Diffraction Contrast Profiles of Voids

ABSTRACTThe incorporation of triple crystal x-ray diffraction (TCD) under conditions of a nearly grazing incident x-ray beam provides a unique capability to characterize surface and subsurface structural damage. The effects of bromine-methanol chemical-mechanical (CM) polishing on the surface quality of GaAs were investigated by inclined Bragg plane triple crystal x-ray diffraction. GaAs samples polished under varying conditions of Br2 concentration, total polish time, polish wheel rotation speed, and force exerted on the samples were analyzed using TCD profiles from inclined (220) planes, with the samples oriented at both the exact Bragg condition, θB, and at deviations from the exact Bragg condition. As the deviation from the 220 reciprocal lattice point was increased, multiple peaks corresponding to both the dynamic and the kinematic components were observed. The peak positions and the relative intensities of the various peaks were used to characterize the effects of the CM polishing variables on the GaAs surfaces.

A model is presented to describe a spherical void shrinkage at the center of a quasi-spherical grain dominated by lattice self-diffusion. The model is based on the difference in chemical potential between the spherical void surface and the grain boundary interface. The quantitative calculations for pure iron predicted that only small, micron-sized spherical voids could be wholly healed within hours at high temperature. The spherical void shrinkage process can be greatly promoted with an increase in temperature, which depends strongly on crystal lattices, particularly the initial radius of the spherical void and the grain size. The time to eliminate a spherical void with an identical radius within grains is close to that for grain boundaries, while different shrinkage processes were undergone, at fixed temperatures, and related to spherical void size, void spacing, and the grain size.

The dynamical theory for perfect crystals in the Laue case was reformulated using the Riemann surface, as used in complex analysis. In the two-beam approximation, each branch of the dispersion surface is specified by one sheet of the Riemann surface. The characteristic features of the dispersion surface are analytically revealed using four parameters, which are the real and imaginary parts of two quantities specifying the degree of departure from the exact Bragg condition and the reflection strength. By representing these parameters on complex planes, these characteristics can be graphically depicted on the Riemann surface. In the conventional case, the absorption is small and the real part of the reflection strength is large, so the formulation is the same as the traditional analysis. However, when the real part of the reflection strength is small or zero, the two branches of the dispersion surface cross, and the dispersion relationship becomes similar to that of the Bragg case. This is because the geometrical relationships among the parameters are similar in both cases. The present analytical method is generally applicable, irrespective of the magnitudes of the parameters. Furthermore, the present method analytically revealed many characteristic features of the dispersion surface and will be quite instructive for further numerical calculations of rocking curves.

The apodized transmitting volume Bragg grating (TVBG) with the amplitude of the refractive index modulation (RIM) dropped to zero at both the surfaces is discussed. The proposed method for apodization is based on the recording of two identical uniform TVBGs with slightly different directions of their Bragg wave vectors in a single wafer. As a result, slow sinusoidal moire modulation occurs in the direction perpendicular to the averaged direction of the two wave vectors of Bragg modulation. The cutting of a specimen at the planes of the two closest zeros of the moire envelope produces the apodized TVBG. The longitudinal sinusoidal semi-period profile of RIM requires its specific maximum value to achieve 100% diffraction efficiency at the exact Bragg condition. Such an apodized TVBG demonstrates a significant suppression of the sidelobes in the diffraction efficiency depending on the angular or the wavelength detuning, in comparison to the diffraction operation of a uniform TVBG.

A diamond phase retarder was applied to control the polarization states of a hard X-ray free-electron laser (XFEL) in the photon energy range 5-20 keV. The horizontal polarization of the XFEL beam generated from the planar undulators of the SPring-8 Angstrom Compact Free-Electron Laser (SACLA) was converted into vertical or circular polarization of either helicity by adjusting the angular offset of the diamond crystal from the exact Bragg condition. Using a 1.5 mm-thick crystal, a high degree of circular polarization, 97%, was obtained for 11.56 keV monochromatic X-rays, whereas the degree of vertical polarization was 67%, both of which agreed with the estimations including the energy bandwidth of the Si 111 beamline monochromator.

The wave amplitudes in the vicinity of the focus in monochromatic focusing are calculated in the approximation where each point of the surface of a weakly bent single crystal reflects an X-ray wave as a planar crystal, while the reflection coefficient is a coordinate function of the deviation from the exact Bragg condition. These amplitudes are calculated for all the meridional diffraction geometries (those for plane and spherical waves and the Johann and aberration-free schemes). For all these schemes, the quantitative characteristic of the process of polychromatic focusing—the intensity integrated over the pass band—is introduced and calculated. The analytical expressions of polyprofiles necessary for the consideration of these schemes are also derived.

For a solid surface or interface that is subjected to transverse loading, the influence of its flexural resistibility to bending deformation becomes significant. A spherical inhomogeneity or void embedded in an infinite elastic medium under the application of nonhydrostatic loads represents a typical example. In this work, we consider the most fundamental loading of a far-field unidirectional tension. Analytical displacements and stresses are developed by the coupling of a Steigmann–Ogden surface mechanical model, the simple method of Boussinesq displacement potentials, the semi-inverse method of elasticity, and Legendre series representations of spherical harmonics. The problem is then solved by converting the equilibrium equations of displacement into a linear system with respect to the Legendre series coefficients. The developed solutions are general in the sense that they may reduce to their classical or Gurtin–Murdoch counterparts as special cases. Analytical expressions reveal that the derived solution depends on four dimensionless ratios from among surface material parameters, shear moduli ratio, and inhomogeneity or void radius. In particular, instead of depending on both flexural parameters in the moment–curvature relation, one fixed combination is sufficient to represent the surface flexural rigidity. This is in contrast with the influence of the in-plane elastic stiffness, in which both surface Lamé parameters matter. Parametric studies further demonstrate that, for metallic inhomogeneities or voids with radii between 10 nm and 100 nm, the effects of surface flexural rigidity on stress distributions and stress concentrations are significant.

Large amplitude vibration of horizontally curved beams: a finite element approach

Half-wave frequency response phenomenon of a tightly moored submerged sphere under monochromatic wave action simulated by using the body-exact approach

A new type of chopper-monochromator for thermal neutrons based on multiple bragg reflections in one vibrating single crystal

This research investigates using an inerter system to control the impact-induced vibration response of a single degree of freedom(SDOF) and two degrees of freedom(TDOF) vibration system. An analytic model of the SDOF system with an inerter is first derived, and simulation is performed to compare the inerter performance in suppressing the maximum acceleration response under shock load. Next, a more complex TDOF vibration model with an inerter is derived, and the effectiveness of the inerter in reducing the large acceleration amplitude is evaluated. The energy analysis is conducted to investigate the energy transfer mechanism during impact. The simulation study shows that one can significantly decrease the maximum acceleration response with an appropriate selection of the inerter parameters. For the SDOF vibration system with an inerter, response reduction is greatly influenced by the system’s natural frequency. In the TDOF vibration system, the maximum acceleration response attenuation is caused by two factors. For a large inerter radius, the acceleration response reduction is mainly influenced by energy transfer between unsprung and inerter mass. However, for a big inerter mass, attenuation of the acceleration response is caused by decreasing the system’s natural frequency. It is observed from the simulation that the maximum acceleration response can be reduced up to 35% by adjusting the inerter radius of gyration. Furthermore, the optimum condition for reducing the acceleration response occurs when the inerter mass is half the unsprung mass ( m i = 0.5 m u). An experimental study is conducted to validate the simulation results.

Numerical study on the influence of input power and tube shape on a single-phase natural circulation for passive residual heat removal heat exchanger

Near-resonant interaction of longitudinal plasma waves

Nonlinear oscillation analysis of a pendulum wrapping on a cylinder

We report million-atom reactive molecular dynamic simulations of shock initiation of β-cyclotetramethylene tetranitramine (β-HMX) single crystals containing nanometer-scale spherical voids. Shock induced void collapse and subsequent hot spot formation as well as chemical reaction initiation are observed which depend on the void size and impact strength. For an impact velocity of 1 km s(-1) and a void radius of 4 nm, the void collapse process includes three stages; the dominant mechanism is the convergence of upstream molecules toward the centerline and the downstream surface of the void forming flowing molecules. Hot spot formation also undergoes three stages, and the principal mechanism is kinetic energy transforming to thermal energy due to the collision of flowing molecules on the downstream surface. The high temperature of the hot spot initiates a local chemical reaction, and the breakage of the N-NO2 bond plays the key role in the initial reaction mechanism. The impact strength and void size have noticeable effects on the shock dynamical process, resulting in a variation of the predominant mechanisms leading to void collapse and hot spot formation. Larger voids or stronger shocks result in more intense hot spots and, thus, more violent chemical reactions, promoting more reaction channels and generating more reaction products in a shorter duration. The reaction products are mainly concentrated in the developed hot spot, indicating that the chemical reactivity of the hmx crystal is greatly enhanced by void collapse. The detailed information derived from this study can aid a thorough understanding of the role of void collapse in hot spot formation and the chemical reaction initiation of explosives.