Scattering of X-rays and Neutrons

1997 ◽  
Author(s):  
Philip Coppens
Keyword(s):  
Resonance Scattering ◽  
Periodic Lattice ◽  
X Rays ◽  
X Ray ◽  
Emit Radiation ◽  
Harmonic Vibrations ◽  
Atomic Nuclei ◽  
X Ray Scattering ◽  
Quantum Mechanical Theory ◽  
Ray Scattering

This chapter starts with a discussion of the classical treatment of X-ray scattering, followed by a brief overview of the quantum-mechanical theory in the first Born approximation. The scattering of a periodic arrangement is derived by considering the crystal as a convolution of the unit cell contents and a periodic lattice. The atomic description of the charge density, which is the basis for structure analysis, is introduced. The origin of resonance anomalous scattering is discussed. While its effect must be accounted for before charge densities can be derived from the X-ray scattering amplitudes, resonance scattering itself can give invaluable information on the electronic states of the resonating atoms. The final section of this chapter deals with the scattering of neutrons by atomic nuclei. Nuclear neutron scattering is independent of the distribution of the electrons, and can provide atomic positions and thermal amplitudes unbiased by the bonding effects which are the subject of this book. In the classical theory of scattering (Cohen-Tannoudji et al. 1977, James 1982), atoms are considered to scatter as dipole oscillators with definite natural frequencies. They undergo harmonic vibrations in the electromagnetic field, and emit radiation as a result of the oscillations.

Resonant Inelastic X-ray Scattering at the ESRF: Hard and Soft X-rays

2012 ◽  
Vol 25 (4) ◽  
pp. 9-15 ◽  
Author(s):  
L. Braicovich ◽  
N. B. Brookes ◽  
G. Ghiringhelli ◽  
M. Minola ◽  
G. Monaco ◽  
...  
Keyword(s):  
X Rays ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

A multi-length-scale USAXS/SAXS facility: 10–50 keV small-angle X-ray scattering instrument

2013 ◽  
Vol 46 (5) ◽  
pp. 1508-1512 ◽  
Author(s):  
Byron Freelon ◽  
Kamlesh Suthar ◽  
Jan Ilavsky
Keyword(s):  
Small Angle ◽  
Soft Matter ◽  
High Energy ◽  
X Rays ◽  
X Ray ◽  
X Ray Scattering ◽  
Wide Range ◽  
And Performance ◽  
New Facility ◽  
Ray Scattering

Coupling small-angle X-ray scattering (SAXS) and ultra-small-angle X-ray scattering (USAXS) provides a powerful system of techniques for determining the structural organization of nanostructured materials that exhibit a wide range of characteristic length scales. A new facility that combines high-energy (HE) SAXS and USAXS has been developed at the Advanced Photon Source (APS). The application of X-rays across a range of energies, from 10 to 50 keV, offers opportunities to probe structural behavior at the nano- and microscale. An X-ray setup that can characterize both soft matter or hard matter and high-Zsamples in the solid or solution forms is described. Recent upgrades to the Sector 15ID beamline allow an extension of the X-ray energy range and improved beam intensity. The function and performance of the dedicated USAXS/HE-SAXS ChemMatCARS-APS facility is described.

A new high-resolution small-angle X-ray scattering apparatus using a fine-focus rotating anode, point-focusing collimation and a position-sensitive proportional counter

1984 ◽  
Vol 17 (5) ◽  
pp. 337-343 ◽  
Author(s):  
O. Yoda
Keyword(s):  
High Resolution ◽  
Small Angle ◽  
Proportional Counter ◽  
Anisotropic Scattering ◽  
Photon Flux ◽  
X Rays ◽  
X Ray ◽  
X Ray Scattering ◽  
Position Sensitive ◽  
Ray Scattering

A high-resolution small-angle X-ray scattering camera has been built, which has the following features. (i) The point collimation optics employed allows the scattering cross section of the sample to be directly measured without corrections for desmearing. (ii) A small-angle resolution better than 0.5 mrad is achieved with a camera length of 1.6 m. (iii) A high photon flux of 0.9 photons μs−1 is obtained on the sample with the rotating-anode X-ray generator operated at 40 kV–30 mA. (iv) Incident X-rays are monochromated by a bent quartz crystal, which makes the determination of the incident X-ray intensity simple and unambiguous. (v) By rotation of the position-sensitive proportional counter around the direct beam, anisotropic scattering patterns can be observed without adjusting the sample. Details of the design and performance are presented with some applications.

Collimating Montel mirror as part of a multi-crystal analyzer system for resonant inelastic X-ray scattering

2016 ◽  
Vol 23 (4) ◽  
pp. 880-886 ◽  
Author(s):  
Jungho Kim ◽  
Xianbo Shi ◽  
Diego Casa ◽  
Jun Qian ◽  
XianRong Huang ◽  
...  
Keyword(s):  
Energy Resolution ◽  
Incident Beam ◽  
X Rays ◽  
X Ray ◽  
X Ray Scattering ◽  
Angular Acceptance ◽  
Crystal Analyzer ◽  
Present Design ◽  
Photon Source ◽  
Ray Scattering

Advances in resonant inelastic X-ray scattering (RIXS) have come in lockstep with improvements in energy resolution. Currently, the best energy resolution at the IrL3-edge stands at ∼25 meV, which is achieved using a diced Si(844) spherical crystal analyzer. However, spherical analyzers are limited by their intrinsic reflection width. A novel analyzer system using multiple flat crystals provides a promising way to overcome this limitation. For the present design, an energy resolution at or below 10 meV was selected. Recognizing that the angular acceptance of flat crystals is severely limited, a collimating element is essential to achieve the necessary solid-angle acceptance. For this purpose, a laterally graded, parabolic, multilayer Montel mirror was designed for use at the IrL3-absorption edge. It provides an acceptance larger than 10 mrad, collimating the reflected X-ray beam to smaller than 100 µrad, in both vertical and horizontal directions. The performance of this mirror was studied at beamline 27-ID at the Advanced Photon Source. X-rays from a diamond (111) monochromator illuminated a scattering source of diameter 5 µm, generating an incident beam on the mirror with a well determined divergence of 40 mrad. A flat Si(111) crystal after the mirror served as the divergence analyzer. From X-ray measurements, ray-tracing simulations and optical metrology results, it was established that the Montel mirror satisfied the specifications of angular acceptance and collimation quality necessary for a high-resolution RIXS multi-crystal analyzer system.

Improved Signal-to-Background Ratio in Small-Angle X-ray Scattering Experiments with Synchrotron Radiation using an Evacuated Cell for Solutions

1997 ◽  
Vol 30 (1) ◽  
pp. 49-54 ◽  
Author(s):  
J.-M. Dubuisson ◽  
T. Decamps ◽  
P. Vachette
Keyword(s):  
Synchrotron Radiation ◽  
Small Angle ◽  
X Rays ◽  
X Ray ◽  
Tight Contact ◽  
X Ray Scattering ◽  
Quartz Capillary ◽  
Conventional Cell ◽  
Capillary Walls ◽  
Ray Scattering

An evacuated, temperature-controlled cell has been built for use on the small-angle X-ray scattering instrument D24 at the synchrotron radiation facility LURE. The sample is placed in a quartz capillary sealed in a stainless-steel holder using a vacuum-tight glue. Several O rings provide a vacuum path upstream and downstream from the cell, so that the X-ray beam only meets the capillary walls and the solution under study between the slits and the beam stop, while the sample is maintained under atmospheric pressure. The cell temperature is controlled via a water circulation through a copper sheath in tight contact with the steel holder. The use of this cell results in a marked reduction of the background, as observed in two series of parallel experiments using a conventional cell and this evacuated cell. The decrease ranges from a factor of 2 at s 1 values larger than 0.008 Å−1 to more than 15 at s = 0.00116 Å−1, where s is the modulus of the scattering vector (s = 2sin θ/λ, 2θ is the scattering angle and λ is the wavelength of the X-rays).

Specular and Off-Specular X-Ray Scattering as Quantitative Structural Probes of Multilayers. Application to MN/IR(111) Superlattices

1995 ◽  
Vol 382 ◽  
Author(s):  
H.M. Fischer ◽  
H.E. Fischer ◽  
M. Bessiere ◽  
J.-F. Bobo ◽  
O. Lenoble ◽  
...  
Keyword(s):  
Deposition Temperature ◽  
Surface Defects ◽  
Single Layer ◽  
Scattering Data ◽  
Length Scale ◽  
X Rays ◽  
Interfacial Roughness ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

ABSTRACTDiffuse scattering of X rays is a particularly useful tool for studying interface and surface defects in single layer films. We have extended this technique to the study of multilayers. The samples are Mn/Ir(111) superlattices where Mn is pseudomorphic to Ir. We have studied three typical samples prepared at different substrate temperatures. Using theoretical analyses and simulations of both specular and off-specular X-ray scattering data at small angles as well as large angles, we show that large length-scale interfacial roughness is mainly due to the formation of terraces during growth at low deposition temperature, whereas small length-scale interfacial roughness occurs preferably at high deposition temperature and is mainly due to an atomic interdiffusion (i.e. the formation of an interface alloy) which manages to maintain a high degree of crystallographic order.

Apparatus for the simultaneous measurement of the X-ray absorption factor developed for a small-angle X-ray scattering beamline

2007 ◽  
Vol 40 (4) ◽  
pp. 791-795 ◽  
Author(s):  
Takeshi Morita ◽  
Yoshitada Tanaka ◽  
Kazuki Ito ◽  
Yoshihiro Takahashi ◽  
Keiko Nishikawa
Keyword(s):  
Small Angle ◽  
Performance Test ◽  
X Rays ◽  
Absorption Factor ◽  
X Ray ◽  
X Ray Scattering ◽  
X Ray Absorption ◽  
Scattering Measurement ◽  
Ray Scattering

A novel apparatus has been developed that enables the simultaneous determination of the absorption factor during measurement of small-angle X-ray scattering (SAXS) intensities of a sample. It was designed especially for the use of relatively low-energy X-rays at SAXS beamlines of synchrotron facilities. The X-ray intensity of transmittance is measured by a silicon PIN photodiode, which is implanted in a direct beamstop set in a vacuum chamber. Since the assembly transmits an attenuated direct beam to a detector during the scattering measurement, a zero-angle position can be monitored without additional operation. It was confirmed that the linearity between the signal from the photodiode and the intensity of X-rays is good and the photodiode is applicable for the desired purpose. For a performance test, the absorption factors of a supercritical fluid were measured with a wide density range.

X-RAY SCATTERING STUDIES OF CHARGE STRIPES IN La2-xSrxNiO4 (x=0.20-0.33)

2002 ◽  
Vol 16 (11n12) ◽  
pp. 1633-1640 ◽  
Author(s):  
P. D. HATTON ◽  
M. E. GHAZI ◽  
S. B. WILKINS ◽  
P. D. SPENCER ◽  
D. MANNIX ◽  
...  
Keyword(s):  
Correlation Length ◽  
Surface Region ◽  
Crystalline Lattice ◽  
X Rays ◽  
Near Surface ◽  
X Ray ◽  
X Ray Scattering ◽  
Charge Stripe ◽  
A Charge ◽  
Ray Scattering

The La 2-x Sr x NiO 4 system is isostructural with the high T C superconducting cuprate La 2-x Sr x CuO 4 and is a prototypical system for the understanding of strongly correlated electron-phonon coupling, and the resultant effects on material properties. X-ray scattering studies have been performed on La5/3Sr1/3NiO4 that demonstrate the two-dimensional nature of these charge stripes. Such studies, demonstrate the very high correlation length of the stripes (~ 2000 Å) at low temperatures. We have undertaken a series of experiments measuring the wavevector and charge stripe correlation length on a variety of crystals with the compositions La 2-x Sr x NiO 4 (x=0.20, 0.25, 0.275, 0.30 and 0.33) using ~10 keV X-rays. The results demonstrate that for x=0.275, and above, the charge stripes are highly correlated in a well-ordered crystalline lattice. Measurements of the incommensurability, ε, as a function of temperature for the series revealed that it is commensurate and temperature independent for the x=0.33 sample. For other compositions it is incommensurate and also temperature dependent. However for the x=0.20 and 0.25 crystals a much reduced correlation length was observed suggestive of a charge stripe glass. However, such experiments are sensitive to such charge ordering only in the near (top few micron) surface region. High energy X-rays however can probe the charge stripe ordering within the bulk of the single crystal by utilising the dramatic increase in penetration depth. We have used 130 keV X-rays and demonstrate that in La5/3Sr1/3NiO4 the charge stripes are far less correlated in the bulk than in the near surface region. This reduced correlation length (~300 Å), consistent with neutron scattering measurements, is indicative of a charge stripe glass, reminiscent of that observed below x=0.25, in the near surface region.

scholarly journals Amorphous boron oxide at megabar pressures via inelastic X-ray scattering

2018 ◽  
Vol 115 (23) ◽  
pp. 5855-5860 ◽  
Author(s):  
Sung Keun Lee ◽  
Yong-Hyun Kim ◽  
Paul Chow ◽  
Yunming Xiao ◽  
Cheng Ji ◽  
...  
Keyword(s):  
Oxide Glass ◽  
X Rays ◽  
Oxide Glasses ◽  
Earth’S Core ◽  
Earth's Core ◽  
X Ray ◽  
Mantle Boundary ◽  
Core Mantle Boundary ◽  
X Ray Scattering ◽  
Ray Scattering

Structural transition in amorphous oxides, including glasses, under extreme compression above megabar pressures (>1 million atmospheric pressure, 100 GPa) results in unique densification paths that differ from those in crystals. Experimentally verifying the atomistic origins of such densifications beyond 100 GPa remains unknown. Progress in inelastic X-ray scattering (IXS) provided insights into the pressure-induced bonding changes in oxide glasses; however, IXS has a signal intensity several orders of magnitude smaller than that of elastic X-rays, posing challenges for probing glass structures above 100 GPa near the Earth’s core–mantle boundary. Here, we report megabar IXS spectra for prototypical B2O3 glasses at high pressure up to ∼120 GPa, where it is found that only four-coordinated boron ([4]B) is prevalent. The reduction in the [4]B–O length up to 120 GPa is minor, indicating the extended stability of sp3-bonded [4]B. In contrast, a substantial decrease in the average O–O distance upon compression is revealed, suggesting that the densification in B2O3 glasses is primarily due to O–O distance reduction without the formation of [5]B. Together with earlier results with other archetypal oxide glasses, such as SiO2 and GeO2, the current results confirm that the transition pressure of the formation of highly coordinated framework cations systematically increases with the decreasing atomic radius of the cations. These observations highlight a new opportunity to study the structure of oxide glass above megabar pressures, yielding the atomistic origins of densification in melts at the Earth’s core–mantle boundary.

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