Measurement of stress/strain in single-crystal samples using diffraction

2006 ◽  
Vol 39 (3) ◽  
pp. 320-325 ◽  
Author(s):  
Hanfei Yan ◽  
I. C. Noyan
Keyword(s):  
Single Crystal ◽  
Strain Analysis ◽  
Incident Beam ◽  
Diffraction Theory ◽  
Secondary Peak ◽  
Bending Strain ◽  
Integrated Intensity ◽  
Cantilever Bending ◽  
Incident Beam Energy ◽  
Tip Displacement

Diffraction profiles from an Si-single-crystal strip deformed in cantilever bending are presented as a function of tip displacement and incident-beam energy. Data obtained with slit-based diffracted-beam optics contain a secondary peak in addition to the primary 004 reflection for all energies when the bending strain is finite. This secondary peak can be identified as a `mirage' peak, predicted by dynamical diffraction theory to occur in weakly deformed single-crystal samples. The integrated intensity of this mirage peak increases with increasing energy and tip displacement and exceeds the primary peak intensity at higher values. The mirage peak disappears when a monochromator is used in the diffracted-beam path. Data that show the effect of these mirage peaks on X-ray diffraction strain analysis are presented, and it is shown that a diffracted-beam monochromator may be used to eliminate these errors.

Diffraction profiles of elastically bent single crystals with constant strain gradients

2007 ◽  
Vol 40 (2) ◽  
pp. 322-331 ◽  
Author(s):  
Hanfei Yan ◽  
Özgür Kalenci ◽  
I. C. Noyan
Keyword(s):  
Single Crystal ◽  
Strain Gradient ◽  
Bragg Reflection ◽  
Incident Beam ◽  
Sample Surface ◽  
Intersection Point ◽  
Diffraction Peak ◽  
Specimen Surface ◽  
Diffraction Profile ◽  
Integrated Intensity

This work presents a set of equations that can be used to predict the dynamical diffraction profile from a non-transparent single crystal with a constant strain gradient examined in Bragg reflection geometry with a spherical incident X-ray beam. In agreement with previous work, the present analysis predicts two peaks: a primary diffraction peak, which would have still been observed in the absence of the strain gradient and which exits the specimen surface at the intersection point of the incident beam with the sample surface, and a secondary (mirage) peak, caused by the deflection of the wavefield within the material, which exits the specimen surface further from this intersection point. The integrated intensity of the mirage peak increases with increasing strain gradient, while its separation from the primary reflection peak decreases. The directions of the rays forming the mirage peak are parallel to those forming the primary diffraction peak. However, their spatial displacement might cause (fictitious) angular shifts in diffractometers equipped with area detectors or slit optics. The analysis results are compared with experimental data from an Si single-crystal strip bent in cantilever configuration, and the implications of the mirage peak for Laue analysis and high-precision diffraction measurements are discussed.

scholarly journals Accurate Determination of Structure Factors by Pendellosung Methods Using White Radiation

1988 ◽  
Vol 41 (3) ◽  
pp. 433 ◽  
Author(s):  
T Takama ◽  
S Sato
Keyword(s):  
Single Crystal ◽  
Accurate Determination ◽  
Diffraction Theory ◽  
Specimen Thickness ◽  
Dynamical Diffraction ◽  
Laue Spot ◽  
Exit Surface ◽  
Structure Factors ◽  
Integrated Intensity

This paper describes two experimental techniques measuring the Pendellosung beats using white radiation, developed in the authors' laboratory. The intensity of a Laue spot diffracted from a parallel-sided single crystal is successively measured at different Bragg angles, i.e. with different wavelengths. The values of structure factors are evaluated from extremum positions in the measured beats on the basis of the dynamical diffraction theory. In the first method, the integrated intensity diffracted from the whole exit surface is measured, and in the second, the measurement is made only at the centre of the Borrmann fan on the exit surface of a specimen. A discussion is given on the accuracy associated with the following origins of errors: (1) polarisation of incident white radiation, (2) measurement of specimen thickness, (3) measurement of wavelength, (4) determination of extremum positions, and (5) effect of defects in the crystal.

Instrumentation for detecting channelling radiation in the high-voltage electron microscope

1983 ◽  
Vol 41 ◽  
pp. 318-319
Author(s):  
J. H. Butler ◽  
C. J. Humphreys
Keyword(s):  
Monochromatic Light ◽  
Incident Beam ◽  
Laboratory Frame ◽  
Relativistic Electrons ◽  
Voltage Electron ◽  
Dipole Emission ◽  
Sinusoidal Oscillations ◽  
Pass Through ◽  
Incident Beam Energy ◽  
Increasing Function

Electromagnetic radiation is emitted when fast (relativistic) electrons pass through crystal targets which are oriented in a preferential (channelling) direction with respect to the incident beam. In the classical sense, the electrons perform sinusoidal oscillations as they propagate through the crystal (as illustrated in Fig. 1 for the case of planar channelling). When viewed in the electron rest frame, this motion, a result of successive Bragg reflections, gives rise to familiar dipole emission. In the laboratory frame, the radiation is seen to be of a higher energy (because of the Doppler shift) and is also compressed into a narrower cone of emission (due to the relativistic “searchlight” effect). The energy and yield of this monochromatic light is a continuously increasing function of the incident beam energy and, for beam energies of 1 MeV and higher, it occurs in the x-ray and γ-ray regions of the spectrum. Consequently, much interest has been expressed in regard to the use of this phenomenon as the basis for fabricating a coherent, tunable radiation source.

Optimizing conditions for x-ray microchemical analysis in analytical electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 548-549 ◽  
Author(s):  
N. J. Zaluzec
Keyword(s):  
Solid Angle ◽  
Analytical Electron Microscopy ◽  
Incident Beam ◽  
Thin Foil ◽  
Experimental Conditions ◽  
X Ray ◽  
Microchemical Analysis ◽  
Analytical Electron ◽  
Image Position ◽  
Incident Beam Energy

The ultimate sensitivity of microchemical analysis using x-ray emission rests in selecting those experimental conditions which will maximize the measured peak-to-background (P/B) ratio. This paper presents the results of calculations aimed at determining the influence of incident beam energy, detector/specimen geometry and specimen composition on the P/B ratio for ideally thin samples (i.e., the effects of scattering and absorption are considered negligible). As such it is assumed that the complications resulting from system peaks, bremsstrahlung fluorescence, electron tails and specimen contamination have been eliminated and that one needs only to consider the physics of the generation/emission process.The number of characteristic x-ray photons (Ip) emitted from a thin foil of thickness dt into the solid angle dΩ is given by the well-known equation

LACBED with Quantitative Anomalous Absorption Corrections

1990 ◽  
Vol 48 (2) ◽  
pp. 528-529
Author(s):  
C.J. Rossouw ◽  
L.J. Allen ◽  
P.R. Miller
Keyword(s):  
Momentum Transfer ◽  
Scattering Amplitude ◽  
Incident Beam ◽  
Waller Factor ◽  
Beam Momentum ◽  
Anomalous Absorption ◽  
Quantitative Calculation ◽  
Ewald Sphere ◽  
Image Position ◽  
Incident Beam Energy

An Einstein model for thermal diffuse scattering (TDS) has enabled quantitative calculation of the absorptive potential V'(r). This allows anomalous absorption to be accounted for in LACBED contrast. Fourier coefficients Vg-h of the absorptive component from each atom α are calculated from integrals of the formwhere fα is the scattering amplitude and M(Q) the Debye-Waller factor. Integration over the Ewald sphere (dΩ) requires the momentum transfer q to have values up to 2ko (the incident beam momentum). Dynamical ‘dechannelling’ is accounted for by the terms g ≠ h. The crystal absorptive potential is obtained by coherently summing over these atomic absorptive potentials within the unit cell. Unlike the elastic potential, the absorptive potential is a strong function of incident beam energy Eo, since the range of momentum transfer q and associated solid angles dΩ change with the Ewald sphere radius.Fig. 1 shows a LACBED pattern of the zeroth order beam from Si aligned along a <001> zone axis.

Algorithms for determining the phase of RHEED oscillations

2015 ◽  
Vol 48 (6) ◽  
pp. 1927-1934 ◽  
Author(s):  
Zbigniew Mitura ◽  
Sergei L. Dudarev
Keyword(s):  
Experimental Data ◽  
Direct Method ◽  
Incident Beam ◽  
Diffraction Theory ◽  
High Energy ◽  
Angle Of Incidence ◽  
High Energy Electron ◽  
Dynamical Diffraction ◽  
Glancing Angle ◽  
Low Symmetry

Oscillations of reflection high-energy electron diffraction (RHEED) intensities are computed using dynamical diffraction theory. The phase of the oscillations is determined using two different approaches. In the first, direct, approach, the phase is determined by identifying the time needed to reach the second oscillation minimum. In the second approach, the phase is found using harmonic analysis. The two approaches are tested by applying them to oscillations simulated using dynamical diffraction theory. The phase of RHEED oscillations observed experimentally is also analysed. Experimental data on the variation of the phase as a function of the glancing angle of incidence, derived using the direct method, are compared with the values computed using both the direct and harmonic methods. For incident-beam azimuths corresponding to low-symmetry directions, both approaches produce similar results.

Inference on fission timescale from neutron multiplicity measurement in18O+184W

2022 ◽  
Author(s):  
Niraj Kumar Rai ◽  
Aman Gandhi ◽  
M T Senthil Kannan ◽  
Sujan Kumar Roy ◽  
Saneesh Nedumbally ◽  
...  
Keyword(s):  
Excitation Energy ◽  
Beam Energy ◽  
Incident Beam ◽  
Fission Process ◽  
Incident Beam Energy ◽  
Neutron Evaporation ◽  
Neutron Multiplicities ◽  
Nuclear Dissipation ◽  
Fission Yields ◽  
Primary Compound

Abstract The pre-scission and post-scission neutron multiplicities are measured for the 18O + 184W reaction in the excitation energy range of 67.23−76.37 MeV. Langevin dynamical calculations are performed to infer the energy dependence of fission decay time in compliance with the measured neutron multiplicities. Different models for nuclear dissipation are employed for this purpose. Fission process is usually expected to be faster at a higher beam energy. However, we found an enhancement in the average fission time as the incident beam energy increases. It happens because a higher excitation energy helps more neutrons to evaporate that eventually stabilizes the system against fission. The competition between fission and neutron evaporation delicately depends on the available excitation energy and it is explained here with the help of the partial fission yields contributed by the different isotopes of the primary compound nucleus.

DIFFRACTION OF 3.2 CM. ELECTROMAGNETIC WAVES BY CYLINDRICAL OBJECTS

1954 ◽  
Vol 32 (6) ◽  
pp. 372-380 ◽  
Author(s):  
A. B. McLay ◽  
S. T. Wiles
Keyword(s):  
Electromagnetic Waves ◽  
Incident Beam ◽  
Diffraction Theory ◽  
Central Peak ◽  
Beam Direction ◽  
Cylinder Axis ◽  
Scalar Diffraction ◽  
Conducting Cylinder ◽  
Scalar Diffraction Theory ◽  
Diffraction Patterns

Diffraction patterns of a brass tube and a hard rubber rod, each a cylinder of 1 in. diameter, in a nearly plane beam of square-wave modulated 3 cm. waves with electric vector parallel to the cylinder axis, have been measured in several planes transverse to the incident beam direction. Experimental results for the conducting cylinder agree closely with calculations based on scalar diffraction theory. Patterns of the dielectric rod show a pronounced central peak immediately behind the rod and other intensity effects differing from the conducting cylinder patterns, particularly in the vicinity of the shadow.

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