Aidan Heerdegen

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.

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.

Diffuse scattering resulting from macromolecular frustration

Distinctive diffuse scattering in the form of diffuse rings around Bragg positions has been observed in the diffraction patterns of a crystal of the N-terminal fragment of the Gag protein from Feline Foamy Virus. It is shown that these are caused by geometric frustration as molecules try to pack on the triangular b-c mesh of the space group P6(1)22. In order to explain the strong diffuse scattering it is necessary for the crystal to contain occupational disorder such that each unit cell contains one or other of two different molecular arrangements, A and B. The frustration arises because the nearest-neighbour packing prefers neighbouring cells to be AB or BA, which cannot be achieved on all three sides of a triangle simultaneously. To explain the observation that reciprocal sections hk5n, where n = integer, contain only Bragg peaks it is necessary that A and B are identical molecular arrangements differing only by a translation of 0.2c. The implications of the disorder for solving the structure of the protein by conventional techniques as well as the possibility of using the diffuse scattering for this purpose are discussed.

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.

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.

A room-temperature X-ray diffuse scattering study of form (II) of the trimorphic molecular system p-(N-methylbenzylidene)-p-methylaniline

Three-dimensional X-ray diffuse scattering data have been collected at room temperature for form (II) of the trimorphic molecular system p-(N-methylbenzylidene)-p-methylaniline. Although this polymorph has been reported to have a perfectly normal ordered average structure, strong and highly structured diffuse scattering was observed, indicating that substantial thermal disorder is present. A diffuse scattering analysis has been carried out using Monte Carlo simulation techniques. Narrow streaks of intensity extending between Bragg peaks in the h0l section were found to arise from planes of diffuse scattering in three dimensions. These are caused by highly correlated molecular displacements along chains of end-to-end disposed molecules running in the a-c direction, corresponding to methyl-methyl intermolecular interactions. A second significant feature--rods of diffuse scattering running in the b* direction--indicates that molecular layers normal to b have a tendency to undergo lateral displacements with little correlation between layers. Finally, the internal flexibility of the molecule is required for a best fit. Changes in the two dihedral angles are found to be strongly correlated and show large excursions (> +/- 20 degrees) from the average values. All of these features suggest possible mechanisms for the way in which form (II) might transform to other polymorphs.

Assessing Local Structure in PbZn 1/3 Nb 2/3 O 3 Using Diffuse Scattering and Reverse Monte Carlo Refinement

We use an extensive X-ray diffuse scattering dataset collected from the relaxor ferroelectric PbZn1/3Nb2/3O3 to study the feasibility of refining a nanoscale structure with the reverse Monte Carlo method. Six integer and non-integer reciprocal sections are used with a total number of nearly 105 symmetry-independent data points. Very good agreement between observed and calculated diffuse scattering patterns is achieved with rather subtle diffuse intensity modulations being satisfactorily reproduced. The correlations within the refined local structure are related to the possible physical mechanisms behind them. We discuss the ambiguity of the obtained results and feasible constraining schemes.

Disorder in pentachloronitrobenzene, C6Cl5NO2 :a diffuse scattering study

Monte Carlo computer simulation has been used to interpret and model observed single-crystal diffuse X-ray scattering data for pentachloronitrobenzene, C(6)Cl(5)NO(2). Each site in the crystal contains a molecule in one of six different basic orientations with equal probability. However, no short-range order amongst these different orientations has been detected. The strong, detailed and very distinctive diffraction patterns can be accounted for almost entirely on the assumption of random occupancy of each molecular site, but with very large local relaxation displacements that tend to increase the neighbouring distances for contacts involving NO(2)...NO(2) and NO(2)...Cl with a corresponding reduction for those involving Cl...Cl. The results show that the mean NO(2)...NO(2) distance is increased by approximately 0.6 Angstrom, compared with that given by the average structure determination.

Simultaneous fitting of X‐ray and neutron diffuse scattering data

Conventional crystallographic refinement uses the Bragg-peak intensities and gives the single-site average crystal structure. Information about short-range order and local order is contained in the diffuse scattering that is distributed throughout reciprocal space. Models of the short-range order in materials can now be automatically refined. The complementarity of X-ray and neutron diffraction data, and the value of simultaneously refining a structural model against both types of data, has long been known. This paper presents the first refinement of a short-range-order model against comprehensive X-ray and neutron diffuse scattering data simultaneously. The sample is the organic molecular crystal benzil, C(14)H(10)O(2) (for neutron work H is replaced by D). The technique gives new insights into local order in crystalline materials, including the dynamic correlation structure indicative of the dynamics of molecules in the crystalline state, and successfully overcomes limitations of using only the X-ray data set.

Atomistic modeling of diffuse scattering in cubic PbZrO3

We present a joint theoretical and experimental study on diffuse scattering in cubic PbZrO. A comprehensive synchrotron data-set reveals -oriented diffuse streaks emanating from Bragg reflections and showing a strong intensity variation in the vicinity of selected points. The intensity distribution on the section reveals another system of weaker but much sharper -type diffuse lines extended along directions. These lines are slightly bent and intersect the -oriented diffuse streaks a little off the points of the Brillouin zone. Molecular dynamics simulations with an ab initio derived shell model allow one to assign observed diffuse intensity to correlations coming from different atomic species. It is shown that interactions between the Pb-related modes and the octahedra tilting modes are manifested in subtle diffuse scattering features.