Monolithic Crystal Bender for Dynamical Sagittal Focusing with Compensation for Anticlastic Curvature and Twist Distortions

1997 ◽  
Vol 7 (C2) ◽  
pp. C2-317-C2-318
Author(s):  
S. Müllender ◽  
J. Goulon ◽  
P. W. Loeffen ◽  
Ph. Marion ◽  
A. Filipponi ◽  
...  
Keyword(s):  
Anticlastic Curvature

Characterization and on-line adjustment of the sagittal-bent Laue crystal profile

2018 ◽  
Vol 25 (5) ◽  
pp. 1346-1353
Author(s):  
Weiwei Dong ◽  
Quan Cai ◽  
Fugui Yang ◽  
Xu Liu ◽  
Jiaowang Yang ◽  
...  
Keyword(s):  
Ray Tracing ◽  
Crystal Surface ◽  
Great Influence ◽  
High Energy ◽  
Double Crystal ◽  
X Ray ◽  
Bent Crystal ◽  
On Line ◽  
Condition Adjustment ◽  
Anticlastic Curvature

The sagittal-bent Laue monochromator can provide an ideal way to focus high-energy X-ray beams. However, the anticlastic curvature induced by sagittal bending has a great influence on the crystal performance. Thus, characterizing the bent-crystal shape is very important for predicting the performance of the bent-crystal monochromator. In this paper the crystal profile is measured by off-line optical metrology and on-line X-ray experiments. The off-line results showed that the bent-crystal surface could be well fitted to a saddle surface apart from a redundant cubic term which was related to the different couples applied on the crystal. On-line characterization of the meridional and the sagittal radius of the bent crystal includes double-crystal topography and ray-tracing measurement. In addition, the double-crystal topography experiment could be used as a quick diagnostic method for the bending condition adjustment. The sagittal radius of the bent crystal was characterized through a ray-tracing experiment by using a particularly designed tungsten mask. Moreover, rocking curves under different bending conditions were measured as well. The results were highly consistent with analytical results derived from the elastic theory. Furthermore, radii along different vertical positions under various bending conditions were measured and showed a quadratic relationship between the vertical positions and the meridional radii.

Evaluation of two methods to minimize the anticlastic curvature of cylindrical bent crystals

2008 ◽  
Vol 15 (2) ◽  
pp. 140-143 ◽  
Author(s):  
Liangjie Feng ◽  
Le Kang ◽  
Zhongliang Li ◽  
Feixun Zhao ◽  
Chaoyin Xu
Keyword(s):  
Anticlastic Curvature ◽  
Bent Crystals

Anticlastic Curvature of Elastically Bent Crystals for Sagittal Focusing

1993 ◽  
Vol 307 ◽  
Author(s):  
J. P. Quintana ◽  
V. I. Kushnir ◽  
P. Georgopoulos
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Width Ratio ◽  
Crystal Length ◽  
Poisson Coefficient ◽  
Anticlastic Curvature ◽  
Bent Crystals

ABSTRACTFinite element results are presented for the case of an elastically bent isotropic rectangular crystal with clamped boundary conditions. Results show that the anticlastic curvature can be eliminated in the center of the crystal provided the crystal length to width ratio fits a “golden aspect ratio” which is dependent on the Poisson coefficient ν. For ν=0.262 (appropriate for Si(111)), this ratio is approximately equal to 1.42.

The Bending of a Long Strip Reinforced by Transverse Ribs

1965 ◽  
Vol 69 (650) ◽  
pp. 131-133
Author(s):  
G. G. Pope
Keyword(s):  
Middle Surface ◽  
Elastic Strip ◽  
Finite Deflection ◽  
Engineering Applications ◽  
Surface Stresses ◽  
Small Deflection ◽  
Cylindrical Form ◽  
Deflection Analysis ◽  
Anticlastic Curvature ◽  
Free Edges

When a long unreinforced flat elastic strip with free edges is bent to a uniform curvature about transverse axes in its own plane, anticlastic curvature is produced due to the influence of Poisson's ratio. Provided that the applied curvature is sufficiently small, the anticlastic curvature is constant across the strip and is proportional to the applied curvature. A finite deflection analysis shows, however, that the anticlastic deformation is reduced by the action of middle surface stresses, and the deformed strip approaches asymptotically a cylindrical form as the applied curvature is increased. Nevertheless, in some engineering applications it is necessary to limit the anticlastic deformation when the applied curvature is small, and for this purpose transverse ribs can be attached to the strip. In this note a small deflection analysis is given of the effect of uniformly spaced rigid ribs on the deformation of such a strip.

Anticlastic curvature in draw-bend springback

2005 ◽  
Vol 42 (5-6) ◽  
pp. 1287-1307 ◽  
Author(s):  
J.F. Wang ◽  
R.H. Wagoner ◽  
D.K. Matlock ◽  
F. Barlat
Keyword(s):  
Anticlastic Curvature

scholarly journals Dupin's indicatrix: a tool for quantifying periclinal folds on maps

2003 ◽  
Vol 140 (6) ◽  
pp. 721-726 ◽  
Author(s):  
RICHARD J. LISLE
Keyword(s):  
Remote Sensing ◽  
Aspect Ratio ◽  
Principal Curvature ◽  
Quantitative Assessment ◽  
Tangent Plane ◽  
New Method ◽  
Principal Curvatures ◽  
Remote Sensing Images ◽  
Geometrical Figure ◽  
Anticlastic Curvature

The elliptical and hyperbolic outcrop patterns characteristic of periclinal folds can be used to classify structures according to different curvature attributes. Elliptical patterns indicate domal-basinal structures with synclastic curvature, that is, principal curvatures of the same sign. Hyperbolic patterns are diagnostic of anticlastic curvature (saddle-like structures). Such outcrop geometries are geological examples of Dupin's indicatrix, the geometrical figure obtained by sectioning a curved surface on a plane parallel and almost coincident with the tangent plane. The aspect ratio of Dupin's indicatrix is theoretically related to the ratio of the principal curvature values for the part of the structure being considered. This new method allows quantitative assessment of structures on maps and on remote sensing images. Illustrations are given from Wyoming, USA, and Yorkshire, England.

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