scholarly journals Pushing the limits: determining the average structure in the presence of strong diffuse scattering

2013 ◽  
Vol 69 (a1) ◽  
pp. s420-s420 ◽  
Author(s):  
Rangana Warshamanage ◽  
Anthony Linden ◽  
Hans-Beat Bürgi
Keyword(s):  
Diffuse Scattering ◽  
Average Structure

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

2007 ◽  
Vol 64 (1) ◽  
pp. 23-32 ◽  
Author(s):  
T. R. Welberry ◽  
D. J. Goossens
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Diffuse Scattering ◽  
Simulation Methods ◽  
Neutron Sources ◽  
X Ray ◽  
Average Structure

Studies of diffuse scattering had a prominent place in the first issue ofActa Crystallographica60 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.

scholarly journals Average structures of the disordered β-phase of Pigment Red 170: a single-crystal X-ray diffraction study

2014 ◽  
Vol 70 (2) ◽  
pp. 283-295 ◽  
Author(s):  
Rangana Warshamanage ◽  
Anthony Linden ◽  
Martin U. Schmidt ◽  
Hans-Beat Bürgi
Keyword(s):  
Single Crystal ◽  
Diffuse Scattering ◽  
Bragg Diffraction ◽  
X Ray Diffraction ◽  
Group Setting ◽  
X Ray ◽  
Space Groups ◽  
Average Structure ◽  
Β Phase ◽  
Layer Stacking

The β-phase of the industrially important Pigment Red 170 (β-P.R. 170) has a structure with severe layer stacking disorder. The single-crystal X-ray diffraction pattern consists of a difficult-to-disentangle mix of Bragg diffraction superimposed on rods of diffuse scattering which impede the estimation of accurate Bragg intensities. Two average monoclinic structure models with the same unit-cell dimensions, but different extents of disorder in the layers and different space groups seem plausible, one with the non-conventional space group settingB21/g(No. 14,Z′ = 2) and one inP21/a(No. 14,Z′ = 4). Disordered molecules related by a translation of 0.158bare present in all layers of theB21/gmodel and in every second layer of theP21/amodel. Layer-to-layer contacts are practically the same in both models. According to order–disorder theory, both models are valid superposition structures. Structure-factor calculations show that the pattern of strong and weak Bragg reflections is very similar for the two models.Rfactors indicate that theB21/gmodel is the most economic representation of the average structure. However, given the limitations in data processing, theP21/amodel should not be discarded and further insight sought from a detailed analysis of the experimental diffuse scattering. The difficulties encountered in this analysis raise the question of whether or not the concept of an average structure is applicable in practice to β-P.R. 170.

An insight into real and average structure from diffuse X-ray scattering – a case study

2016 ◽  
Vol 72 (4) ◽  
pp. 571-583 ◽  
Author(s):  
Michał Leszek Chodkiewicz ◽  
Anna Makal ◽  
Roman Gajda ◽  
Dragoslav Vidovic ◽  
Krzysztof Woźniak
Keyword(s):  
Diffuse Scattering ◽  
Organic Salt ◽  
X Ray ◽  
Average Structure ◽  
X Ray Scattering ◽  
The Difference ◽  
The Relationship ◽  
Insight Into ◽  
Ray Scattering

Two-dimensional diffuse X-ray scattering from an organic salt [N-(3-(2,6-dimethylanilino)-1-methylbut-2-enylidene)-2,6-dimethylanilinium chloride, C21H27N2+Cl−] was interpreted with the help of an analytical model of diffuse scattering. An analysis of the relationship between symmetry and diffuse scattering for the studied system has been undertaken. The symmetry of the system explains the extinction pattern, taking the form of curves, on the diffuse scattering planes. We have also tested the relationship between the average structure model and scattering intensities. Two models, differing in their representation of overlapping atoms, were used. In the case of diffuse scattering the difference between resulting intensities is immense, while for the Bragg intensities it is much smaller. This sensitivity of diffuse scattering could potentially be used to improve the description of the average structure.

Structural complexity of a polar perhydrotriphenylene inclusion compound brought to light by synchrotron radiation

2001 ◽  
Vol 57 (4) ◽  
pp. 579-590 ◽  
Author(s):  
Thomas Weber ◽  
Michael A. Estermann ◽  
Hans-Beat Bürgi
Keyword(s):  
Synchrotron Radiation ◽  
Diffuse Scattering ◽  
Molecular Form ◽  
Three Dimensional ◽  
Structural Complexity ◽  
Form Factors ◽  
Guest Molecules ◽  
Positional Disorder ◽  
Average Structure ◽  
Area Detector

The complex diffraction pattern of the heavily disordered co-crystals of perhydrotriphenylene and 1-(4-nitrophenyl)piperazine (5C18H30·C10H13N3O2) has been investigated with synchrotron radiation and an area detector. Five (almost) complete, three-dimensional data sets have been obtained from the tips and the centre of a needle-like crystal at room temperature and 120 K. They revealed a rich variety of features including one,- two- and three-dimensional diffuse scattering, as well as incommensurate satellites. At the centre and one tip of the crystal the symmetry appears to be orthorhombic, whereas at the other tip the symmetry of the satellites and of some of the diffuse scattering is clearly monoclinic, indicating that the crystal is not homogeneous. Most of the scattering could be assigned to R/S occupational disorder of the chiral host molecules, to positional disorder of the guest molecules or to local distortions of the average structure. Assignments are based on the disorder deduced from the average structure and the molecular form factors of host and guest molecules which show characteristic patterns in reciprocal space. Two smaller, orthorhombic twin fragments and an additional phase with hexagonal symmetry have also been found.

scholarly journals Aravaite, Ba2Ca18(SiO4)6(PO4)3(CO3)F3O: modular structure and disorder of a new mineral with single and triple antiperovskite layers

2018 ◽  
Vol 74 (6) ◽  
pp. 492-501 ◽  
Author(s):  
Biljana Krüger ◽  
Hannes Krüger ◽  
Evgeny V. Galuskin ◽  
Irina O. Galuskina ◽  
Yevgeny Vapnik ◽  
...  
Keyword(s):  
Diffuse Scattering ◽  
Structure Refinement ◽  
New Mineral ◽  
Stacking Sequence ◽  
Single Crystal Diffraction ◽  
Qualitative Modelling ◽  
One Dimensional ◽  
Average Structure ◽  
Layer Sequence ◽  
Swiss Light Source

The crystal structure of the new mineral aravaite Ba2Ca18(SiO4)6(PO4)3(CO3)F3O [R{\bar 3}m, a = 7.12550 (11), c = 66.2902 (13) Å, V = 2914.81 (8) Å3, Z = 3] was solved from single-crystal diffraction data, collected using synchrotron radiation at the X06DA beamline of the Swiss Light Source. The unit cell of this modular mineral contains six layers of {Ba(PO4)1.5(CO3)0.5}3.5− (T-layer), three triple antiperovskite layers (tAP) {(F2OCa12)(SiO4)4}4+, and three single antiperovskite layers (sAP) {(FCa6)(SiO4)2}3+. The structure refinement confirms a model with a layer sequence of T–sAP–T–tAP as an average structure of this mineral. However, one-dimensional diffuse scattering observed parallel to c* implies imperfections in the stacking sequence of the average structure. Qualitative modelling of disorder confirms that the alternating sequence of T–sAP and T–tAP blocks is disturbed. The blocks occurring in this new mineral are known from other so-called hexagonal intercalated antiperovskite structures: T–sAP (stracherite and zadovite group), T–tAP (ariegilatite and nabimusaite group).

scholarly journals Topology and temperature dependence of the diffuse X-ray scattering in Na0.5Bi0.5TiO3ferroelectric single crystals

2015 ◽  
Vol 48 (5) ◽  
pp. 1543-1550 ◽  
Author(s):  
Semën Gorfman ◽  
Dean S. Keeble ◽  
Alessandro Bombardi ◽  
Pam A. Thomas
Keyword(s):  
Temperature Dependence ◽  
Diffuse Scattering ◽  
Structural Changes ◽  
Structural Disorder ◽  
X Ray ◽  
Average Structure ◽  
X Ray Scattering ◽  
Starting Point ◽  
Lower Temperature ◽  
Ray Scattering

The results of high-resolution measurements of the diffuse X-ray scattering produced by a perovskite-based Na0.5Bi0.5TiO3ferroelectric single crystal between 40 and 620 K are reported. The study was designed as an attempt to resolve numerous controversies regarding the average structure of Na0.5Bi0.5TiO3, such as the mechanism of the phase transitions between the tetragonal,P4bm, and rhombohedral | monoclinic,R3c | Cc, space groups and the correlation between structural changes and macroscopic physical properties. The starting point was to search for any transformations of structural disorder in the temperature range of thermal depoling (420–480 K), where the average structure is known to remain unchanged. The intensity distribution around the {032} pseudocubic reflection was collected using a PILATUS 100K detector at the I16 beamline of the Diamond Light Source (UK). The data revealed previously unknown features of the diffuse scattering, including a system of dual asymmetric L-shaped diffuse scattering streaks. The topology, temperature dependence, and relationship between Bragg and diffuse intensities suggest the presence of complex microstructure in the low-temperatureR3c | Ccphase. This microstructure may be formed by the persistence of the higher-temperatureP4bmphase, built into a lower-temperatureR3c | Ccmatrix, accompanied by the related long-range strain fields. Finally, it is shown that a correlation between the temperature dependence of the X-ray scattering features and the temperature regime of thermal depoling is present.

Calculation of structure images of crystalline defects

1978 ◽  
Vol 36 (1) ◽  
pp. 282-283
Author(s):  
M.A. O'Keefe ◽  
Sumio Iijima
Keyword(s):  
Diffuse Scattering ◽  
Computing Time ◽  
Continuous Distribution ◽  
Sampling Interval ◽  
Reciprocal Space ◽  
Objective Lens ◽  
Lattice Images ◽  
Slice Method ◽  
Space Cell ◽  
Beam Lattice

We have extended the multi-slice method of computating many-beam lattice images of perfect crystals to calculations for imperfect crystals using the artificial superlattice approach. Electron waves scattered from faulted regions of crystals are distributed continuously in reciprocal space, and all these waves interact dynamically with each other to give diffuse scattering patterns.In the computation, this continuous distribution can be sampled only at a finite number of regularly spaced points in reciprocal space, and thus finer sampling gives an improved approximation. The larger cell also allows us to defocus the objective lens further before adjacent defect images overlap, producing spurious computational Fourier images. However, smaller cells allow us to sample the direct space cell more finely; since the two-dimensional arrays in our program are limited to 128X128 and the sampling interval shoud be less than 1/2Å (and preferably only 1/4Å), superlattice sizes are limited to 40 to 60Å. Apart from finding a compromis superlattice cell size, computing time must be conserved.

Recent applications of TEM to the study of interfaces

1990 ◽  
Vol 48 (4) ◽  
pp. 308-309
Author(s):  
C. Barry Carter
Keyword(s):  
High Resolution ◽  
Sample Preparation ◽  
Grain Boundaries ◽  
Diffuse Scattering ◽  
Imaging Techniques ◽  
Amorphous Material ◽  
Contrast Imaging ◽  
Current State ◽  
Actual Nature ◽  
High Resolution Images

This paper will review the current state of understanding of interface structure and highlight some of the future needs and problems which must be overcome. The study of this subject can be separated into three different topics: 1) the fundamental electron microscopy aspects, 2) material-specific features of the study and 3) the characteristics of the particular interfaces. The two topics which are relevant to most studies are the choice of imaging techniques and sample preparation. The techniques used to study interfaces in the TEM include high-resolution imaging, conventional diffraction-contrast imaging, and phase-contrast imaging (Fresnel fringe images, diffuse scattering). The material studied affects not only the characteristics of the interfaces (through changes in bonding, etc.) but also the method used for sample preparation which may in turn have a significant affect on the resulting image. Finally, the actual nature and geometry of the interface must be considered. For example, it has become increasingly clear that the plane of the interface is particularly important whenever at least one of the adjoining grains is crystalline.A particularly productive approach to the study of interfaces is to combine different imaging techniques as illustrated in the study of grain boundaries in alumina. In this case, the conventional imaging approach showed that most grain boundaries in ion-thinned samples are grooved at the grain boundary although the extent of this grooving clearly depends on the crystallography of the surface. The use of diffuse scattering (from amorphous regions) gives invaluable information here since it can be used to confirm directly that surface grooving does occur and that the grooves can fill with amorphous material during sample preparation (see Fig. 1). Extensive use of image simulation has shown that, although information concerning the interface can be obtained from Fresnel-fringe images, the introduction of artifacts through sample preparation cannot be lightly ignored. The Fresnel-fringe simulation has been carried out using a commercial multislice program (TEMPAS) which was intended for simulation of high-resolution images.

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