Crystal Physics, Diffraction, Theoretical and General Crystallography

A formula has been derived for the mean-square error in the phases of crystal reflections determined through the multiwavelength anomalous scattering method. The error is written in terms of a simple function of the positions in the complex plane of the 'centres' corresponding to the different wavelengths. For the case of three centres, the mean-square error is inversely proportional to the area of the triangle formed by them. The theoretical values are in good agreement with those obtained by earlier workers from computer simulations. The present method makes it easier to optimize the number and the actual wavelengths to be employed in the multiwavelength method. The maximum benefits of this method are expected in experiments employing synchrotron radiation or neutrons.

Neutron-diffraction study of structure and conformation of nucleotide uridine-5 phosphate (disodium salt)

Acta Crystallographica Section A: Foundations of Crystallography covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic disordered materials, and the corresponding Bragg, satellite and diffuse scattering, thermal motion and symmetry aspects. Spatial resolutions range from the subatomic domain in charge-density studies to nanodimensional imperfections such as dislocations and twin walls. The chemistry encompasses metals, alloys, and inorganic, organic and biological materials. Structure prediction and properties such as the theory of phase transformations are also covered.

The nonplanar peptide unit III. Quantum chemical calculations for related compounds and experimental X-ray diffraction data

The possible nonplanar distortions of the amide group in formamide, acetamide, N-methylacetamide, and N-ethylacetamide have been examined using CNDO/2 and INDO methods. The predictions from these methods are compared with the results obtained from X-ray and neutron diffraction studies on crystals of small open peptides, cyclic peptides, and amides. It is shown that the INDO results are in good agreement with observations, and that the dihedral angles N and defining the nonplanarity of the amide unit are correlated approximately by the relation N = -2, while C is small and uncorrelated with . The present study indicates that the nonplanar distortions at the nitrogen atom of the peptide unit may have to be taken into consideration, in addition to the variation in the dihedral angles (,), in working out polypeptide and protein structures.

A note on Sommerfeld's diffraction problem

A direct transform technique is found to be most suitable for attacking two-dimensional diffraction problems. As a first example of the application of the technique, the well-known Sommerfeld problem is reconsidered and the solution of the problem of diffraction, by a half-plane, of a cylindrical pulse is made use of in deducing the solution of the problem of diffraction of a plane wave by a soft half-plane. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Apparent shortening of the Csp(3)-Csp(3) bond analysed via a variable-temperature X-ray diffraction study in racemic 1,1 '-binaphthalene-2,2 '-diyl diethyl bis(carbonate)

Crystal structure determination at room temperature [292 (2) K] of racemic 1,1'-binaphthalene-2,2'-diyl diethyl bis(carbonate), C26H22O6, showed that one of the terminal carbon-carbon bond lengths is very short [Csp(3)-Csp(3) = 1.327 (6) angstrom]. The reason for such a short bond length has been analysed by collecting data sets on the same crystal at 393, 150 and 90 K. The values of the corrected bond lengths clearly suggest that the shortening is mainly due to positional disorder at two sites, with minor perturbations arising as a result of thermal vibrations. The positional disorder has been resolved in the analysis of the 90 K data following the changes in the unit-cell parameters for the data sets at 150 and 90 K, which appear to be an artifact of a near centre of symmetry relationship between the two independent molecules in the space group P (1) over bar at these temperatures. Indeed, the unit cell at low temperature (150 and 90 K) is a supercell of the room-temperature unit cell.

X-ray scattering and diffraction enhanced imaging studies of in vitro breast tissues

This thesis is a study of the x-ray scattering properties of tissues and tumours of the breast. Clinical radiography is based on the absorption of the x-rays when passing right through the human body and gives information about the densities of the tissues. Besides being absorbed, x-rays may change their direction within the tissues due to elastic scattering or even to refraction. The phenomenon of scattering is a nuisance to radiography in general, and to mammography in particular, because it reduces the quality of the images. However, scattered x-rays bear very useful information about the structure of the tissues at the supra-molecular level. Some pathologies, like breast cancer, produce alterations to the structures of the tissues, being especially evident in collagen-rich tissues. On the other hand, the change of direction due to refraction of the x-rays on the tissue boundaries can be mapped. The diffraction enhanced imaging (DEI) technique uses a perfect crystal to convert the angular deviations of the x-rays into intensity variations, which can be recorded as images. This technique is of especial interest in the cases were the densities of the tissues are very similar (like in mammography) and the absorption images do not offer enough contrast. This thesis explores the structural differences existing in healthy and pathological collagen in breast tissue samples by the small-angle x-ray scattering (SAXS) technique and compares these differences with the morphological information found in the DEI images and the histo-pathology of the same samples. Several breast tissue samples were studied by SAXS technique in the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. Scattering patterns of the different tissues of the breast were acquired and compared with the histology of the samples. The scattering signals from adipose tissue (fat), connective tissue (collagen) and necrotic tissue were identified. Moreover, a clear distinction could be done between the scattering signals from healthy collagen and from collagen from an invasive tumour. Scattering from collagen is very characteristic. It includes several scattering peaks and scattering features that carry information about the size and the spacing of the collagen fibrils in the tissues. It was found that the collagen fibrils in invaded tumours were thinner and had a d-spacing length 0,7% longer that fibrils from healthy tumours. The scattering signals from the breast tissues were compared with the histology by building colour-coded maps across the samples. They were also imaged with the DEI technique. There was a total agreement between the scattering maps, the morphological features seen in the images and the information of the histo- pathological examination. The thesis demonstrates that the x-ray scattering signal can be used to characterize tissues and that it carries important information about the pathological state of the breast tissues, thus showing the potential of the SAXS technique as a possible diagnostic tool for breast cancer.

Search for a Light Higgs Boson in Central Exclusive Diffraction: Method and Detectors

By detecting leading protons produced in the Central Exclusive Diffractive process, p+p → p+X+p, one can measure the missing mass, and scan for possible new particle states such as the Higgs boson. This process augments - in a model independent way - the standard methods for new particle searches at the Large Hadron Collider (LHC) and will allow detailed analyses of the produced central system, such as the spin-parity properties of the Higgs boson. The exclusive central diffractive process makes possible precision studies of gluons at the LHC and complements the physics scenarios foreseen at the next e+e− linear collider. This thesis first presents the conclusions of the first systematic analysis of the expected precision measurement of the leading proton momentum and the accuracy of the reconstructed missing mass. In this initial analysis, the scattered protons are tracked along the LHC beam line and the uncertainties expected in beam transport and detection of the scattered leading protons are accounted for. The main focus of the thesis is in developing the necessary radiation hard precision detector technology for coping with the extremely demanding experimental environment of the LHC. This will be achieved by using a 3D silicon detector design, which in addition to the radiation hardness of up to 5×10^15 neutrons/cm2, offers properties such as a high signal-to- noise ratio, fast signal response to radiation and sensitivity close to the very edge of the detector. This work reports on the development of a novel semi-3D detector design that simplifies the 3D fabrication process, but conserves the necessary properties of the 3D detector design required in the LHC and in other imaging applications.

Systematic study on crystal-contact engineering of diphthine synthase: influence of mutations at crystal-packing regions on X-ray diffraction quality

It is well known that protein crystallizability can be influenced by site-directed mutagenesis of residues on the molecular surface of proteins, indicating that the intermolecular interactions in crystal-packing regions may play a crucial role in the structural regularity at atomic resolution of protein crystals. Here, a systematic examination was made of the improvement in the diffraction resolution of protein crystals on introducing a single mutation of a crystal-packing residue in order to provide more favourable packing interactions, using diphthine synthase from Pyrococcus horikoshii OT3 as a model system. All of a total of 21 designed mutants at 13 different crystal-packing residues yielded almost isomorphous crystals from the same crystallization conditions as those used for the wild-type crystals, which diffracted X-rays to 2.1 angstrom resolution. Of the 21 mutants, eight provided crystals with an improved resolution of 1.8 angstrom or better. Thus, it has been clarified that crystal quality can be improved by introducing a suitable single mutation of a crystal-packing residue. In the improved crystals, more intimate crystal-packing interactions than those in the wild-type crystal are observed. Notably, the mutants K49R and T146R yielded crystals with outstandingly improved resolutions of 1.5 and 1.6 angstrom, respectively, in which a large-scale rearrangement of packing interactions was unexpectedly observed despite the retention of the same isomorphous crystal form. In contrast, the mutants that provided results that were in good agreement with the designed putative structures tended to achieve only moderate improvements in resolution of up to 1.75 angstrom. These results suggest a difficulty in the rational prediction of highly effective mutations in crystal engineering.

Characterisation of properties of coniferous wood tracheids by x-ray diffraction, laser scattering and microscopy

In recent years there has been growing interest in selecting suitable wood raw material to increase end product quality and to increase the efficiency of industrial processes. Genetic background and growing conditions are known to affect properties of growing trees, but only a few parameters reflecting wood quality, such as volume and density can be measured on an industrial scale. Therefore research on cellular level structures of trees grown in different conditions is needed to increase understanding of the growth process of trees leading to desired wood properties. In this work the cellular and cell wall structures of wood were studied. Parameters, such as the mean microfibril angle (MFA), the spiral grain angles, the fibre length, the tracheid cell wall thickness and the cross-sectional shape of the tracheid, were determined as a function of distance from the pith towards the bark and mutual dependencies of these parameters were discussed. Samples from fast-grown trees, which belong to a same clone, grown in fertile soil and also from fertilised trees were measured. It was found that in fast-grown trees the mean MFA decreased more gradually from the pith to the bark than in reference stems. In fast-grown samples cells were shorter, more thin-walled and their cross-sections were rounder than in slower-grown reference trees. Increased growth rate was found to cause an increase in spiral grain variation both within and between annual rings. Furthermore, methods for determination of the mean MFA using x-ray diffraction were evaluated. Several experimental arrangements including the synchrotron radiation based microdiffraction were compared. For evaluation of the data analysis procedures a general form for diffraction conditions in terms of angles describing the fibre orientation and the shape of the cell was derived. The effects of these parameters on the obtained microfibril angles were discussed. The use of symmetrical transmission geometry and tangentially cut samples gave the most reliable MFA values.

Unraveling the packing pattern leading to gelation using SS NMR and X-ray diffraction: direct observation of the evolution of self-assembled fibers

A detailed understanding of the mode of packing patterns that leads to the gelation of low molecular mass gelators derived from bile acid esters was carried out using solid state NMR along with complementary techniques such as powder X-ray diffraction (PXRD), differential scanning calorimetry (DSC), thermogravimetric analysis (TGA) and polarizing optical microscopy (POM). Solid state C-13{H-1} cross polarization (CP) magic angle spinning (MAS) NMR of the low molecularmass gel in its native state was recorded for the first time. A close resemblance in the packing patterns of the gel, xerogel and bulk solid states was revealed upon comparing their C-13{H-1} CPMAS NMR spectral pattern. A doublet resonance pattern of C-13 signals in C-13{H-1}CPMAS NMR spectra were observed for the gelator molecules, whereas the non-gelators showed simple singlet resonance or resulted inthe formation of inclusion complexes/solvates. PXRD patterns revealed a close isomorphous nature of the gelators indicating the similarity in the mode of the packing pattern in their solid state. Direct imaging of the evolution of nanofibers (sol-gel transition) was carried out using POM, which proved the presence of self-assembled fibrillar networks (SAFINs) in the gel. Finally powder X-ray structure determination revealed the presence of two non-equivalent molecules in an asymmetric unit which is responsible for the doublet resonance pattern in the solid state NMR spectra.

Diffraction and Total Cross-Section at the Tevatron and the LHC

At the Tevatron, the total p_bar-p cross-section has been measured by CDF at 546 GeV and 1.8 TeV, and by E710/E811 at 1.8 TeV. The two results at 1.8 TeV disagree by 2.6 standard deviations, introducing big uncertainties into extrapolations to higher energies. At the LHC, the TOTEM collaboration is preparing to resolve the ambiguity by measuring the total p-p cross-section with a precision of about 1 %. Like at the Tevatron experiments, the luminosity-independent method based on the Optical Theorem will be used. The Tevatron experiments have also performed a vast range of studies about soft and hard diffractive events, partly with antiproton tagging by Roman Pots, partly with rapidity gap tagging. At the LHC, the combined CMS/TOTEM experiments will carry out their diffractive programme with an unprecedented rapidity coverage and Roman Pot spectrometers on both sides of the interaction point. The physics menu comprises detailed studies of soft diffractive differential cross-sections, diffractive structure functions, rapidity gap survival and exclusive central production by Double Pomeron Exchange.

An electron diffraction investigation of the molecular structure of methyl azide

The molecular structure of methyl azide has been studied by the sector-microphotometer and the sector-visual methods of electron diffraction and the parameters determined as follows: C-N = 1.47 ± 0.02 Å., N1-N2 = 1.24 ± 0.01 Å., N2-N3 = 1.12 ± 0.01 Å. and