A comparative study of the propagation of vectorial nonparaxial beams in the use of different approaches

Starting from the vectorial Rayleigh diffraction integral formula and using a simple expansion of the nucleus in the Rayleigh formula, an analytical propagation equation of vectorial nonparaxial Gaussian beams in free space is derived, which permits us to perform numerical calculations in comparison with the expression derived by Ciattoni et al. and with the direct numerical integration of the Rayleigh formula. It is found that as usual the use of expansion of vectorial Rayleigh diffraction integral is sufficient to provide satisfactory numerical results as compared with the direct integration of the Rayleigh formula. The above two analytical expressions are valid under certain conditions, however both are applicable in the far field.     

α-Fe2O3-In2O3 mixed oxide nanoparticles synthesized under hydrothermal supercritical conditions

α-Fe₂O₃-In₂O₃ mixed oxide nanoparticles system has been synthesized by hydrothermal supercritical and postannealing route, starting with (1−x)Fe(NO₃)₃·9H₂O·xIn(NO₃)₃·5H₂O aqueous solution (x=0-1). X-ray diffraction and Mössbauer spectroscopy have been used to study the phase structure and substitutions in the nanosized samples. The concentration regions for the existence of the solid solutions in the α-Fe₂O₃-In₂O₃ nanoparticle system together with the solubility limits of In³⁺ ions in the hematite lattice and of Fe³⁺ ions in the cubic In₂O₃ structure have been evidenced. In general, the substitution level is considerably lower than the nominal concentration x. A justification of the processes leading to the formation of iron and indium phases in the investigated supercritical hydrothermal system has been given.     

Application of the Volterra filter in experimental diffraction data processing

The effective signal in x-ray diffraction analysis of material properties often contains high frequency (noise) and low frequency (trend) components as additive parts. It is necessary to extract the effective signal from the noise to ensure high quality of signal processing. Digital filters of Volterra type are proposed for filtering purposes and a comparison of Volterra filtration implemented on x-ray diffraction data versus results from a set of other digital filters is given.     

纵波模拟演示装置

介绍了一种纵波模拟演示装置，并给出了其结构要点及演示效果，实现了对纵波行波的演示。     

Measurement of wire diameter by optical diffraction

A combined interference and diffraction pattern, in the form of equidistant interference fringes, resulting from illuminating a vertical metallic wire by a laser beam is analyzed to measure the diameter of four standard wires. The diameters range from 170 to 450 μm. It is found that the error in the diameter measurements increases for small metallic wires and for small distances between the wire and the screen due to scattering effects. The intensity of the incident laser beam was controlled by a pair of sheet polaroids to minimize the scattered radiation. The used technique is highly sensitive, but requires controlled environmental conditions and absence of vibration effects. The expanded uncertainty for k=2 is calculated and found to decrease from U(D)=±1.45 μm for the wire of nominal diameter 170 μm to ±0.57 μm for the diameter 450 μm.     

Solid state phase equilibria in the Gd-Si-B system at 1270 K

Solid state phase equilibria in the ternary Gd-Si-B phase diagram have been proposed at 1270 K using X-ray diffraction, scanning electron microscopy and electron probe microanalysis. Prior to this work, the binary systems Gd-B, Gd-Si and Si-B have also been reinvestigated. The main characteristic of the ternary diagram is the occurrence of two new ternary compounds Gd₅Si₂B₈ and Gd₅Si₃B_0.64. The former crystallizes in tetragonal symmetry, space group P4/mbm with unit cell parameters a=7.2665(3), c=8.2229(7) Å, the second one presents hexagonal symmetry, space group P6₃/mcm with unit cell parameters a=8.5080(4),c=6.4141(2) Å. The X-ray structures of the two structurally related phases Gd₅Si₃B_0.64 and host binary Gd₅Si₃ have been refined from three-dimensional single-crystal intensity data to the final R values of 0.036 (R_w=0.046) and 0.046 (R_w=0.055) for 457 and 401 reflections, respectively with [F>4σ(F)]. Both structures exhibit the Mn₅Si₃-type structure, with in addition for Gd₅Si₃B_0.64 a partial occupancy by boron of the normally vacant interstitial site at the center of the Gd₆ octahedron, which corresponds to the origin of the unit cell. Bonding between the interstitial boron atoms and the gadolinium ones forming the Gd₆B polyhedra is indicated by the decrease in the corresponding Gd-Gd distances and consequently in the unit cell volume. Finally, the Gd-Si-B phase diagram is compared with the previously reported Er-Si-B, at 1070 K.     

均匀分层介质中标准矢量波函数的构成

研究了在均匀分层介质中构成标准矢量波函数的必要条件。研究结果表明在均匀分层介质中构成标准矢量波函数一般需遵循Morse-Feshbach判据外，领示矢量只能选取与折射率变化方向一致的那根坐标轴单位矢量。但在某些特定的条件下，对领示矢量的选取条件可以放宽为只需遵循Morse-Feshbach判据即可。     

ON INTERACTION OF SHOCK AND SOUND WAVE （I）

This paper studies the interaction of shock and gradient wave (sound wave) of solutions to the system of inviscid isentropic gas dynamics as a model for the corresponding problems for nonlinear hyperbolic systems. The problem can be reduced to a boundary value problem in a wedged dormain, By using the method of constructing asymptotic solutions and Newton‘siteration process it is proved that if a weak shock hits a gradient wave, then the grandient wave will split into two gradient waves, while the shock continuses propagating. In this paper the author reduces the problem to a standard form and constructs asymptotic solution of the problem. The existence of the genuine solution will he given in the following paper.     

CsBr高压X光研究

 采用同步辐射X光源和能散法，对CsBr粉末样品进行高压原位X光衍射实验。由金刚石对顶压砧高压装置（DAC）产生高压，用已知状态方程的Pt粉末作内标，由Pt的衍射数据确定样品压力，最高压力达64.4 GPa。实验结果表明：室温常压下原始CsBr样品是具有简单立方结构的晶体，其晶格常数α＝0.428 5 nm。高压下CsBr的结构有所变化，在51.3~58.4 GPa的压力范围内，(110)线和(211)线发生劈裂，从而形成了四方相。     

Electron diffraction investigation of PPTA/nylon 3T blends from shear-oriented anisotropic solutions

Nematic solutions of PPTA and nylon 3T were prepared in H₂SO₄ Optical microscopy was used to ascertain the phase behaviour of the blends. In the studied concentration range, no phase separation was observed. The solutions were shear-oriented and coagulated, and the resulting samples were studied by x-ray and electron diffraction. Nylon 3T crystallised even at a low concentration, which is indicative of a phase separation. Electron diffraction investigations of the oriented samples showed that well-oriented areas, which were predominantly composed of PPTA, adjoined areas where the major component, nylon 3T, showed no orientation. The relative proportion of the unoriented areas increased with increasing nylon concentration. It was concluded that, upon coagulation, the nylon was segregated into separate phases and crystallised unoriented, whereas for PPTA, crystallisation proceeded with very little chain rearrangement therefore preserving the orientation.