Bragg Angle θB Research Articles

Pure Nuclear Bragg Reflection due to Combined Magnetic and Quadrupole Interaction in Fe3O4

A pure nuclear Bragg reflection due to the combined magnetic and quadrupole interaction in the B-site Fe of Fe3O4 has been investigated. The 10 10 0 reflection (Bragg angle θB = 46.48°), which is e...

The seed energy fluctuation of hard X-ray self-seeding free electron laser

Self-seeding free electron lasers (FELs) are capable of generating fully coherent X-ray pulses. However, the stability of output pulse energy of hard X-ray self-seeding (HXRSS) FEL is poor. This letter reports the seed energy stability investigation of HXRSS FEL. For the purpose of a more stable HXRSS FEL, this work suggests a relatively broad bandwidth ρt of crystal monochromator, a relatively long electron bunch with energy jitter (r.m.s.) down to a quarter of FEL Pierce parameter ρ, and a larger Bragg angle θB to improve the seed energy stability. Moreover, the angle jitter (r.m.s.) between the SASE pulse incident direction and the crystal surface should be less than (ρ tan θB)/2, and the relative time jitter (r.m.s.) between the electron bunch and the seed should be less than half of the seed bump duration Tt.

Coherent X-Rays Generated by Relativistic Electrons in a Tungsten Monocrystal

In an experiment conducted at the Tomsk synchrotron "Sirius", the photon yield of parametric X-ray radiation generated by 500 MeV electrons in a tungsten monocrystal in Bragg geometry has been studied. The (111) tungsten monocrystal, having a thickness of 1.7 mm and a surface mosaicity of not more than 80², was oriented at the Bragg angle θB= 45°to the direction of the electron beam. The photons were detected at the angle 2θB= 90° relative to the electron beam. A comparison of PXR angular distributions with calculations has been carried out with taking into account the actual conditions of the experiment.

Aiming for the theoretical limit of sensitivity of Bonse-Hart USANS instruments

The basis of the Double-Crystal Diffractometer (DCD), used for ultra-small angle neutron scattering (USANS), is that the reflectivity function is very near 1.0 for |y| < 1, where y = (θ - θB)/ δΘD, falls off rapidly for |y| >1, eventually decreasing as y −2. In the Bonse-Hart multi-bounce crystal the reflectivity function R(y) transforms into Rm(y) and in the wings, for large |y|, theoretically decreases as y−2m after m consecutive Bragg reflections inside the channel-cut crystal. Here θ and θB are respectively the diffraction angle and the Bragg angle (for given wavelength) and δΘD is the width of the Darwin plateau. However, the experimental reflectivity Rmexp(y) obtained for m = 3 exceeds the theoretical prediction by over two orders of magnitude in the range of the far wings, which creates limitations for USANS studies of weakly scattering objects.We used the pulsed-source neutron time-of-flight (TOF) technique to study this discrepancy in more detail. Two identical Si(111) crystals, a slab-shaped single-bounce and a channel-cut triple-bounce, were measured at the nominal Bragg angle θB = 24.4o in the TOF powder diffractometer GPPD at IPNS, in the range 0.2 < λ < 4.0 Å of the first seven Bragg reflections from Si(111) family. Cadmium shielding protected the detectors from view of the first-bounce crystal. The experimental data obtained from the single-bounce crystal shows thermal diffuse (phonon) scattering (TDS) filling the region between the Bragg reflections, and exhibiting the symmetry of the reciprocal lattice. With appropriate shielding installed, the triple-bounce Bragg reflections, in contrast, are TDS-free in the range 0.6 < λ < 3.0 Å; however, the intensity of TDS grows in the range λ < 0.5 Å, reaching the level of TDS registered for the single-bounce reflections (777) and (888). The growth of TDS correlates with the increase of the Cd transmission T(λ) in the range 0.2 < λ < 0.5 Å, which in the vicinity of (888) reflection is T(λ) ≈ 0.9. Therefore, the Cd shielding of the triple-bounce crystal becomes ineffective and the parasitic single-bounce back-face reflection and TDS, blocked for 0.5 < λ < 3.0 Å, reappear for λ< 0.5 Å.It is practically impossible to separate this parasitic scattering from the triple-bounce reflection at steady state neutron beam lines except by the use of highly curved neutron guides. However, the TOF-USANS instrument, which is currently under construction at SNS, allows separation of the orders of Bragg reflections and the residual TDS in time-of-flight and thus the discovered parasitic effect cannot compromise its sensitivity. Thus, we expect to approach the theoretical limit of sensitivity for the SNS TOF-USANS instrument.

The diffraction focusing of X-rays upon backscattering from a bent crystal covered with epitaxial film: Sensitivity with respect to the interplanar spacing mismatch between film and substrate

The diffraction focusing of an X-ray wave reflected from a thick bent crystal covered with an epitaxial film is theoretically studied in the case when the Bragg angle θB is close to π/2. It is shown that the X-ray wave focusing upon backscattering from this system is sensitive with respect to the relative interplanar spacing mismatch Δd/d between the epitaxial film and the thick crystal substrate. It is suggested that this effect can be employed for evaluating Δd/d with an accuracy on the order of 10−10.

On the spherical X-ray wave focusing upon backscattering from a biaxially bent crystal

It is shown that a spherical X-ray wave incident at the Bragg angle θB≈π/2 onto a biaxially bent crystal exhibits independent diffraction in two mutually perpendicular planes. An analytical formula for the size of the diffraction reflection region in the backscattering mode is derived and the analytical expression for the wave intensity distribution at the two-dimensional focus is refined.

Parametric X Rays in the Region of Anomalous Dispersion

The influence of anomalous dispersion on the intensity of parametric x rays (PXR) is experimentally investigated in the present work. An experiment conducted with an inner electron beam generated by the Tomsk synchrotron with energy E 0 = 900 MeV is discussed. A Ge monocrystal 0.17 mm thick oriented so that Bragg's angle ΘB between the electron momentum direction and the (111) plane is 9°30′ is used as a target. The experimental data are compared with the results of calculations in the context of the kinematic PXR theory.

Extreme asymmetric X-ray Bragg reflection of semiconductor heterostructures near the edge of total external reflection

Synchrotron radiation has been used to measure the rocking curves from a (GaIn)(AsP) single layer grown on an InP (100)-oriented substrate. For angles of incidence ΦB = (ΘB − ϕ) ≤ 0.7° measured at the Bragg angle ΘB (ϕ is the angle between the diffracting lattice plane and the surface), the rocking curve (RC) is very strongly influenced by total external reflection (TER). This causes a decrease in the full width at half-maximum (FWHM) and an asymmetrical shape for the RC for small ΦB. Both of these effects are due to the Bragg-angle shift from the actual incident angle Φ which is not considered in the conventional dynamical theory. In this paper the essential influence of TER on any thin-layer rocking curve is investigated using a numerical solution of the extended dynamical theory. The pattern can be interpreted up to ΦB ≥ ΘC (ΘC is the angle of TER) by semiempirical incorporation of the results of the extended theory with the coupling formalism of Barrels, Hornstra & Lobeek [Acta Cryst. (1986). A42, 539–545].

Demonstration of reduced source size broadening with a Johann focusing elliptical spectrograph and theory of the second-order source broadening

A Johann focusing elliptical spectrograph has been developed for the measurement of high-resolution x-ray spectra from a spatially extended source. The instrument was designed for the study of high-density, high-temperature plasmas produced by z-pinch implosion or ion-beam bombardment on pulsed-power accelerators. We have constructed and tested this instrument, and have demonstrated an improvement in resolution over what we obtain with a standard circular detector when viewing an extended source. Analytic results for the second-order source broadening due to a finite source size have been obtained and verified by ray tracing. Also given is a simple parametric equation for the Johann crossover curve in terms of either the ellipse sweep angle λ or the Bragg angle θB.

X-ray reflection from and transmission through a plane-parallel dielectric plate with cosine-like polarizability (symmetrical Laue case)

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Solution of the two-dimensional stationary schrödinger equation with cosine-like coefficient (in view of X-ray diffraction)

Inside and outside of a semi-infinite dielectric medium with cosine-like polarizability, which is modulated parallel to a vacuo-dielectric plane boundary (symmetrical Laue case), the X-ray field expressions are obtained if the incident plane wave is under Bragg condition. The represented results are related to a transparent as well as to an absorbing medium. Results are correct if the Bragg angle θB is close to π/2. [Russian Text Ignored].