Use of coherent X-ray diffraction to map strain fields in nanocrystals

Abstract A new method is proposed to analyze the internal strains inside nanometer-sized crystals. The method employs a coherent beam of X-rays to obtain a continuous diffraction pattern in the immediate vicinity of each of the Bragg reflections. The symmetric part of the diffraction is given by the Fourier transform of the crystal’s shape, while the asymmetric part can be associated with the strain. Iterative Fourier transform methods can then be applied to reveal the strain as a three-dimensional spatial image.

[1]  B. C. Wang Resolution of phase ambiguity in macromolecular crystallography. , 1985, Methods in enzymology.

[2]  J. Miao,et al.  Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens , 1999, Nature.

[3]  Crowther Ra,et al.  The use of non-crystallographic symmetry for phase determination. , 1969 .

[4]  B. Warren,et al.  X-Ray Diffraction , 2014 .

[5]  Ian K. Robinson,et al.  RECONSTRUCTION OF SURFACE MORPHOLOGY FROM COHERENT X-RAY REFLECTIVITY , 1997 .

[6]  G. Bricogne Maximum entropy and the foundations of direct methods , 1984 .

[7]  Rick P. Millane,et al.  Phase retrieval in crystallography and optics , 1990 .

[8]  S. Sinha,et al.  X-ray scattering with partial coherent radiation: The exact relationship between “resolution” and “coherence” , 1998 .

[9]  Rick P. Millane,et al.  RECONSTRUCTING SYMMETRIC IMAGES FROM THEIR UNDERSAMPLED FOURIER INTENSITIES , 1997 .

[10]  M. Laue,et al.  Die äußere Form der Kristalle in ihrem Einfluß auf die Interferenzerscheinungen an Raumgittern , 1936 .

[11]  I. Robinson,et al.  Coherent x-ray diffraction imaging of silicon oxide growth , 1999 .

[12]  I. Robinson,et al.  Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction. , 2001, Physical review letters.

[13]  M. Fink,et al.  Imaging Processes and Coherence in Physics , 1980 .

[14]  D. Sayre Prospects for long-wavelength X-ray microscopy and diffraction , 1980 .

[15]  Strain profiles in epitaxial films from x-ray Bragg diffraction phases , 2000 .

[16]  Robinson,et al.  Crystal truncation rods and surface roughness. , 1986, Physical review. B, Condensed matter.

[17]  R. Gerchberg A practical algorithm for the determination of phase from image and diffraction plane pictures , 1972 .

[18]  D. Blow,et al.  Determination of phases by the conditions of non-crystallographic symmetry , 1963 .