Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-25T18:01:28.808Z Has data issue: false hasContentIssue false
  • English
  • Français

Anticlastic Curvature of Elastically Bent Crystals for Sagittal Focusing

Published online by Cambridge University Press:  15 February 2011

J. P. Quintana ,
V. I. Kushnir  and
P. Georgopoulos
J. P. Quintana
Affiliation:
DND-CAT Synchrotron Research Center, Robert R.McCormick School of Engineering and Applied Science, Northwestern University, Evanston, Illinois 60208
V. I. Kushnir
Affiliation:
Advanced Photon Source - XFD/362, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439-4815
P. Georgopoulos
Affiliation:
DND-CAT Synchrotron Research Center, Robert R.McCormick School of Engineering and Applied Science, Northwestern University, Evanston, Illinois 60208
Get access

Abstract

Finite 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.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 307: Symposium L – Applications of Synchrotron Radiation Techniques to Materials Science , 1993 , 349
Copyright
Copyright © Materials Research Society 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Sparks, C.J. Jr., Borie, B.S., Hastings, J.B. Nuci. Instr. and Methods, 172, p.237 (1980)CrossRefGoogle Scholar
2. Sparks, C.J. Jr., Ice, G.E., Wong, J., Batterman, B.W.. Nucl. Instr. and Methods, 195, p. 73 (1982)Google Scholar
3. Batterman, B.W. and Berman, L.. Nucl. Instr. and Methods, 208, p. 327 (1983)CrossRefGoogle Scholar
4. Mills, D.M., Henderson, C., Batterman, B.W.. Nucd. Instr. and Methods, A246, p.356 (1986)Google Scholar
5. Matsushita, T., Ishikawa, T., Oyanagi, H.. Nucl. Instr. and Methods, A246, p.377 (1986)Google Scholar
6. Knapp, G.S., Ramanathan, M., Nian, H.L., Macrander, A.T., Mills, D.M.. Rev. Sci. Instr., 63 (1), p.465 (1992)Google Scholar
7. Timoshenko, S., Woinowsky-Krieger, S.. Theory of Plates and Shells. McGraw-Hill, New York, 1959., pp 82–84.Google Scholar
8. Swanson Analysis Systems, Inc. Houston, Penn. USA.Google Scholar
9. Ferrer, S., Krisch, M., de Bergevin, F. and Zontone, F., Nuc. Instr. and Methods, A311, p. 444 (1992)Google Scholar
10. Kushnir, V.I., Quintana, J.P., Georgopoulos, P., Nuc. Instr. and Methods, (In press)Google Scholar