Optics InfoBase > Virtual Journal for Biomedical Optics > Volume 4 > Issue 2 > Page 20522
Structure of confined fluids by x-ray interferometry using diffraction gratings
K. Nygard, D. K. Satapathy, O. Bunk, A. Diaz, E. Perret, J. Buitenhuis, F. Pfeiffer, C. David, and F. van der Veen »View Author Affiliations
1Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
2European Synchrotron Radiation Facility, B.P. 220, F-38042 Grenoble Cedex 9, France
3Forschungszentrum Jülich, D-52425 Jülich, Germany
4École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
5ETH Zürich, CH-8093 Zürich, Switzerland
Optics Express, Vol. 16, Issue 25, pp. 20522-20529 (2008)
http://dx.doi.org/10.1364/OE.16.020522
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Abstract
We develop a novel method for structure determination of confined fluids using diffraction-grating-based x-ray interferometry. Within this approach, diffraction from a microfluidic array, which acts both as confinement and transmission diffraction grating, provides the reference wave, whereas the density modulations of the confined fluid, acting as a weak phase object, generate the object wave. The ensemble-averaged density profile of the fluid perpendicular to the confining channel is then unambiguously obtained from the interference between the reference and object waves by direct Fourier inversion.
© 2008 Optical Society of America
OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(100.5070) Image processing : Phase retrieval
(340.7450) X-ray optics : X-ray interferometry
ToC Category:
Diffraction and Gratings
History
Original Manuscript: September 15, 2008
Revised Manuscript: October 28, 2008
Manuscript Accepted: November 24, 2008
Published: November 26, 2008
Virtual Issues
Vol. 4, Iss. 2 Virtual Journal for Biomedical Optics
Citation
K. Nygard, D. K. Satapathy, O. Bunk, A. Diaz, E. Perret, J. Buitenhuis, F. Pfeiffer, C. David, and F. van der Veen, "Structure of confined fluids by x-ray interferometry using diffraction gratings," Opt. Express 16, 20522-20529 (2008)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-16-25-20522
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References
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- Since Δβ/Δδ ~ 10-2 in the present study (Δδ denoting the average change in the imaginary part of the refractive index across the grating-fluid interface), absorption can be neglected.
- It follows from the definition of (x) that A0 = 0.
- The reference diffraction efficiencies |0 m are obtained from the diffraction efficiencies |e m of the empty grating as |0 m _ (m_=0 |m/m_=0 |e m) |e m.
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- H. N. Chapman, A. Barty, S. Marchesini, A. Moy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006). [CrossRef]
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- H. N. Chapman, A. Barty, S. Marchesini, A. Moy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006). [CrossRef]
- B. Bhushan, J. N. Israelachvili, and U. Landmann, "Nanotribology: friction, wear and lubrication at the atomic scale," Nature (London) 374, 607-616 (1995). [CrossRef]
- M. J. Zwanenburg, J. H. H. Bongaerts, J. F. Peters, D. O. Riese, and J. F. van der Veen, "X-ray waveguiding studies of ordering phenomena in confined fluids," Phys. Rev. Lett. 85, 5154-5157 (2000). [CrossRef] [PubMed]
- K. Nygård, D. K. Satapathy, O. Bunk, F. Pfeiffer, C. David, and J. F. van der Veen, "Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects," Appl. Phys. Lett. 92, 214105 (2008). [CrossRef]
- D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008). [CrossRef] [PubMed]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007). [CrossRef]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007). [CrossRef]
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- J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens," Nature (London) 400, 342-344 (1999). [CrossRef]
- H. N. Chapman, A. Barty, S. Marchesini, A. Moy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006). [CrossRef]
- K. Nygård, D. K. Satapathy, O. Bunk, F. Pfeiffer, C. David, and J. F. van der Veen, "Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects," Appl. Phys. Lett. 92, 214105 (2008). [CrossRef]
- D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008). [CrossRef] [PubMed]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007). [CrossRef]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007). [CrossRef]
- A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005). [CrossRef]
- W. J. Huisman, J. F. Peters, M. J. Zwanenburg, S. A. de Vries, T. E. Terry, D. Abernathy, and J. F. van der Veen, "Layering of a liquid metal in contact with a hard wall," Nature (London) 390, 379-381 (1997). [CrossRef]
- H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, "Observation of five-fold local symmetry in liquid lead," Nature (London) 408, 839-841 (2000). [CrossRef] [PubMed]
- D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008). [CrossRef] [PubMed]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007). [CrossRef]
- A. Diaz and J. F. van der Veen, "Theory of X-ray scattering from a complex fluid confined by a nanocavity array," Thin Solid Films 515, 5645-5653 (2007). [CrossRef]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007). [CrossRef]
- A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005). [CrossRef]
- H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, "Observation of five-fold local symmetry in liquid lead," Nature (London) 408, 839-841 (2000). [CrossRef] [PubMed]
- T. Terwilliger, S.-H. Kim, and D. Eisenberg, "Generalized method of determining heavy-atom positions using the difference Patterson function," Acta Crystallogr. Sect. A 43, 1-5 (1987). [CrossRef]
- C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003). [CrossRef] [PubMed]
- C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003). [CrossRef] [PubMed]
- D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008). [CrossRef] [PubMed]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007). [CrossRef]
- A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005). [CrossRef]
- C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003). [CrossRef] [PubMed]
- D. K. Saldin, R. Harder, H. Vogler, W. Moritz, and I. K. Robinson, "Solving the structure completion problem in surface crystallography," Comput. Phys. Commun. 137, 12-24 (2001). [CrossRef]
- H. N. Chapman, A. Barty, S. Marchesini, A. Moy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006). [CrossRef]
- H. N. Chapman, A. Barty, S. Marchesini, A. Moy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006). [CrossRef]
- G. J. Maalouf, J. C. Hoch, A. S. Stern, H. Szöke, and A. Szöke, "Holographic methods in x-ray crystallography. III. First numerical results," Acta Crystallogr. Sect. A 49, 866-871 (1993). [CrossRef]
- H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, "Observation of five-fold local symmetry in liquid lead," Nature (London) 408, 839-841 (2000). [CrossRef] [PubMed]
- H. N. Chapman, A. Barty, S. Marchesini, A. Moy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006). [CrossRef]
- W. J. Huisman, J. F. Peters, M. J. Zwanenburg, S. A. de Vries, T. E. Terry, D. Abernathy, and J. F. van der Veen, "Layering of a liquid metal in contact with a hard wall," Nature (London) 390, 379-381 (1997). [CrossRef]
- B. Bhushan, J. N. Israelachvili, and U. Landmann, "Nanotribology: friction, wear and lubrication at the atomic scale," Nature (London) 374, 607-616 (1995). [CrossRef]
- H. N. Chapman, A. Barty, S. Marchesini, A. Moy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006). [CrossRef]
- D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008). [CrossRef] [PubMed]
- O. H. Seeck, H. Kim, D. R. Lee, D. Shu, I. D. Kaendler, J. K. Basu, and S. K. Sinha, "Observation of thickness quantization in liquid films confined to molecular dimension," Europhys. Lett. 60, 376-382 (2002). [CrossRef]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007). [CrossRef]
- A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005). [CrossRef]
- O. H. Seeck, H. Kim, D. R. Lee, D. Shu, I. D. Kaendler, J. K. Basu, and S. K. Sinha, "Observation of thickness quantization in liquid films confined to molecular dimension," Europhys. Lett. 60, 376-382 (2002). [CrossRef]
- T. Terwilliger, S.-H. Kim, and D. Eisenberg, "Generalized method of determining heavy-atom positions using the difference Patterson function," Acta Crystallogr. Sect. A 43, 1-5 (1987). [CrossRef]
- J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens," Nature (London) 400, 342-344 (1999). [CrossRef]
- H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, "Observation of five-fold local symmetry in liquid lead," Nature (London) 408, 839-841 (2000). [CrossRef] [PubMed]
- B. Bhushan, J. N. Israelachvili, and U. Landmann, "Nanotribology: friction, wear and lubrication at the atomic scale," Nature (London) 374, 607-616 (1995). [CrossRef]
- O. H. Seeck, H. Kim, D. R. Lee, D. Shu, I. D. Kaendler, J. K. Basu, and S. K. Sinha, "Observation of thickness quantization in liquid films confined to molecular dimension," Europhys. Lett. 60, 376-382 (2002). [CrossRef]
- H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, "Observation of five-fold local symmetry in liquid lead," Nature (London) 408, 839-841 (2000). [CrossRef] [PubMed]
- G. J. Maalouf, J. C. Hoch, A. S. Stern, H. Szöke, and A. Szöke, "Holographic methods in x-ray crystallography. III. First numerical results," Acta Crystallogr. Sect. A 49, 866-871 (1993). [CrossRef]
- C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003). [CrossRef] [PubMed]
- H. N. Chapman, A. Barty, S. Marchesini, A. Moy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006). [CrossRef]
- J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens," Nature (London) 400, 342-344 (1999). [CrossRef]
- D. K. Saldin, R. Harder, H. Vogler, W. Moritz, and I. K. Robinson, "Solving the structure completion problem in surface crystallography," Comput. Phys. Commun. 137, 12-24 (2001). [CrossRef]
- H. N. Chapman, A. Barty, S. Marchesini, A. Moy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006). [CrossRef]
- K. Nygård, D. K. Satapathy, O. Bunk, F. Pfeiffer, C. David, and J. F. van der Veen, "Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects," Appl. Phys. Lett. 92, 214105 (2008). [CrossRef]
- D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008). [CrossRef] [PubMed]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007). [CrossRef]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007). [CrossRef]
- D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008). [CrossRef] [PubMed]
- M. J. Zwanenburg, J. H. H. Bongaerts, J. F. Peters, D. O. Riese, and J. F. van der Veen, "X-ray waveguiding studies of ordering phenomena in confined fluids," Phys. Rev. Lett. 85, 5154-5157 (2000). [CrossRef] [PubMed]
- W. J. Huisman, J. F. Peters, M. J. Zwanenburg, S. A. de Vries, T. E. Terry, D. Abernathy, and J. F. van der Veen, "Layering of a liquid metal in contact with a hard wall," Nature (London) 390, 379-381 (1997). [CrossRef]
- D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008). [CrossRef] [PubMed]
- K. Nygård, D. K. Satapathy, O. Bunk, F. Pfeiffer, C. David, and J. F. van der Veen, "Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects," Appl. Phys. Lett. 92, 214105 (2008). [CrossRef]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007). [CrossRef]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007). [CrossRef]
- A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005). [CrossRef]
- H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, "Observation of five-fold local symmetry in liquid lead," Nature (London) 408, 839-841 (2000). [CrossRef] [PubMed]
- H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, "Observation of five-fold local symmetry in liquid lead," Nature (London) 408, 839-841 (2000). [CrossRef] [PubMed]
- M. J. Zwanenburg, J. H. H. Bongaerts, J. F. Peters, D. O. Riese, and J. F. van der Veen, "X-ray waveguiding studies of ordering phenomena in confined fluids," Phys. Rev. Lett. 85, 5154-5157 (2000). [CrossRef] [PubMed]
- D. K. Saldin, R. Harder, H. Vogler, W. Moritz, and I. K. Robinson, "Solving the structure completion problem in surface crystallography," Comput. Phys. Commun. 137, 12-24 (2001). [CrossRef]
- H. N. Chapman, A. Barty, S. Marchesini, A. Moy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006). [CrossRef]
- D. K. Saldin, R. Harder, H. Vogler, W. Moritz, and I. K. Robinson, "Solving the structure completion problem in surface crystallography," Comput. Phys. Commun. 137, 12-24 (2001). [CrossRef]
- D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008). [CrossRef] [PubMed]
- K. Nygård, D. K. Satapathy, O. Bunk, F. Pfeiffer, C. David, and J. F. van der Veen, "Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects," Appl. Phys. Lett. 92, 214105 (2008). [CrossRef]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007). [CrossRef]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007). [CrossRef]
- J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens," Nature (London) 400, 342-344 (1999). [CrossRef]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007). [CrossRef]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007). [CrossRef]
- O. H. Seeck, H. Kim, D. R. Lee, D. Shu, I. D. Kaendler, J. K. Basu, and S. K. Sinha, "Observation of thickness quantization in liquid films confined to molecular dimension," Europhys. Lett. 60, 376-382 (2002). [CrossRef]
- C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003). [CrossRef] [PubMed]
- H. N. Chapman, A. Barty, S. Marchesini, A. Moy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006). [CrossRef]
- O. H. Seeck, H. Kim, D. R. Lee, D. Shu, I. D. Kaendler, J. K. Basu, and S. K. Sinha, "Observation of thickness quantization in liquid films confined to molecular dimension," Europhys. Lett. 60, 376-382 (2002). [CrossRef]
- C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003). [CrossRef] [PubMed]
- O. H. Seeck, H. Kim, D. R. Lee, D. Shu, I. D. Kaendler, J. K. Basu, and S. K. Sinha, "Observation of thickness quantization in liquid films confined to molecular dimension," Europhys. Lett. 60, 376-382 (2002). [CrossRef]
- H. N. Chapman, A. Barty, S. Marchesini, A. Moy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006). [CrossRef]
- C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003). [CrossRef] [PubMed]
- G. J. Maalouf, J. C. Hoch, A. S. Stern, H. Szöke, and A. Szöke, "Holographic methods in x-ray crystallography. III. First numerical results," Acta Crystallogr. Sect. A 49, 866-871 (1993). [CrossRef]
- A. Szöke, "Holographic methods in x-ray crystallography. II. Detailed theory and connection to other methods of crystallography," Acta Crystallogr. Sect. A 49, 853-866 (1993). [CrossRef]
- G. J. Maalouf, J. C. Hoch, A. S. Stern, H. Szöke, and A. Szöke, "Holographic methods in x-ray crystallography. III. First numerical results," Acta Crystallogr. Sect. A 49, 866-871 (1993). [CrossRef]
- G. J. Maalouf, J. C. Hoch, A. S. Stern, H. Szöke, and A. Szöke, "Holographic methods in x-ray crystallography. III. First numerical results," Acta Crystallogr. Sect. A 49, 866-871 (1993). [CrossRef]
- W. J. Huisman, J. F. Peters, M. J. Zwanenburg, S. A. de Vries, T. E. Terry, D. Abernathy, and J. F. van der Veen, "Layering of a liquid metal in contact with a hard wall," Nature (London) 390, 379-381 (1997). [CrossRef]
- T. Terwilliger, S.-H. Kim, and D. Eisenberg, "Generalized method of determining heavy-atom positions using the difference Patterson function," Acta Crystallogr. Sect. A 43, 1-5 (1987). [CrossRef]
- C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003). [CrossRef] [PubMed]
- D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008). [CrossRef] [PubMed]
- K. Nygård, D. K. Satapathy, O. Bunk, F. Pfeiffer, C. David, and J. F. van der Veen, "Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects," Appl. Phys. Lett. 92, 214105 (2008). [CrossRef]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007). [CrossRef]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007). [CrossRef]
- A. Diaz and J. F. van der Veen, "Theory of X-ray scattering from a complex fluid confined by a nanocavity array," Thin Solid Films 515, 5645-5653 (2007). [CrossRef]
- A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005). [CrossRef]
- M. J. Zwanenburg, J. H. H. Bongaerts, J. F. Peters, D. O. Riese, and J. F. van der Veen, "X-ray waveguiding studies of ordering phenomena in confined fluids," Phys. Rev. Lett. 85, 5154-5157 (2000). [CrossRef] [PubMed]
- W. J. Huisman, J. F. Peters, M. J. Zwanenburg, S. A. de Vries, T. E. Terry, D. Abernathy, and J. F. van der Veen, "Layering of a liquid metal in contact with a hard wall," Nature (London) 390, 379-381 (1997). [CrossRef]
- D. K. Saldin, R. Harder, H. Vogler, W. Moritz, and I. K. Robinson, "Solving the structure completion problem in surface crystallography," Comput. Phys. Commun. 137, 12-24 (2001). [CrossRef]
- A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005). [CrossRef]
- D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008). [CrossRef] [PubMed]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007). [CrossRef]
- H. N. Chapman, A. Barty, S. Marchesini, A. Moy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006). [CrossRef]
- A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005). [CrossRef]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007). [CrossRef]
- M. J. Zwanenburg, J. H. H. Bongaerts, J. F. Peters, D. O. Riese, and J. F. van der Veen, "X-ray waveguiding studies of ordering phenomena in confined fluids," Phys. Rev. Lett. 85, 5154-5157 (2000). [CrossRef] [PubMed]
- W. J. Huisman, J. F. Peters, M. J. Zwanenburg, S. A. de Vries, T. E. Terry, D. Abernathy, and J. F. van der Veen, "Layering of a liquid metal in contact with a hard wall," Nature (London) 390, 379-381 (1997). [CrossRef]
Acta Crystallogr. Sect. A
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007). [CrossRef]
- A. Szöke, "Holographic methods in x-ray crystallography. II. Detailed theory and connection to other methods of crystallography," Acta Crystallogr. Sect. A 49, 853-866 (1993). [CrossRef]
- G. J. Maalouf, J. C. Hoch, A. S. Stern, H. Szöke, and A. Szöke, "Holographic methods in x-ray crystallography. III. First numerical results," Acta Crystallogr. Sect. A 49, 866-871 (1993). [CrossRef]
- T. Terwilliger, S.-H. Kim, and D. Eisenberg, "Generalized method of determining heavy-atom positions using the difference Patterson function," Acta Crystallogr. Sect. A 43, 1-5 (1987). [CrossRef]
Appl. Phys. Lett.
- K. Nygård, D. K. Satapathy, O. Bunk, F. Pfeiffer, C. David, and J. F. van der Veen, "Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects," Appl. Phys. Lett. 92, 214105 (2008). [CrossRef]
Comput. Phys. Commun.
- D. K. Saldin, R. Harder, H. Vogler, W. Moritz, and I. K. Robinson, "Solving the structure completion problem in surface crystallography," Comput. Phys. Commun. 137, 12-24 (2001). [CrossRef]
Europhys. Lett.
- O. H. Seeck, H. Kim, D. R. Lee, D. Shu, I. D. Kaendler, J. K. Basu, and S. K. Sinha, "Observation of thickness quantization in liquid films confined to molecular dimension," Europhys. Lett. 60, 376-382 (2002). [CrossRef]
J. Opt. Soc. Am. A
- H. N. Chapman, A. Barty, S. Marchesini, A. Moy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006). [CrossRef]
J. Opt. Soc. Am. B
- P. W. Wachulak, M. C. Marconi, R. A. Bartels, C. S. Menoni, and J. J. Rocca, "Soft x-ray laser holography with wavelength resolution," J. Opt. Soc. Am. B 25, 1811-1814 (2008). [CrossRef]
Nature (London)
- J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens," Nature (London) 400, 342-344 (1999). [CrossRef]
- W. J. Huisman, J. F. Peters, M. J. Zwanenburg, S. A. de Vries, T. E. Terry, D. Abernathy, and J. F. van der Veen, "Layering of a liquid metal in contact with a hard wall," Nature (London) 390, 379-381 (1997). [CrossRef]
- H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, "Observation of five-fold local symmetry in liquid lead," Nature (London) 408, 839-841 (2000). [CrossRef] [PubMed]
- B. Bhushan, J. N. Israelachvili, and U. Landmann, "Nanotribology: friction, wear and lubrication at the atomic scale," Nature (London) 374, 607-616 (1995). [CrossRef]
Opt. Express
- J. N. Clark, G. J. Williams, H. M. Quiney, L. Whitehead, M. D. de Jonge, E. Hanssen, M. Altissimo, K. A. Nugent, and A. G. Peele, "Quantitative phase measurement in coherent diffractive imaging," Opt. Express 16, 3342-3348 (2008). [CrossRef] [PubMed]
Phys. Rev. E
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007). [CrossRef]
Phys. Rev. Lett.
- M. J. Zwanenburg, J. H. H. Bongaerts, J. F. Peters, D. O. Riese, and J. F. van der Veen, "X-ray waveguiding studies of ordering phenomena in confined fluids," Phys. Rev. Lett. 85, 5154-5157 (2000). [CrossRef] [PubMed]
- D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008). [CrossRef] [PubMed]
- C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003). [CrossRef] [PubMed]
Physica B
- A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005). [CrossRef]
Thin Solid Films
- A. Diaz and J. F. van der Veen, "Theory of X-ray scattering from a complex fluid confined by a nanocavity array," Thin Solid Films 515, 5645-5653 (2007). [CrossRef]
Other
- Since Δβ/Δδ ~ 10-2 in the present study (Δδ denoting the average change in the imaginary part of the refractive index across the grating-fluid interface), absorption can be neglected.
- It follows from the definition of (x) that A0 = 0.
- The reference diffraction efficiencies |0 m are obtained from the diffraction efficiencies |e m of the empty grating as |0 m _ (m_=0 |m/m_=0 |e m) |e m.
2008, Nygård, Appl. Phys. Lett.
- K. Nygård, D. K. Satapathy, O. Bunk, F. Pfeiffer, C. David, and J. F. van der Veen, "Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects," Appl. Phys. Lett. 92, 214105 (2008). [CrossRef]
- D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008). [CrossRef] [PubMed]
- A. Diaz and J. F. van der Veen, "Theory of X-ray scattering from a complex fluid confined by a nanocavity array," Thin Solid Films 515, 5645-5653 (2007). [CrossRef]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007). [CrossRef]
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007). [CrossRef]
- H. N. Chapman, A. Barty, S. Marchesini, A. Moy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006). [CrossRef]
- A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005). [CrossRef]
- C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003). [CrossRef] [PubMed]
- O. H. Seeck, H. Kim, D. R. Lee, D. Shu, I. D. Kaendler, J. K. Basu, and S. K. Sinha, "Observation of thickness quantization in liquid films confined to molecular dimension," Europhys. Lett. 60, 376-382 (2002). [CrossRef]
- D. K. Saldin, R. Harder, H. Vogler, W. Moritz, and I. K. Robinson, "Solving the structure completion problem in surface crystallography," Comput. Phys. Commun. 137, 12-24 (2001). [CrossRef]
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