Determination of dispersion and polarization of thermal plane waves in crystals

1971 ◽  
Vol 134 (3-4) ◽  
Author(s):  
P. L. La Fleur
Keyword(s):  
Intensity Distribution ◽  
Phonon Scattering ◽  
Reciprocal Lattice ◽  
Plane Waves ◽  
Lattice Points ◽  
X Ray Diffraction ◽  
Diffraction Intensity ◽  
Reciprocal Lattice Point ◽  
X Ray

AbstractThe dispersion of the thermal plane waves (phonons) in crystals can be determined from the x-ray diffraction intensity distribution around a reciprocal lattice point. In the method presented here no higher-order phonon-scattering corrections are necessary. It is shown furthermore that polarizations and dispersion of the phonons can be determined from the intensity distributions around six properly chosen reciprocal lattice points.

Protein crystals can be incommensurately modulated

2008 ◽  
Vol 41 (3) ◽  
pp. 600-605 ◽  
Author(s):  
Jeffrey J. Lovelace ◽  
Cameron R. Murphy ◽  
Lee Daniels ◽  
Kartik Narayan ◽  
Clarence E. Schutt ◽  
...  
Keyword(s):  
Diffraction Pattern ◽  
Reciprocal Lattice ◽  
Lattice Points ◽  
Chemical Crosslinking ◽  
X Ray Diffraction ◽  
X Ray ◽  
Periodic State ◽  
Orientation Matrix ◽  
Aperiodic Crystals ◽  
Future Work

For a normal periodic crystal, the X-ray diffraction pattern can be described by an orientation matrix and a set of three integers that indicate the reciprocal lattice points. Those integers determine the spacing along the reciprocal lattice directions. In aperiodic crystals, the diffraction pattern is modulated and the standard periodic main reflections are surrounded by satellite reflections. The successful indexing and refinement of the main unit cell andqvector usingTWINSOLVE, developed by Svensson [(2003). Lund University, Sweden], are reported here for an incommensurately modulated, aperiodic crystal of a profilin:actin complex. The indexing showed that the modulation is along thebdirection in the crystal, which corresponds to an `actin ribbon' formed by the crystal lattice. Interestingly, the transition to the aperiodic state was shown to be reversible and the diffraction pattern returned to the periodic state during data collection. It is likely that the protein underwent a conformational change that affected the neighbouring profilin:actin molecules in such a way as to produce the observed modulation in the diffraction pattern. Future work will aim to trap the incommensurately modulated crystal state, for example using cryocooling or chemical crosslinking, thus allowing complete X-ray data to be collected.

Characterization of Reactive Ion Etch Damage in GaAs by Triple Crystal X-Ray Diffraction

1993 ◽  
Vol 324 ◽  
Author(s):  
Victor S. Wang ◽  
Richard J. Matyi ◽  
Karen J. Nordheden
Keyword(s):  
Bias Voltage ◽  
Diffuse Scattering ◽  
Reciprocal Lattice ◽  
Surface Region ◽  
Perfect Crystal ◽  
X Ray Diffraction ◽  
Reciprocal Lattice Point ◽  
Near Surface ◽  
X Ray ◽  
Imperfect Crystal

AbstractTriple crystal x-ray diffraction (TCXD) is a non-destructive structural characterization tool capable of the separation and direct observation of the dynamic (perfect crystal) and the kinematic (imperfect crystal) components of the total intensity diffracted by a crystal. Specifically, TCXD can be used to measure the magnitude of the diffuse scattering arising from defects in the crystal structure in the immediate vicinity of a reciprocal lattice point. In this study, the effects of BC13 reactive ion etching (RIE) on the near-surface region of GaAs were investigated by analyzing the changes in the diffuse scattering using both the symmetric 004 reflection as well as the highly asymmetric and more surface sensitive 113 reflection. While the results from the 004 reflections revealed little difference between the unetched and the BC13-etched samples, maps of the diffracted intensity around the 113 reflections showed an unexpected and reproducible decrease in the extent of the diffuse scattering in the transverse direction (perpendicular to the < 113 > direction) as the RIE bias voltage was increased. This decrease suggests that the degree of etch damage induced in the GaAs near-surface region is reduced with increasing bias voltage and ion energy. Additionally, the symmetry and orientation of the kinematic scattering was altered. Possible mechanisms for these results willbe discussed.

High Resolution X-ray Diffraction of GaN Grown on Sapphire Substrates

1996 ◽  
Vol 449 ◽  
Author(s):  
A. Saxler ◽  
M. A. Capano ◽  
W. C. Mitchel ◽  
P. Kung ◽  
X. Zhang ◽  
...  
Keyword(s):  
Metalorganic Chemical Vapor Deposition ◽  
Reciprocal Lattice ◽  
Chemical Vapor ◽  
Lattice Points ◽  
Structural Quality ◽  
X Ray Diffraction ◽  
X Ray ◽  
Sapphire Substrates ◽  
Primary Mechanism

ABSTRACTX-ray rocking curves are frequently used to assess the structural quality of GaN thin films. In order to understand the information given by the line shape, we need to know the primary mechanism by which the curves are broadened. The GaN films used in this study were grown by low pressure metalorganic chemical vapor deposition (MOCVD) on (00•1) sapphire substrates. GaN films with both broad and very narrow (open detector linewidth of 40 arcseconds for the (00•2) GaN reflection) rocking curves are examined in this work. Reciprocal space maps of both symmetric and asymmetric reciprocal lattice points are used to determine that the cause of the broadening of GaN rocking curves is a limited in-plane coherence length.

Determination by high-resolution X-ray diffraction of shape, size and lateral separation of buried empty channels in silicon-on-nothing architectures

2007 ◽  
Vol 40 (2) ◽  
pp. 338-343 ◽  
Author(s):  
Marco Servidori
Keyword(s):  
High Resolution ◽  
Lattice Point ◽  
Reciprocal Lattice ◽  
Reciprocal Lattice Vector ◽  
X Ray Diffraction ◽  
Lattice Vector ◽  
Reciprocal Lattice Point ◽  
One Dimensional ◽  
X Ray ◽  
Planar Array

High-resolution multi-crystal X-ray diffraction was employed to characterize silicon-on-nothing samples made by a one-dimensional periodic planar array of buried empty channels. When the channels are normal to the scattering plane, under the constraint of lattice continuity from the perfect substrate to the surface, this periodic array gives rise to a well defined Fraunhofer diffraction in a scan crossing a selected reciprocal lattice point and normal to the reciprocal lattice vector (transverse or ω scan). In a longitudinal scan (ω/2θ scan crossing the reciprocal lattice point and parallel to the reciprocal lattice vector) interference fringes are observed. By analysis of the ω scan and numerical fit of the ω/2θ scan, the period of the buried empty channels and their shape, size and lateral gap were easily determined, thanks to the high-resolution optics used for the measurements.

scholarly journals Improved crystal orientation and physical properties from single-shot XFEL stills

2014 ◽  
Vol 70 (12) ◽  
pp. 3299-3309 ◽  
Author(s):  
Nicholas K. Sauter ◽  
Johan Hattne ◽  
Aaron S. Brewster ◽  
Nathaniel Echols ◽  
Petrus H. Zwart ◽  
...  
Keyword(s):  
Crystal Orientation ◽  
Degrees Of Freedom ◽  
Reciprocal Lattice ◽  
Single Shot ◽  
X Ray Diffraction ◽  
Reciprocal Lattice Point ◽  
X Ray ◽  
Structure Factors ◽  
Rotational Degrees Of Freedom ◽  
Diffraction Patterns

X-ray diffraction patterns from still crystals are inherently difficult to process because the crystal orientation is not uniquely determined by measuring the Bragg spot positions. Only one of the three rotational degrees of freedom is directly coupled to spot positions; the other two rotations move Bragg spots in and out of the reflecting condition but do not change the direction of the diffracted rays. This hinders the ability to recover accurate structure factors from experiments that are dependent on single-shot exposures, such as femtosecond diffract-and-destroy protocols at X-ray free-electron lasers (XFELs). Here, additional methods are introduced to optimally model the diffraction. The best orientation is obtained by requiring, for the brightest observed spots, that each reciprocal-lattice point be placed into the exact reflecting condition implied by Bragg's law with a minimal rotation. This approach reduces the experimental uncertainties in noisy XFEL data, improving the crystallographicRfactors and sharpening anomalous differences that are near the level of the noise.

Materials characterization from diffraction intensity distribution in the γ-direction

2014 ◽  
Vol 29 (2) ◽  
pp. 113-117 ◽  
Author(s):  
Bob B. He
Keyword(s):  
Intensity Distribution ◽  
Crystal Size ◽  
Profile Analysis ◽  
Structure Refinement ◽  
Size Analysis ◽  
Phase Identification ◽  
X Ray Diffraction ◽  
Diffraction Intensity ◽  
X Ray ◽  
Orientation Relations

Two-dimensional X-ray diffraction (XRD2) pattern can be described by the diffraction intensity distribution in both 2θ and γ-directions. The XRD2 images can be reduced to two kinds of profiles: 2θ-profile and γ-profile. The 2θ-profile can be evaluated for phase identification, crystal structure refinement, and many applications with many existing algorithms and software. In order to evaluate the materials structure associated with the intensity distribution along γ-angle, either the XRD2 pattern should be directly analyzed or the γ-profile can be generated by 2θ-integration. A γ-profile contains information on texture, stress, crystal size, and crystal orientation relations. This paper introduces the concept and fundamental algorithms for stress, texture, and crystal size analysis by the γ-profile analysis.

High-resolution x-ray diffraction study of In0.25Ga0.75Sb/InAs superlattice

1999 ◽  
Vol 14 (5) ◽  
pp. 1744-1751 ◽  
Author(s):  
A. Vigliante ◽  
H. Homma ◽  
J. T. Zborowski ◽  
T. D. Golding ◽  
S. C. Moss
Keyword(s):  
High Resolution ◽  
Structural Parameters ◽  
Reciprocal Lattice ◽  
Lattice Points ◽  
Diffuse Interface ◽  
X Ray Diffraction ◽  
Group V ◽  
X Ray ◽  
Strained Layer Superlattice ◽  
Ir Detection

An In0.25Ga0.75Sb/InAs strained-layer superlattice, grown by molecular-beam epitaxy (MBE) on a GaSb[001] substrate, has been characterized by four-circle x-ray diffractometry. This system, proposed by Maliot and Smith for ir detection application, is challenging because of the two group V species and the likelihood of cross-incorporation of the different elements during growth, leading possibly to interdiffusion and thus, to a more diffuse interface. High-resolution x-ray diffraction (XRD) profiles were obtained about several reciprocal lattice points in order to extract a reliable set of structural parameters. The profiles were then successfully modeled by computer simulation. The presence of many sharp higher-order satellite reflections in the XRD profiles is a measure of the high quality of the superlattices. The normal and lateral structural coherence was also measured and will be discussed.

X-Ray Line Profile Analysis for Single Crystals

2014 ◽  
pp. 242-270
Keyword(s):  
Single Crystals ◽  
Intensity Distribution ◽  
Profile Analysis ◽  
Reciprocal Lattice ◽  
Lattice Points ◽  
Polycrystalline Materials ◽  
Line Profile Analysis ◽  
Line Profiles ◽  
X Ray ◽  
Lattice Misorientation

The features of the dislocation structure in plastically deformed single crystals can be determined from diffraction line broadening. Both the measuring and the evaluation procedures of X-ray line profiles are somewhat different from the methods used for polycrystalline materials. In this chapter, these procedures are overviewed, and their effectiveness is illustrated by representative examples. It is shown that the intensity distribution in the vicinity of the reciprocal lattice points can be mapped by rocking the single crystal about appropriate axes. From the detected intensity distribution, the density, the slip systems, and the arrangement of dislocations, as well as the lattice misorientation can be determined. The average misorientation obtained from rocking curve measurement can be related to the density of geometrically necessary dislocations. It is also shown that the inhomogeneous distribution of dislocations in plastically deformed single crystals usually results in asymmetric line profiles. The evaluation of these peaks enables the determination of the long-range internal stresses besides the dislocation densities in the dislocation cell walls and interiors.

Structural Characterization of Reactive Ion Etched Semiconductor Nanostructures Using X-Ray Reciprocal Space Mapping

1995 ◽  
Vol 406 ◽  
Author(s):  
G. Bauer ◽  
A. A. Darhuber ◽  
V. Holy
Keyword(s):  
Quantum Dot ◽  
Reciprocal Lattice ◽  
Space Mapping ◽  
Reciprocal Space ◽  
Lattice Points ◽  
Scanning Electron Micrographs ◽  
X Ray Diffraction ◽  
Reciprocal Space Mapping ◽  
Entire Volume ◽  
X Ray

AbstractWe have studied GaAs/AlAs periodic quantum dot arrays using high resolution x-ray diffraction (reciprocal space mapping) around the (004) and (113) reciprocal lattice points. From the distribution of the diffracted intensities we deduced the average strain status of the dots. From the numerical simulations it is evident that random elastic strain fields are present, which extend through almost the entire volume of the quantum dot. The simulations of the x-ray measurements revealed that the crystalline part of the dots is considerably smaller as scanning electron micrographs would indicate.

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