A Direct Approach to the Problem of Diffraction by a Half-Plane under Mixed Boundary Conditions

A general direct technique of solving a mixed boundary value problem in the theory of diffraction by a semi-infinite plane is presented. Taking account of the correct edge-conditions, the unique solution of the problem is derived, by means of Jones' method in the theory of Wiener-Hopf technique, in the case of incident plane wave. The solution of the half-plane problem is found out in exact form. (The far-field is derived by the method of steepest descent.) It is observed that it is not the Wiener-Hopf technique which really needs any modification but a new technique is certainly required to handle the peculiar type of coupled integral equations which the Wiener-Hopf technique leads to. Eine allgemeine direkte Technik zur Lösung eines gemischten Randwertproblems in der Theorie der Beugung an einer halbunendlichen Ebene wird vorgestellt. Unter Berücksichtigung der korrekten Eckbedingungen wird mit der Methode von Jones aus der Theorie der Wiener-Hopf-Technik die eindeutige Lösung für den Fall der einfallenden ebenen Welle hergeleitet. Die Lösung des Halbebenenproblems wird in exakter Form angegeben. (Das Fernfeld wurde mit der Methode des steilsten Abstiegs bestimmt.) Es wurde bemerkt, daß es nicht die Wiener-Hopf-Technik ist, die wirklich irgend welcher Modifikationen bedurfte. Gewiß aber wird eine neue Technik zur Behandlung des besonderen Typs gekoppelter Integralgleichungen benötigt, auf die die Wiener-Hopf-Technik führt.

Diffraction of a cylindrical pulse by a half plane under mixed boundary conditions

The general time dependent source problem has been solved by the method of transforms (Laplace, Lebedev–Kontorovich in succession) and the solution is obtained in the form of an infinite series involving Legendre functions. The solutions in the case of harmonic time dependence and the incident plane wave have been derived from the above solution and are presented in the form of an infinite series. In the case of an incident plane wave, the series has been summed and the final solution involves an improper integral which behaves like a complementary error function for large values of the argument. Finally, the far field evaluation has been shown. The results are compared with those of Sommerfeld's half-plane diffraction problem with unmixed boundary conditions.

Diffraction of a cylindrical pulse by a metallic half plane

A direct transform technique is applied to the initial and boundary value problem involving diffraction of a cylindrical pulse by a half plane, on which impedance type of boundary conditions must be met by the total field. The solution to the time harmonic incident plane wave is deduced as a particular case of the general time-dependent problem considered here and we avoid the Wiener–Hopf technique which leads to very complicated factorization and which masks the role of the impedance factor Z′ (a small quantity) in the expression for the scattered field.

A furnace for in situ synchrotron Laue diffraction and its application to studies of solid-state phase transformations

The design of a new microfurnace for use for Laue diffraction studies of solid-state transformations is described. The furnace operates in the temperature range 298-573 K with a thermal stability of about ± 0.1 K. The potential of the synchrotron-radiation Laue diffraction technique for studies of structural phase transitions is demonstrated. Experimental data on phase transitions in caesium periodate, potassium tetrachlorozincate and pentaerythritol are presented.

Two forms of Pf1 Inovirus: X-ray diffraction studies on a structural phase transition and a calculated libration normal mode of the asymmetric unit

Inovirus is a helical array of alpha-helical protein asymmetric units surrounding a DNA core. X-ray fibre diffraction studies show that the Pf1 species of Inovirus can undergo a reversible temperature-induced transition between two similar structural forms having slightly different virion helix parameters. Molecular models of the two forms show no evidence for altered interactions between the protein and either the solvent or the viral DNA; but there are significant differences in the shape and orientation of the protein asymmetric unit, related to the changes in the virion parameters. Normal modes involving libration of whole asymmetric units are in a frequency range with appreciable entropy of libration, and the structural transition may be related to changes in libration.

Crystallization and Preliminary X-ray Diffraction Analysis of Crystals of Thermoascus aurantiacus Xylanase

Crystals suitable for high resolution X-ray diffraction analysis have been grown of the 29,774-Da protein, xylanase (1,-4-beta-xylan xylanohydrolase EC 3.2.1.8) from the thermophilic fungus Thermoascus aurantiacus. This protein, an endoxylanase demonstrates the hydrolysis of β-(1-4)-Image -xylose linkage in xylans and crystallizes as monoclinic pinacoids in the presence of ammonium sulphate buffered at pH 6·5, and also with neutral polyethylene glycol 6000. The crystals belong to space group P 21 and have cell dimensions, a = 41·2 Å, b = 67·76 Å, c = 51·8 Å; β = 113·2°.

Two forms of PF1 INOVIRUS: X-ray diffraction studies on a structural phase transition and a calculated libration normal mode of the assymetric unit

Inovirus is a helical array of agr-helical protein asymmetric units surrounding a DNA core. X-ray fibre diffraction studies show that the Pf1 species of Inovirus can undergo a reversible temperature-induced transition between two similar structural forms having slightly different virion helix parameters. Molecular models of the two forms show no evidence for altered interactions between the protein and either the solvent or the viral DNA; but there are significant differences in the shape and orientation of the protein asymmetric unit, related to the changes in the virion parameters. Normal modes involving libration of whole asymmetric units are in a frequency range with appreciable entropy of libration, and the structural transition may be related to changes in libration.

Structural refinement using high-resolution powder X-ray diffraction data of Ca0.5Ti2P3O12, a low-thermal-expansion material

The structures of Ca0.5Ti2P3O12 and Sr0.5Ti2P3O12, low-thermal-expansion materials, have been refined by the Rietveld method using high-resolution powder X-ray diffraction (XRD) data. The assignment of space group R[3 with combining macron] to NASICON-type compounds containing divalent cations is confirmed. 31P magic-angle spinning nuclear magnetic resonance (MASNMR) data are presented as supporting data. A comparison of changes in the polyhedral network resulting from the cation distribution, is made with NaTi2P3O12 and Nb2P3O12. Factors that may govern thermal expansion in this family of compounds are discussed.

X-ray diffraction line profile analysis of deformation microstructure in boron modified Ti-6Al-4V alloy

X-ray diffraction line profile analysis (XRDLPA) techniques have been applied to investigate the deformed microstructure of a recently developed boron modified two-phase titanium alloy Ti-6Al-4V. The alloy was hot compressed at 750 degrees C up to 50% height reduction at two different strain rates (10(-3) S-1 and 1 S-1). Microstructural parameters like average domain size, average microstrain within the domain and dislocation density of the two phases were determined using X-ray diffraction line profile analysis. The results indicate an increase in the microstrain and dislocation density for the alpha-phase and decrease for the beta-phase in the case of boron modified alloys as compared to the normal material. Microstructural modifications viz, the grain refinement and the presence of hard, brittle TiB particles in the case of boron modified alloy are held responsible for the observed difference in the dislocation density. (C) 2010 Elsevier Inc. All rights reserved.

An electron diffraction study of quasicrystals in Ti-37 at% Mn and Ti-24 at% Mn-13 at% Fe alloys

Electron diffraction studies were carried out to establish the icosahedral phase formation in rapidly quenched Ti-37 at% Mn and Ti-24 at% Mn-13 at% Fe alloys. Distortions in the diffraction spots and diffuse intensities in the diffraction patterns were investigated. The existence of a rational approximant structure and a decagonal like phase are also reported.

A structural study of Li2S---B2S3 glasses by neutron diffraction

The radial distribution functions (RDFs) of five xLi2S.(1 - x)B2S3 glasses (x = 0.55, 0.60, 0.67, 0.71 and 0.75) have been determined from neutron diffraction experiments performed at the Institut Laue-Langevin, Grenoble. These glasses are prepared by casting a molten mixture of boron, sulphur and Li2S inside a controlled atmosphere glovebox. Addition of the Li2S Modifier is found gradually to suppress all peaks corresponding to interatomic distances > 3.5 angstrom, which implies that the structural entities present in these glasses become segmented, and therefore more ionic, as x increases. The assumption of the existence of four main structural entities based on four- and three-coordinated borons (the latter carrying bridging and/or non-bridging sulphurs) accounts for all the peaks present in the RDFs as a function of composition. Furthermore, in the most modified glass (x = 0.75), that which contains only 'isolated' BS33- triangles, there seems to be evidence for either octahedral or tetrahedral coordination of Li+ by S- ions

A novel method for diameter estimation of small opaque objects using Fraunhofer diffraction

A novel optical method is proposed and demonstrated, for real-time dimension estimation of thin opaque cylindrical objects. The methodology relies on free-space Fraunhofer diffraction principle. The central region, of such tailored diffraction pattern obtained under suitable choice of illumination conditions, comprises of a pair of `equal intensity maxima', whose separation remains constant and independent of the diameter of the diffracting object. An analysis of `the intensity distribution in this region' reveals the following. At a point symmetrically located between the said maxima, the light intensity varies characteristically with diameter of the diffracting object, exhibiting a relatively stronger intensity modulation under spherical wave illumination than under a plane wave illumination. The analysis reveals further, that the said intensity variation with diameter is controllable by the illumination conditions. Exploiting these `hitherto unexplored' features, the present communication reports for the first time, a reliable method of estimating diameter of thin opaque cylindrical objects in real-time, with nanometer resolution from single point intensity measurement. Based on the proposed methodology, results of few simulation and experimental investigations carried-out on metallic wires with diameters spanning the range of 5 to 50 mu m, are presented. The results show that proposed method is well-suited for high resolution on-line monitoring of ultrathin wire diameters, extensively used in micro-mechanics and semiconductor industries, where the conventional diffraction-based methods fail to produce accurate results.