scholarly journals X-ray interference fringes from a weakly bent plane-parallel crystal with negative strain gradient

2019 ◽  
Vol 75 (6) ◽  
pp. 842-850
Author(s):  
Tomoe Fukamachi ◽  
Sukswat Jongsukswat ◽  
Dongying Ju ◽  
Riichirou Negishi ◽  
Keiichi Hirano ◽  
...  
Keyword(s):  
Strain Gradient ◽  
Transmission Condition ◽  
Dynamical Theory ◽  
Perfect Crystal ◽  
Back Surface ◽  
Propagation Length ◽  
Transmitted Beam ◽  
X Ray ◽  
Plane Parallel ◽  
Interference Fringes

Under the anomalous transmission condition in the Bragg mode, X-ray interference fringes were observed between two beams with different hyperbolic trajectories in a very weakly bent plane-parallel perfect crystal with negative strain gradient. The origin of the fringes was analysed based on the dynamical theory of diffraction for a distorted crystal. In the reflected beam from the entrance surface, the interference fringes were observed between once- and twice-reflected beams from the back surface. In the transmitted beam from the back surface, the interference fringes were observed between the direct beam and once-reflected beam from the entrance surface. In the emitted beam from the lateral surface, the interference fringes were observed between the beams after different numbers of reflections in the crystal. The multiply reflected beams were formed by a combined result of long propagation length along the beam direction with large divergence of the refracted beams when the strain gradient was negative. The period of these interference fringes was sensitive to very weak strain, of the order of 10−7.

scholarly journals Strain distribution in an Si single crystal measured by interference fringes of X-ray mirage diffraction

2013 ◽  
Vol 46 (5) ◽  
pp. 1261-1265 ◽  
Author(s):  
Sukswat Jongsukswat ◽  
Tomoe Fukamachi ◽  
Dongying Ju ◽  
Riichirou Negishi ◽  
Keiichi Hirano ◽  
...  
Keyword(s):  
Single Crystal ◽  
Strain Gradient ◽  
Residual Strain ◽  
Strain Distribution ◽  
X Rays ◽  
X Ray ◽  
Plane Parallel ◽  
Rod Theory ◽  
Interference Fringes ◽  
Incident Plane

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.

Investigation of the phase shift in X-ray forward diffraction using an X-ray interferometer

1998 ◽  
Vol 5 (3) ◽  
pp. 967-968 ◽  
Author(s):  
Keiichi Hirano ◽  
Atsushi Momose
Keyword(s):  
Phase Shift ◽  
Silicon Crystal ◽  
Dynamical Theory ◽  
Perfect Crystal ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Bragg Geometry

The phase shift of forward-diffracted X-rays by a perfect crystal is discussed on the basis of the dynamical theory of X-ray diffraction. By means of a triple Laue-case X-ray interferometer, the phase shift of forward-diffracted X-rays by a silicon crystal in the Bragg geometry was investigated.

Theory of moiré fringes on X-ray diffraction topographs of bicrystals

1999 ◽  
Vol 55 (3) ◽  
pp. 413-422 ◽  
Author(s):  
Michael Ohler ◽  
Jürgen Härtwig
Keyword(s):  
Optical Properties ◽  
Dynamical Theory ◽  
Perfect Crystal ◽  
X Ray Diffraction ◽  
X Ray ◽  
Moiré Fringes ◽  
Diffraction Geometry

The theory of moiré fringes on X-ray diffraction topographs of bicrystals is derived from the dynamical theory of X-ray diffraction for the reflection (Bragg) and the transmission (Laue) case. The influence on the moiré fringes of the diffraction geometry, of the geometry of the sample, of its optical properties and of the topographic method is investigated. The perfect-crystal theory is also expanded to weakly deformed bicrystals.

The covalent bond in silicon

1967 ◽  
Vol 298 (1455) ◽  
pp. 379-394 ◽  
Keyword(s):  
Electron Distribution ◽  
Radial Function ◽  
Covalent Bond ◽  
Dynamical Theory ◽  
Perfect Crystal ◽  
X Ray ◽  
Distribution Study ◽  
Atom Scattering ◽  
Antisymmetric Component ◽  
Absolute Basis

A detailed electron distribution study of the covalent bond in silicon is discussed. The study is based on the strategy employed earlier to define the covalent bond in diamond, and estimates of the bonded-atom scattering power, including results for 222, that have been obtained in three different X -ray experiments at room temperature are considered. Two of these involve the conventional approach via intensity measurement, that of Gottlicher & Wolfel (G. W. ) on powders and that of DeMarco & Weiss (D. M. W. ) on perfect single crystals, while the third by Hattori, Kuriyama, Katagaw a & Kato (H. K. K. K. ) involves the measurement of spacing in X -ray Pendellösung fringes observed in wedge-shaped perfect crystal specimens and their interpretation by the dynamical theory of Kato. It is shown that only the results obtained by H. K. K. K. are capable of detailed analysis in term s of the criteria now available from the earlier study of diamond, from which we conclude that the fringe-spacing method has yielded data for the low-angle reflexions which are superior to the data obtained m re conventionally by G. W. and D. M. W. The covalent bond in silicon is described comprehensively by two non-spherical components as in diamond. The major (antisymmetric) component involves the radial function F 3 ( r ) = 1⋅11 r 2 exp (─ 0⋅88 r 2 ), and the minor (cubo-centrosymmetric) the function G 4 ( r ) = ─ 0⋅32 1 r 2 exp (─0⋅88 r 2 ). The origin of these components lies in an electron redistribution of the spherical unbonded atom involving 0⋅127 electron per bond, and this leads to a peak of + 0⋅25 e/Å 3 at the mid-point of the covalent bond. The consequences of this study are considered in relation to future attempts to examine aspects of electron distribution in atoms of different weight. The suitability of diamond and silicon as standards for scaling intensity data to the strict absolute basis so essential to such studies is also noted.

THE SIMULATION OF MODULATED PENDELLÖSUNG FRINGES OF PERFECT CRYSTALS FOR SPHERICAL X-RAY WAVE

1989 ◽  
Vol 03 (04) ◽  
pp. 319-323
Author(s):  
S.S. JIANG ◽  
Y. QIU
Keyword(s):  
Theoretical Calculation ◽  
Fringe Pattern ◽  
Dynamical Theory ◽  
Perfect Crystal ◽  
Experimental Result ◽  
X Ray Diffraction ◽  
Fringe Visibility ◽  
X Ray ◽  
Computer Based ◽  
Polarization States

The modulation in Pendellösung fringe visibility in perfect crystal is due to the interference between σ and π polarization states of X-ray wave. It is simulated by superposition of two polarization states by computer based on spherical X-ray wave dynamical theory and compared with fringe pattern on X-ray diffraction section topograph. It is found that the agreement between experimental result and theoretical calculation is satisfactory.

scholarly journals Extinction in Polycrystalline Materials

1985 ◽  
Vol 38 (3) ◽  
pp. 507 ◽  
Author(s):  
TM Sabine
Keyword(s):  
Grain Size ◽  
Parallel Plate ◽  
Experimental Tests ◽  
Dynamical Theory ◽  
Perfect Crystal ◽  
Polycrystalline Materials ◽  
Plane Parallel ◽  
Extinction Factor ◽  
Plane Parallel Plate ◽  
Crystal Grains

An expression is given for an extinction factor appropriate to powders composed of spherical perfect crystal grains or subgrains. This factor extrapolates to the dynamical theory value for the plane parallel plate in the symmetric Bragg case. Experimental tests of the theory have been made by nelitron diffraction experiments on polycrystalline specimens of MgO of controlled grain size. Agreement is excellent to an extinction level of y = 0�60.

X-ray Bragg reflexion from perfect crystals – dependence on geometrical factors with particular regard to the zero-level-of-interaction limit

1978 ◽  
Vol 364 (1719) ◽  
pp. 569-589 ◽  
Keyword(s):  
Dynamical Theory ◽  
Perfect Crystal ◽  
Crystal Thickness ◽  
X Ray ◽  
Maximum Reflectivity ◽  
First Case ◽  
Imperfect Crystal ◽  
The Difference ◽  
Geometrical Factors ◽  
Parameter Values

The variation of X-ray Bragg reflexion properties of centro-symmetric perfect crystals (both absorbing and non-absorbing) with thickness and degree of asymmetry of the reflexion is explored systematically by direct numerical evaluation of the dynamical theory. In particular, it is shown that well-defined universal limits exist where the integrated reflectivity of a perfect crystal (i. e. dynamical theory) approaches asymptotically that for an ideally imperfect crystal (i. e. kinematical approximation) of the same material under the same diffraction conditions. That is, in these limits the level of extinction goes to zero with zero gradient when plotted against an appropriate parameter. The first case occurs when the crystal thickness tends to zero, while the second case occurs when the degree of asymmetry tends toward the asymmetric limits. In each case it is shown that the level of interaction , as indicated for example by the maximum reflectivity, also goes to zero. If absorption is small it is found that the integrated reflectivity for a finite crystal can exceed that for the corresponding semi-infinite crystal, a particular example being the difference between the Ewald and Darwin results which occur for zero and negligible absorption respectively. If absorption and anomalous dispersion are both large, then for some range of parameter values the integrated reflectivity for a perfect crystal can exceed that for an ideally mosaic crystal leading to the phenomenon of negative extinction . A cautionary message arising from the present investigations relates to the dubious practical value of theoretical results for variation of diffraction properties with asymmetry, when these are based on the assumption of zero absorption.

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