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Phys. Rev. Lett. 87, 195505 (2001) [4 pages]

[Issue 19 – 5 November 2001 ]

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Reconstruction of the Shapes of Gold Nanocrystals Using Coherent X-Ray Diffraction

I. K. Robinson, I. A. Vartanyants^*, G. J. Williams, M. A. Pfeifer, and J. A. Pitney^§

Department of Physics, University of Illinois, Urbana, Illinois 61801

Inverse problems arise frequently in physics: The magnitude of the Fourier transform of some function is measurable, but not its phase. The "phase problem" in crystallography arises because the number of discrete measurements (Bragg peak intensities) is only half the number of unknowns (electron density points in space). Sayre first proposed that oversampling of diffraction data should allow a solution, and this has recently been demonstrated. Here we report the successful phasing of an oversampled hard x-ray diffraction pattern measured from a single nanocrystal of gold.

©2001 The American Physical Society

URL: http://link.aps.org/abstract/PRL/v87/e195505
DOI: 10.1103/PhysRevLett.87.195505
PACS: 61.10.Dp, 42.30.Rx, 68.35.Md, 81.07.Bc

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References

1. L. Pauling, The Nature of the Chemical Bond and the Structure of Molecules and Crystals (Cornell University, Ithaca,1939).
2. H. Schenk, Direct Methods of Solving Crystal Structures (Plenum, New York,1991).
3. B. C. Wang, Methods Enzymol. 115, 90–112 (1985) [CAS].
4. M. G. Rossmann and D. M. Blow, Acta Crystallogr. Sect. A 16, 39–45 (1963) [CAS].
5. G. Bricogne, Acta Crystallogr. Sect. A 40, 410–445 (1984).
6. D. Sayre, Imaging Processes and Coherence in Physics, Springer Lecture Notes in Physics Vol. 112 (Springer-Verlag, Berlin,1980), p. 229.
7. J. Miao, D. Sayre, and H. N. Chapman, J. Opt. Soc. Am. A 15, 1662–1669 (1998) [ADS][ SPIN][ INSPEC].
8. R. P. Millane, J. Opt. Soc. Am. A 7, 394–411 (1990) [ADS][ SPIN][ INSPEC].
9. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, Nature (London) 400, 342–344 (1999) [CAS][ INSPEC].
10. D. Gabor, Nature (London) 161, 777 (1948).
11. J. J. Barton, Phys. Rev. Lett. 61, 1356 (1988) [SPIRES].
12. G. R. Harp, D. K. Saldin, and B. P. Tonner, Phys. Rev. Lett. 65, 1012 (1990) [SPIRES].
13. J. Wilder et al., Phys. Rev. Lett. 86, 2337 (2001).
14. T. Gog et al., Phys. Rev. Lett. 76, 3132 (1996) [SPIRES].
15. M. Tegze et al., Phys. Rev. Lett. 82, 4847 (1999) [SPIRES].
16. Q. Shen and R. Colella, Nature (London) 329, 232 (1987) [ADS][CAS][ INSPEC].
17. Y. Yacoby et al., J. Phys. Condens. Matter 12, 3929 (2000) [CAS][ INSPEC].
18. P. Cloetens et al., Appl. Phys. Lett. 75, 2912 (1999) [ADS][CAS][ SPIN][ INSPEC].
19. M. Sutton et al., Nature (London) 352, 608–610 (1991) [ADS][ INSPEC].
20. R. H. T. Bates, Optik (Stuttgart) 61, 247–262 (1982) [ INSPEC].
21. R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 35, 237–246 (1972) [ INSPEC].
22. J. R. Fienup, Appl. Opt. 21, 2758–2369 (1982) [ADS][ SPIN][ INSPEC].
23. R. P. Millane and W. J. Stroud, J. Opt. Soc. Am. A 14, 568–579 (1997) [ADS][CAS][ SPIN][ INSPEC].
24. J. C. Heyraud and J. J. Métois, Acta Metall. 28, 1789–1797 (1980) [CAS][ INSPEC].
25. M. Wortis, in Chemistry and Physics of Solid Surfaces VII, edited by R. Vanselow and R. Howe (Springer-Verlag, Berlin,1988), p. 367.
26. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Oxford,1984).
27. I. A. Vartanyants and I. K. Robinson (to be published).
28. M. von Laue, Ann. Phys. (Leipzig) 26, 55–85 (1936).
29. I. K. Robinson, Phys. Rev. B 33, 3830 (1986).
30. W. H. Press et al., Numerical Recipes (Cambridge University, Cambridge, England,1988).

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