature is found to be 175 (4) K. Conflicting reports concerning the different coordinate system settings in the low‐temperature and high‐temperature phases are discussed. It is also shown that the high‐temperature Cmcm phase is not pseudo‐tetragonal as commonly assumed. The crystal structure of SnSe is investigated through high‐resolution synchrotron powder X‐ray diffraction in the range 100–855 K. The temperature dependence of the lattice constants, fractional coordinates, site occupancy factors and atomic displacement parameters is studied.
Following the interest generated by two previous blind tests of crystal structure prediction (CSP1999 and CSP2001), a third such collaborative project (CSP2004) was hosted by the Cambridge Crystallographic Data Centre. A range of methodologies used in searching for and ranking the likelihood of predicted crystal structures is represented amongst the 18 participating research groups, although most are based on the global minimization of the lattice energy. Initially the participants were given molecular diagrams of three molecules and asked to submit three predictions for the most likely crystal structure of each. Unlike earlier blind tests, no restriction was placed on the possible space group of the target crystal structures. Furthermore, Z′ = 2 structures were allowed. Part‐way through the test, a partial structure report was discovered for one of the molecules, which could no longer be considered a blind test. Hence, a second molecule from the same category (small, rigid with common atom types) was offered to the participants as a replacement. Success rates within the three submitted predictions were lower than in the previous tests – there was only one successful prediction for any of the three `blind' molecules. For the `simplest' rigid molecule, this lack of success is partly due to the observed structure crystallizing with two molecules in the asymmetric unit. As in the 2001 blind test, there was no success in predicting the structure of the flexible molecule. The results highlight the necessity for better energy models, capable of simultaneously describing conformational and packing energies with high accuracy. There is also a need for improvements in search procedures for crystals with more than one independent molecule, as well as for molecules with conformational flexibility. These are necessary requirements for the prediction of possible thermodynamically favoured polymorphs. Which of these are actually realised is also influenced by as yet insufficiently understood processes of nucleation and crystal growth.
Full three‐dimensional diffuse scattering data have been recorded for both polymorphic forms [(I) and (II)] of aspirin and these data have been analysed using Monte Carlo computer modelling. The observed scattering in form (I) is well reproduced by a simple harmonic model of thermally induced displacements. The data for form (II) show, in addition to thermal diffuse scattering (TDS) similar to that in form (I), diffuse streaks originating from stacking fault‐like defects as well as other effects that can be attributed to strain induced by these defects. The present study has provided strong evidence that the aspirin form (II) structure is a true polymorph with a structure quite distinct from that of form (I). The diffuse scattering evidence presented shows that crystals of form (II) are essentially composed of large single domains of the form (II) lattice with a relatively small volume fraction of intrinsic planar defects or faults comprising misoriented bilayers of molecular dimers. There is evidence of some local aggregation of these defect bilayers to form small included regions of the form (I) structure. Evidence is also presented that shows that the strain effects arise from the mismatch of molecular packing between the defect region and the surrounding form (II) lattice. This occurs at the edges of the planar defects in the direction only.
Semiconducting indium sulfide (In2S3) has recently attracted considerable attention as a buffer material in the field of thin film photovoltaics. Compared with this growing interest, however, detailed characterizations of the crystal structure of this material are rather scarce and controversial. In order to close this gap, we have carried out a reinvestigation of the crystal structure of this material with an in situ X‐ray diffraction study as a function of temperature using monochromatic synchrotron radiation. For the purpose of this study, high quality polycrystalline In2S3 material with nominally stoichiometric composition was synthesized at high temperatures. We found three modifications of In2S3 in the temperature range between 300 and 1300 K, with structural phase transitions at temperatures of 717 K and above 1049 K. By Rietveld refinement we extracted the crystal structure data and the temperature coefficients of the lattice constants for all three phases, including a high‐temperature trigonal γ‐In2S3 modification. We report on the high‐resolution structure analysis of In2S3 powder with monochromatic synchrotron light in the temperature range between 300 and 1300 K. Three modifications could be identified with the two phase transitions taking place at 717 K and above 1049 K. Crystal structure parameters and their temperature dependence for all three phases were extracted from the diffraction data by Rietveld refinement.
Rietveld neutron powder profile analysis of the compound Na0.5Bi0.5TiO3 (NBT) is reported over the temperature range 5–873 K. The sequence of phase transitions from the high‐temperature prototypic cubic structure (above 813 K), to one of tetragonal (673–773 K) and then rhombohedral structures (5–528 K) has been established. Coexisting tetragonal/cubic (773–813 K) and rhombohedral/tetragonal (with an upper temperature limit of 145 K between 528 and 673 K) phases have also been observed. Refinements have revealed that the rhombohedral phase, space group R3c, with aH = 5.4887 (2), cH = 13.5048 (8) Å, V = 352.33 (3) Å3, Z = 6 and Dx = 5.99 Mg m−3, exhibits an antiphase, a−a−a− oxygen tilt system, ω = 8.24 (4)°, with parallel cation displacements at room temperature. The tetragonal phase, space group P4bm, with aT = 5.5179 (2), cT = 3.9073 (2) Å, V = 118.96 (1) Å3, Z = 2 and Dx = 5.91 Mg m−3, possesses an unusual combination of in‐phase, a0a0c+ oxygen octahedra tilts, ω = 3.06 (2)°, and antiparallel cation displacements along the polar axis. General trends of cation displacements and the various deviations of the octahedral network from the prototypic cubic perovskite structure have been established and their systematic behaviour with temperature is reported. An investigation of phase transition behaviour using second harmonic generation (SHG) to establish the centrosymmetric or non‐centrosymmetric nature of the various phases is also reported.
The structural chemistry of hybrid organic–inorganic lead iodide materials has become of increasing significance for energy applications since the discovery and development of perovskite solar cells based on methylammonium lead iodide. Seven new hybrid lead iodide compounds have been synthesized and structurally characterized using single‐crystal X‐ray diffraction. The lead iodide units in materials templated with bipyridyl, 1,2‐bis(4‐pyridyl)ethane, 1,2‐di(4‐pyridyl)ethylene and imidazole adopt one‐dimensional chain structures, while crystallization from solutions containing piperazinium cations generates a salt containing isolated [PbI6]4− octahedral anions. Templating with 4‐chlorobenzylammonium lead iodide adopts the well known two‐dimensional layered perovskite structure with vertex shared sheets of composition [PbI4]2− separated by double layers of organic cations. The relationships between the various structures determined, their compositions, stability and hydrogen bonding between the protonated amine and the iodide ions of the PbI6 octahedra are described.
In surficial environments, the fate of many elements is influenced by their interactions with the phyllomanganate vernadite, a nano‐sized and turbostratic variety of birnessite. To advance our understanding of the surface reactivity of vernadite as a function of pH, synthetic vernadite (δ‐MnO2) was equilibrated at pH ranging from 3 to 10 and characterized structurally using chemical methods, thermogravimetry and modelling of powder X‐ray diffraction (XRD) patterns. With decreasing pH, the number of vacant layer sites increases in the octahedral layers of δ‐MnO2 (from 0.14 per layer octahedron at pH 10 to 0.17 at pH 3), whereas the number of layer Mn3+ is, within errors, equal to 0.12 per layer octahedron over the whole pH range. Vacant layer sites are capped by interlayer Mn3+ sorbed as triple corner‐sharing surface complexes (TC sites). The increasing number of interlayer Mn3+ with decreasing pH (from 0.075 per layer octahedron at pH 10 to 0.175 at pH 3) results in the decrease of the average Mn oxidation degree (from 3.80 ± 0.01 at pH 10 to 3.70 ± 0.01 at pH 3) and in the lowering of the Na/Mn ratio (from 27.66 ± 0.20 at pH 10 to 6.99 ± 0.16 at pH 3). In addition, in‐plane unit‐cell parameters are negatively correlated to the number of interlayer Mn at TC sites and decrease with decreasing pH (from b = 2.842 Å at pH 10 to b = 2.834 Å at pH 3), layer symmetry being systematically hexagonal with a = b× 31/2. Finally, modelling of X‐ray diffraction (XRD) patterns indicates that crystallite size in the ab plane and along the c* axis decreases with decreasing pH, ranging respectively from 7 nm to 6 nm, and from 1.2 nm to 1.0 nm (pH 10 and 3, respectively). Following their characterization, dry samples were sealed in polystyrene vials, kept in the dark, and re‐analysed 4 and 8 years later. With ageing time and despite the dry state, layer Mn3+ extensively migrates to the interlayer most likely to minimize steric strains resulting from the Jahn–Teller distortion of Mn3+ octahedra. When the number of interlayer Mn3+ at TC sites resulting from this migration reaches the maximum value of ∼ 1/3 per layer octahedron, interlayer species from adjacent layers share their coordination sphere, resulting in cryptomelane‐like tunnel structure fragments (with a 2 × 2 tunnel size) with a significantly improved layer stacking order.
The lattice parameters of three perovskite‐related oxides have been measured with high precision at room temperature. An accuracy of the order of 10−5 has been achieved by applying a sophisticated high‐resolution X‐ray diffraction technique which is based on the modified Bond method. The results on cubic SrTiO3 [a = 3.905268 (98) Å], orthorhombic DyScO3 [a = 5.442417 (54), b = 5.719357 (52) and c = 7.904326 (98) Å], and orthorhombic NdGaO3 [a = 5.428410 (54), b = 5.498407 (55) and c = 7.708878 (95) Å] are discussed in view of possible systematic errors as well as non‐stoichiometry in the crystals.
The structure factors of diamond were determined by synchrotron radiation X‐ray powder diffraction at 800 K at sin gθ/λ ≤ 2.2 Å−1 reciprocal resolution. The structure factors were estimated using six powder profiles measured on beamline BL02B2 at SPring‐8 (Hyogo, Japan). A high reciprocal resolution at sin gθ/λ ≤ 2.2 Å−1 was required to reveal the temperature dependence of the charge density, due to the high Debye temperature of gθD = 1860 K of diamond. Wide 2gθ angle data with the highest counting statistics are crucial for accurate data analysis. The periodic noise of every six‐pixel step was observed in the highest counting statistics imaging plate (IP) data scanned by a BAS2500 IP scanner. It was found that the noise originated from the six‐sided polygonal mirror in the scanner. The intensity fluctuation at every six‐pixel step was also found in the Fourier series expansion of the powder profiles. The ratio of the maximum fluctuation was estimated as 0.4% by summing all six‐pixel step data. The powder profiles were corrected by multiplying the ratios. The intensity fluctuation in the background region was reduced to less than 50% of the uncorrected data. The weak 888 Bragg reflection, with an intensity of 0.005% of that of the 111 Bragg reflection at 800 K, was readily observed in the corrected data. Finally, the structure factors determined at 800 K were successfully applied to a charge‐density study by multipole modelling. The reliability factors and multipole parameters at 800 K are in agreement with those at 300 K. The differences in the charge density at the bond midpoint and ∇2ρ at the bond‐critical point were less than 1% and 2%, respectively. The structure factors of diamond at 800 K at sin gθ/λ ≤ 2.2 Å−1 were determined from multiple overlaid powder profiles. Data correction was essential to extract the Bragg intensities of the weak reflections. The quality of the final charge density determined at 800 K was nearly comparable with that of room‐temperature data.
Hydrochlorothiazide (HCT), C7H8ClN3O4S2, is a diuretic BCS (Biopharmaceutics Classification System) class IV drug which has primary and secondary sulfonamide groups. To modify the aqueous solubility of the drug, co‐crystals with biologically safe co‐formers were screened. Multi‐component molecular crystals of HCT were prepared with nicotinic acid, nicotinamide, succinamide, p‐aminobenzoic acid, resorcinol and pyrogallol using liquid‐assisted grinding. The co‐crystals were characterized by FT‐IR spectroscopy, powder X‐ray diffraction (PXRD) and differential scanning calorimetry. Single crystal structures were obtained for four of them. The N—H...O sulfonamide catemer synthons found in the stable polymorph of pure HCT are replaced in the co‐crystals by drug‐co‐former heterosynthons. Isostructural co‐crystals with nicotinic acid and nicotinamide are devoid of the common sulfonamide dimer/catemer synthons. Solubility and stability experiments were carried out for the co‐crystals in water (neutral pH) under ambient conditions. Among the six binary systems, the co‐crystal with p‐aminobenzoic acid showed a sixfold increase in solubility compared with pure HCT, and stability up to 24 h in an aqueous medium. The co‐crystals with nicotinamide, resorcinol and pyrogallol showed only a 1.5–2‐fold increase in solubility and transformed to HCT within 1 h of the dissolution experiment. An inverse correlation is observed between the melting points of the co‐crystals and their solubilities.
In recent years powder X‐ray diffraction has proven to be a valuable alternative to single‐crystal X‐ray diffraction for determining electron‐density distributions in high‐symmetry inorganic materials, including subtle deformation in the core electron density. This was made possible by performing diffraction measurements in vacuum using high‐energy X‐rays at a synchrotron‐radiation facility. Here we present a new version of our custom‐built in‐vacuum powder diffractometer with the sample‐to‐detector distance increased by a factor of four. In practice this is found to give a reduction in instrumental peak broadening by approximately a factor of three and a large improvement in signal‐to‐background ratio compared to the previous instrument. Structure factors of silicon at room temperature are extracted using a combined multipole–Rietveld procedure and compared with ab initio calculations and the results from the previous diffractometer. Despite some remaining issues regarding peak asymmetry, the new diffractometer yields structure factors of comparable accuracy to the previous diffractometer at low angles and improved accuracy at high angles. The high quality of the structure factors is further assessed by modelling of core electron deformation with results in good agreement with previous investigations. The present state of X‐ray electron‐density determination from powder‐diffraction data is briefly reviewed together with the first results from a new large‐diameter in‐vacuum diffractometer.