[show abstract][hide abstract] ABSTRACT: In X-ray interference fringes accompanied by mirage diffraction, variations have been observed in the spacing and position of the fringes from a plane-parallel Si single crystal fixed at one end as a function of distance from the incident plane of the X-rays to the free crystal end. The variations can be explained by distortion of the sample crystal due to gravity. From the variations and positions of the fringes, the strain gradient of the crystal has been determined. The distribution of the observed strain agrees with that expected from rod theory except for residual strain. When the distortion is large, the observed strain distribution does not agree with that expected from rod theory.
[show abstract][hide abstract] ABSTRACT: Interference fringes from a Si plane-parallel crystal have been observed
in the topography of the transmitted beam in the Bragg mode when the
crystal is very weakly bent. The period of the interference fringes
becomes large as the distance from the incident point of the X-ray to
the emitted point of the beam increases. The interference fringes are
caused by interference between the transmitted beams in the Bragg mode
with twice internal reflections from the bottom and top surfaces and
those without any internal reflection. When these interference fringes
are observed, another interference fringes are observed in the emitted
beams from the lateral surface even when the distance from the incident
point to the crystal edge is 13.5 mm. This indicates that X-rays
propagate over a long distance, i.e., over a centimeter distance in the
crystal, and the very weakly bent crystal acts as an X-ray waveguide.
Journal of the Physical Society of Japan 09/2012; 81(9):4804-. · 2.09 Impact Factor
[show abstract][hide abstract] ABSTRACT: Two experimental approaches are studied to determine a parameter of the
strain gradient in an elastically bent crystal. In one approach, the
parameter is determined by measuring the third peak of the X-ray mirage
interference fringes and in the other, by measuring the region where no
mirage diffraction beam reaches on the lateral surface of the crystal.
Using the X-rays from synchrotron radiation, the mirage fringes have
been observed in the 220 reflection of the Si crystal whose strain is
controlled in cantilever bending. These two approaches both give
accurate values of the parameter of the strain gradient, showing good
agreement with the values calculated using elastic theory. In addition,
the residual strain due to gravity is observed by measuring mirage
fringes when the bending force becomes zero.
Japanese Journal of Applied Physics 07/2012; 51(7):6702-. · 1.07 Impact Factor
[show abstract][hide abstract] ABSTRACT: When the dispersion angle of X-rays in a perfect crystal is large,
interference fringes are observed between the beams in the Bragg-Laue
mode and Bragg-Bragg-Laue mode in the emitted beams from the lateral
surface. If the crystal is weakly bent, X-rays propagate along a path of
hyperbolic form and are diffracted from the incident surface, which is
called mirage diffraction. Under the condition, mirage interference
fringes between two mirage diffraction beams are observed not only from
the incident surface but also from the lateral surface. Two approaches
are proposed to determine strain parameters in the bent crystal by using
the mirage interference fringes from the incident surface or the lateral
surface. In one approach, the third peak of the mirage interference
fringes is used. In the other, the region is used where no direct beam
reaches to the lateral surface. The resultant strain parameters
determined by the two approaches show excellent agreement. Some
characteristics and advantages of using mirage interference fringes are
[show abstract][hide abstract] ABSTRACT: In X-ray section topography of Si 220 diffraction in a multiple Bragg-Laue mode, a moiré pattern is observed when the incident beam is divided into two parts by inserting a platinum wire in the middle of the beam. The moiré pattern can be explained by the summation of two interference fringes corresponding to the two incident beams. The coherency of the X-rays from the bending-magnet beamline is estimated using the moiré pattern.
[show abstract][hide abstract] ABSTRACT: A novel two-beam X-ray interferometer using two multiple Bragg--Laue
(MBL) mode interferometers has been developed. The first MBL
interferometer was utilized not only as a monochromator to generate a
highly coherent beam but also as a beam splitter. The second MBL
interferometer was used as an analyzer. By using this two-beam X-ray
interferometer, interference fringes were observed as a function of the
thickness of a phase plate inserted in one path of incident X-rays. The
visibility of the measured fringes is approximately 25%. Some advantages
of this MBL interferometer are pointed out.
Journal of the Physical Society of Japan 07/2011; 80(8):3001. · 2.09 Impact Factor
[show abstract][hide abstract] ABSTRACT: Interference fringes in multiple Bragg-Laue mode have been measured from the lateral surface of an Si plane-parallel crystal by changing the distance L between the incident point of X-rays and the crystal edge for two sample crystals with different thicknesses H. The period of the interference fringes becomes large when the distance L becomes large or the thickness H becomes small. When the ratio L/H is larger than 15, a shorter period of oscillation appears in addition to the interference fringes. These variations are explained by considering the beams in multiple Bragg-Laue modes based on the dynamical theory of diffraction. When L/H is less than 15, the measured fringes are well reproduced by taking account of interference between beams in the Bragg-Laue and the Bragg-Bragg-Laue modes. The short period of the oscillations observed for L/H > 15 is reproduced by adding the intensities of the beams in higher-order Bragg-Laue mode. The interference fringes calculated by taking the visibility into account show good agreement with the measured ones.
Acta crystallographica. Section A, Foundations of crystallography 03/2011; 67(Pt 2):154-9. · 49.93 Impact Factor
[show abstract][hide abstract] ABSTRACT: Topographies of Si 220 reflection in the Bragg mode have been observed from a weakly bent single crystal. When bending is very weak, a novel interference fringe is observed instead of mirage diffraction fringes. The period of this fringe increases with the distance between the incident point of X-rays and the exit point of the diffracted beam. This interference fringe is caused by the interference between a mirage diffraction beam and the reflected beam from the bottom surface. When this interference fringe is observed, the interference fringes are also observed from the lateral surface even when the distance from the incident point to the crystal edge is 12 mm; X-rays propagate over a long distance, i.e., over a centimeter distance in the crystal.
Journal of The Physical Society of Japan - J PHYS SOC JPN. 01/2011; 80.
[show abstract][hide abstract] ABSTRACT: Interference fringes are measured in the diffraction from the surface as well as from the lateral surface of an Si single-crystal strip which is deformed in cantilever bending as a function of the tip displacement. The interference fringes are observed only when the bending strain is applied. Both interference fringes change conspicuously by increasing the bending strain. The number of the interference fringes changes, and the positions and heights of the peaks in the fringes change. These variations can be explained by the change of the interference between the beams in multiple Bragg-Laue modes and those of mirage diffraction based on the dynamical theory of diffraction.
Acta crystallographica. Section A, Foundations of crystallography 05/2010; 66(Pt 3):421-6. · 49.93 Impact Factor
[show abstract][hide abstract] ABSTRACT: X-ray interference fringes in the beams diffracted from a lateral surface of a thin plane-parallel crystal are measured and analyzed using Wagner's approach [Wagner (1956), Z. Phys. 146, 127-168]. It is found that the fringes are caused by the interference between the internal waves excited by the incident beam in both the Bragg-Laue case and the Bragg-Bragg-Laue case. The period of the interference fringes is shown to be proportional to the distance between the incident point of the X-ray and the crystal edge, and to be inversely proportional to the crystal thickness.
Acta crystallographica. Section A, Foundations of crystallography 08/2009; 65(Pt 4):253-8. · 49.93 Impact Factor
[show abstract][hide abstract] ABSTRACT: By using X-rays from synchrotron radiation, we measured the rocking curves due to only the imaginary part of the atomic scattering factor in Laue case. The interference fringes are observed which are totally different from the Pendellösung fringe. The fringes of the diffracted and transmitted rocking curves are in-phase with each other. We studied the origin of the in-phase fringes by using the complex dispersion surface and the electric field in the crystal, and also the relation with a coupled pendulum.
Physica Status Solidi (A) Applications and Materials 06/2009; 206(8):1865 - 1869. · 1.46 Impact Factor
[show abstract][hide abstract] ABSTRACT: X-Ray rocking curves from side surface of a thin plane-parallel Ge crystal are measured under the condition where the dispersion of the refracted angle is quite large. In the diffracted beams from side surface are observed, which are analysed by using Wagner's approach for Bragg–(Bragg)m–Laue case. The origin of the fringes is explained by the interference between diffraction beams in Bragg–Laue case and that in Bragg–Bragg–Laue case.
Physica Status Solidi (A) Applications and Materials 06/2009; 206(8):1855 - 1859. · 1.46 Impact Factor
[show abstract][hide abstract] ABSTRACT: By measuring X-rays from a bent Si single crystal, we have observed the amplification of the reflected beams from the surface. The amplification is observed when the incident angle is adjusted to minimize the effective linear absorption coefficient due to the dynamical diffraction effect. When we increase the width of the incident X-rays along the incident azimuth, we observe on increase in reflected beam intensity. The amplification can be explained by the addition of the electric fields of the propagating beams along hyperbolic trajectories in the bent crystal to those of the reflected beams.
Journal of the Physical Society of Japan 01/2009; 78(10). · 2.09 Impact Factor
[show abstract][hide abstract] ABSTRACT: X-ray rocking curves in the Bragg-Laue case diffracting from the side surface of a plane-parallel crystal have been measured using a high-resolution optical system. The full width at half-maximum of the rocking curves is approximately three times narrower than that measured from the top surface. The characteristics of the transmitted beam from the side surface are almost the same as those through a thin crystal in the Bragg case. The rocking curves and the direction of X-ray energy flow in the crystal observed in the experiment can be reproduced using Wagner's approach [Wagner (1956), Z. Phys. 146, 127-168].
Acta Crystallographica Section A Foundations of Crystallography 10/2008; 64(Pt 5):515-8. · 2.24 Impact Factor
[show abstract][hide abstract] ABSTRACT: Variations of peak position of the rocking curve in the Bragg case are measured from a Ge thin crystal near the K-absorption edge. The variations are caused by a phase change of the real part of the atomic scattering factor. Based on the measurement, the values of the real part are determined with an accuracy of better than 1%. The values are the most reliable ones among those reported values so far as they are directly determined from the normal atomic scattering factors.
Acta Crystallographica Section A Foundations of Crystallography 04/2008; 64(Pt 2):321-5. · 2.24 Impact Factor
[show abstract][hide abstract] ABSTRACT: X-ray interference fringes in diffraction beam from side surface of a thin plane-parallel crystal in Bragg-(Bragg)m-Laue case are measured and analyzed by using Wagner's approach. The origin of the interference fringes is explained by interference between the diffraction beam in Bragg-Laue case and that in Bragg-Bragg-Laue case. A part of the beams from side surface cannot be explained by the interference effect, but can be explained by the effect of confined beam.
Journal of The Physical Society of Japan - J PHYS SOC JPN. 01/2008; 77(10).
[show abstract][hide abstract] ABSTRACT: We have observed the interference fringes that are in phase with each other in the diffracted and transmitted rocking curves of GaAs 200 reflection near the K-absorption edge of As. The fringes are in contrast with the well-known Pendellösung fringes that are anti-phase with each other in the diffracted and transmitted waves. The origin of the in-phase interference fringe is analyzed to be due to the diffraction only by the imaginary part of the atomic scattering factor. It is also shown that the interference fringes become typical Pendellösung fringes when the diffraction is caused only by the real part.
Journal of the Physical Society of Japan 01/2008; 77(2). · 2.09 Impact Factor
[show abstract][hide abstract] ABSTRACT: It is shown that the locus of the f' + if'' plot in the complex plane, f' being determined from measured f'' by using the dispersion relation, looks like a semicircle very near the absorption edge of Ge. The semicircular locus is derived from a quantum theory of X-ray resonant scattering when there is a sharp isolated peak in f'' just above the K-absorption edge. Using the semicircular behavior, an approach is proposed to determine the anomalous scattering factors in a crystal by fitting known calculated values based on an isolated-atom model to a semicircular focus. The determined anomalous scattering factors f' show excellent agreement with the measured values just below the absorption edge. In addition, the phase determination of a crystal structure factor has been considered by using the semicircular behavior.
Acta Crystallographica Section A Foundations of Crystallography 12/2005; 61(Pt 6):553-6. · 2.24 Impact Factor