Darren Goossens

Diffuse scattering study of aspirin forms (I) and (II).

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 b direction only.

Diffuse X-ray scattering from benzil, C14H10O2: analysis via automatic refinement of a Monte Carlo model

A recently developed method for fitting a Monte Carlo computer-simulation model to observed single-crystal diffuse X-ray scattering has been used to study the diffuse scattering in benzil, diphenylethanedione, C(6)H(5)-CO-CO-C(6)H(5). A model involving 13 parameters consisting of 11 intermolecular force constants, a single intramolecular torsional force constant and a local Debye-Waller factor was refined to give an agreement factor, R = [summation operator omega(Delta I)(2)/summation operator omega I(obs)(2)](1/2), of 14.5% for 101,324 data points. The model was purely thermal in nature. The analysis has shown that the diffuse lines, which feature so prominently in the observed diffraction patterns, are due to strong longitudinal displacement correlations. These are transmitted from molecule to molecule via a network of contacts involving hydrogen bonding of an O atom on one molecule and the para H atom of the phenyl ring of a neighbouring molecule. The analysis also allowed the determination of a torsional force constant for rotations about the single bonds in the molecule. This is the first diffuse scattering study in which measurement of such internal molecular torsion forces has been attempted.

Single-crystal neutron diffuse scattering and Monte Carlo study of the relaxor ferroelectric PbZn1/3Nb2/3O3 (PZN)

Full three-dimensional diffuse neutron scattering data have been recorded from a single crystal of Pb(Zn 1/3 Nb 2/3 )O 3 (PZN) at 300 K using the time-of-flight Laue technique on the SXD single-crystal instrument at ISIS. The data show a series of diffuse rods of scattering oriented parallel to each of the six (11 0) crystal directions. Monte Carlo simulation has been used to demonstrate that the diffuse rods are caused by planar nanodomains oriented normal to the (1 1 0) directions. Within these domains, there are correlated displacements of the atoms away from their average site positions. In order to explain the systematic absence of some rods of scattering in the (h k 1) data but the presence of all rods in the (h k 0) data, it is necessary that the displacement of an O atom is of opposite sign to that of its neighbouring Pb atoms. This is explained in terms of a model based on the fact that Pb 2+ possesses a lone pair of electrons, giving the Pb ion directionality.

The interpretation and analysis of diffuse scattering using Monte Carlo simulation methods.

Studies of diffuse scattering had a prominent place in the first issue of Acta Crystallographica 60 years ago at a time when conventional crystallography (determination of the average structure from Bragg peaks) was in its infancy. Since that time, conventional crystallography has developed enormously while diffuse-scattering analysis has seemingly lagged well behind. The paper highlights some of the extra difficulties involved in the measurement, interpretation and analysis of diffuse scattering and plots the progress that has been made. With the advent of the latest X-ray and neutron sources, area detectors and the ever-increasing power of computers, most disorder problems are now tractable. Two recent contrasting examples are described which highlight what can be achieved by current methods.

Different Models for the Polar Nanodomain Structure of PZN and Other Relaxor Ferroelectrics

Computer simulations have been carried out to test the recently proposed model for the nanodomain structure of relaxor ferroelectrics such as lead zinc niobate (PZN). In this recent model it was supposed that the polar nanodomains are three-dimensional, that the observed diffuse rods of scattering originate from the boundaries between domains and that the Pb displacements may be directed along \langle {100} \rangle, \langle {111} \rangle or \langle {110} \rangle. This is in marked contrast to a previously published model, which described the polar domains as thin plates with Pb displacements confined to the \langle {110} \rangle directions within the essentially two-dimensional domains. The present results confirm that \langle {100} \rangle and \langle {111} \rangle types of Pb displacement are viable possibilities, but the number of domain boundaries required to produce sufficiently strong diffuse rods of scattering means that individual domains cannot be described as three-dimensional and must still be relatively thin. The current work has been carried out with no direct involvement of the B-site cation ordering, which many workers assume is necessary to understand the formation of the polar nanodomains. While it may be true that the B-site cation distribution could provide an underlying perturbation field that might ultimately limit the extent of any polar domain, it is certainly not necessary to produce the observed scattering effects.

Single-crystal diffuse scattering studies on polymorphs of molecular crystals. I. The room-temperature polymorphs of the drug benzocaine

The drug benzocaine (ethyl 4-aminobenzoate), commonly used as a local anaesthetic, is a bimorphic solid at room temperature. Form (I) is monoclinic P2(1)/c, while the metastable form (II) is orthorhombic P2(1)2(1)2(1). Three-dimensional diffuse X-ray scattering data have been collected for the two forms on the 11-ID-B beamline at the Advanced Photon Source (APS). Both forms show strong and highly structured diffuse scattering. The data have been interpreted and analysed using Monte Carlo (MC) modelling on the basis that the scattering is purely thermal in origin and indicates the presence of highly correlated molecular motions. In both forms (I) and (II) broad diffuse streaks are observed in the 0kl section which indicate strong longitudinal displacement correlations between molecules in the 031 directions, extending over distances of up to 50 A. Streaks extending between Bragg peaks in the hk0 section normal to [100] correspond to correlated motions of chains of molecules extending along a that are linked by N-H...O=C hydrogen bonds and which occur together as coplanar ribbon pairs. The main difference between the two forms is in the dynamical behaviour of the ribbon pairs and in particular how they are able to slide relative to each other. While for form (I) a model involving harmonic springs is able to describe the motion satisfactorily, as simple excursions away from the average structure, there is evidence in form (II) of anharmonic effects that are precursors of a phase transition to a new low-temperature phase, form (III), that was subsequently found.

A combined diffraction (XRD, electron and neutron) and electrical study of Na3MoO3F3

Abstract Na3MoO3F3, a member of the A2BMVIO3F3 family of elpasolite-related oxyfluorides, has been prepared by the reaction of NaF with MoO3 at 650°C. It is shown by a combined X-ray, electron and neutron diffraction study, that the true symmetry of Na3MoO3F3 is not monoclinic (pseudo-orthorhombic) as previously reported but instead triclinic (metrically rhombohedral) P1. The superstructure unit cell is given by a=−aR+bR, b=cR, c=(aR+bR+cR), when expressed with respect to the underlying rhombohedral parent structure. Neutron diffraction refinement of the rhombohedral sub-structure shows O and F to be fully ordered with alternate (111)R planes being occupied by O and then F. The nature of the distortion away from the high temperature Fm 3 m parent structure is consistent with a combination of φφφ type rotations of the octahedral framework together with ppp type displacements of the octahedral cations, which is not observed in any of the closely related A2BMVIO3F3 family members. Bond valence arguments are used to give a plausible explanation for this difference in behavior.

Diffuse neutron scattering in benzil, C14D10O2, using the time-of-flight Laue technique

Diffuse neutron scattering data have been recorded for the molecular crystal d-benzil, C 14 D 10 O 2 , using the time-of-flight Laue technique on the SXD and PRISMA instruments at ISIS. Using SXD it was possible to access a large fraction of the total three-dimensional reciprocal space out to a Q value of 15 A -1 , using only four individual exposures and by making use of the 3m Laue symmetry of the crystal. By segregating the scattered data according to the incident neutron energy used, patterns were obtained from those neutrons in the range of ∼20 meV to 150 meV, which showed little sign of inelastic effects and so could be compared with previously analysed X-ray data. For neutron energies of <20 meV, interesting inelastic effects were observed, which have been used to obtain an estimate for the energy of phonons associated with a vibrational mode in which an intramolecular mode couples to a low-energy shearing motion of the hydrogen-bonded network linking neighbouring molecules. The estimated value of 8.95 cm -1 (1.11 meV) for this mode is less than the lowest energy mode reported from spectroscopic measurements for hydrogenous benzil (∼16 cm -1 ). A model previously derived from analysis of X-ray data observed over a limited range of Q has been used to calculate neutron patterns over the full Q range. Comparison with the present neutron data has shown that while the model gives a good description of the form of the diffuse patterns, the magnitudes of the atomic displacements arc underestimated by a factor of ∼2.25.

Diffuse scattering and partial disorder in complex structures

This review discusses the state of the field of single-crystal diffuse scattering (SCDS), including detectors, data collection and the modelling techniques. High quality, three-dimensional volumes of SCDS data can now be collected at synchrotron light sources, allowing increasingly detailed and quantitative analyses to be undertaken.

A refinement strategy for Monte Carlo modelling of diffuse scattering from molecular crystal systems

A new strategy for modelling diffuse scattering from molecular crystals using Monte Carlo simulation is described. The use of harmonic (Hookes law) springs to represent effective intermolecular interactions is preserved, in order to minimize computer requirements, but use is now made of a simple empirical formula to specify spring constants and provide an objective means for limiting the number of springs needed to be used. The method has been tested on diffuse scattering data obtained for form I of paracetamol.