Diffuse scattering and phason modes in the i-AlPdMn quasicrystalline phase

2005 ◽  
Vol 220 (12) ◽  
Author(s):  
Marc de Boissieu ◽  
Sonia Francoual
Keyword(s):  
Elastic Constant ◽  
Elastic Constants ◽  
Intensity Distribution ◽  
Diffuse Scattering ◽  
Hydrodynamic Theory ◽  
Quasicrystalline Phase ◽  
X Rays ◽  
X Ray ◽  
Long Wavelength ◽  
Diffusive Modes

AbstractWe review results obtained in the study of the diffuse scattering in the i-AlPdMn quasicrystal. Most of the diffuse scattering is the result of long wavelength phason modes. The shape and intensity distribution of the diffuse scattering is well reproduced using the generalised elasticity theory and two phason elastic constants. The temperature dependence of the diffuse scattering indicates a softening of the phason elastic constant as the temperature is lowered. Using coherent X-rays and photo-correlation X-ray spectroscopy, it is shown that phason modes are collective diffusive modes, in agreement with the hydrodynamic theory of long wavelength fluctuations in quasicrystals.

X-Ray Diffuse Scattering Investigation of Defects in Ion Implanted and Annealed Silicon

1998 ◽  
Vol 524 ◽  
Author(s):  
C. H. Chang ◽  
U. Beck ◽  
T. H. Metzger ◽  
J. R. Patel
Keyword(s):  
Ion Implantation ◽  
Point Defect ◽  
Point Defects ◽  
Diffuse Scattering ◽  
Grazing Incidence ◽  
X Rays ◽  
Scattered Intensity ◽  
X Ray ◽  
Defect Clusters ◽  
Point Defect Clusters

ABSTRACTTo characterize the point defects and point defect clusters introduced by ion implantation and annealing, we have used grazing incidence x-rays to measure the diffuse scattering in the tails of Bragg peaks (Huang Scattering). An analysis of the diffuse scattered intensity will allow us to characterize the nature of point defects or defect clusters introduced by ion implantation. We have also observed unexpected satellite peaks in the diffuse scattered tails. Possible causes for the occurrence of the peaks will be discussed.

Determination of X-ray Elastic Constants in a Ti-14Al-21Nb Nb Alloy and a Ti-14Al-21Nb/SiC Metal Matrix Composite

1990 ◽  
Vol 34 ◽  
pp. 689-698 ◽  
Author(s):  
J. Jo ◽  
R. W. Hendricks ◽  
W. D. Brewer ◽  
Karen M. Brown
Keyword(s):  
Residual Stress ◽  
Plastic Deformation ◽  
Elastic Constant ◽  
Theoretical Calculation ◽  
Metal Matrix Composite ◽  
Elastic Constants ◽  
Metal Matrix ◽  
Intrinsic Value ◽  
X Ray

Residual stress values in a material are governed by the measurements of the atomic spacings in a specific crystallographic plane and the elastic constant for that plane. It has been reported that the value of the elastic constant depends on microstructure, preferred orientation, plastic deformation and morphology [1], Thus, the theoretical calculation of the elastic constant may deviate from the intrinsic value for a real alloy.

Implementation of the self-consistent Kröner–Eshelby model for the calculation of X-ray elastic constants for any crystal symmetry

2019 ◽  
Vol 34 (2) ◽  
pp. 103-109
Author(s):  
Arnold C. Vermeulen ◽  
Christopher M. Kube ◽  
Nicholas Norberg
Keyword(s):  
Elastic Constants ◽  
Ultrasonic Waves ◽  
The Self ◽  
Crystal Symmetry ◽  
Intermediate Step ◽  
X Rays ◽  
X Ray ◽  
Eshelby Inclusion ◽  
Eshelby Model ◽  
Self Consistent

In this paper, we will report about the implementation of the self-consistent Kröner–Eshelby model for the calculation of X-ray elastic constants for general, triclinic crystal symmetry. With applying appropriate symmetry relations, the point groups of higher crystal symmetries are covered as well. This simplifies the implementation effort to cover the calculations for any crystal symmetry. In the literature, several models can be found to estimate the polycrystalline elastic properties from single crystal elastic constants. In general, this is an intermediate step toward the calculation of the polycrystalline response to different techniques using X-rays, neutrons, or ultrasonic waves. In the case of X-ray residual stress analysis, the final goal is the calculation of X-ray Elastic constants. Contrary to the models of Reuss, Voigt, and Hill, the Kröner–Eshelby model has the benefit that, because of the implementation of the Eshelby inclusion model, it can be expanded to cover more complicated systems that exhibit multiple phases, inclusions or pores and that these can be optionally combined with a polycrystalline matrix that is anisotropic, i.e., contains texture. We will discuss a recent theoretical development where the approaches of calculating bounds of Reuss and Voigt, the tighter bounds of Hashin–Shtrikman and Dederichs–Zeller are brought together in one unifying model that converges to the self-consistent solution of Kröner–Eshelby. For the implementation of the Kröner–Eshelby model the well-known Voigt notation is adopted. The 4-rank tensor operations have been rewritten into 2-rank matrix operations. The practical difficulties of the Voigt notation, as usually concealed in the scientific literature, will be discussed. Last, we will show a practical X-ray example in which the various models are applied and compared.

X-Ray Diffuse Scattering from Cobalt Precipitates in Copper

1986 ◽  
Vol 82 ◽  
Author(s):  
B. C. Larson ◽  
S. Iida ◽  
J. Z. Tischler ◽  
J. D. Lewis ◽  
G. E. Ice ◽  
...  
Keyword(s):  
Crystal Lattice ◽  
Size Distribution ◽  
Diffuse Scattering ◽  
Large Angle ◽  
Host Lattice ◽  
Internal Strain ◽  
X Rays ◽  
X Ray ◽  
Scattering Measurements

ABSTRACTLarge-angle diffuse scattering has been investigated for the purpose of studying coherent precipitates in a crystal lattice. Detailed calculations have been made of the scattering near Bragg reflections from cobalt precipitates in a copper host lattice. These calculations have been compared to x-ray diffuse scattering measurements made on aged (570°C for 17 hr.) Cu-0.95%Co crystals with x-rays of three different wavelengths at the NSLS. The results indicate that the size distribution, the concentration, and the internal strain of the precipitates can be determined from such diffuse scattering measurements.

SECONDARY RADIATION FROM X-RAY FILTERS: I. SINGLE-METAL FILTERS

1942 ◽  
Vol 20a (11) ◽  
pp. 185-194
Author(s):  
G. A. Wrenshall ◽  
H. J. Nichols
Keyword(s):  
Intensity Distribution ◽  
Ionization Chamber ◽  
Operating Conditions ◽  
Secondary Radiation ◽  
X Rays ◽  
X Ray ◽  
Chamber Method ◽  
Aluminium Copper ◽  
Standard Operating

Using an ionization chamber method, the intensity distribution and quality of forward transmitted secondary X-rays from filters of aluminium, copper, tin, and lead have been measured under standard operating conditions. Geometrical arrangements of X-ray tube, defining apertures, filter, and receiver commonly used in medical and industrial radiology are employed. Suggestions for minimizing the intensity of the secondary radiation reaching the receiver from single-metal filters are submitted.

Helium Path Diffractometry and its Application to Determination of Retained Austenite and Macrostress in Steel

1962 ◽  
Vol 6 ◽  
pp. 85-90
Author(s):  
Robert A. McCune
Keyword(s):  
Retained Austenite ◽  
Intensity Increase ◽  
X Rays ◽  
X Ray ◽  
Long Wavelength ◽  
Gauge Block ◽  
Background Ratio ◽  
Ray Path

AbstractThe helium X-ray path has long been used, in spectrography to increase the intensity of the long-wavelength X-rays. The same principle has been applied to diflractometry. Up to threefold intensity increase is observed with chromium Ka radiation with very little increase In background. The peak to background ratio, therefore, is Improved by almost the same factor as the increase in intensity. Application of the technique is illustrated by analysis of gauge block steel for retained austcnite and macrostress.

Adaptation of the X-Ray Diffraction Technique to the Analysis of Residual Stress in Carbo-Nitrided Steel Layers

2005 ◽  
Vol 490-491 ◽  
pp. 125-130
Author(s):  
Jean Michel Sprauel ◽  
H. Michaud
Keyword(s):  
Residual Stress ◽  
Carbon Content ◽  
Diffuse Scattering ◽  
Volume Fraction ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Quantitative Phase ◽  
Nitrided Steel ◽  
Stress Components

X-ray diffraction is used to analyse the fatigue behaviour of carbo-nitrided steel layers. Measurements are therefore carried out on the two major phases of the material, i.e. the martensite (a') and the retained austenite (g). On such gear material, X-ray residual stress evaluations are particularly difficult for three reasons. First, the studied material is multiphase. For that reason, in each phase, the stress component in the direction normal to the surface is non negligible. Second, the diffraction peaks obtained on the martensite are broadened, due to the overlap of different reflections of the tetragonal structure. Third, the material contains also carbide and nitride clusters, which lead to incoherent and diffuse scattering of X-rays thus making quantitative phase determination difficult. In our paper the methods used to solve these problems are presented. The development of a new quantitative phase analysis method which accounts for the variation of diffuse scattering of X-rays is shown first. The second part deals with an iterative micromechanical model implemented for the evaluation of the carbon content and the residual stress components of each phase. These methods are used for analysing the evolution with cycling fatigue of all the parameters derived from our enhanced analysis (phase volume fraction, carbon content, stress components, peak width).

scholarly journals The Radiation Transfer of Soft X-rays

1997 ◽  
Vol 166 ◽  
pp. 337-340 ◽  
Author(s):  
Jürgen Kerp ◽  
Jochen Pietz
Keyword(s):  
Power Law ◽  
Intensity Distribution ◽  
Galactic Halo ◽  
Background Radiation ◽  
Plasma Temperature ◽  
Intensity Variation ◽  
Background Intensity ◽  
X Rays ◽  
Energy Bands ◽  
X Ray

AbstractWe discuss the link between the halo plasma temperature and the power-law spectral index of the extragalactic background radiation. This link is of strong influence for the derivation of the Galactic halo intensity distribution. In principal, we can distinguish between two combinations of Galactic halo plasma temperature and power-law slope. The first combination consists of a halo plasma of Thalo = 106 K and an E−2 approximation of the extragalactic background radiation. The second combination is Thalo = 106.2 K and an E−1.5. Both combinations are in agreement with recent observational results, thus it is not feasible to discriminate between both models on the basis of X-ray data available. But, the soft X-ray background intensity distribution in the ¼ keV and ¾ keV ROSAT energy bands differs significantly. The Thalo = 106 K and an E−2 allows a patchy ¼ keV intensity distribution while the Thalo = 106.2 K and an E−1.5 predicts a much smoother intensity variation since the hotter halo plasma accounts for a significant fraction of the ¾ keV background radiation.

scholarly journals Interface Evolution in a W/Si Multilayer after Rapid Thermal Annealing Studied by X-ray Reflectivity and Diffuse Scattering

1997 ◽  
Vol 30 (5) ◽  
pp. 642-646 ◽  
Author(s):  
M. Jergel ◽  
V. Holý ◽  
E. Majková ◽  
S. Luby ◽  
R. Senderák
Keyword(s):  
Thermal Annealing ◽  
Rapid Thermal Annealing ◽  
Diffuse Scattering ◽  
Grazing Incidence ◽  
Interface Roughness ◽  
X Rays ◽  
Interface Evolution ◽  
X Ray ◽  
Scattering Measurements ◽  
Highly Correlated

An interface study of the effect of rapid thermal annealing (RTA) in the temperature range 523–1273 K for 5–40 s on a nominally [(50 Å Si/10 Å W) × 9] amorphous multilayer (ML) deposited on an Si(100) wafer was performed by X-ray reflectivity and diffuse-scattering measurements at grazing incidence. The results of the X-ray reflectivity and diffuse-scattering measurements were evaluated by Fresnel optical computational code and within the distorted-wave Born approximation, respectively. Up to the 773 K/5 s annealing step, the r.m.s. interface roughness decreases by 30%, which brings about a reflectivity increase of 20% on the first Bragg maximum. There is a small overall increase of the r.m.s. interface roughness across the ML in the as-deposited state and the interface profiles are highly correlated. From the very beginning of RTA, the fractal interface behaviour is gradually lost and the lateral correlation length increases, this process being accompanied by a decrease of the interface conformality. This tendency continues during the 773 K/20 s annealing; however, the r.m.s. roughness evolution is reversed. During the 1023 K/5 s annealing, the interfaces are no longer `seen' by the X-rays and, during the 1273 K/5 s annealing, a total collapse of the ML structure takes place.

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